Physico-Chemistry of Solid-Gas Interfaces

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Physical Chemistry of Solid-Gas Interfaces


Physical Chemistry of Solid-Gas Interfaces Concepts and Methodology for Gas Sensor Development

René Lalauze Series Editor Dominique Placko

First published in France in 2006 by Hermes Science/Lavoisier entitled “Physico-chimie des interfaces solide-gaz 1 et 2” First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc. Translated from the French by Zineb Es-Skali and Matthieu Bourdrel. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 6 Fitzroy Square London W1T 5DX UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd, 2008 © LAVOISIER, 2006 The rights of René Lalauze to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Lalauze, René. [Physico-chimie des interfaces solide-gaz. English] Physical chemistry of solid-gas interfaces : concepts and methodology for gas sensors development / René Lalauze. p. cm. Includes bibliographical references and index. ISBN 978-1-84821-041-7 1. Gas-solid interfaces. 2. Gas detectors. I. Title. QD509.G37L3513 2008 681'.2--dc22 2008022737 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-041-7 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.

Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter 1. Adsorption Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1. The surface of solids: general points . . . . . . . . . . . . . . . . . . . . 1.2. Illustration of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. The volumetric method or manometry . . . . . . . . . . . . . . . . 1.2.2. The gravimetric method or thermogravimetry. . . . . . . . . . . . 1.3. Acting forces between a gas molecule and the surface of a solid. . . . 1.3.1. Van der Waals forces . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2. Expression of the potential between a molecule and a solid. . . . 1.3.3. Chemical forces between a gas species and the surface of a solid 1.3.4. Distinction between physical and chemical adsorption . . . . . . 1.4. Thermodynamic study of physical adsorption . . . . . . . . . . . . . . . 1.4.1. The different models of adsorption . . . . . . . . . . . . . . . . . . 1.4.2. The Hill model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3. The Hill-Everett model . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4. Thermodynamics of the adsorption equilibrium in Hill’s model . 1.4.4.1. Formulating the equilibrium . . . . . . . . . . . . . . . . . . . 1.4.4.2. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5. Thermodynamics of adsorption equilibrium in the Hill-Everett model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5. Physical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2. Adsorption isotherms of mobile monolayers . . . . . . . . . . . . 1.5.3. Adsorption isotherms of localized monolayers . . . . . . . . . . . 1.5.3.1. Thermodynamic method . . . . . . . . . . . . . . . . . . . . . 1.5.3.2. The kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4. Multilayer adsorption isotherms . . . . . . . . . . . . . . . . . . . . 1.5.4.1. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . .

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1 2 3 4 4 4 6 7 8 8 8 9 10 10 10 11

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12 13 13 15 15 16 17 18 18

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1.6. Chemical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 2. Structure of Solids: Physico-chemical Aspects . . . . . . . . . . . . 29 2.1. The concept of phases . . . . . . . . . . . . . . . . . . . . 2.2. Solid solutions . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Point defects in solids . . . . . . . . . . . . . . . . . . . . 2.4. Denotation of structural members of a crystal lattice. . 2.5. Formation of structural point defects . . . . . . . . . . . 2.5.1. Formation of defects in a solid matrix . . . . . . . 2.5.2. Formation of defects involving surface elements . 2.5.3. Concept of elementary hopping step . . . . . . . . 2.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . .

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29 31 33 34 36 36 37 38 38

Chapter 3. Gas-Solid Interactions: Electronic Aspects . . . . . . . . . . . . . . 39 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Electronic properties of gases . . . . . . . . . . . . . . . . . . . . . . 3.3. Electronic properties of solids . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Energy spectrum of a crystal lattice electron. . . . . . . . . . . 3.3.2.1. Reminder about quantum mechanics principles . . . . . . 3.3.2.2. Band diagrams of solids . . . . . . . . . . . . . . . . . . . . 3.3.2.3. Effective mass of an electron . . . . . . . . . . . . . . . . . 3.4. Electrical conductivity in solids . . . . . . . . . . . . . . . . . . . . . 3.4.1. Full bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. Partially occupied bands . . . . . . . . . . . . . . . . . . . . . . 3.5. Influence of temperature on the electric behavior of solids . . . . . 3.5.1. Band diagram and Fermi level of conductors . . . . . . . . . . 3.5.2. Case of intrinsic semiconductors . . . . . . . . . . . . . . . . . 3.5.3. Case of extrinsic semiconductors . . . . . . . . . . . . . . . . . 3.5.4. Case of materials with point defects. . . . . . . . . . . . . . . . 3.5.4.1. Metal oxides with anion defects, denoted by MO1x . . . 3.5.4.2. Metal oxides with cation vacancies, denoted by M1xO . 3.5.4.3. Metal oxides with interstitial cations, denoted by M1+xO 3.5.4.4. Metal oxides with interstitial anions, denoted by MO1+x . 3.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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39 39 40 40 41 41 45 52 55 55 56 57 57 61 62 64 65 66 67 67 68

Chapter 4. Interfacial Thermodynamic Equilibrium Studies . . . . . . . . . . 69 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Interfacial phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Solid-gas equilibriums involving electron transfers or electron holes . 4.3.1. Concept of surface states . . . . . . . . . . . . . . . . . . . . . . . .

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69 70 71 72

Table of Contents

4.3.2. Space-charge region (SCR) . . . . . . . . . . . . . . . . . . . . . . . 4.3.3. Electronic work function . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3.1. Case of a semiconductor in the absence of surface states . . 4.3.3.2. Case of a semiconductor in the presence of surface states . . 4.3.3.3. Physicists’ and electrochemists’ denotation systems . . . . . 4.3.4. Influence of adsorption on the electron work functions . . . . . . 4.3.4.1. Influence of adsorption on the surface barrier VS . . . . . . . 4.3.4.2. Influence of adsorption on the dipole component VD. . . . . 4.4. Solid-gas equilibriums involving mass and charge transfers . . . . . . 4.4.1. Solids with anion vacancies . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Solids with interstitial cations . . . . . . . . . . . . . . . . . . . . . 4.4.3. Solids with interstitial anions. . . . . . . . . . . . . . . . . . . . . . 4.4.4. Solids with cation vacancies . . . . . . . . . . . . . . . . . . . . . . 4.5. Homogenous semiconductor interfaces. . . . . . . . . . . . . . . . . . . 4.5.1. The electrostatic potential is associated with the intrinsic energy level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2. Electrochemical aspect . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3. Polarization of the junction . . . . . . . . . . . . . . . . . . . . . . . 4.6. Heterogenous junction of semiconductor metals . . . . . . . . . . . . . 4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

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73 77 77 78 79 80 80 90 91 92 94 94 96 97

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103 104 107 107 108

Chapter 5. Model Development for Interfacial Phenomena . . . . . . . . . . . 109 5.1. General points on process kinetics. . . . . . . . . . . . . . . . . . . . 5.1.1. Linear chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1.1. Pure kinetic case hypothesis . . . . . . . . . . . . . . . . . 5.1.1.2. Bodenstein’s stationary state hypothesis . . . . . . . . . . 5.1.1.3. Evolution of the rate according to time and gas pressure 5.1.1.4. Diffusion in a homogenous solid phase. . . . . . . . . . . 5.1.2. Branched processes . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Electrochemical aspect of kinetic processes . . . . . . . . . . . . . . 5.3. Expression of mixed potential . . . . . . . . . . . . . . . . . . . . . . 5.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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109 111 114 118 119 121 125 126 133 136

Chapter 6. Apparatus for Experimental Studies: Examples of Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. General points. . . . . . . . . . . . . . . . . . . . . . . 6.2.1.1. Theoretical aspect of Tian-Calvet calorimeters 6.2.1.2. Seebeck effect. . . . . . . . . . . . . . . . . . . . 6.2.1.3. Peltier effect . . . . . . . . . . . . . . . . . . . . . 6.2.1.4. Tian equation . . . . . . . . . . . . . . . . . . . .

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137 138 138 139 139 140 140

viii


6.2.1.5. Description of a Tian-Calvet device. . . . . . . . . . . . . . . . 6.2.1.6. Thermogram profile . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1.7. Examples of applications . . . . . . . . . . . . . . . . . . . . . . 6.3. Thermodesorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2. Theoretical aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3. Display of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3.1. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3.2. Nickel oxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Vibrating capacitor methods . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1. Contact potential difference . . . . . . . . . . . . . . . . . . . . . . . 6.4.2. Working principle of the vibrating capacitor method . . . . . . . . 6.4.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2.2. Theoretical study of the vibrating capacitor method . . . . . . 6.4.3. Advantages of using the vibrating capacitor technique . . . . . . . 6.4.3.1. The materials studied . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3.2. Temperature conditions . . . . . . . . . . . . . . . . . . . . . . . 6.4.3.3. Pressure conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4. The constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4.1. The reference electrode . . . . . . . . . . . . . . . . . . . . . . . 6.4.4.2. Capacitance modulation . . . . . . . . . . . . . . . . . . . . . . . 6.4.5. Display of experimental results . . . . . . . . . . . . . . . . . . . . . 6.4.5.1. Study of interactions between oxygen and tin dioxide . . . . . 6.4.5.2. Study of interactions between oxygen and beta-alumina . . . 6.5. Electrical interface characterization . . . . . . . . . . . . . . . . . . . . . . 6.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2. Direct-current measurement . . . . . . . . . . . . . . . . . . . . . . . 6.5.3. Alternating-current measurement . . . . . . . . . . . . . . . . . . . . 6.5.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3.2. Principle of the impedance spectroscopy technique . . . . . . 6.5.4. Application of impedance spectroscopy – experimental results . . 6.5.4.1. Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.4.2. Experimental results: characteristics specific to each material 6.5.5. Evolution of electrical parameters according to temperature . . . . 6.5.6. Evolution of electrical parameters according to pressure . . . . . . 6.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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142 144 146 156 156 157 161 161 163 172 172 176 176 176 179 179 179 181 181 181 182 182 184 185 187 187 189 191 191 191 196 196 197 202 208 212

Chapter 7. Material Elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1. The compression of powders . . . . . . . . . . . . . 7.2.1.1. Elaboration process and structural properties

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215 216 216 216

Table of Contents

7.2.1.2. Influence of the morphological parameters on the electric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2. Reactive evaporation. . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.1. Experimental device . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.2. Measure of the source temperature . . . . . . . . . . . . . . . 7.2.2.3. Thickness measure . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.4. Experimental process . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.5. Structure and properties of the films . . . . . . . . . . . . . . 7.2.3. Chemical vapor deposition: deposit contained between 50 and 300 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.2. Device description . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.3. Structural characterization of the material . . . . . . . . . . . 7.2.3.4. Influence of the experimental parameters on the physico-chemical properties of the films. . . . . . . . . . . . . 7.2.3.5. Influence of the structure parameters on the electric properties of the films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4. Elaboration of thick films using serigraphy . . . . . . . . . . . . . 7.2.4.1. Method description. . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4.2. Ink elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4.3. Structural characterization of thick films made with tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1. General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2. Material elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3. Material shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3.1. Mono-axial compression . . . . . . . . . . . . . . . . . . . . . 7.3.3.2. Serigraphic process. . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4. Characterization of materials . . . . . . . . . . . . . . . . . . . . . . 7.3.4.1. Physico-chemical characterization of the sintered materials 7.3.4.2. Physico-chemical treatment of the thick films. . . . . . . . . 7.3.5. Electric characterization. . . . . . . . . . . . . . . . . . . . . . . . . 7.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

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217 219 219 222 222 224 224

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250 252 252 253

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254 255 255 257 261 261 262 263 263 266 273 275

Chapter 8. Influence of the Metallic Components on the Electrical Response of the Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1. Methods to deposit the metallic parts on the sensitive element . 8.2.2. Role of the metallic elements on the sensors’ response . . . . . 8.2.3. Role of the metal: catalytic aspects . . . . . . . . . . . . . . . . . 8.2.3.1. Spill-over mechanism . . . . . . . . . . . . . . . . . . . . . .

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277 278 278 279 282 283

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8.2.3.2. Reverse spill-over mechanism . . . . . . . . . . . . . . . . . . . 8.2.3.3. Electronic effect mechanism . . . . . . . . . . . . . . . . . . . . 8.2.3.4. Influence of the metal nature on the involved mechanism. . . 8.3. Case study: tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1. Choice of the samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2. Description of the reactor . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3.1. Influence of the oxygen pressure on the electric conductivity 8.3.3.2. Influence of the reducing gas on the electric conductions . . . 8.4. Case study: beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1. Device and experimental process . . . . . . . . . . . . . . . . . . . . 8.4.2. Influence of the nature of the electrodes on the measured voltage . 8.4.2.1. Study of the different couples of metallic electrodes . . . . . . 8.4.2.2. Electric response to polluting gases . . . . . . . . . . . . . . . . 8.4.3. Influence of the electrode size . . . . . . . . . . . . . . . . . . . . . . 8.4.3.1. Description of the studied devices . . . . . . . . . . . . . . . . . 8.4.3.2. Study of the electric response according to the experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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284 284 286 288 288 289 291 291 295 296 297 298 299 301 303 303

. 304 . 306 . 307

Chapter 9. Development and Use of Different Gas Sensors . . . . . . . . . . . 309 9.1. General points on development and use . . . . . . . . . . . . . . . . . . 9.2. Examples of gas sensor development . . . . . . . . . . . . . . . . . . . . 9.2.1. Sensors elaborated using sintered materials . . . . . . . . . . . . . 9.2.2. Sensors produced with serigraphed sensitive materials . . . . . . 9.3. Device designed for the laboratory assessment of sensitive elements and/or sensors to gas action . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1. Measure cell for sensitive materials . . . . . . . . . . . . . . . . . . 9.3.2. Test bench for complete sensors . . . . . . . . . . . . . . . . . . . . 9.3.3. Measure of the signal . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3.1. Measure of the electric conductance . . . . . . . . . . . . . . 9.3.3.2. Measure of the potential. . . . . . . . . . . . . . . . . . . . . . 9.4. Assessment of performance in the laboratory . . . . . . . . . . . . . . . 9.4.1. Assessment of the performances of tin dioxide in the presence of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2. Assessment of beta-alumina in the presence of oxygen . . . . . . 9.4.2.1. Device and experimental process . . . . . . . . . . . . . . . . 9.4.2.2. Electric response to the action of oxygen. . . . . . . . . . . . 9.4.3. Assessment of the performances of beta-alumina in the presence of carbon monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3.1. Measurement device . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

. . . .

309 310 310 312

. . . . . . .

. . . . . . .

316 317 319 319 319 322 322

. . . .

. . . .

322 327 327 327

. . 329 . . 329

Table of Contents

9.4.3.2. Electric results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5. Assessment of the sensor working for an industrial application . . . . . 9.5.1. Detection of hydrogen leaks on a cryogenic engine . . . . . . . . . 9.5.1.1. Context of the study . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1.2. Study of performances in the presence of hydrogen . . . . . . 9.5.1.3. Test carried out in an industrial environment . . . . . . . . . . 9.5.2. Application of the resistant sensor to atmospheric pollutants in an urban environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2.1. Measurement campaign conducted at Lyon in 1988 . . . . . . 9.5.2.2. Measurement campaign conducted at Saint Etienne in 1998 . 9.5.3. Application of the potentiometric sensor to the control of car exhaust gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3.1. Strategy implemented to control the emission of nitrogen oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3.2. Strategy implemented to control nitrogen oxide traps . . . . . 9.5.3.3. Results relative to the nitrogen oxides traps . . . . . . . . . . . 9.6. Amelioration of the selectivity properties . . . . . . . . . . . . . . . . . . 9.6.1. Amelioration of the selective detection properties of SnO2 sensors using metallic filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.1.1. Development of a sensor using a rhodium filter. . . . . . . . . 9.6.1.2. Development of a sensor using a platinum filter . . . . . . . . 9.6.2. Development of mechanical filters . . . . . . . . . . . . . . . . . . . 9.6.2.1. Development of a sensor detecting hydrogen . . . . . . . . . . 9.6.2.2. Development of a protective film for potentiometric sensors . 9.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

xi

329 332 333 333 333 337

. 341 . 342 . 345 . 347 . . . .

347 349 350 352

. . . . . . .

352 352 354 356 356 356 359

Chapter 10. Models and Interpretation of Experimental Results . . . . . . . 361 10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Nickel oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1. Kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2. Simulation of a kinetic model using analog electric circuits. . . . 10.2.2.1. Simulation of the curves displaying a maximum . . . . . . . 10.2.2.2. Simulation of the curves displaying a plateau . . . . . . . . . 10.2.3. Physical significance of the measured electric conductivity . . . . 10.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1. Physico-chemical and physical aspects of a phenomenon taking place at the electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.1. Oxygen species present at the surface of the device. . . . . . 10.3.1.2. Origin of the electric potential . . . . . . . . . . . . . . . . . . 10.3.2. Expression of the model . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2.1. The electrode potential. . . . . . . . . . . . . . . . . . . . . . . 10.3.2.2. Expression of the coverage degree . . . . . . . . . . . . . . . .

. . . . . . . .

361 362 365 370 370 377 380 380

. . . . . .

380 380 384 385 385 389

xii


10.3.2.3. Expression of the theoretical potential difference at the poles of the device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3. Simulation of the results obtained with oxygen . . . . . . . . . . . . 10.3.3.1. Behavior as a function of temperature and pressure. . . . . . . 10.3.3.2. Behavior as a function of electrode size. . . . . . . . . . . . . . 10.3.3.3. Evolution of the surface potential . . . . . . . . . . . . . . . . . 10.3.4. Simulation of the phenomenon in the presence of CO . . . . . . . . 10.3.4.1. Description of the mechanisms considered . . . . . . . . . . . . 10.3.4.2. Oxidation mechanisms of carbon monoxide . . . . . . . . . . . 10.3.4.3. Results of the simulation. . . . . . . . . . . . . . . . . . . . . . . 10.4. Tin dioxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2. Proposition for a physico-chemical model . . . . . . . . . . . . . . . 10.4.3. Phenomenon at the electrodes and role of the thickness of the sensitive film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3.1. Calculation of the conductance G as a function of the thickness of the film . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3.2. Mathematical simulation. . . . . . . . . . . . . . . . . . . . . . . 10.5. Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

394 395 395 397 399 401 401 402 405 409 409 410 415 416 423 428

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

Preface

Produced with the collaboration of Christophe Pijolat and Jean Paul Viricelle, this book is the fruit of research carried out over a long period of time by the Microsystems, Instrumentation and Chemical Sensors department at the Ecole des Mines, Saint Etienne, France. The abilities of this laboratory on the subject of modeling and instrumentation on heterogenous systems have enabled us to develop and study different devices for the detection of gas. The theoretical models based on kinetic concepts constitute the course of reflection and progress in a scientific area that is still little understood. A large part of this book refers to PhD and scientific reports. My thanks go out to all the authors. I would also like to thank the translators of this book from French, Zineb EsSkali and Matthieu Bourdrel.


Chapter 1

Adsorption Phenomena1

1.1. The surface of solids: general points The concept of form, which can be associated with that of surface, is characteristic of a solid. On a crystallographic level, every solid can be identified by its atomic or molecular arrangement. This arrangement, which is specific to each solid, constitutes a solid phase. Generally, the identification of such a structure (atomic positions, cohesive energy) is defined in the hypothesis of an infinite crystal, which implies a similar environment for all atoms. Near the surface, this is no longer true and it is important to imagine a new local structure of atoms or electrically charged species. In the particular case of ionic species, to submit to the local electroneutrality, it will often be necessary to take the solid’s environment into account. The material and the different phases in contact with it will thus reach equilibrium. Thus appears the concept of interface: a privileged area of the solid, from which all interactions likely to occur between a solid and different surrounding compounds upon its contact will start and develop. Depending on the nature of these compounds, there will be talk of solid-solid, solid-liquid or gas-solid reactions.

2


To conceptualize the solid-gas reactions on which we will concentrate, it is essential to start by simply picturing a molecule of gas bonding with a solid. The bonded molecule could remain independent from its support or react with it. In the first hypothesis, the reversible process at work is one of adsorption, which then constitutes the overall reaction. It is called the adsorption-desorption phenomenon (see Figure 1.1a). In the second hypothesis, adsorption will be the first step of a more complex process. It has, in this case, a non-reversible character due to which a new compound, GS for instance, will form. The nature of the observed phenomenon will depend on the thermodynamic conditions (pressure, temperature) as well as on the chemical affinity of the present species. It is also possible in adsorption phenomena to distinguish between physical and chemical adsorption. Chemical adsorption or chemisorption is characterized by a simple electron transfer between the gas in physisorbed state and the solid. This transfer results in the forming of a reversible chemical bond between the two compounds (see Figure 1.1b). Once again, the appearance of the chemisorption process is directly related to the environment’s thermodynamic conditions.

Figure 1.1. The different interaction modes between a gas and a solid: a) physical adsorption, b) chemisorption, c) non-reversible reaction

1.2. Illustration of adsorption Volumetric and gravimetric methods are the most explicit and common methods used to display and quantify adsorption.

Adsorption Phenomena

3

1.2.1. The volumetric method or manometry In a closed system, the bonding of a gas molecule with a solid contributes to lowering the partial pressure of the gas and measuring the variation of this pressure is enough to access the necessary information. To conduct an experiment, one uses two containing vessels A and B (see Figure 1.2) are used. Vessel A is connected to a device that measures pressure in it or in vessel A+B if A and B are joined by a valve V1. Gas is introduced in vessel A using valve V2 under pressure Pa . The solid sample is put in vessel B. A simple gas expansion in vessel A+B is enough to allow us to measure pressure Pa b .

Figure 1.2. Adsorption-measuring device using the volumetric method

Generally, the number of gas molecules introduced, n, is given, either by:

n1

PaVa

when vessel A is isolated from vessel B, or by:

n2

Pa b (Va Vb )

after the expansion of the gas in vessel A+B.

Va and Vb are, respectively, the volumes of vessel A and B. If there is no solid sample in vessel B, we naturally find that:

n1 = n2

4


If there is a solid sample, we generally note that:

n1 > n2 The difference n1-n2 is the amount of gas bonded to the solid. This experiment, if conducted under different gas pressure conditions, gives us adsorption isotherms, which plot n against P at a given temperature. 1.2.2. The gravimetric method or thermogravimetry When a molecule of gas bonds with a solid, it changes the mass of the solid and simply weighing the solid gives us information about the bonded amount given the system’s parameters. This method allows us to easily verify that the process is reversible (see Figure 1.3).

Figure 1.3. Evolution of a solid sample’s mass gain ǻm under changing pressure: if t < t0: P = P0 if t0 < t < t1: P = P1 > P0 if t > t1: P = P0 a) reversible process; b) non-reversible process

1.3. Acting forces between a gas molecule and the surface of a solid 1.3.1. Van der Waals forces By analogy with molecular interactions, we can use forces known as Van der Waals forces to interpret the source of the physical adsorption processes which are G favored by very low temperatures. These forces, denoted by F for instance, are associated with a scalar potential ĳ:

G F

grad M

The scalar potentials are additive and the global scalar potential is the sum of the potential of attraction M a and the potential of repulsion M r :


M

5

Ma Mr

where:

C r6

Ma

Mr

B rn

and:

r represents the intermolecular distance, while the constant C consists of three contributions: – the Keesom interaction or Keesom force, which only applies to polar molecules and originates from the attraction between several molecules’ permanent dipoles; – the induction interaction or Debye force, which originates from a molecule’s polarizability. It is caused by the attraction between permanent dipoles and other dipoles that are induced by the permanent dipoles; – London’s dispersion force, which originates from the attraction between molecules’ instantaneous dipoles. This is generally the most powerful attraction. As for the expression of M r , this is an empirical expression for which we generally choose n = 12. The global scalar potential M between two molecules is thus given by:

M

B C r 12 r 6

If we take into account the fact that the potential reaches a minimal value, M 0 , at equilibrium, meaning for an intermolecular distance r0, we then obtain:

ª § r0 · 6 § r0 ·12 º ¸ ¨ ¸ » «¬ © r ¹ © r ¹ »¼

M M 0 «2¨

6


1.3.2. Expression of the potential between a molecule and a solid In the hypothesis that all of the supposed semi-infinite crystal’s n molecules interact with the gas molecule, and that the potentials are additive, the global potential ĭ can be expressed as follows:

)a

¦M

a

for the attraction potential

)r

¦M

r

for the repulsion potential

n

and: n

These summations can be replaced with integrals:

)a

³ M dn

)r

³ M dn

a

and: r

where dn = N dv, and N represents the number of molecules per volume unit. The volume element used in the integrals is the volume between the spherical caps of radius r and r+dr, (see Figure 1.4), so: dV

Sdr

:r 2 dr

ȍ is the solid angle, and if Į is the maximum angle formed by the sphere’s radius and the solid’s surface normal, then:

:

2S (1 cos D )

where cos Į = Z / r , and Z is the distance between the molecule G and the solid.


7

Figure 1.4. Domain of integration in solid

The potential of attraction then becomes: )a

SNC 6Z 3

and the potential of repulsion now is: )r

SBN 45Z 9

Thus, in the case of a gas molecule interacting with a solid, the 1/r3 Van der Waals potential becomes a 1/r6 potential of attraction, and a 1/r12 potential becomes a 1/r9 potential of repulsion. The solid seems to be a thousand times more attractive or repulsive than a simple molecule. 1.3.3. Chemical forces between a gas species and the surface of a solid In an upcoming chapter, we will go into more detail about this physico-chemical aspect, which is crucial in explaining the workings of chemical sensors. For now, we will merely point out that if a gas atom has free electrons, a chemical bond between the gas and the solid becomes a possibility, and there are two extreme polarization possibilities that can be observed, either:

G e G or:

G G e

-

8


1.3.4. Distinction between physical and chemical adsorption The difference between physical and chemical adsorption is due to the difference between the natures of forces that keep the gas molecules on the solid’s surface. Let us analyze the ĭ = f ® curve: it goes through a minimum defined by ĭ0 and r0. In physical adsorption (see Figure 1.5), the value of ĭ0 is so much smaller than that observed for chemical adsorption (1 instead of 5 or 6 Joules per mole); r0, on the contrary, is lower for chemical adsorption. At last, physical adsorption can be represented as a non-activated and therefore spontaneous process that is likely to take place at very low temperatures. On the contrary, chemisorption is an activated process and the ĭ = f ® curve goes first through a maximum marked by the activation energy value EA. The necessity of activation is related to the fact that electron transfer, from the gas or the solid, requires an energy input; this implies the existence of a kinetic process.

Figure 1.5. Plot aspect of ĭ = f ® in case of a): physisorption; b): chemisorption

1.4. Thermodynamic study of physical adsorption 1.4.1. The different models of adsorption In order to build a thermodynamic model of physical adsorption, it is important to take note of a few experimental results. The adsorption isotherms acquired through the volumetric or the gravimetric method allow us to make sure that the


9

quantity n of bonded molecules is a function of gas pressure and temperature. These results involve a divariant system. Thereby, at the very least, all proposed models will have to meet this condition. It is important to note that the adsorption process can in no case whatsoever be identified with a simple condensation process. Indeed, condensation is a monovariant process that owes its origin to gas saturation. Saturation is achieved at a pressure P greater than or equal to the saturation vapor pressure P0, which varies with temperature only. On the other hand, adsorption is observed at gas pressure values that are lower than P0. The various thermodynamic models that have been proposed are grounded on such considerations. 1.4.2. The Hill model To take into account a system’s divariance, Hill deems it necessary to take surface effects into consideration. With this aim in mind, he supposes that the adsorption film, that is to say the adsorbent + adsorbed block, is easily assimilated to a solution where the adsorbent is formed by the free sites on the solid’s surface, and the adsorbed species are the gas molecules that have settled on those sites. In this case, the possible variables are pressure, temperature and the quantities of matter for the adsorbent (ns) and the adsorbed (na) species. There are 2 independent components (adsorbent + adsorbed + gas – an equilibrium relation between these three components). There are 2 exterior parameters (P and T) and there are 2 phases (solid and gaseous). Thus, the variance v is:

v 1 3 2

2

We can therefore plot: – isotherms na = f (P) where T = constant; – isobars na = f (P) where P = constant; – isosters P = f (T) where na = constant.

10


1.4.3. The Hill-Everett model Unlike the previous model, where the surface acts through the surface ns of its species, Hill and Everett describe surface effects using a physical parameter, namely the force field of the solid. In effect, this model considers that adsorption can be described as a localized condensation process that tends to progressively cover the entire surface when the gas pressure increases. A fluctuation in the fraction of covered surface necessarily induces a fluctuation in the energy of the contact between the two phases. This energy term is the product of an extensive quantity AS, which is the contact surface between the two phases, with an intensive quantity PS, which is comparable with a surface pressure. PS is identified with the variation of the surface tension coefficient Ȗ during the covering, that is to say: PS

Ȗ0 Ȗ

In this case, there are 3 exterior parameters: pressure, temperature and surface pressure. Assuming that there is only one independent component, the variance is given by:

v 1 3 2

2

There is in effect only one component: a solid + a gas – an equilibrium relation. At P = P0 (saturation vapor pressure), we will assume that the entire surface is covered and that there is no longer any change in the solid’s force field; the conditions we now have are those of a simple condensation, for which v = 1 + 2 – 2 = 1. 1.4.4. Thermodynamics of the adsorption equilibrium in Hill’s model 1.4.4.1. Formulating the equilibrium In the adsorbed phase, the change dG in enthalpy G is given by Gibbs’ equation:

dG where: μ1

Sdt VdP P1dn1 dn2

§ GG · and: μ2 ¨ Gn ¸ 1 ¹ P ,T , n2 ©

§ GG · ¨ Gn ¸ 2 ¹ P ,T , n1 ©


11

For component 1 (the adsorbed species) in the solution, we have:

§ Gμ · S1dT V 1dP ¨¨ 1 ¸¸ dn1 © Gn1 ¹ P ,T ,n2

dμ1

S1 being the differential molar entropy of component 1, and V1 the differential molar volume of component 1, we know that:

dP1

d(

GG G ) (dG ) , S1 Gn1 Gn1

GS1 and V1 Gn1

GV1 Gn1

Let us suppose that dn2 = 0, which would imply that the quantity n 2 of adsorbent is a constant. This assumption works all the better for the fact that the value of n 1 is very much lower than that of n 2 . As to the gas phase, it is pure, so we have:

dPG

SG dT VG dP

SG and VG representing the molar entropy and the molar volume of the gas. At equilibrium, necessarily, d ȝ1 = d ȝG, hence the following equilibrium equation:

S

G

§ Gμ · S1 dT VG V 1 dP ¨¨ 1 ¸¸ dn1 © Gn1 ¹ P ,T ,n2

0

1.4.4.2. Isotherm equation To make things simpler, we will make a few hypotheses: – the volume of the gaseous phase is far greater than that of the adsorbed phase:

VG !! V1 – the gas is ideal:

PVG

RT

12


The process being isothermal dT = 0 leads to:

RT

§ Gμ1 · ¨¨ ¸¸ dn1 © Gn1 ¹ P ,T ,n2

dP P

if: ȝ1 = ȝ0 + RT Ln nS, where nS is the number of fixed moles per surface unit. Then:

§ Gμ1 ·§ GnS ¸¸¨¨ ¨¨ © GnS ¹© Gn1

§ Gμ1 · ¸¸ ¨¨ © Gn1 ¹

· ¸¸ ¹

thus:

RTd ( LnP)

RT ( LnS )

which brings us to:

nS

DP

in which we recognize Henry’s law. 1.4.5. Thermodynamics of adsorption equilibrium in the Hill-Everett model In this case, the effects due to the surface tension between the condensed phase and the solid need to be taken into account when using Gibbs’ equation. To this end, we can start by expressing the internal energy changes dUS of the condensed phase:

dU S

TdS S PdVS PS dAS P S dnS

A new additional energy term appears when we distance ourselves from the classic model, which is a function of P and T only, that is, PS dAS. SS, VS, AS and dnS stand for entropy, volume, contact surface and the condensed phase’s number of moles. We can finally give the expressions for US and GS using the fact that, for a compound in a pure phase, GS = ȝS nS:


US

TS S PVS PS AS P S nS

GS

U S TS S PVS PS AS

13

and:

If we consider G to be an exact differential, then we arrive at:

s s dT v s dP a s dPS P s dn s

dG S Since:

dG

nS dP S P S dnS

dμS

s s dT v s dP a s PS

then:

where s s

SS

nS

, vs

VS

nS

and a s

AS

nS

.

If ī denotes the quantity of matter per surface unit, as in 1/aS, the equilibrium condition:

dP S

dPG

becomes:

S G s S dT VG v S dP

1 dPS *

0

This equation expresses the equilibrium condition in a Hill-Everett system. 1.5. Physical adsorption isotherms 1.5.1. General points Physical adsorption isotherms are generally obtained experimentally using a volumetric or gravimetric method. Before we try to obtain meaningful results from the theoretical expressions we have arrived at using Hill’s or Hill and Everett’s

14


hypotheses, we can already point out a few things concerning the mobility of the layers that become adsorbed on the surface of a solid. There are two borderline cases to be considered: – molecules that are adsorbed in the form of mobile layers; – molecules that are perfectly located on some of the solid’s sites. The existence of these borderline cases can be explained by the non-uniformity of the solid’s surface potential and the fact that this is typically related partly to the periodicity of a crystal lattice and the nature of the solid’s constituents. This periodicity (see Figure 1.6) can be described as there being E1 sites of lower energy, separated by higher E2 energy levels. The probability of a molecule moving from one stable site to another is thus proportional to E2 – E1. The E2 – E1 difference represents the energy barrier related to this species’ surface movement. If kT >> E2 – E1, the probability of a hopping step is high, and it is then said that the layer is mobile. If kT is for a constituent A in a solid or liquid solution; – < A > is for a pure solid or liquid phase of a compound A. In the situation we are considering, the adsorption reaction is expressed by:

s G s > appears here as the new species, and we therefore have a G – s solution in s. This model is fully compatible with Hill’s model. To express the equation of the isotherm, there are two complementary and equally effective methods available.

16


1.5.3.1. Thermodynamic method If we apply the mass action law to the previous equilibrium, we have:

K

G s !! P s !!

where K is the equilibrium constant. It is given by:

K

§ 'H q · K 0 exp¨ ¸ © RT ¹

Adsorption is an exothermic process, which leads to ǻH° < 0. A negative value for ǻH° means that it is the reverse reaction that takes place if the temperature increases; therefore, adsorption is more likely to take place at low temperatures. In an ideal solution, if S denotes the number of free sites, S0 denotes the number of sites, and ș represents the fraction of sites that are in use, which is expressed as:

T

S0 S S0

G s !!

then:

s !!

S S0

1T

which brings us to:

K

T 1 T P

Thus:

T

KP 1 KP

This relation, which is called the Langmuir isotherm, demonstrates that the percentage coverage of the surface is a homographic function of pressure. This


17

function is an accurate way to represent most adsorption-related experimental results. Note that, at low surface coverage fractions ( ș N D N A p ( x) n( x)@

[4.7]

The electroneutral condition in the bulk:

N D N A

nV pV

[4.8]

then makes it possible to rewrite [4.7] in the following way:

U ( x) q>nv pv n( x) p( x)@

[4.9]

at equilibrium; the general expression for Poisson’s equation becomes:

d 2V ( x) dx 2

q ª § qV ( x) ·º qV ( x) · § nV ¨1 exp ¸ pV ¨1 exp ¸ « kT ¹»¼ kT ¹ HH 0 ¬ © ©

[4.10]

Solving this equation yields the expression of the potential barrier V(x) as a function of the characteristic quantities of the system. We are going to show how the surface potential barrier VS (and consequently the electronic work function), which is obtained using the expression for V(x) when x = 0, is related to the surface charge and the concentration in adsorbed species.

Interfacial Thermodynamic Equilibrium Studies

77

4.3.3. Electronic work function The electronic work function ) in a solid is defined as the difference between ~ of the electrons in the solid and the electrostatic the electrochemical potential μ potential –qVe of the electrons in the vacuum near the surface of the solid:

ĭ

~ qV μ e

[4.11]

~ μ

§ wG · ¨ ¸ © wn ¹ P ,T

[4.12]

where

G being the free enthalpy of the system. Statistical thermodynamics make it possible to demonstrate that the Fermi energy EF is equal to the partial derivative of the free enthalpy G:

EF

§ wG · ¨ ¸ © wn ¹ P ,T

[4.13]

Using [4.12] and [4.13], we arrive at the conclusion that the Fermi energy is equal to the electronic electrochemical potential. Under such conditions, the work function is the amount of energy required by an electron trapped in the solid, and whose energy is equal to the Fermi energy, in order to reach the vacuum with a zero velocity. The Fermi level is the highest energy level occupied by electrons at 0°K temperature; the work function, as we have defined it above, therefore represents the lowest amount of energy that has to be supplied so that one of the solid’s electrons is extracted without gaining kinetic energy. 4.3.3.1. Case of a semiconductor in the absence of surface states In this ideal case, where there are not any surface or space charges, the energy bands are horizontal. The work function )0 is the sum of two contributions (see Figure 4.3a):

)0

F HV

[4.14]

78


where F referred to as the electron affinity of the semiconductor, represents the difference between the energy of the electrons in a vacuum and at the bottom of the conduction band.

HV represents the difference between the energy corresponding to the bottom of the conduction band and the Fermi energy, that is HV = EC – EF. HV is sometimes referred to as the work function in the bulk. The quantity HV is mainly dependent on the doping process and the temperature; we will see that this is one of the characteristics of the bulk of the solid.

Figure 4.3. Formation of potential barrier in the presence of surface states

4.3.3.2. Case of a semiconductor in the presence of surface states The presence of charged surface states leads to the formation of a barrier potential VS at the surface; in the hypothesis that the surface states are due to adsorbed species. A dipole layer can form, which leads to an additional energy jump –qVD. The electron affinity of the semiconductor becomes F – qVD. The work function ) is then expressed (see Figure 4.3b):

)

F H V q(VS VD )

[4.15]

The quantities F and HV, which are characteristic of the ideal semiconductor with no surface states, are not affected by the adsorption of foreign species at the surface. Consequently, the change in the electron work function ') during adsorption is written:

')

q ( 'V S 'V D )

[4.16]


79

where 'VS and 'VD denote the corresponding variations of the surface barrier and the dipole component. 4.3.3.3. Physicists’ and electrochemists’ denotation systems Physicists and electrochemists do not necessarily use the same symbols and/or the same designations, particularly to describe the energy quantities involved in the use of semiconductors. Figure 4.4 and Table 4.1 present the two systems generally used.

Figure 4.4. Energy quantities involved in semiconductors

Table 4.1. Matching of denotations

80


4.3.4. Influence of adsorption on the electron work functions We have just seen that the adsorption of foreign species (atoms or gas molecules) on the surface of the semiconductor shows in the band diagram, where surface states appear, and that the presence of these states causes a change in the electronic work function ) because of a variation of the surface VS and the appearance of a dipole component VD. We intend to relate these two quantities to the concentration in chemisorbed species N, which is expressed in the number of atoms per surface unit. 4.3.4.1. Influence of adsorption on the surface barrier VS Boundary layer theory The electronic transfers between solids and surface states are at the root of the first electronic theories about chemisorption, which were simultaneously developed by Aigrain and Dugas2, Weisz, Hauffe and Engell3. Suppose there is, on the surface, an electronegative species X (or electronacceptor) like oxygen and whose electron affinity A is greater than the electronic work function ) of a semiconductor: it will tend to trap an electron coming from the solid, according to the following equation:

X e o X The difference A-) represents the adsorption energy. During this chemisorption process, the surface acquires a negative charge and the bands bend upwards. The potential barrier VS decreases, causing a rise in the electronic work function ) until the Fermi level and the energy level of the gas become the same, which would mean that the equilibrium had been reached and the chemisorption process had stopped. Figures 4.5a and 4.5b represent the bands of a semiconductor n in the presence of electron acceptor-type molecules at the beginning of adsorption and at adsorption equilibrium. The chemisorption of an electropositive molecule results in an electron transfer towards the solid, provided that the work function ) is greater than the ionization energy I of the adsorbed gas. The adsorption energy is )-I. The surface acquires a positive charge during the process of chemisorption which leads to a rise in the potential barrier VS, and therefore a decrease of the work function ).


81

Figure 4.6 shows the energy diagrams of p-type semiconductor in the presence of donor-type molecules.

Figure 4.5. Semiconductor n in the presence of acceptor-type molecules: (a) at beginning of adsorption, (b) at adsorption equilibrium

Figure 4.6. Semiconductor p in the presence of donor-type molecules

Within the framework of the boundary layer theory, Aigrain and Dugas4 solved the Poisson equation for an n-type semiconductor with fully-ionized donor-type impurities, the boundary conditions being:

U ( x) qN D U ( x) 0

when 0 x 1 when x ! l

82


Moreover, we will suppose that all impurities are fully ionized at working temperature, which, for the electron concentration, means that:

n

N D

ND

over the entire domain, that is to say: 0 < x < l. In such a case, the electroneutral condition is written:

N

xN D

xN D

N represents the concentration in surface states and is expressed in number of atoms per surface unit. Solving equation [4.6] results in a parabolic variation for VS:

VS

aN 2

This is the Schottky barrier. There is a second possibility where the ionization of the impurity levels is no longer considered to be full when x < l and which yields a linear relation between VS and N:

VS

aN

This is the Mott barrier. Some authors consider that, during the chemisorption process, the Mott barrier intervenes at the beginning of adsorption, when the levels are not all ionized, while the Schottky barrier is involved at the end of the process, when the ionization is almost complete. Theoretical study of the surface barrier VS A full mathematical processing performed by Wolkenstein5 allows us to estimate the variations of the surface barrier VS depending on the surface charge, then depending on the surface concentration N of the adsorbed species. 4.3.4.1.1. Variations of the potential barrier VS as a function of the surface charge V Let us briefly recall the calculations leading to the expression for VS as a function of ı, which represents the surface charge and is expressed in number of charges per surface unit.


83

The Poisson equation can be written:

U

d 2V dx 2

HH 0

The potential V(x) at a depth x is expressed, according to [4.2], by:

V ( x ) I ( x ) IV when x = f:

M ( x) MV and:

V(x) 0 when x = 0:

M ( 0) M S and:

V(0)

VS

The volume charge density U is a function of x; it can also be expressed as a function of the potential I, which is related to x. Integrating Poisson’s equation with I gives us: IV

³I

H 0H ³

U (M )dI

f

X

2 f d V dV d 2V dI dx H H dx 0 ³ X dx 2 dx dx 2 dx

If we consider that dV / dx x

f

0 and express

IV

³I

U (M )dI as a function of V

by a variable transformation V = I - IV, integrating the previous expression yields the relation:

§ dV · ¨ ¸ © dx ¹

2

2

V

HH³ 0

0

U (V )dV

[4.17]

84


when x = 0, V = VS, and equation [4.17] leads to: 2

§ dV · ¨ ¸ © dx ¹ x

0

2

VS

HH³ 0

0

U (V )dV

[4.18] is a first relation between dV / DX x

[4.18]

0

and VS.

We will demonstrate that we can obtain a second relation between dV / dx x and V .

0

The electroneutrality condition at the interface is expressed by the fact that the surface charge V and the volume charge ȡ are equal, hence:

V

f

³ U ( x)dx 0

However, integrating Poisson’s equation leads to: f

§ dV · H 0H ¨ ¸ © dx ¹ 0

f

³ U x dx 0

Combining the two previous relations gives us:

§ dV · ¨ ¸ © dx ¹ x

0

V H 0H

[4.19]

Relations [4.18] and [4.19] thus make it possible to write the following relation between the potential barrier at the surface VS and the surface charge V:

V2 2H 0H

VS

³ U (V )dV 0

[4.20]

For a semiconductor containing both a singly-ionized donor-type impurity D, of concentration ND, as well as a singly-ionized acceptor-type impurity A, of concentration NA, the density U(V) can be expressed using relation [4.7]:

U (V ) q>N D N A p(V ) n(V )@

[4.21]


85

The concentrations of electrons n(V) and of holes p(V) are given by [4.4] and [4.5], while [3.23] and [3.25], found in Chapter 3, yield the concentrations of

ionized acceptor-type species N A and in ionized donor-type species N D . This means that the ionization state of donors and acceptors changes according to the band curvature and therefore according to the value of x. We are going to

express N A and N D as functions of V; note therefore that relation [3.23] of Chapter 3 involves the difference EA – EF, which breaks down into:

E A EF

E A Ei Ei E

which, according to [4.1], yields:

E A EF

E A Ei qMV qV

Consequently, the concentration N A is related to V through: N A

NA 1 § qV · 1 exp¨ ¸ a © kT ¹

[4.22]

where: a

§ E Ei qIV · exp¨ A ¸ kT © ¹

Similarly, the concentration N D is: N D

ND 1 § qV · 1 exp¨ ¸ b © kT ¹

where:

b

§ E ED qIV · exp¨ i ¸ kT ¹ ©

[4.22]

86


Using [4.5], [4.6], [4.22] and [4.23], which relate n(V), p(V), N A and N D to V, the integration of equation [4.20] leads to a general formula relating to the surface barrier VS to the surface charge:

§ § qV · · § § qVS · · V2 nV ¨ exp¨ S ¸ 1¸ pV ¨ exp¨ ¸ 1¸ 2H0H kT © © kT ¹ ¹ © © kT ¹ ¹ § qV · 1 a exp¨ S ¸ © kT ¹ NA log 1 a

[4.24]

§ qVS · 1 bexp¨ ¸ © kT ¹ ND log 1 b Two borderline cases present themselves: – 1st case The impurities are virtually non-ionized, hence the following conditions: qV qV B @..... >B @ V1 k1>A1 @ - k1 n >A n @.... >A 2 @

and:

Vn

G >A @..... >A @ H n kn 1 k >B @ >B1 @.... >Bn-1 @ n n

Note that, for this type of species, A1 and Bn do not influence V1 and Vn in the same way. Based on this type of consideration, and after making a comparison between some experimental results, we will be able to validate the working hypotheses and therefore also validate a kinetic process. To make this task easier, we must choose the nature of the experiments to be conducted and the parameters that will control these experiments with great care. 5.1.1.2. Bodenstein’s stationary state hypothesis This hypothesis consists of supposing that after a period of time during which the reaction takes off, steady-state conditions will establish themselves, characterized by constant intermediate compound concentrations. Such a hypothesis implies that the reaction time is long enough for the steady-state conditions to be reached, and this is especially true for systems that are open to inlet and outlet reactants. Mathematically, we only need to express the condition:

d >X 1 @ d >X i @ d >X n 1 @ ----------dt dt dt

0

Just as for the pure kinetic cases, this relation naturally results in V1 = V2 = … Vn, but the processes are no longer necessarily at equilibrium. We are then led to solve a system of algebraic equations with n-1 undetermined variables:

V1 V2 ………….

Vi 1 Vi ………….

Vn 1 Vn

Model Development for Interfacial Phenomena

119

Solving this system makes it possible to express all the concentrations of intermediate species as functions of the physico-chemical system’s parameters. The rates all being equal, the kinetic process can be described by either one of them by copying out, in the expression of its rate, the rates of the affected intermediate species Xi. The solutions are necessarily different from those we have obtained using the hypothesis of pure kinetic cases because they only involve kinetic constants ki, unlike the pure cases which bring into play the kinetic constants ki as well as the equilibrium constants Ki. The stationary state hypothesis therefore supplies us with a more general solution without requiring any details of the nature of a possible rate limiting process. 5.1.1.3. Evolution of the rate according to time and gas pressure We will deal with this kinetic aspect using the two examples that are the most appropriate for this book, that is to say that of chemisorption and that of an adsorption-reaction type of process. – Case of chemisorption Suppose we have the reaction:

Gs Gs Since it is an elementary step, we can write:

dș dt

V

G H k P( 1 ș) k ș

In such a case, the mathematical solution is easy to find. We have:

dT G G H k P (k P k )

dt

and:

ș

G G H kP G H 1 exp ( (k P k )t kP k

>

@

120


With the knowledge of T, we can relate the rate to time. We therefore arrive at:

V

>

G G H k P exp (k P k )t

@

if we consider that:

t

ti

0 Vi

G kP

and that:

t

tf

f Vf

0

Vi representing the initial process rate. Also note that the maximum rate value is reached immediately, and that the rate decreases non-stop over time. In that case, the changes in the rate according to P are relatively complex. – Case of an adsorption-reaction process If we assume that the adsorption process, as we have just described it, is associated with a chemical reaction, and if we hypothesize that there is a rate limiting process and that the reverse reaction is distinctly advanced, then we can write that:

Gs Gs If the step is at equilibrium, it follows that:

T

K1P 1 K1P

Moreover, for the second step that imposes its rate, we will have:

(G s ) A AG s and:

G V2 k 2T >A @


121

If the system is open for A, we will also have:

>A @

C te

Under such conditions, the rate of the global process is expressed by:

V

V2

G k 2 >A @K1 P 1 K1 P

The rate here is independent of time (the process is equivalent to a stationary state), rather, it is a homographic function of pressure. 5.1.1.4. Diffusion in a homogenous solid phase3,4,5 Within the context of linear processes, it is necessary to mention the case of diffusion processes in a homogenous phase. The most typical case involves the migration of a chemical species in a solid phase. It can be, for example, the migration of an oxygen ion through the lattice of a metallic oxide thanks to the oxygen vacancies. In such a case, the positions occupied by oxygen are of the same nature for all of the hopping steps. Consequently, these lattice positions are characterized by the same energy value. Every hopping step that corresponds to an elementary step is characterized by G H identical activation energy values ( and ( , the former being for the forward reaction and the latter for the reverse one. It is therefore an athermal reaction for which (see Figure 5.2):

ǻH q

G H EE

Every hopping step being the same, all kinetic constants are identical and are identified with a diffusion coefficient D expressed by:

D

G E D0 exp ( ) RT

H E D0 exp ( ) RT

We will retain D as the dimension of a kinetic constant.

122


We can also suppose that such a process will generate a diffusing species concentration gradient with boundary conditions fixing the concentration values at the inlet and outlet interface of the homogenous scattering region. Under such conditions, the concentration of the scattering species C(x,t) is a function of time and of the diffusion distance x, which is initialized at the inlet interface (see Figure 5.3). Note that if we suppose the system to be open at x=0, the vacancy concentration will be kept constant. If J(x, t) represents the flow of particles crossing the energy barrier E per time unit between two stable lattice positions, then (see Figure 5.2):

J x,t

G H J x,t J x,t

This flow, which is identified with the rate of an elementary step, is expressed by:

G J x,t

DC (x,t) for the forward reaction

and by:

H J x,t DC xa ,t

DC(x,t) aD

į C x,t įx

for the reverse reaction

a, which represents here the distance between two consecutive hopping steps, can be identified with a crystal lattice parameter.

Figure 5.2. Energy diagram of a hopping step in a crystal lattice


123

To be more precise, a coefficient D has to be added to the expression of the flow. This takes into account the probability of finding a free site; it follows that:

J x ,t

DaD

į Cx,t Gx

This relation is the first Fick’s law. Moreover, at the t + įt instant, we will have: J x ,t Gt

DaD

G C x,t Gt Gx

§ GC G 2C x ,t · dt ¸¸ DaD¨¨ x ,t G x2 © Gx ¹

Figure 5.3. Evolution of the vacancy concentration gradient according to the x coordinates and time t

We can then perform a mass balance for a volume element of a single unit section and of a width dx, during a time duration dt (see Figure 5.4). In our case, dx will be considered as equal to the lattice parameter a.

124


Figure 5.4. Element of a scattering zone

Thus, the number of particles going into this volume element at the abscissa x and at the instant t equals that of the outgoing particles at the abscissa x+a and at the instant t+dt added to that of the particles that have accumulated or been depleted inside the volume element:

J x,t įt ĮaD

J x,t

įC x,t įt

dt

Using the previously established relations, we obtain:

DaD

GC x ,t Gt

DaD

G 2C x ,t dx 2

dt

which leads to:

GC x ,t Gx

G 2 C x ,t Gt 2

This is the second Fick’s law. In the hypothesis of a stationary state, which requires a system that is open for inlet and outlet reactants, C0 and Ce being the respective constant inlet and outlet concentrations, we obtain:

GC x ,t Gx

0

G 2 C x ,t Gt 2


125

which leads to:

GC x ,t Gt

C 0 Ce e

that is to say a constant linear concentration gradient:

C0 Ce e

A

This result only applies in the hypothesis of an open system to inlet and outlet reactants. “e” represents the distance between the system’s inlet and outlet. 5.1.2. Branched processes

In some cases, the process can no longer be described as a simple linear process, as multiple chains appear and sometimes split into branches. The approach for linear processes does stay the same when applied to each chain. However, the ramification nodes have to be taken into account as they are presented in Figure 5.5.

Figure 5.5. Branched processes

126


As an example, we will present the two cases seen in Figure 5.5 with the hypothesis that the forward reactions are distinctly advanced, which amounts to completely disregarding the reverse reactions. In the first case, there is no interaction between the intermediate species (see Figure 5.5a): d>X 2 @ dt

G G G V1A V1B V2

thus:

d>X 2 @ Į X1A ȕ X1B Ȗ>X 2 @ dt

> @ > @

In the second case, there are interactions between the intermediate species and therefore: d>X 2 @ G G V1 V2 dt

d <X2 > dt

Į ¢¡ X1A ¯±° ¢¡ X1B ¯°± Ȗ < X 2 >

Here we are presented with quadratic expressions that make this case harder to solve mathematically. In conclusion we hold that expressing the kinetics of a reaction process is a relatively difficult approach which will require the researcher to: – acquire as much information as they can about the experimental results obtained through different analysis techniques; – imagine a realistic kinetic process and its experimental conditions; – introduce hypotheses also compatible with the nature of the process; – simulate and validate the obtained kinetic models. 5.2. Electrochemical aspect of kinetic processes We have previously mentioned that the activation energy value can be changed when there is movement of charged species. In such a case, an electrochemical


127

phenomenon is observed. We will explore this subject through an oxidationreduction reaction which brings into play a solid-gas interface. This case is typical of chemisorption. Generally speaking, the reaction is: oxidizing agent De reducing agent

The rate V of this reaction is defined as the number of electron grams dn extracted from the reducing agent during dt and per surface unit, therefore:

V -

1 dn G H V V Vred Voxy D dt

dn/dt is therefore proportional to the density of the current i, for which the following convention was adopted: the current is considered to be positive in the case of an oxidation, and negative in the case of a reduction, thus leading to:

i

q

dn dt

iOx iRe d

where:

iox

qGk ox >Re d @

and:

ired

qGkRe d >Oxy @

~ ~ Suppose EOx and ERe d are the energy values that define the activation energies respectively corresponding to the kinetic constants k Ox and k Red , where:

kOx

~ EOx ) k exp( RT 0 Ox

and: k Re d

0 k Re d exp(

~ ERe d ) RT

128


As a result of the existence of an electrically charged interface, these energy quantities have to take the diffusion potential VD into account or rather take into account the fractions ĮVD or ȕVD as they are expressed and presented in Figure 4.15. Thus: H E ȕqVD

~ E Ox

and:

G E ĮqVD

~ E Red

It follows that:

H ( E EqVD ) k exp( ) RT 0 Ox

k Ox and:

0 k Re d exp(

k Re d

G ( E DqVD ) ) RT

It is now possible to choose: G k1

k

kRe d

0 Re d

G H E1 exp( ) and k 2 RT

H E2 k exp( ) RT 0 Ox

G DqVD ) k exp( RT

and: kOx

H EqVD k exp( ) RT

The global current is then expressed as: i

G EqVD DqVD ªH º ) Re d k exp( ) Ox » qG «k exp( RT RT ¬ ¼


129

Thus, at equilibrium, which is when i = 0, we have:

VD

G >Ox@ ) RT k (ln H ln * * >Re d @ q (D E ) k

This expression leads us to Nernst’s law. Į* and ȕ* stand for the value of these coefficients at equilibrium, considering that Į + ȕ* = 1. *

The idea that D and E are functions of time is based on the fact that the surface potential value, and therefore the curve V = f(x,t), changes during the shift towards equilibrium. Therefore, the coefficients D and E which describe this curve, may from now on be associated with such an evolution type. Given the extent to which these coefficients affect kinetic parameters, we will clarify them for two particular cases: that of an abrupt junction in a closed medium, and then in an open medium – the latter being typical of adsorption. – First case: abrupt junction in a closed medium, case of the p-n junction Suppose we have an oxidant medium as medium 1 and a reducing medium as medium 2:

Qt

U1 x1

U 2 x2

with Qt charge per surface unit and

U

the charge density.

If –x1 d x d 0, we will have:

U1 0 and

d 2V dx 2

U 1 HH 0

If 0 d x d +x2, we will have:

U2 t 0 and

d 2V dx 2

U 2 HH 0

Q(t) denotes the charge initiating at the interface as charge transfers are taking place and until the system reaches equilibrium.

130


G

If [ stands for the electric field, then we have, for medium 1 and 2 (see Figure 5.6):

G

[1

G U1 ( x x1 ) and [ 2 HH 0

dV dx

dV dx

U2 ( x x2 ) HH 0

therefore:

G

[1 max

G U1 ( x1 ) [ 2 max HH 0

U2 ( x2 ) HH 0

However, we have: x xp

V

G

³ [ dx = area of triangle ABC

x xn

and:

DV

x 0G ³ [ dx = area of triangle AOC x xn

Figure 5.6. Outline of the electrical field at the interface (see Figure 4.13)


131

Under such conditions:

D

surface of triangle A, 0, C surface of triangle A, B, C

S1

U1 ( x12 ) 2HH 0

S1 S0

where:

with x1 = xn and: S0

U1

2HH 0

( x12 x1 x 2 )

with x2 = xp which yields:

D

1 x 1 2 x1

1 1

U1 U2

and:

E 1-D

1 1

x1 x2

1 1

U1 U2

Note that U1 and U 2 , which here represent the volume concentration of defects in the two considered mediums, keep the same value even while the external parameters change. These results lead to the conclusion that the D and E coefficients, at least for a closed system and in the case of an abrupt junction, are independent of the charge value and consequently of time. – Second case: abrupt junction in an open medium In the particular case of an adsorption process that is characterized by a system that is open to the gas and a single chemisorbed layer, medium 1 can be described

132


using a surface density of charges q N(P, t), as well as the width of a space-charge region x1, which is limited by that of an adsorbed monolayer. We will adopt that width value as a reference, keeping it constant and equal to a single unit. Consequently, N(P, t) represents the number of chemisorbed molecules in the monolayer per surface unit at the point in time t. Thus:

Q( P , t )

qa

N ( P ,t ) a

qN ( P ,t )

Ux 2

As for medium 2, nothing has changed since the previous situation: it is now the x2 parameter that varies according to the carried charge value and the charge density, which is related to the concentration of intrinsic defects in the oxide, is constant. Under such conditions, the D coefficient, which is the ratio:

D

area of triangle A, 0, C area of triangle A, B, C

S1 S0

can be expressed as:

D

1 1 x2

1

1 qN ( P , t )

U2

In such a case, the D and E coefficients are functions of the chemisorbed amount N(P, t) and, as a result, of gas pressure and time. However, this situation allows us to suppose that x2 is much larger then x1. Indeed, if we suppose that the medium fraction of covered surface is 0.5, and that the ratio of defects in the oxide is in the order of 1%, then the x2 / x1 ratio is in the order of 20. This calculation is done on the hypothesis that the molecular volume of the considered species is the same in both phases. Under such conditions, we can consider that D is negligible compared to E, and go back to a situation similar to the one we found ourselves in with heterogenous junctions of semiconductor metals, whose space charge region and, as a result, its potential barrier, is fully supported by the semiconductor.


133

5.3. Expression of mixed potential The same solid-gas interface can be the scene of multiple simultaneous and independent oxidation-reduction reactions. This has to be taken into consideration when modeling the electrical response of some electrochemical sensors, particularly those located in a gaseous atmosphere containing oxidant and reducing gases. We will approach this study by considering two electrochemical reactions of the following type:

Ox1 įe Re d1 1 where VD is the scattering potential of reaction 1, and:

Ox2 įe Re d 2 where VD2 is the diffusion potential of reaction 2. The catalytic oxidation of carbon monoxide by oxygen on metallic oxide, is a typical example. Thus, Rideal’s hypothesis, which supposes the presence of interactions between the adsorbed oxygen and the carbon monoxide, leads to:

O2 2e 2s 2(O s ) and:

2CO2 2e 2s l 2CO 2(O s) the global reaction being:

Ox1 Re d 2 l Ox2 Re d1 and also, in the present case:

CO O2 l CO2

134


Let us go back to the global system and consider separately the two reactions out of equilibrium. They are each at the origin of an electric current characterized by: i10

G ªH º E qV 1 D qV 1 qG «k exp( 1 D )>Re d1 @ k exp( 1 D )>Ox1 @» RT RT ¬ ¼

i20

G ªH º E qV 2 D qV 2 qJ «k exp( 2 D )>Re d 2 @ k exp( 1 D )>Ox2 @» RT RT ¬ ¼

If both reactions are taken into account, then the current i will represent the summation of both phenomena. However, it should be made clear that there is only one possibility for the electrical diffusion barrier potential and the profile of V=f(x). This results in the same value VM for the potential barrier as well as the Į and ȕ coefficients in both cases, so:

D

D1 D 2

E

E1 E 2

and:

VM is referred to as the mixed potential. We can now express i as i = i1 + i2, where: i1

G EqVM DqVM ªH º qG «k exp( )>Re d1 @ k exp( )>Ox1 @» RT RT ¬ ¼

i2

G EqVM DqVM ªH º qJ «k exp( )>Re d 2 @ k exp( )>Ox2 @» RT RT ¬ ¼

and:

To reach a simple expression of VM using i1 and i2, it is necessary, from a mathematical standpoint, to suppose that the forward global reaction is distinctly advanced. We will therefore only use the first term of i2 and i1 while expressing this condition:

Ox1 Re d 2 o Ox2 Re d1


135

and: i

G EqVM DqVM ª H º q «Jk2 exp( )>Re d 2 @ Gk1 exp( )>Ox1 @» RT RT ¬ ¼

The i = 0 condition, which expresses the stationary character of the process, yields the expression for VM: G Gk >Ox @ RT ln H 1 1 q(D E ) Jk2 >Re d 2 @

VM

If we take into account the fact that Į + ȕ = 1, we obtain, for the present case:

G RT Gk1 >Ox1 @ ln( H ) q Jk2 >Re d 2 @

VM

This model applies to the catalytic oxidation of CO. It is however advisable to take into consideration the fact that, in such a case, the two reactions are not independent, and have a shared reaction intermediate that is the chemisorbed species (O s ) , whose concentration is denoted by ș. It is possible here to express the stationary character of the reaction using the reaction intermediate. Thus, we have:

>

1 d (O s) dt 2

@

V1 V2

i1 i2

0

In the present case, making the same hypotheses as before, and considering that Ȗ = į = 2, we arrive at:

VM

G k1 PO2 (1 T ) RT ln( H ) q k 2 PCOT

Note that VM depends on the concentration of the involved species, on the values of the kinetic constants and therefore on the nature of the solid.

136


5.4. Bibliography 1. M. SOUSTELLE, Modélisation macroscopique des transformations physico-chimiques, Masson, Paris, 1990. 2. A. SOUCHON, Utilisation de la microcalorimétrie pour l'étude des réactions hétérogènes Application à l’oxydation du niobium par les gaz, Thesis, Grenoble, 1977. 3. M. SOUSTELLE, “La théorie des sauts élémentaires dans les réactions gaz-métal, résolution par la méthode des zones”, C.R. Acad. Sci., 270C, 2-032, 1970. 4. M. SOUSTELLE, “Etude théoriques des demi-réactions d’interfaces en cinétique hétérogène gaz-solide, I – les demi-réactions d’interface externe”, J. Chim. Phys., 67, 240, 1970. 5. M. SOUSTELLE, “Etude théoriques des demi-réactions d’interfaces en cinétique hétérogène gaz-solide, I – les demi-réactions d’interface interne”, J. Chim. Phys., 67, 1173, 1970.

Chapter 6

Apparatus for Experimental Studies: Examples of Applications

6.1. Introduction A physico-chemical approach to phenomena relating to the behavior of materials, and more specifically to that of interfaces associated with a gas detection device, demands the use of specific methods of investigation and analysis. The gaseous atmosphere is an important determining factor so it is essential to be able to conduct the investigations in the presence of a gas. Many analysis techniques for solids use methods involving radiation-matter interactions, which requires us to operate under ultra vacuum. However, this state of the art technology, including ESCA and ionization probes, is not necessarily the most appropriate to deal with this type of situation. Nowadays, however, physico-chemists do have some particularly effective tools at their disposal, which allow them to study phenomena that involve heterogenous equilibriums affecting at least one gaseous element. The purpose of this chapter is to describe and illustrate using concrete examples some methods that could supply us with relevant data, at least within the investigative field of this book. Moreover, we will see in Chapter 10 how these results can be utilized in order to model certain phenomena.

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Regarding the investigative methods specific to this type of study, there are four techniques used by the “laboratory of processes granular mediums”, which are: – calorimetry using a Tian-Calvet calorimeter; – surface potential using a vibrating capacitor apparatus; – temperature programmed desorption; – complex impedance spectrometry. 6.2. Calorimetry 6.2.1. General points As we have already mentioned, it is reasonable to believe that measuring the heat released during a physico-chemical process through time yields useful information about process kinetics. Thus, in the case of solid-gas heterogenous interactions, the calorimetric method seems to be a particularly appropriate solution. In general, if W denotes the heat released in a calorimetric cell over time, which is expressed in Joules/second, then we can assume that a fraction W1 of this amount raises the internal enclosure’s temperature, while the remainder W2 is evacuated from the internal to the external enclosure, constituting what we refer to as a thermal leak. We thus have: W

W1 W2

From a technological point of view, it is possible to distinguish three types of calorimeters: – isothermal calorimeters, in which we attempt to fulfill the condition W1 = 0. The heat flux W2 is then measured, leading to W; – adiabatic calorimeters, in which we attempt to fulfill the condition W2 = 0. The rise in temperature is proportional to W1 so measuring it leads to W; – conduction calorimeters of the Tian-Calvet kind, which constitute an intermediate solution to isothermal and adiabatic calorimeters. We will limit our interest in this book to the study of the Tian-Calvet calorimeter.

Apparatus for Experimental Studies

139

6.2.1.1. Theoretical aspect of Tian-Calvet calorimeters1, 2 The microcalorimetric cell, which is where the process we are studying takes place, is connected to the external enclosure through a thermoelectric cell. The cell contains platinum – rhodium-coated platinum thermocouples connected in series and electrically isolated from the cell. There must be enough thermocouples to record the entire flux emitted by the internal enclosure (see Figure 6.1).

Figure 6.1. Diagrammatic representation of a flux calorimeter

We will see how it is possible to measure W1 and W2 using these thermocouples. 6.2.1.2. Seebeck effect Suppose we have a conductor chain A/B/A that is closed using a voltmeter. If the two metal junctions A/B and B/A are not at the same temperature, we note the formation of an electromotive force E that is proportional to the temperature difference 'T:

E D 'T

140


6.2.1.3. Peltier effect If the temperature values of the same chain’s two junctions A/B and B/A are identical, and we have a current i, there is a power transfer W from one junction to the other, which results in a difference in temperature between the two junctions. 6.2.1.4. Tian equation In the case of a Tian-Calvet calorimeter, we note that the presence of a temperature difference between the internal and external enclosure will lead to the creation of an electromotive force that is proportional to this difference (Seebeck effect). Consequently, a current will flow in the thermocouples between the internal and external enclosure. There is then a thermal exchange that is proportional to i (Peltier effect). Thus, the two effects add up and the expression of the flux W2 exchanged between the internal and external enclosure is obtained:

W2

I

P(T i T e )

ș e and ș i respectively denote the temperature of the external and internal enclosure. We then only have to calibrate the current i generated by the thermocouples using a known power to obtain the value of the flux I. In this case, a percentage of the released heat W1 contributes to raising the internal enclosure’s temperature by dș during the time dt. Knowing that μ denotes the internal enclosure’s heat capacity, we have:

W1

P

dT dt

P

d ('T ) if T e = constant dt

This relation is due to the fact that Q the exchanged heat. In these circumstances, the condition W

mc'T and that W1

dQ / dt , Q being

W1 W2 obviously becomes:


W

P'T P

141

d ('T ) dt

This relation is referred to as the Tian equation. It allows us to relate the total energy to only one variable ș. If we assume that the signal Ȝ provided by the calorimeter is proportional to the electromotive force E, and therefore to ǻș, then the Tian equation becomes:

W

D ('O W

d ('O ) ) dt

As a result, determining W is determining Į, W and d ('O ) / dt . ǻȜ represents the change in calorimetric signal between the equilibrium and outof-equilibrium states Ȝ0 and Ȝ. As for d ( 'O ) / dt , there are two possible cases to be considered: – the process is slow enough that we can consider Ĳ d ( 'O ) / dt to be negligible compared to 'O , and, under such conditions, the measured flux leads to W; – the process is rapid, and we have to calculate d ( 'O ) / dt first using the slope of the recorded signal ǻȜ = f(t) at multiple points in time. As for Į and W , it is important to conduct a calibration using a known thermal power. The easiest method consists of producing an electrical Joule effect EJ inside the calorimeter’s measurement cell (see Figure 6.2). Under steady-state conditions, when the delivered power is constant, the calorimeter produces a constant signal equal to Ȝp and is therefore proportional to EJ. As a result:

D

EJ where 'O 'O

O p O0

142


Figure 6.2. Set-up for the calibration of a calorimeter

To access the value of Ĳ, we have to reach steady-state conditions and record the curve obtained during the shift toward equilibrium after we achieve the condition EJ = 0. The equation of this curve is:

'O W

d ('O ) dt

0

Integration then yields:

Ln('O )

t c st

W

It is possible, using the response curve, to plot Ln(ǻȜ) according to t. The slope of the obtained line equals: 1 .

W

6.2.1.5. Description of a Tian-Calvet device Some of the devices produced by the SETARAM company make it possible to work at temperatures that reach 800°C; the thermostated calorimetric block contains two identical microcalorimetric cells set up to form a differential system (see Figure 6.3).


143

access to the reactor cell

Figure 6.3. Section of a Tian-Calvet microcalorimeter as produced by the SETARAM company

The importance of such a set-up lies in its allowing us to avoid the effect of any possible changes in external temperature, șe being the temperature of the reference enclosure. The reactor is made up of two identical quartz tubes immersed in the two microcalorimetric cells, thus preserving the symmetry of the equipment (see Figure 6.4). At the microcalorimeter’s outlet, the tubes can be connected to the same gas pumping or gas admittance equipment.

144


Figure 6.4. Schematic view of the gas admittance set-up

6.2.1.6. Thermogram profile We have just seen that the recorded calorimetric signal is representative of the process rate. Yet, for many processes including adsorption, the initial rate value is the highest. This value Vi = Į decreases with time to finally reach a zero value at equilibrium (see Figure 6.5, curve b, which shows the reality of the thermal process that takes place inside the cell). To express such behavior, the calorimetric signal must shift, starting from the initial instant, from a value representing a post-reaction equilibrium where V = 0 to the value corresponding to the initial rate Vi = Į, which in this case equals 40. The time W of this transient state will depend on the response time of the equipment. Concretely speaking, the signal will increase from a zero value representing the equilibrium to a maximum value VM = 20 where it will meet the real curve, b.


145

Figure 6.5. Evolution of the calorimeter’s response to the action of an adsorbed gas

The thermogram, which is obtained using curves a and b, will therefore contain a curve that shows a maximum, as can be seen in Figure 6.5.

Figure 6.6. Evolution of the calorimeter’s response in case stationary conditions have been reached

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After the reaction has taken off, it is possible to observe other situations due especially to the existence of a stationary process. In such a case, the calorimetric signal will be constant at a value lower than or equal to the initial value. If the time duration t needed to reach the stationary state is higher than Ĳ, the response curve will look like curves a and c of Figure 6.6. In the opposite situation, the response curve will look like curves a and d. 6.2.1.7. Examples of applications To illustrate the importance of this technique, we will present some experimental results regarding three types of materials. These studies deal with: – interaction between oxygen and nickel oxide; – interaction between oxygen and beta-alumina associated with metals; – interaction between oxygen and tin dioxide associated with metals. 6.2.1.7.1. Study of interaction between oxygen and nickel oxide3 The conducted physico-chemical research concerning the interaction between this material and oxygen has yielded some original electrical responses to the effect of this gas. To complete these observations from a kinetic angle, these experiments were conducted again using calorimetry. – Process conditions The sample, which is in pulverulent form, is first degassed for two days under a residual pressure of 1.33x10-4 Pa at 800°C. It is then admitted into the calorimeteric cell, which is at a controlled temperature of 700°C. Having achieved thermal equilibrium, we successively insert multiple amounts of oxygen under pressures ranging from 0.133 to 300 Pa. – Experimental results Figure 6.7 perfectly illustrates the observed results. Note first that these results could very well be of a mere adsorption process. The kinetic processes become relatively fast as soon as the gas is admitted then progressively decrease until equilibrium.


147

As a matter of fact, beyond 7x10-2 Pa, the results start to become more and more complex, at least when it comes to this experiment. Indeed, we note the appearance of an incipient stationary state characterized by a constant signal whose value differs from the one corresponding to the equilibrium. A point worth noting is that introducing additional oxygen has practically no effect on the calorimetric signal. Other results, presented in Figure 6.8, confirm this tendency and show that the time duration of the state we assumed to be stationary can reach three days when the oxygen pressure is 13.3 Pa. We will also note that once the equilibrium value has again been reached, the situation is similar to the initial one, and there is another peak in the device’s response after it has admitted a gas that is under a pressure of 106 Pa.

Figure 6.7. Calorimetric response of nickel oxide to the action of oxygen 8x10-3 < P < 0.4 Torr (1 Torr = 133 Pa)

148


Figure 6.8. Calorimetric response of nickel oxide to the action of oxygen 0.05 < P < 1.5 Torrs (1 Torr = 133 Pa)

Such phenomena can be interpreted as a reaction mechanism, involving an adsorption step associated with the formation of cation vacancies that diffuse inwards from the oxide’s surface until the cation vacancies are uniformly distributed in the bulk. The presence of stationary conditions as they have been presented in Chapter 5 corresponds to the period of time where cation vacancies are filling up the bulk. All of these results are perfectly compatible with such kinetic laws, and especially with the pressure laws. What is more, they confirm the tendencies we have observed in the electrical results of Figures 6.9 and 6.10, that is to say the presence of a transient state, accompanied by a peak and a shift towards equilibrium under oxygen pressure lower than 13.3 Pa, the presence of a more complex state accompanied by a peak and an evolution towards a stationary state under oxygen pressure higher than 13.3 Pa.


Figure 6.9. Evolution of nickel oxide’s electrical conductivity as a function of time and for different oxygen injections: curve a: P = 8 Pa , curve b: P = 10.6 Pa

Figure 6.10. Evolution of nickel oxide’s electrical conductivity as a function of time after the injection of oxygen at 40 Pa (1 torr = 133 Pa)

149

150


6.2.1.7.2. Study of interaction between oxygen and beta-alumina associated with metals4 The research conducted on the development of an electrochemical sensor made of ionic materials led to many investigations concerning beta-alumina associated with metallic elements, such as gold or platinum and used in electrodes. In order to locate and count the different oxygen species found on the surface of the materials in question, calorimetric experiments were conducted on different samples. These samples are made with beta-alumina only, beta-alumina associated with gold or platinum, with gold and with platinum. The purely metallic samples appear as foils with a surface in the order of 10 cm2, and a width of 0.1 mm. The alumina samples appear as sintered pellets made using 200 mg of alumina. We can associate alumina with metals by cathode sputtering of the metal in question. The 500 nm thick sputtering partially covers the surface of the alumina pellet. The most typical results are presented in Figures 6.11 and 6.12. Observing Figure 6.11 leads us to the conclusion that the interaction between oxygen and beta-alumina is a perfectly reversible endothermic process at temperatures between 200 and 400°C.

Figure 6.11. Corrected thermograms obtained at 300°C using beta-alumina for different changes in oxygen pressure (10 to 104 Pa)

The endothermic character of the process is a particularly interesting fact that excludes the possibility of a mere adsorption process, which is usually associated


151

with an exothermic reaction. A plausible explanation of this phenomenon would be that the adsorbed oxygen has dissolved in the crystal lattice. Figure 6.12 illustrates the effect of gold and platinum on the thermograms. There is quite a significant decrease of the heat produced by oxygen in the presence of a metal, the platinum having a bigger effect than gold.

Figure 6.12. Comparison between the thermograms obtained with beta-alumina only and those obtained with alumina and gold or platinum for a change in oxygen pressure of 10 to 104 Pa

The histogram in Figure 6.13 sums up this kind of situation, leading us to the conclusion that the effects of gold or platinum are all the more visible since the working temperature is low. Moreover, it confirms the fact that the effects we observed on the beta-alumina only as the temperature varied are suggestive of an endothermic process, which is characterized by an increase in the amount of formed species, and as a result, by an increase of the matching heat quantity as temperature rises. The role played by metals can be interpreted by considering the formation of a new exothermic oxygen species whose bound amount constantly decreases while the temperature rises. The exothermic nature of this species makes it possible to explain why its contribution to the heat exchange continually decreases with temperature; the calorimetric signal corresponding to the composite material of alumina + metal then joins up with the signal corresponding to alumina alone.

152


Figure 6.13. Heat exchange of the different samples, and at different temperatures, for a change in oxygen pressure of 10 to 104 Pa

6.2.1.7.3. Study of the interaction between oxygen and tin dioxide associated with metallic elements We have just seen that the presence of a metal could have direct consequences on the nature of surface chemical states for an ionic oxide. These results, which are particularly interesting when it comes to understanding the kinetic processes of gas-solid interactions, have led us to conduct similar investigations on tin dioxide. These experiments are related to those we will present in Chapter 7 and which concern the role of electrodes. Once again, we will study tin dioxide, tin dioxide associated with gold or platinum, gold and finally platinum. – Experimental protocol The experiments are conducted on tin dioxide samples that were initially sintered at 800°C under a residual oxygen pressure of 10 Pa. The samples used weighed 150 mg, and the specific surface of this material was in the order of 5 m2/g. Regarding tin dioxide associated with gold or platinum, we used 150 mg plates covered with a 450 nm-thin layer of metal that was deposited by cathode sputtering.


153

Gold and platinum are used in the form of metal foils with a 2.10-2 m² surface area and a 0.1 mm width. – Results obtained with the different samples a) Tin dioxide only The interaction between tin dioxide and oxygen has been studied for three different changes in oxygen pressure ranging from 10 to 200 Pa, from 10 to 2x103 Pa, and from 10 to 5x103 Pa. These experiments were conducted in isothermal conditions at 300 and 400°C. We have plotted the thermograms we obtained at 400°C under three different oxygen pressure values in Figure 6.14. We can see that an increase in oxygen pressure yields an exothermic signal, and that the signal amplitude increases with pressure.

Figure 6.14. Thermograms obtained with a tin dioxide sample at a temperature of 400°C and for different changes in oxygen pressure (10 to 5x103 Pa)

We can also see that the process is relatively fast and that its time duration, which is in the order of 300 seconds, does not seem to be affected much by the admitted amount of oxygen. The reverse process, which is much slower but perfectly reversible, has a duration in the order of 30 minutes.

154


These results perfectly fit those of an adsorption process. b) Pure metals Unlike the previous results, those obtained with gold or platinum-only metal foils have not shown any sign of heat exchange during the multiple gas injections, at least not with the experimental conditions and sensitivity ranges used for the tin dioxide samples. c) Gold or platinum-covered tin dioxide The effects of gold or platinum, which are presented in Figure 6.15, result in a noticeable increase of the emitted heat, platinum having a bigger effect than gold.

Figure 6.15. Thermograms obtained with the different types of samples at a temperature of 400°C and for changes in oxygen pressure of 5x103 Pa

The influence of oxygen pressure confirms this tendency, as can be seen in Figure 6.16


155

Figure 6.16. Heat exchange (-Q in mJ) with the different types of samples for changes in oxygen pressure ranging from 10 to 5x103 Pa, at 400°C

It is tempting to take into consideration the results we obtained using pure metals and come to the conclusion that oxygen is more reactive towards tin dioxide associated with metals because of a synergic effect between metal and oxide. In order to eliminate the exclusive action of metal, complementary experiments were conducted using equal metal surface areas in both cases, that is to say for pure metals and also for metal associated with tin dioxide. In the second case, it comes down to sputtering the metal on a 1 mm x 10 mm surface; the metal then appears as a line. If we take into account the sintered material’s specific surface area, we obtain a surface area of approximately the same magnitude as the metal-only sample, that is to say 2 dm2. Figure 6.17 clearly confirms the influence of the oxide-supported metal even when the oxide and metal are present in equal amounts. Indeed, just as we expected, the interaction between oxygen and tin dioxide results, using an exothermic process, in the formation of at least one chemisorbed oxygen species on the surface of the oxide.

156


Figure 6.17. Thermograms obtained with the different types of samples at a temperature of 400°C and for changes in oxygen pressure of 20 Pa

In order to interpret the role of deposited metal, we can imagine the creation of a new chemisorbed oxygen species of exothermic nature but whose formation enthalpy is higher in absolute value than the other species. This hypothesis could be correlated to the fact that the oxide-metal interface can induce the creation of new adsorption sites with higher energy than that of tin dioxide. 6.3. Thermodesorption 6.3.1. Introduction This technique, which is based on the exothermic nature of adsorption, allows us, by using a programmed temperature increase, to analyze the chemical species initially bound to the surface of a solid and which are desorbed under the influence of temperature. Detecting and/or analyzing desorbed molecules is possible with the use of different detectors, such as thermistors, or analyzers, such as chromatography or mass spectrometry. This analysis could also be conducted by maintaining the sample under a dynamic vacuum or inert gas vector flow.


157

The choice of a detector depends most often on the nature and the quality of the expected information: – thermistors provide only quantitative information, without specifying the nature of bound species; – chromatography provides quantitative as well as qualitative information, but in a discontinuous way; – mass spectrometry provides continuous quantitative and qualitative information using samples that are, usually, maintained under a dynamic vacuum of 10-4 Pa. These devices are designed to analyze charged species obtained after the desorbed element is ionized. The gathered information is therefore characterized by a m/e ratio where m is the mass of the element chosen by the experimenter and charge e is identified with the ionicity degree of the element in question. Some elements can thus appear with different ionicity degrees. The experimental results presented in this chapter were all obtained through mass spectrometry. The equipment we used consisted of 5 (see Figure 6.18): – a heating reactor made up of a laboratory tube and a programmed temperature furnace which reaches a temperature of 900ºC; – a mass spectrometer chosen based on its performances and the nature of species to be detected. The information delivered by this analyzer is representative of an ionized material flux marked by the m/e ratio. Through a continuous scan adapted to the m/e ratio, we will be able to monitor all of the masses, or even continually monitor one or multiple m/e ratios that the experimenter will have had to provide; – two turbomolecular pumps capable of creating a separate residual atmosphere. Note that turbomolecular pumps maintain atmospheres with no trace of oil in them, which averts hydrocarbon pollution. The first vacuum pump controls the gaseous atmosphere of the reactor, and allows us to degass the solid sample beforehand at a moderate temperature. The second pump controls the residual pressure in the mass spectrometer. 6.3.2. Theoretical aspect 6, 7 We have just seen that the information delivered by the mass spectrometer is representative of a material flux and therefore, in this case, of a desorption rate.

158


We have seen, however, that a desorption process can be considered an elementary step:

n( X s ) X n ns [X] represents the concentration of the species X - s in its adsorbed state, and n is its stoichiometric coefficient.

Figure 6.18. Diagrammatic representation of a thermodesorption set-up associated with a mass spectrometer

The rate Vd is therefore:

Vd

H Ed d >X @ )>X @ n k d exp( dt RT


159

Given the temperature and pressure range of study, we will assume that the adsorption component Va is negligible compared to Vd. Thus, concerning the monoatomic adsorbed oxygen, we will have:

2(O s ) O2 2 s where n = 2 X also being a function of temperature T, the changes in desorption rate can be expressed as:

dVd dT

H H H E Ed Ed dX 2 )>X @ 2kd exp( )>X @ k exp( 2 d RT RT RT dT

It is possible, using this relation, to prove that the rate reaches a maximum value that corresponds with the temperature. To do so, we will choose a variation law for temperature as a function of time:

T

T0 at

a being the heating rate. It follows that:

dVd dT

dVd dt dt dT

1 dVd a dt

The maximum rate VdM is obtained using the equation:

dVd dT

0

This maximum rate will therefore correspond to a temperature value T = TM and a concentration value [X] = [XM]. We will thus have:

H E >x@ RT 2

2 Vd a M

160


Therefore:

H E RTM2

H 2H E )> X M @ k0 exp( a RTM

We can also demonstrate, using some mathematical approximations, that when n = 2:

>X M @ >X 0 @ 2

The previous expression can be written a different way:

a Ln 2 TM

H H E E Ln H Ln> X 0 @ RTM Rk0

Determining the system’s parameters, and especially the activation energy requires an analysis of multiple spectra obtained with different heating rates. This

procedure 2 M

Ln(a / T )

easily

leads

us

to

the

value

of

H E

by

H E,

plotting

f (1 / TM ) . A specific temperature value TM indeed corresponds to

each value of a. The slope of the obtained line equals

L E/R.

In fact, observing noticeable variations of the rate curve as temperature changes requires there to be very high variations of the heating rate. Ratios of the order of 100 are sometimes necessary, which can pose some technological problems. On a purely qualitative level, this procedure is not necessary. We can then analyze two types of spectra: – those obtained through a scan of the m/e ratio. Such spectra make it possible for us to quickly analyze the nature of present species; – those obtained using a chosen value of the m/e ratio. Since they are more precise, such spectra allow us, if need be, to better describe the species, particularly when it comes to their binding energy to the solid. It is important to note that depending on the diversity of adsorption sites and/or


161

temperature, a species of a given chemical nature can be differently adsorbed; each possibility being characterized by the value of its binding energy to the solid. Thus, a mere perusal of the spectra obtained using the same sample but different values of the m/e ratio will lead us, on the one hand, to information of a chemical nature and, on the other, to information concerning energy; both with regards to the entire set of adsorbed species on the solid’s surface. Based on a few experimental results, we will show the importance of this technique in solving the problems regarding the analysis of surface chemical states. 6.3.3. Display of results These are experimental results from, on the one hand, a study on tin dioxide and, on the other, a study on nickel oxide. These two materials are studied here under different oxygen pressure values and either have or have not been subjected to some gaseous treatments. 6.3.3.1. Tin dioxide8 Particularly used as the sensitive element in gas sensors, this material has been the subject of a large number of investigations in the thermodesorption field. This presentation will focus more specifically on the effect the presence of adsorbed sulfur dioxide has on the binding energies of the hydroxyl groups present on the tin oxide’s surface. The experiments were conducted on two types of sintered samples. These two samples differ from one another in respect of a sulfur dioxide gaseous treatment that was conducted upon one, but not the others, at 500°C for 15 minutes. Generally, the surface of a material that has not been subjected to a sulfur dioxide treatment is rich in hydroxyl groups, and the thermodesorption spectrum presented in Figure 6.19 is typical of this kind of situation. The desorption of these species, which is marked by the ratio value m/e = 18, takes place over a temperature ranging from 100 to 800°C, with a very noticeable peak around 550°C. There are also three slight bumps located at 180, 380 and 750°C. Figure 6.19 also indicates an oxygen spectrum characterized by m/e = 32. Weak traces of carbon monoxide and carbon dioxide were also detected but are not presented in this diagram.

162


We note a profound change in the water spectrum of the sample that was subjected to a sulfur dioxide treatment (see Figure 6.20). We observe, indeed, that the peak at 550°C has practically disappeared, contrary to the peak corresponding to 180°C. We also note that there are, at high temperatures, new species marked by the ratio value m/e = 48.

Figure 6.19. Thermodesorption spectrum of the hydroxyl groups (m/e = 18) and oxygen (m/e = 32) bound to tin dioxide prior to treatment

These species are characterized by a sharp thermodesorption peak located between 700 and 800°C. This peak is very clearly associated with a simultaneous oxygen desorption. The signal corresponding to m/e = 48, which can be attributed to the SO+ ion, expresses the presence of a sulfur compound that is surely different from sulfur dioxide. This is based on the fact that the ratio of the m/e = 32 and m/e = 48 is about 2 in the present case, while it is around 0.4 when it comes to sulfur dioxide. The value of 0.4 was determined during the calibration of the mass spectrometer.


163

Figure 6.20. Thermodesorption spectrum of the hydroxyl groups (m/e = 18) and oxygen (m/e = 32) bound to tin dioxide after the sulfur dioxide treatment

The sulfur compound present on the tin dioxide’s surface could be SO or SO3. These results therefore seem to indicate that sulfur dioxide reacts with tin dioxide and produces a relatively stable species that is only desorbed once high temperatures are reached. This species, which causes the changes we observed on the spectrum marked by m/e =18, could therefore compete with hydroxyl groups by occupying sites that were initially occupied by the hydroxyl groups, which would be forced to occupy sites of lower energy. 6.3.3.2. Nickel oxide9 It was deemed necessary, in a study on the evolution of the electrical behavior of this material in the presence of gases, and particularly in the presence of sulfur dioxide, to better analyze and control its chemical surface states under different temperature and oxygen pressure conditions. The samples studied were in pulverulent form and weighed 1 g. The heating rate was 14°C/min.

164


A preliminary analysis (see Figure 6.21) leads to the observation that there is large water desorption at 180 and 470°C. The two peaks probably express a dehydration followed by a dehydroxylation of the oxide. The m/e = 48 ratio value corresponds to the carbon dioxide, which is desorbed at 180, 410 and 610°C. Desorption of oxygen leads to a much more intense and complex spectrum. It reaches its maximum at 520°C, and also presents many oscillations that show the presence of multiple adsorbed species with different energies.

Figure 6.21. Thermodesorption spectrum of nickel oxide sinters exposed to air

To better grasp and characterize these different species, we adopted a protocol that consisted of controlling the temperature TA that corresponds to oxygen admittance on a perfectly degassed sample. It is reasonable to think that the concentration of each adsorbed species, which is related to its adsorption or desorption rate, is a function of temperature and oxygen treatment time. – Influence of temperature and adsorption time From a practical standpoint, the sample that is degassed for one night at 750°C is subjected to 100 Pa pressure oxygen at the temperature TA and for a time t. After that, the sample is quickly cooled, then degassed at degassing temperature TD.

10-3 Pa for an hour at the

The effects of introducing the gas at the temperature TA are shown in Figure 6.22 for four different temperature values, with an oxygen exposure time t of one hour and a degassing temperature of 20°C.


165

These results perfectly display the considerable evolution of the oxygen’s energy state depending on the adsorption temperature. Moreover, they allow us to observe the evolution of multiple coexisting species according to temperature.

Figure 6.22. Oxygen thermodesorption spectrum as a function of adsorption temperature TA

Figure 6.23 presents the results obtained with a sample that was exposed to oxygen at 500°C, and for a time duration of 1, 15 and 60 minutes. This particularly interesting spectrum shows that, in this case, the oxygen exposure time causes the disappearance of a species, marked by a peak at 400°C, apparently to the benefit of the species corresponding to the peak located around 500°C.

166


Figure 6.23. Oxygen thermodesorption spectrum as a function of adsorption time

Using these results, which show how complex this oxide’s surface chemical states are, six different oxygen species were identified and marked by the temperature of their desorption peak TM (see Table 6.1). Adsorbed species

01

02

03

04

05

06

TM(ºC)

320

410

520

640

740

860

Table 6.1. Desorption temperature of the different species

It is possible, by identifying each desorption curve with a Gaussian curve, to “decompose” each spectrum and evaluate the effect of each species as a function of time and temperature of adsorption TA. Figures 6.24 and 6.25 give two examples of the “decomposition” of spectra, each corresponding to a different adsorption temperature: TA= 750 and 400°C, and with respective exposure times of 30 seconds and 15 minutes.


167

Figure 6.24. “Decomposition” example where the adsorption temperature is 750°C

Figure 6.25. “Decomposition” example where the adsorption temperature is 400°C

Figures 6.26 and 6.27 give the evolution model of species “320” and “410” for different adsorption temperature values; we will note that species “300” is still present when the sample is exposed to oxygen at 750°C. – Influence of desorption temperature It is possible, based on the previously obtained results, to prepare various samples characterized by the number of species on their surface by choosing the right values for the desorption temperature TD. The method consists of successively eliminating some species by desorption, starting with the most weakly bound ones.

168


Figure 6.26. Amount of chemisorbed oxygen in the “320°C” form: adsorption kinetics as a function of TA

Figure 6.27. Amount of chemisorbed oxygen in the “410°C” form: adsorption kinetics as a function of TA

Figure 6.28 gives the thermodesorption spectrum of four samples that were degassed at 250, 400, 500 and 600°C. These samples had initially been exposed to oxygen at 600°C.


169

Figure 6.28. Thermodesorption spectrum of oxygen obtained with nickel oxide at 600°C and degassing at different temperatures TD

Table 6.2 sums up the surface states specific to each sample that is referred to by a number from 1 to 5. sample

TD

species bounded at the surface

1

250

06 + 05 + 04 + 03 + 02

2

400

06 + 05 + 04

3

500

06 + 05

4

600

06

5

750

no adsorbed species

Table 6.2. Evolution of the nature of adsorbed species as a function of desorption temperature

– Reactivity to sulfur dioxide In order to better interpret nickel oxide’s reaction to sulfur dioxide, it might be interesting to consider this problem from the angle of the selective contribution of one or multiple oxygen species. Selecting 5 different sample types enables us to

170


conduct a certain number of tests. Each sample is subjected to the action of pure sulfur dioxide at 250°C and is then analyzed by thermodesorption. The spectra retained are those corresponding to the ratio values m/e = 32 and 48. Regarding samples 2 to 5, the spectrum in Figure 6.29 shows simple desorption of sulfur dioxide, the mass ratio keeping a constant value of 0.4. The interaction between nickel oxide and sulfur dioxide therefore comes down to a simple adsorption process. The results we obtained for sample 1 (see Figure 6.30) are much more interesting if we consider the appearance of new species on the spectrum beyond 600°C. In such a case, the signal ratio is no longer constant, and its value greatly exceeds 1. This leads to the idea that a species that is much more stable than adsorbed sulfur dioxide is present on the nickel oxide’s surface, and that this species, which is present in sample 1 only, is a result of the interaction between sulfur dioxide and the oxygen species that is most weakly bound to the solid.

Figure 6.29. Thermodesorption spectrum obtained with nickel oxide after sulfur dioxide adsorption at 250°C: samples 2 to 5


171

Figure 6.30. Thermodesorption spectrum obtained with nickel oxide after sulfur dioxide adsorption at 250°C: sample 1

.

.

.

Figure 6.31. Heat exchange during adsorption of sulfur dioxide at 250°C as a function of its pressure and for different nickel oxide pretreatments

In addition, this difference of behavior was brought forth by calorimetric experiments conducted at 250°C (see Figure 6.31). The results show that the heat of reaction between oxygen and nickel oxide is distinctly higher for sample 1. This confirms the fact that sample 1 has a much greater reaction to sulfur dioxide.

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6.4. Vibrating capacitor methods As we have already mentioned with regard to adsorption processes, the formation of new surface states, such as atomic rearrangements or the presence of chemisorbed gaseous species, influences the equilibrium states of this same surface. These surface states generally lead to the creation of a potential barrier VS at the surface of the material. This potential can vary according to experimental conditions, particularly the partial pressure of the gases present in the gaseous environment. There are various experimental methods that can lead us to the value of VS. Physico-chemists consider the vibrating capacitor method to be one of the most efficient because it allows us to work under gas and at different temperature. In general, this method allows us to measure the work function of a solid or its variations simply by measuring the contact potential between the concerned solid and a reference solid. 6.4.1. Contact potential difference10 Suppose we have two solids R and S characterized by their respective ~ and P ~ (see Figure 6.32a) and that when thermal electrochemical potentials P R S equilibrium is reached – considered separately in each phase – we have:

P~R ! P~S If the ends of these two solids are electrically connected, the system approaches a state of thermodynamic equilibrium whereby electrons in both solids will have the same electrochemical potential, thus:

P~R

P~S

It is possible to demonstrate that the shift of the system towards equilibrium generates an electron flux from the solid with the highest electrochemical potential towards the other solid. This electron transfer comes with the appearance of a negative charge on the solid S, and a positive one on the solid R, revealing a difference in potential between two solids.


173

The difference in potential between two points M and P on the surface of solids R and S is referred to as the Volta potential difference or the contact potential difference; it is expressed using the relation:

VRS

VeR VeS

where VeR and VeS represent the electrostatic potential of electrons on the nearsurface layer of solids R and S. Figure 6.32b represents the energy diagram of the two solids R and S at thermodynamic equilibrium. According to the definition of the electronic work function (see Chapter 4), the electrostatic potentials VEr and VeS are expressed the following way:

VeR

1 (IR ~ ȝR ) q

Figure 6.32. Energy diagram of solids R and S

174


and:

VeS

1 (IS ~ ȝS ) q

which yields the following expression for the contact potential difference:

VRS

VeR VeS

1 IR IS q

The contact potential difference between two solids R and S equals the difference between their work functions multiplied by 1 / q . Depending on each case, measuring the contact potential difference can yield either the absolute value of the work function or the work function changes of a solid: – if solid R’s work function has been precisely determined using another method, we can deduce the value of the work function IS of solid S using the contact potential difference VRS between R and S:

IS

qVRS IR

– if the work function of one of the two solids, say solid R, is stable under the chosen experimental conditions, then we have:

IR

0

As a result, the changes ') S in work function of the solid S equal those of the contact potential difference multiplied by the factor q:

'IS

qVRS

In the particular case of a metal semiconductor system, whose energy diagram is given in Figure 6.33, the contact potential difference is obtained using the relation:

VRS

IS I R q


175

where:

IS

F H V q(VS VD )

(see Chapter 4, equation [4.15])

As a result:

VRS

F HV qVS VD IR q

We have already seen that the only parameter of a semiconductor that can vary during the adsorption of gases on its surface is the surface barrier VS and the dipole component VD; therefore, choosing a metal R whose work function IR is constant under the working conditions leads to:

'VRS

(VS VD )

Figure 6.33. Energy diagram of a metal semiconductor system

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6.4.2. Working principle of the vibrating capacitor method11, 12 6.4.2.1. Introduction In this method, solids R and S constitute the electrodes of a capacitor whose capacitance will be denoted by C. When the two electrodes are electrically connected through a resistance R, the capacitor charges up with the potential difference VRS, which is the contact potential difference between the two solids. We will denote it by VDPC throughout this chapter. Under such conditions, the electrical charge Q carried by the capacitor’s electrodes equals:

Q CVDPC The principle method, owed to Kelvin, consists of distancing one of the capacitor’s electrodes from the other; the subsequent change in capacitance ǻC leads to a change in carried charge ǻQ while the electrode is moving:

'Q VDPC 'C If an opposite direct voltage is added to the circuit and fixed at a value U0 so that distancing the electrodes will no longer create a charge variation, then we are allowed to say that U0 has the algebraic value of the opposite of the contact potential difference VDPC. The vibrating capacitor method known as the Kelvin-Zisman method was developed by Zisman based on the previous method. Instead of simply distancing the electrodes from each other, Zisman periodically vibrates an electrode, thus creating an alternating current that is easier to detect. 6.4.2.2. Theoretical study of the vibrating capacitor method Suppose we have a plane capacitor, whose section area is denoted by S and whose electrodes are l0 apart from each other and made of solids R and S. Its capacitance C0 is:

C0

H 0H

S l0

İ represents the dielectric constant of the medium between the two electrodes.


177

When an electrode is moved according to a sinusoidal law of amplitude l1 and (mechanical) pulsation Z, the distance between electrodes l varies as a function of time according to:

l

l0 l1 sin Zt

Inserting the modulation amplitude m

l

l1 / l0 leads to:

l0 (1 m sin Zt )

Under such conditions, the capacitor’s capacitance C equals:

C

H 0HS

l0 1 m sin Zt

At low modulation amplitudes, that is to say when m 2Ld, the conductivity is controlled by the resistance of the neck between two grains; – if L60 Pa), which is then quickly out of use. The films containing tungsten oxide have different electric properties, and cannot be used to detect gases. For some applications, it is important that we can explore films under high pressure. Thus, to solve the oxidation, we have to use a mix of oxygen + nitrogen at the desired pressure, so that the oxygen pressure is less than 50 Pa. Generally, we use oxygen until the pressure reaches 35 Pa and air until it reaches 160 Pa. We then note that the average reaction speed is the same under a pressure of 35 Pa of oxygen and under a pressure of 175 Pa of air, which corresponds to an oxygen partial pressure of 35 Pa. It is possible to mix the oxygen with another inert gas. We then note that the molar mass of this gas has a great influence on the texture and the density: thus, with the same total pressure, an increase of the molar mass implies a decrease of the film density (Table 7.2).

228


66 Pa O2 M = 32 g

66 Pa O2

66 Pa O2

+ 200 Pa H2

+ 200 Pa A2

(M = 4 g)

(M = 40 g)

0.022

0.0125

266 Pa O2 or air

Relative density d/dSnO

2

0.0266

0.0167

at 2.5 cm Table 7.2. Relative density variation

It is then normal to note that the films deposited in the same oxygen or air pressure are identical, because the molar masses of oxygen and nitrogen are close (32 and 28 respectively). Thus, at a constant total pressure, the oxygen pressure acts only on the deposit speed. – Size and composition of the grains The X-ray diffraction pictures on the annealed samples do not show the rays typical of SnO2 (Figure 7.6). Nevertheless, the films deposited under a pressure close to 2 Pa, and therefore composed before firing of a mixture of metal and oxide, after firing contain different tin oxides, as well as a low quantity of metal. The measure of the width of the diffraction rays shows that the size of the grains is about 50 or 60 Å after annealing, and does not depend much upon the deposit pressure. – Surface analysis (Figure 7.8) The results obtained using the Auger spectroscopy show that the oxygen concentration at the surface of the films increases with the pressure. Remember that this method allows an analysis not far below the surface, that is to say below 10 Å. We can also detect impurity (sulfur and carbon), especially on the most compact films. After evaporation, tungsten traces can be observed on the films in an oxygen partial pressure greater than 60 Pa. As was explained before, these traces come from the filament oxidization and confirm the necessity to limit the oxygen partial pressure during the deposit. A great part of the impurities on the compact films disappear thanks to ionic abrasion. So, it seems that the impurities are concentrated on the surface of such films.

Material Elaboration

229

Figure 7.8. Influence of the oxygen pressure on the AUGER spectrum, E =3 keV

– Electric conductivity measure The electric conductivity measures mentioned here are made using the four points method, at a temperature of 500°C in dry air. This conductivity, which is defined by the quotient of surface conductivity compared to the thickness of the film, is the average conductivity of the film. It is necessary to divide this value by relative density in order to know the conductivity of a grain or the conductivity of the compact material composing the film. The conductivity V (S/cm) greatly decreases when the depositing pressure increases (Figure 7.9).

230


Figure 7.9. Conductivity at 500°C in dry air according to the deposit pressures

The peculiar values observed between 2 and 10 Pa correspond to the crackled films already mentioned. The conductivity of these films greatly drops, and it is sometimes impossible to measure. Furthermore, the density of the films decreases when the pressure increases: this can partially explain the part of the curve where the conductivity Vdecreases. If, as in Figure 7.10, we plot V as a function of the density d, we obtain a curve which can be modeled by the following expression:

V

kd a

with 3 < a < 3.3. Thanks to the percolation theory, we know the laws which rule the electric conductivity of a mixture of insulating and conducting powders. Thus, if n is the conducting powder proportion, the conductivity V of the mixture is calculated using the following expression:

V

( n nS ) a

nS is called the percolation threshold and represents the value of n under which the mixture is no longer conductive.


231

Figure 7.10. Conductivity at 500°C in air as a function of the relative density

This theory can be applied to the porous conductors, if we imagine that the pores and the grains of the material are the two constituents of the mixture. In this peculiar case, the percolation threshold necessarily tends towards zero, because there will always be an electric charge transfer in the material. This case has been studied by Deptuck et al.,6 using sintered submicronic silver powder. This powder is prepared using silver evaporation in inert gas. They then find the value of the exponent: a = 2.15 ± 0.25. This value is smaller than the one we found, which seems to indicate the film’s porosity is not the factor responsible for the decrease of V with the pressure. Another factor could be the increase of the oxygen concentration noted on the grain’s surface during the Auger analysis. The intrinsic conductivity of each grain is in effect controlled by the oxygen stoichiometry deviation. In this case, the phenomenon can be limited to the surface of grains, but given their tiny dimensions (50 to 60 Å), we can expect determining effects on the film conductivity. – Reproducibility of the electric measures Often, the reproducibility of the electric measures is weak; for two distinct films deposited using the same method and conditions, there can exist a factor 5 between the measured values. This particularly concerns films deposited under low pressure and thin films.

232


Nevertheless, this error level does not matter much compared with the variations of V according to the studied parameters. Indeed, we have seen that there exists a ratio of 107 between the extreme values measured. This lack of reproducibility seems to be mainly due to an uncertainty concerning the value of the pressure, which is difficult to regulate during the deposit. Indeed, a small variation of the pressure can have an important effect on ı. This value is multiplied by 104 when P increases from 10 to 100 Pa. The variation of ı with the pressure is not as important when the pressure reaches high values (P > 100 Pa). Thus, it will be better to deposit under high pressure if we seek a good reproducibility, although this implies obtaining films whose conductivities will be lower. – Influence of the distance between the source and the substrate For an initial mass m0 of tin in the crucible, we obtain a film whose mass per unit area depends on the evaporation distance. If we want to study, at a constant mass per unit area, the influence of the distance between source and substrate, then we are obliged to vary m0 as a function of the chosen distance. In these conditions, the distance source/substrate seems to have the same influence as the total pressure, be it at the texture level (compact, columnar or spongy), at the density level (see Figure 7.11) or, consequently, at the electric conductivity level (see Figure 7.12). It then appears interesting to draw the iso-density curves (see Figure 7.13) which enable us to characterize the deposit conditions for a given density value and, consequently, for a given conductivity value.


233

Figure 7.11. Influence of the distance between source and substrate on the relative density

Figure 7.12. Influence of the distance between source and substrate on the conductivity (P = 66 Pa)

234


Figure 7.13. Iso-density curves

– Influence of the mass unit area at constant distance To study this influence, we vary the tin mass m0 initially present in the source. The mass unit area and, consequently, the thickness seem to have no observable influence at the texture level, at the density level or at the conductivity level. The thicker films have the advantage of a conductance which is proportional to the thickness and, consequently, greater. Nevertheless, they will be mechanically more fragile. – Influence of the annealing The annealing is performed at a temperature contained between 500 and 650°C, in ambient air for 15 hours. We observe, comparing the different X-ray diffraction spectra, that the annealing increases the size of the grain from 25-35 Å to 50-60 Å. Indeed, we will see in section 7.2.3.3 that there is a relationship between the diffraction ray width halfway up and the size of the grain. The influence of the length and temperature of the annealing have been succinctly studied using the X-ray spectra (Figure 7.14): a) at 500°C, four hours of annealing are necessary to obtain a product, of an apparently structure stable; b) for an annealing of 15 hours, a temperature greater than 450°C is then necessary. Nevertheless, it is advisable to increase these values in order to be certain that the final product will be adequately stabilized (in practice: 600°C during 10 hours).


Figure 7.14. Influence of the annealing on the X-ray diffraction spectra

235

236


7.2.3. Chemical vapor deposition: deposit contained between 50 and 300 Å

7.2.3.1. General points The chemical vapor deposition consists of bringing a volatile compound of the material to be deposited into contact with either another gas in the neighborhood of the concerned surface or with the concerned surface directly in order to provoke a chemical reaction which produces the sought solid. This method, commonly called CVD (chemical vapor deposition), allows the development of a great many materials, including pure elements, solid solutions and composite materials of different substrates. The chemical vapor deposition, though widely used in the industry, proves to be a complex technology, which demands an extensive knowledge of: hydrodynamics of fluids, thermodynamics, kinetics, adsorption and chemistry. The complexity of the involved mechanisms also comes from the great number of interdependent parameters like pressure, temperature, the gaseous phase composition, the gaseous flow and the kind of reactor used. Among the different reactors, we distinguish reactors with a hot inner surface from reactors with a cold inner surface. In a hot inner surface reactor, the whole device is kept at working temperature. This method, which implies a homogenous temperature in the reactor, has the drawback of depositing the material sought on the whole device. In a cold inner surface reactor, the material is deposited on the specified surface, though it is done to the detriment of the temperature homogenity on the surface to cover and in its gaseous neighborhood. For technical reasons linked to conceptual problems and the size of the devices, the device shown in this book is a cold inner surface reactor; indeed, hot inner surface reactors are more specifically used for industrial applications. In general, and especially for this kind of reactor, the process can be split into five main stages: 1) the diffusion of the gaseous phase reagent, through the diffusion-limiting layer, towards the substrate surface. Indeed, there exists, in the neighborhood of the substrate, a film containing some gaseous products stemming from the reaction, and inside which exists a gradient of the reagent concentration; 2) the adsorption of the reagents on the substrate surface;


237

3) the diffusion of chemical species on the surface of the substrate; 4) the germination-growth process of the film; 5) the diffusion of products stemming from the reaction through the diffusionlimiting layer, towards the gaseous phase. The whole of this process is illustrated in Figure 7.15. On the kinetic level, it is obviously the slower part which imposes its speed on the process. We distinguish two growth modes, depending on whether the limiting stage is the mass transfer in vapor phase (diffusion process) or the surface reactions (kinetic process).

Figure 7.15. Process diagram

In general, the phenomena in the vapor phase are furthered by a pressure increase, surface phenomena by a temperature increase.

238


7.2.3.2. Device description 1) Choice of the precursor The tin precursor, chosen to deposit SnO2, is an organometallic compound: tin dibutyldiacetate. In ambient air it is a colorless and viscous liquid compound and does not react with air. It is used because of its physical properties: it has a saturated vapor pressure of about 100 Pa at 100°C, which makes it easily transportable through the use of an inert gas. Furthermore, it is one of the few organostannic compounds that are common. Because of its toxicity, this product has to be handled with care. 2) The CVD device – The CVD reactor The choice of the reactor is very important because it influences the way the reaction happens and can alter the deposit’s nature. We use a reactor with a cold inner surface, cylindrical and vertical. The gas inlet is at the top with a heating device in the middle, and the outflow of the gas at the bottom. This symmetric axial configuration, associated with the regulation of the total pressure in the reactor, is intended to ensure hydrodynamic conditions favorable to realizing a homogenous deposit (the flow of gas is laminar because of the low pressure and the high pumping speed (see Figure 7.16)). The device is composed of a component generating the reagents in the vapor phase, a reactor equipped with a heating system, a pressure regulation system and a gas draining system.


Figure 7.16. Laminar flow of gases in the reactor. Experimental device

Figure 7.17. Device description

239

240


3) Experiment conditions In order to get rid of the problem of stoichiometry and reaction efficiency, we use more oxygen than DBTB so that the stannic precursor is completely consumed. Liquid tin dibutyldiacetate is then put into a jacketed Pyrex balloon at a temperature of 100°C. At this temperature, the saturated vapor pressure is 100 Pa. It is transported by nitrogen current. This is carried out at atmospheric pressure, so that, in conditions of thermodynamic balance between the liquid and gas phases, the DBTD concentration in the gas phase depends on its saturated vapor pressure at the temperature of the liquid. At 100°C, the molar proportion of the DBTD in the nitrogen is about 0.1%. The DBTD is then put into contact with oxygen through the use of a mixer in order to elaborate the reagent. The design of the gas mixer ensures the best homogenization possible. It is made of Pyrex: two independent tanks are linked by a tube. In the first tank, the two gas inlets are facing each other: it creates turbulences and an efficient mix. Then the gases enter the second tank before entering the reactor. Another inlet of nitrogen makes it possible either to dilute the mixture, or to purge the whole gas circuit (see Figure 7.18).

Figure 7.18. Gas mixer description

The gas flows are regulated by flowmeter. The pressure at which the gas flows is the atmospheric pressure, and when there is no deposit, the gas is directed towards a column before being evacuated. We thus recover the DTBD which has not reacted. The introduction of the gases in the reactor is carried out through the use of two electromagnetic valves. The first is a three-way electromagnetic valve which allows us to let in either the reagent mixture (N2 + DBTD + O2) or a nitrogen purge. The second is a two-way electromagnetic valve placed just before the gas entry to the reactor: it is this valve that lets the gases into the reactor.


241

Between these two valves, there is another valve that allows accurate regulation, of very low conductance, which allows us to introduce the gases under a low total pressure. The pressure before the valve is the atmospheric pressure. After the valve, the gases are at the reactor’s pressure (10 to 1,000 Pa). The reduction in pressure, which happens at this valve’s level, implies a great decrease of the gases’ temperature, and a condensation of the tin dibutyldiacetate, which tends to block this valve. In order to solve this problem, a steam-drying at 200°C is performed. – The reactor As stated above, the reactor is a vertical cylinder made of stainless steel. Its inner diameter is 216 mm and its height is 224 mm: thus, the reactor’s volume is 8.2 liters. The reactor is equipped with a circular porthole (Ø 100 mm) on its top part. Thanks to this porthole, we can oversee the depositing process and control the deposit’s thickness and subsequently the depositing speed, using, especially for SnO2, the color of the thin films deposited on the silicon substrate. Two symmetric openings are placed at 4.2 cm of the top; their diameter is 16 mm. The first is used for the gases introduction and the other is used to measure the pressure. On the reactor inner surface, a circular opening is linked to the pumping system. This opening is centered and it must have a sufficient size (here, its diameter is 45 mm). Four openings are placed at the reactor’s bottom and are used for the measure of the temperature and the supply of the heating system in electricity. A copper tube, inside which circulates a fluid, surrounds the reactor outer surface. This tube allows us to better control the temperature of the gaseous phase inside the reactor. Indeed, it is possible to use cold water as the fluid in order to cool down the reactor or, on the contrary, steam-drying to prevent variations of the temperature: thus, this cold inner surface reactor becomes a hot inner surface reactor. In this case, the tube is only used with cold water at the end of the deposit, in order to forcefully stop the reaction by condensing the DBTD molecules on the cooled down surface and also to speed up the cooling of the whole reactor, which has a great thermal inertia. – The furnace This is one of the main parts of the device. Indeed, the CVD reaction is thermally activated and the temperature has a great influence on the speed and the growth method, as well as the deposit texture. The furnace is composed of a brass block which has the shape of a parallelepiped measuring 8 x 8 x 1.6 cm; it is placed at the

242


center of the reactor. It is supported by a vertical axis made of alumina which insulates it from the inside of the reactor (made of stainless steel). The heating of the furnace is accomplished using 4 cylindrical resistances wired up in parallel, so that the total resistance is 35 ȍ. These four resistances are placed inside the stainless steel block. A thermoelectric couple is placed just below the furnace surface. The regulation of the temperature is ensured by a temperature regulator-programmer. The size of the furnace is large enough to have a significant depositing surface (6 x 6 cm) with a homogenous temperature, at least in the depositing zone. Nevertheless, there are also a few drawbacks. Indeed, the necessary power to heat the furnace at the average working temperature (450°C) is large (about 100 W) even at low pressures, that is to say under conditions which do not favor the thermal conduction phenomena. Indeed, it seems that only radiant heating is able to increase the temperature in the whole reactor. – Pressure regulation There are several methods to regulate the pressure in a tank, depending on the inflows of gases and the pumping speed. It is theoretically possible to work in nearstatic conditions if we let in the quantity of gas necessary to attain the desired pressure. To compensate for the decrease of the pressure during the reaction gassolid, we introduce gases in the reactor to maintain the pressure. As these conditions are difficult to implement, we prefer to work in dynamic conditions with a constant pumping speed. The pumping capacities (38 m3/hr) have to be large because of reactor’s volume. These operations are carried out using a micro leak. Depending on the characteristics of the device (reactor volume, conductance, pumping speed), we experimentally determine the flow-pressure curves when the valve is open and closed. 7.2.3.3. Structural characterization of the material – Characterization means The thin films obtained using CVD are characterized by: – the size of the grains which compose the film; – the thickness of the film; – the crystallization state; – the texture.


243

All of these parameters can influence the electric properties of the films. – Size of the grains The size of the grains can be measured in two ways. The first method consists of using an X-ray diffraction peak of the material7. In effect, this peak is representative of the crystallographic field of a SnO2 grain. The size L of the coherent fields can be calculated from the diffraction peak width halfway up, using the Scherrer formula: L

0.9O / ' cos T

In practice, L is calculated for the most intense diffraction rays, and the calculated value is an average. In the case of thin films whose thickness is not greater than 300 ǖ, it is difficult to obtain the X-ray diffraction spectra. In a usual assembly to detect X-ray diffraction, the source is fixed and the sample and the detector rotate at angular speeds of T / t and 2T / t respectively: this method is called: T 2T . Given the large angle of incidence for the beam in the sample and its thinness, the obtained information is representative of the sample’s support and not the sample itself. In order to overcome this drawback, we use a device able to work with a small angle of incidence. In this case, the source and the sample are fixed, and only the detector moves at the speed of 2T / t . The angle of incidence is Į. The advantage of such a method is shown in Figure 7.19.

244


Figure 7.19. X-ray diffractograms with low angle of incidence, using ș-2ș with Į = 0.7°

The second method consists of observing the samples using a scanning electron microscope. This method gives a microscopic representation of the grains. Besides information concerning the grains, it is possible to obtain information on the grain shape, the distribution of the grain size and the shape of the links between the grains. In dark field, we obtain a diffraction diagram which informs us about the crystallization state of the film. This technique entails using very thin samples, which prevent the use of substrates. We can then either deposit the material directly on the grid holder samples, when we deal with very thin films (100 to 300 Å), or retrieve the thicker films (700 Å) using the reaction of the hydrofluoric acid on the silicon substrate. The thickness can be measured by an optical process: – the X reflectometry for thin films (100 to 700 Å); – the optical characterization for intermediate films (500 to 100,000 Å); – the scanning electron microscope for thick films (Figure 7.29).


245

7.2.3.4. Influence of the experimental parameters on the physico-chemical properties of the films 7.2.3.4.1. Influence of the temperature and the pressure on the depositing speed In general, the depositing speed depends on the total pressure in the reactor and the substrate temperature. Figures 7.20 and 7.21 confirm these observations, and it is important to note that it is the total pressure in the reactor which influences the speed. Specifically, as in the case of reactive evaporation, this will allow us, thanks to gases like nitrogen, to control, at the same time, the total pressure to solve kinetic problems and the oxygen pressure to solve chemical problems.

Figure 7.20. Influence of the total pressure on the depositing speed at a temperature of 450°C

Figure 7.21. Influence of the temperature on the depositing speed

246


The duration of the depositing implies a regular increase of the thickness of the film (see Figure 7.22).

Figure 7.22. Influence of the deposit duration on the thickness at 350 and 550°C

7.2.3.4.2. Influence of the depositing temperature on the thickness of the film and the size of the grains To study the size of the grains of the films, X-ray diffraction spectra are used. A great increase in their size is noticed when the depositing temperature increases (see Figure 7.23 and Table 7.3). The results obtained using the scanning electron microscope confirm this fact. Furthermore, they show that the films obtained at high temperature are better crystallized.

Figure 7.23. Influence of the depositing temperature on the grain size (e = 720 Å, non-annealed sample)

Material Elaboration Depositing temperature (ºC)

Depositing duration (mn)

Layer thickness (Å)

Average size of the grains (Å)

425

22.5

720

125

425

205

6500

230

525

21.5

720

155

525

180

7000

280

550

19

720

200

550

990

35,000

| 600

247

Table 7.3. Influence of the temperature and the duration of the depositing on the morphological parameters of the film

Figure 7.24. TEM (transmission electronic microscope) micrographs: evolution of the crystallization state depending of the depositing temperature (magnification = x 200,000)

248


7.2.3.4.3. Influence of the annealing on the crystallization state and the size of the grains Figure 7.25 perfectly shows the influence of annealing on the crystallization state of a film deposited at low temperature, and which was amorphous before the annealing. Furthermore, we note that the size of the grain is a bit altered by the annealing temperature (the diffraction rays become thinner: Figure 7.26). The intensity of these effects also depends on the depositing temperature, as is shown in Figures 7.27 and 7.28.

Figure 7.25. Diffractograms of SnO2 thin films during successive annealings. Depositing temperature = 350°C/e = 720 Å

Figure 7.26. Influence of the annealing temperature on the grain size


249

Figure 7.27. Diffractogram of SnO2 thin films deposited at different temperatures on a non-annealed sample (e = 720 Å)

Figure 7.28. Diffractogram of SnO2 thin films deposited at different temperatures, annealed 17 hrs at 600°C, then 13 hrs at 800°C (e = 720 Å)

7.2.3.4.4. Influence of the depositing temperature on the texture of compact films Here we address the macroscopic texture of thick films deposited at different temperatures. The information, obtained using a scanning electron microscope, allows us to observe an important evolution of the texture, whereby an increase in the temperature changes the film’s structure. From an amorphous structure (Figure 7.29a), it changes into a columnar structure from 450°C on. For temperatures greater than 400°C (see Figures 7.29c and 7.29d), the deposit surface becomes increasingly

250


granular. At 500°C, we assume that the density of the columnar elements is smaller, thus favoring a greater porosity of the material and, subsequently, a better interaction between gas and solid.

Figure 7.29. Evolution of compact film texture according to the temperature

7.2.3.5. Influence of the structure parameters on the electric properties of the films The electric properties of the materials are generally studied using the values of the electric conductance. The conductance is measured under a controlled gaseous atmosphere, and using two metallic electrodes placed at the material surface. 7.2.3.5.1. Influence of the thickness on the electric conductance These results (Figure 7.30) show that the electric conductance is not proportional to the thickness, though the geometric parameters have an influence on the conductance. Furthermore, we observe huge variations in the conductance, which increases from 3 10-9 to 10-5 ȍ-1 when the temperature increases from 80 to 800 Å.


251

Figure 7.30. Influence of the thickness on the conductance in air at 500°C; TD = 450°C, annealed at 600°C

Figure 7.31. Influence of the thickness on the conductance under air for different depositing temperatures

This influence has been studied for different depositing temperatures (see Figure 7.31).

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7.2.3.5.2. Influence of the annealing on the electric conductance The influence of the annealing has been studied on films of intermediate thickness deposited at high and low temperatures. An increase of the annealing length or the temperature results in a quite significant decrease of the measured conductance (in air). The effect of the annealing is even more important than its temperature and is high compared to the depositing temperature. These results shows that the annealing is interesting in order to obtain stable films to be used as material sensitive to the effect of the gases. Indeed, the working temperature of the detection devices is contained between 400 and 500°C. 7.2.4. Elaboration of thick films using serigraphy

7.2.4.1. Method description This method (see Figure 7.32) consists of depositing the sensitive material to form a thick film, using a paste (also called ink). The paste, supported by a screen, including a window that has a thin mesh, is deposited using a scraper on an alphaalumina substrate.

Figure 7.32. Diagram of serigraphy depositing process

First, the substrate being located under the screen, we deposit ink on the screen. The metallic mesh allows the ink to pass through when the ink is under the scraper’s pressure. The structure of deposits is controlled by the presence of a polymeric film covered by a mesh at the places where the paste is not to be deposited.


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This technology, commonly used in the industry, is particularly well adapted to mass production. The quality of the deposited film mostly depends on the physicochemical properties of the paste used. 7.2.4.2. Ink elaboration The paste, of which the ink is made, must possess rheological properties peculiar to the depositing technology. Specifically, it must be sufficiently fluid to cross the mesh under pressure from the scraper, and, after that, regain a sufficient viscosity to stick to the substrate. To make this paste, you have to mix the following ingredients: – the ceramic powder that we want to deposit; – an organic binder; – an organic solvent; – if necessary, a permanent binder. The organic binder allows us to regulate the paste’s viscosity, whereas the solvent helps to homogenize the ink’s constituents. After the elimination of the organic compounds by thermal treatment, the deposit still has to have a good adhesion to the substrate. If that is not the case, we add a permanent binder to the paste which, after fusion, will ensure a good adhesion of the deposit on the substrate. As far as tin dioxide is concerned, however, it seems no commercial ink exists. This has led our laboratory to produce a new paste. The mineral binder is produced using an organic precursor: tin alkoxide. Its thermal decomposition produces tin dioxide. Tin alkoxide allows us to chemically bind the substrate and the initial silicon powder. In practice, the paste is composed of tin dioxide grains (average size 0.5 μm), tin alkoxide and an organic solvent (liquid). The proportions are given in Table 7.4. Component

Quantity

SnO2 (Prolabo)

4g

organic binder

1.7 g

organic solvent

20 Drops

Table 7.4. Ink composition for tin dioxide

The films obtained are steam-dried, after depositing for ten minutes at 100°C, in order to eliminate the solvent; they are then thermally treated at 800°C for 15 hours.

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This method, which prevents the use of a mineral binder different from the deposited compound, also allows us to keep a homogenous electric conductivity in the film. Thick films are generally deposited on two types of substrate: alpha-alumina alone and alpha-alumina with titanium oxide. One deposit has a thickness of 10 μm. This thickness can be controlled by a profilograph. Multiple deposits with thicker films can be made by adding a steamdrying process between the deposits. In this case, the thicknesses are contained between 10 and 80 μm. 7.2.4.3. Structural characterization of thick films made with tin dioxide The specific area of the powder measured by BET is about 7m²/g. The thick films obtained show a comparable area.

Figure 7.33. MEB photograph of a SnO2 serigraphed film of 20 μm, deposited on alpha alumina: a) cross-section (x 500), b) top view (x 5,000)

The MEB pictures shown in Figure 7.33 show that on an alpha-alumina substrate, the films of 20 μm adhere perfectly to the substrate, and that on the whole, these films are not fissured. The greatest magnification shows that the film is porous.


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7.3. Beta-alumina 7.3.1. General properties

For research into the manufacture of gas sensors of a potentiometric type, we have tested different solid electrolytes. The unique property of these sensors is that the two different metallic electrodes are located in the same gaseous phase. This property has prompted us to study particularly the beta-alumina and calcium sulfate. Sodium sulfate, which possesses good electrolytic properties and a good chemical stability towards gases, appeared a good choice for such an application. Unfortunately, this material cannot be used under a ceramic shape because it does not withstand the temperature variations. Indeed, at about 300°C, there is an allotropic change, that is, in the useful field of the sensor: the mechanical tensions this transformation implies favoring the crackling of the sintered material. Beta-alumina, rich in sodium, possesses a good adhesion on the support and a good ionic conduction. Its weak point is linked to its reactions with some gaseous compounds. To overcome these different drawbacks, and to use every advantage provided by these materials, we have chosen to chemically treat sintered beta-alumina: we make beta-alumina react with sulfur dioxide to form sodium sulfate film on the surface of the material. This process takes place at 600°C in 10,000 ppm of sulfur dioxide in the air and it lasts 90 minutes. Thus, we can elaborate a material composed of a superficial film of sodium sulfate which is perfectly stable mechanically (it does not fissure when the temperature varies) and chemically (it does not react with gases). Obtaining and characterizing beta-alumina remains one of the necessary points to produce the sensitive material. The poly-aluminates (formula nAl2O3-mR2O with: R = Na, K, Li or Ag) are called E-alumina. At high temperature (>1,000°C), these compounds crystallize into two forms: E-alumina and E''-alumina whose formulas are 11Al2O3-R2O and 5Al2O3-R2O respectively. Their crystalline structure is constituted of spinel blocks containing aluminum ions and oxide ions separated by symmetric plans composed of oxide ions and R+ ions. E-alumina contains two spinel blocks and a symmetric plan, and E''-alumina contains three spinel blocks and two symmetric plans. Figures 7.34a and 7.34b show the structure of E-alumina mesh and E''-alumina mesh respectively.

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Figure 7.34. (a) Structure of Al2O3-ȕ; (b) structure of Al2O3-ȕ’’

E-alumina belongs to the ionic supra-conductors family, which means that this material displays a structure that, in a certain temperature range, has a good ionic conduction.

In the case of E-alumina, we observe at high temperature a stable compound stemming from this conduction. This property, caused by the cationic site occupation in the mirror plans (also called conduction plans), allows a great mobility of the R+ ions in a direction perpendicular to the c axis. The value of conductivity measured is of a magnitude of 10-1 S.cm-1 at 300°C (see Figure 7.35), for a poly-crystalline sample of E-alumina, though E''-alumina is slightly more conductive.


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Figure 7.35. Conductivity of monocrystalline and polycrystalline sample o f ȕ and ȕ’’ alumina

7.3.2. Material elaboration

Given the complexity of such a material and its reactivity with a gaseous environment, it is necessary to perfectly elaborate it as well as to ensure an exact reproducibility of the product. These difficulties are mostly linked to the composition and control of the obtained product’s micro-structure (sodium oxide evaporation) and the segregation of sodium carbonate. The elaboration process adopted is the sol-gel process pioneered by L. Montanaro and A. Negro (Department of Materials Science and Chemical Engineering, Politecnico of Turin). The organization chart shown in Figure 7.36 depicts the main stages of this process. To an aqueous solution of an organic salt of sodium (sodium acetate or oxalate), easily decomposable, we add, maintaining a constant agitation, aluminum isopropylate.

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The chosen mass proportions are: 7% of sodium oxide (Na2O) and 93% of aluminum oxide (Al2O3), which implies 1 mole of Na2O for 9 moles of Al2O3. At 25°C, the polymerization and condensation reactions lead to the elaboration of a “sol”. At 80°C, the polycondensation can happen, and we then obtain a “gel”. In order to eliminate the water, two solutions are possible: either the gel is placed in a drying oven at 105°C for 24 hours and the product obtained is then ground is an agate mortar, or the gel is dried by hot air pulverization (a method commonly called spray-drying). In order to crystallize the beta-alumina or the beta”-alumina, the amorphous powder, located in an alumina container resistant to high temperatures, is heated at 5°C/mn until the temperature reaches 1,200°C in ambient atmosphere. We maintain these conditions for two hours, then the powder is slowly cooled down until its temperature reaches 1,000°C. Finally, the powder is quenched at ambient temperature. Whether the powder is obtained using sodium oxalate or acetate, the X-rays diffraction spectra shows the presence of the beta-alumina and beta”-alumina stages. In the case of sodium oxalate, the ratio of the beta-alumina/beta’’-alumina stages is calculated using d = 1.976 Å (beta”-alumina stage) and d = 2.690 Å (beta-alumina stage). The value of this ratio is about 0.75.


Figure 7.36. The different stages to obtain E-alumina using a sol-gel process

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Figure 7.37. X-ray diffraction spectra of the powder obtained using sodium acetate or oxalate

These measures, performed using laser granulometry, show that the spray-drying method allows us to obtain a thinner and more homogenous powder than the powder obtained using an agate mortar.

Figure 7.38. Granulometric distribution of the powder obtained using sodium oxalate after steam-drying

Using the BET method, the specific surface area measured is about 1 m2/g after calcination at 1,200°C and will thus be whatever the other conditions are.


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Electric conductivity measures, with an alternating current, allow us to assess ion mobility, and subsequently, the response time of the solid electrolyte. Furthermore, these measures test the reproducibility of the samples using different powders. As is shown Figure 7.39, at 500°C and in air, the conductivity of the product obtained with sodium oxalate is ten times that obtained with sodium acetate.

Figure 7.39. Conductance measure in air according to the temperature

For these reasons, we have decided to use powder prepared using the sol-gel method and to use sodium oxalate. The steam-drying of the product is performed at a temperature of 105°C for 24 hours. The powder is ground in an agate mortar and sifted in order to keep only the grains whose diameter is less than 80 μm. Then the amorphous powder is placed in a heatproof container (made of alumina) and heated at a temperature of 1,200°C under the previously described conditions. 7.3.3. Material shaping

The beta-alumina powder has been conditioned by two different methods: monoaxial compression and serigraphic depositing. 7.3.3.1. Mono-axial compression This method is similar to the one described in the case of tin dioxide, with the elaboration of the material performed using mono-axial cold-compression. With the aid of preliminary samples, we have been able to fix the operating conditions. 500 mg of powder compressed at 450 MPa for 30 seconds. The pellets obtained have a diameter of 13 mm and a thickness of 1.5 mm.

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The temperature for annealing the samples is generally 1,050°C, lasts 1 hour and is realized in air. This temperature enables us to obtain mechanically stable pellets and prevents any phase changes. Furthermore, sodium oxide evaporates. The samples are generally stored in ambient air. Their ageing depends on the time separating the analysis from the heating. 7.3.3.2. Serigraphic process The principle of this depositing method has already been displayed in section 7.2.4: only the compound’s nature changes. – Ink elaboration As for the pulverulent material, the serigraphic ink has been elaborated by L. Montanaro and A. Negro (Department of Materials Science and Chemical Engineering, Politecnico of Turin). The binder used to link the material to the support is a glass material (its fusion temperature is low, about 800°C). In order not to exorbitantly increase the deposit resistivity, we have chosen a sodic glass material (mass proportions: 26.1% Na2O, 12.3% Al2O3, 61.6% SiO2). The glass and the beta-alumina are mixed by grinding in a planarian grinder in a liquid, until the granulometry is less than about 10 μm (which is necessary for depositing). The powder is then mixed for several hours with an organic binder and a dispersion liquid (composition: 10 g of the mix glass/beta-alumina, 0.5 g of PVB and 5 cc of dispersant) – Thermal treatment of the films After the serigraphic depositing of the thick film, the first stage of the drying is enacted at a temperature close to the ambient temperature for 12 hours, in order to evaporate the dispersant liquid without cracking the film. The deposit is then heated in order to thermally decompose the organic binder and to then melt the glass material. When the temperature rises above the fusion temperature of the glass material, the glass material links the film to the substrate, and also links the particles of material between them. In this case, the chosen glass is an ionic conductor which allows us to maintain the conductivity properties necessary for it to act like a solid electrolyte.


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Table 7.5. Heating program

The curve displaying the temperature as a function of time is shown in Table 7.5. Finally, it is important to note that the temperature of the plateau is going to be adapted to the composition ratio E-alumina/glass. – SO2 treatment The chemical treatment of the sintered pellets or the thick films occurs in the presence of sulfur dioxide diluted at 1% in dry air, for 90 minutes at 600°C. Such a treatment is enough to begin the elaboration of sodium sulfate using beta-alumina. 7.3.4. Characterization of materials7, 8

7.3.4.1. Physico-chemical characterization of the sintered materials The characterization of these materials is mostly linked to the effect of the sulfur dioxide treatment. Figures 7.40a and 7.40b make it possible to compare the different analysis, using X-ray diffraction, of a sample of beta-alumina crystallized at high temperature, pellet-shaped and sintered using the previously described process, before and after the SO2 treatment The first is the diffractogram of a sample of beta-alumina not treated with SO2. The characteristic peaks of the beta-alumina can be recognized. If we compare this diffractogram with that of the SO2-treated sample, we can distinguish three peaks, located at 22.6°, 23.6° and 25.5° characteristic of the sodium sulfate (formula Na2SO4).

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Figure 7.40. a) Diffractogram of a beta-alumina pellet not treated with SO2; b) diffractogram of a beta-alumina pellet treated with SO2

A scanning electron microscope allows us to observe the evolution of the betaalumina before and after sulfatation. The photograph (Figure 7.41) shows at great magnification (x 3,500), the sample surface before the SO2 treatment. We note the presence of needle-shaped peaks or inflorescence whose structure is similar to the structure of hydrated sodium carbonate. This compound confirms the reactivity of the beta-alumina even at ambient temperature.


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To prevent the presence of such a phase on the samples, we proceed to the SO2treatment just after the sintering stage in order to prevent a weak homogenity for the sodium sulfate.

Figure 7.41. Photograph of a beta-alumina pellet not treated with sulfur dioxide

Figure 7.42. Photograph of a beta-alumina pellet treated with sulfur dioxide

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Figure 7.43. Photograph of a sodium sulfate pellet after several temperature cycles

If we observe a sample after SO2-treatment (see Figure 7.42), we can see the influence of such a treatment. Indeed, the surface shows a multitude of crystals, anchored in what resembles the formation of a compact and homogenous film, composed of a compound difficult to identify with mere photography. Nevertheless, this evolution of the surface texture has been observed in every SO2-treated sample. In Figure 7.43, showing the sodium sulfate sample, we can observe deep cracks after several temperature cycles. 7.3.4.2. Physico-chemical treatment of the thick films We seek here to characterize different films distinguished by their composition, their sintering temperature or the absence of sulfur dioxide treatment. These films are characterized, on a crystallographic level and on a structural plan, by the X-ray spectrometry and the scanning electron microscope respectively. – Influence of the composition ratio beta-alumina glass Three different compositions have been tested: – 60% of glass and 40% of beta-alumina; – 50% of glass and 50% of beta-alumina; – 40% of glass and 60% of beta-alumina.


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The photographs in Figures 7.44, 7.45 and 7.46 – produced at low magnification (x 55) – show the influence of the composition on the morphology of the films treated at 900°C. In the case of the 50/50 ratio the link to the support is the worst of the three: this is due to the fact that the two materials (glass and beta-alumina) have very different thermal coefficients. We observe on these photographs the trace left by the serigraphy screen; this trace appears because of viscosity phenomena which are a function of the composition. The photographs in Figures 7.47, and 7.48 – obtained with a greater magnification (x 1,600) and realized in the middle of the thick film – show a difference between the depositing made with 40% and 60% of beta-alumina. These films are treated at 1,000°C, but the distinction is valid whatever the heating temperature. The film made with 40% of beta-alumina possesses the properties of wettability which allow the beta-alumina to form an amorphous matrix. Nevertheless, the structure shows cracks and cavities.

Figure 7.44. Photograph of the surface of thick films containing 40% of beta-alumina

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Figure 7.47. Photograph of a thick film containing 40% of beta-alumina not treated with sulfur dioxide (1,000°C/2 hours, x 1600)

Figure 7.48. Photograph of a thick film containing 60% of beta-alumina not treated with sulfur dioxide (1,000°C/2 hrs, x 1600)

Yet, in the film containing 60% of beta-alumina, the structure shows jointed grains. Furthermore, the beta-alumina particles are not necessarily wrapped up in the glass. As in the case of sintered material, these films react in the presence of CO2 and water vapor. This causes the apparition of inflorescences: we can thus assume the formation of sodium carbonate.

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No fundamental change has been observed in the structure when we modify the adhesion temperature of the glass. – Influence of the thermal treatment on the films The presence of glass mixed with beta-alumina, rich in sodium, can provoke, at high temperatures, a certain number of chemical reactions (especially the formation of nepheline). This compound (formula: NaAl(SiO4)) crystallizes into a hexagonal shape characteristic of the Na2O-SiO2-Al2O3 system phase diagram (see Figure 7.49).

Figure 7.49. Na2O-SiO2-Al2O3 system phase diagram

The diffractogram in Figure 7.50 displays the diffraction rays of a thick film containing about 60% of beta-alumina treated at 900°C. Į and ȕ characterize the rays of alpha-alumina and those of beta-alumina respectively, used as substrate for this application. In this figure, we can also distinguish the rays characterizing the


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nepheline. The nepheline can be very clearly identified. The diagram shows five characteristic rays contained between 20° and 30°. The intensity of these rays indicates a great number are present. Diffractograms for different thermal treatments show that the nepheline formation is accompanied by an increase in the annealing temperature, at least for films containing 40% of beta-alumina and a large quantity of glass.

Figure 7.50. Diffractogram of a thick film containing 60% of beta-alumina

– Influence of the sulfur dioxide treatment The photographs in Figures 7.51 and 7.52 show the films obtained after treatment. The films displayed are those that were captured by the photographs in Figures 7.47 and 7.48. In the first, we can clearly observe the influence of this treatment, which turns the amorphous glass matrix on the surface and lets a great number of crystals appear, produced by the reaction of the sulfur dioxide producing sodium sulfate. The film which contains more beta-alumina does not show a great modification of its structure, although we can observe small crystals stemming from compact blocks; this tends to prove that sodium sulfate is formed. These observations show that the material cracking is more noticeable with films containing 40% of beta-alumina.

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Figure 7.51. Photograph of a thick film containing 40% of beta-alumina treated with sulfur dioxide (1,000°C/2 hrs, x 1600)

Figure 7.52. Photograph of a thick film containing 60% of beta-alumina treated with sulfur dioxide (1,000°C/2 hrs, x 1600)


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The influence of the treatment temperature is the same as in previous results. Nevertheless, in the case of films containing 60% of beta-alumina, the cracks become larger and more numerous when the heating temperature increases. In the case of the films containing 40% of beta-alumina, the influence of the SO2-treatment is more difficult to detect, and it becomes more and more difficult when the heating temperature increases. It is not possible to simply observe the adhesion of the sodium sulfate to the support because of the thermal cycle. Only electric tests allow us to check this property. 7.3.5. Electric characterization

Figure 7.53 compares the value of resistance obtained for the sintered material and the 6 thick film samples elaborated at different temperatures and containing different quantities of glass – all of these samples have been treated with sulfur dioxide. These results confirm the great difference between the two elaboration processes, with measured values 2 to 3 times higher for thick films than for sintered beta-alumina. This impedance varies according to the thermal treatment and percentage of glass in the film.

Figure 7.53. Variation of the electric resistance of the sintered material and the thick films according to the temperature

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At 600°C, these results are more clearly depicted in Figure 7.54, which compares the resistance value of the different materials studied and their main components. On the abscissa, there is the percentage of beta-alumina in the mixing beta-alumina + glass. At 0%, the resistance value of a thick film composed solely of glass is displayed and at 100%, those of a sintered pullet composed of beta-alumina only, of sintered pullet of sodium sulfate and a sintered pullet of nepheline, prepared for this study.

Figure 7.54. Comparison of the electric resistance value between the compounds and the different thick films (values obtained at 600°C)

It is important to note that these different compounds have intrinsic resistance (magnitude: kOhm) though the thick films have larger resistance values, even very high sometimes. The greatest values are observed for the films containing 50% of beta-alumina (magnitude MOhm). These films display a lot of cracks which are visible to the naked eye. The deposits containing 60% and 40% of beta-alumina, though, seem to possess a superior conductivity. For the film containing 40% of beta-alumina, this value is independent of the thermal treatment. However, at 60% it decreases when the thermal treatment temperature decreases.


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We can conclude, using these results, that the resistance value of the sensitive material depends largely on the development parameters, and that this resistance value can be used as a quality control in the elaboration process level. 7.4. Bibliography 1. N. YAMAZOE, N. MIURA, “Some basic aspects of semiconductor gas sensors”, Chemical Sensor Technology, vol. 4, Elsevier, 1988. 2. N. MURUKAMI, K. TANAKA, K. SASAKI, K. IHOKURA, “The influence of sintering temperature on the characteristics of SnO2 combustion monitor sensors”, Analyt. Chem. Symp. Ser., vol. 17, 165-170, 1983. 3. S. VINCENT, Influence du traitement thermique sur les propriétés électriques du dioxyde d’étain polycristallin. Application à la détection du méthane, Thesis, INPG-ENSMSE, Saint Etienne, 1992. 4. W. GÖPEL, K. SHIERBAUM, “SnO2 sensors: current status and future prospects”, Sensors and Actuators, B 26-27, 1-12, 1995. 5. P. BREUIL, Elaboration et caractérisation de couches minces de dioxyde d’étain sensibles à l’action des gaz, Thesis, INPG-ENSMSE, Saint Etienne, 1989. 6. D. DEPTUCK, J.P. HARRISON, P. ZAWADZKI, “Measurement of elasticity and conductivity of three dimensional percolation system”, Physical Review Letters, 54, 9, 1985. 7. E. FASCETTA, Etude d’un capteur potentiométrique élaboré à partir d’alumine bêta, Interprétation des phénomènes électrochimiques observés en présence de dioxyde de soufre et de monoxyde de carbone, Thesis, INPG-ENSMSE, Saint Etienne, 1993. 8. C. PUPIER, Etude d’un capteur de gaz sensible au monoxyde de carbone et aux oxydes d’nitrogen élaboré à base d’alumine bêta, Thesis, INPG-ENSMSE, Saint Etienne, 1999.


Chapter 8

Influence of the Metallic Components on the Electrical Response of the Sensors

8.1. Introduction To detect gases, the presence of a metal at the surface of the sensitive part of the sensor is necessary for electrical contacts. Sometimes, the metal is present in order to favor chemical reactions at the surface of the sensitive material. Sensors are always used at temperatures higher than 300°C, so we will use in the two cases the same metal, either gold or platinum or palladium, in both cases: that is, noble metals. The depositing of the metal on the sensitive material is rather difficult. These difficulties are related to the temperature at which the sensor is used and to the adhesion of the metal to the sensitive material (which is often a metallic oxide). The mechanic stability of the device is ensured by a good adhesion of the metal to the surface. The adhesion also influences the electric properties. The properties of the junction between metal and oxide are linked to the structure and as a consequence to electric conductance. Furthermore, such an interface can act as a catalyst to the phenomenon of oxidation or reduction concerned.

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The synergy between the two materials can indeed generate new catalytic effects or amplify catalytic effects which can alter the sensor’s response. The gas-metaloxide system is located at the metal-oxide interface; this zone is called the three boundary point. 8.2. General points 8.2.1. Methods to deposit the metallic parts on the sensitive element We will distinguish the following. – The methods which consist of depositing metallic wire These methods, used with sintered pellets, are especially designed to solve electrode problems. In this case, a part of these wires (diameter 0.1 mm) can be inserted directly into the powder contained in the matrix before the compression. The remaining wires are placed at the surface of the powder. After the compression of the powder, we are able to use the emerging part of the wires. We can also use metallic pastes, which, thanks to the presence of a glue, enable the wire to stick to the substrate. It is generally necessary to steam at 100°C to ensure the evaporation of the solvent, then to anneal the product at about 800°C. These methods are not easily implemented and reproducible, though they have the advantage of combining electrical contacts and wire connections in the same process. – Method of cathodic pulverization or thermal evaporation In this case, the metal is directly deposited as a thin film on the sensitive element. Perfectly controlled, and allowing for a good reproducibility, this process can be used to implant electrodes or for the realization of a catalytic filter. To exploit such technology to its maximum, at least for the sensitive elements deposited as thick or thin films, and to avoid the use of a glue, we can extend the metallic deposit on the substrate by tracks reaching zones exterior to the heating zones of the sensor. The temperature of these zones allows us to solder with tin.

Influence of the Metallic Components

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These devices will be described in detail in Chapter 9, which is devoted to applications. – Method of mixing or impregnation Solely exploited for catalytic property designs, these methods favor the dispersion of the metallic element in the sensitive element or at its surface. For the mixing with sintered pellets, we have only to prepare a mixture of the two powders before the compression operations. This method does not necessarily favor the presence of the metal at the surface of the sample. To achieve this, we employ the impregnation method. The sensitive element is immersed in a liquid precursor of the metallic element to be deposited. An adapted thermal treatment then makes it possible to obtain metallic clusters evenly distributed at the surface of the sensitive element. The metal plays a major role in the device because of its catalytic properties and because of the importance of the heterogenous interfaces generated at the surface of the sensitive element. Consequently, researchers have tried to understand the role played by electrodes in the response of chemical sensors to gas. The results of this research allow us to propose conduction mechanisms that fit these devices and/or systems. 8.2.2. Role of the metallic elements on the sensors’ response We will offer some familiar examples. Studies undertaken in 1986 by C. Pijolat1 demonstrate the influence of the electrode’s nature on the response of a sintered SnO2 sensor to benzene effect. These results (Figure 8.1) show the difference between gold and platinum as the metallic elements used to facilitate the electric contacts by inlaid wires. The effects of the metal are explained by a significant difference in temperature on the response curve. This difference in the sensitivity of the sensors can be attributed to phenomena activated by the temperature, among which electric potential barriers created at the oxide/metal interface.

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Figure 8.1. Electrical conductance of sintered SnO2 as a function of the temperature and according to the nature of electrodes

U. Hoefer,2 working with thin films of SnO2, exploits the results obtained using several electrodes of platinum but separated by different distances. This variation of a geometric parameter allows us to measure different electric resistance. Thus, it is observed that only the zones located near the electrodes are sensitive to gas effect. Furthermore, U. Weimar3 has shown, by complex impedance spectrometry, that in certain conditions, most of the electric phenomena are located near the electrodes. Weimar highlights the importance of the three boundary point: semiconductor/metal (electrode)/gas in the detection of phenomena and speaks of a space-charge area linked to this three boundary point. The extraction of an electron from this depletion zone located near the electrode has an electric effect larger than an extraction initiated far from the electrodes and, subsequently, less depleted.


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Finally, another model has been proposed by K. Varghese.4 According to this model, the material has a capacitive effect because of the accumulation of oxygen compounds in the zone where the SnO2 and the electrodes are in contact. The diagram proposed (Figure 8.2) shows the polarization of electrodes and indicates the presence of a large depletion zone that spreads from the electrode. From these works, we will remember that significant electric phenomena are located on the three boundary point oxide-metal-gas. Maybe this is one of the reasons why most of the commercial devices use interdigitating electrodes, which allows us to multiply the zones which behave like a three boundary point.

Figure 8.2. Model for electrode influence as proposed by K. Varghese

All of these examples are relative to tin dioxide, and subsequently relative to a semiconductor material. Nevertheless, there are comparable studies on solid electrolytes, more specifically beta-alumina. In 1982, D.E. Williams5 proposed a potentiometric sensor, elaborated using betaalumina and two metallic electrodes located in the same gaseous phase. Furthermore, these two electrodes were of different natures and sizes.

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We must remember that a classic potentiometric device works using two identical electrodes located in different compartments. The partial pressure in oxidizing gas or reducing gas, which is different in the two compartments influences the electrochemical potential on each electrode, and subsequently the electric potential between them. The originality of D.E. Williams’ device is the fact that the dissymmetry of the device is no longer linked to a difference in the (oxidizing or reducing) gas partial pressure on each electrode, but to the nature and/or geometry of the electrodes. Again, the role of the metal is not linked to a mere connection problem. 8.2.3. Role of the metal: catalytic aspects In general, we know that the presence of certain metals increases the oxidizing or reducing rate of a gas, and can even lead to selective reactions. Yet, in the case of a sensor, the presence of these catalysts is not limited to a mere reaction between gas and metal, and the electric effects observed seem to indicate that the whole process uses an oxide-metal-gas system. The problem is then to understand the synergy which exists between the catalyst and the sensitive element. As was shown by S. Morrison6 (see Figure 8.3), a simple catalyzing phenomenon with a metal located at the surface of SnO2 would not lead to an evolution of the electric performances of the material

Figure 8.3. Catalyzing mechanism at SnO2 surface according to S. Morrison

To describe this synergy between metal and tin dioxide, different mechanisms have been proposed.


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8.2.3.1. Spill-over mechanism The spill-over is a well-known process in the field of heterogenous catalysis. It has been particularly studied in the case of platinum and palladium. This process is illustrated in Figure 8.4.

Figure 8.4. Spill-over mechanism according to S. Morrison

On contact with the metallic catalyst, the oxygen molecule dissociates. The atoms migrate towards the surface of the oxide support. Then, by reacting with an electron of the oxide, ionization occurs. This consumption amounts to a modification of the oxide space-charge layer. O2 ( gas ) 2 sM 2(O sM )

O sM eOx s (O s ) sM

sM indicates an adsorption site on the metal, and s, an adsorption site on the oxide. Regarding kinetics, the presence of the catalyst makes the regeneration of the O—s compound easier at the surface. As for as the response to H2 action, the proposed model implies a dissociation of H2 on the metal and a reaction with the absorbed oxygen. H 2 ( gas ) 2 sM 2( H sM ) ( H sM ) s ( H s ) sM 2( H s ) (O s ) H 2O ( gas ) eOx 3s

284


In this case, it is the consumption of the absorbed oxygen which leads to an evolution of the electric properties of SnO2. We observe that for oxygen dissociation in the first mechanism, the oxidation of the gas does not happen at the surface of the catalyst. The catalyst only increases the dissociation rate of the concerned gases. We also speak of “chemical sensitization”. A good dispersion of the catalyst is necessary to obtain a large effect. 8.2.3.2. Reverse spill-over mechanism The obverse of the spill-over mechanism, the reverse spill-over mechanism, mentioned by K. Grass,7 consists of an adsorption of the oxygen on tin dioxide, followed by a migration of the adsorbed species towards the metal, as is shown in Figure 8.5. The reaction between the gas and carbon monoxide takes place at the point where metal and oxide are in contact.

Figure 8.5. Reverse spill-over mechanism concerning oxygen, proposed by K. Grass and H. Lintz

Few authors mention such a mechanism and, to our knowledge, no publication gives information on the electric consequences of such a phenomenon on tin dioxide. 8.2.3.3. Electronic effect mechanism A third concept based on an electronic exchange between the metal and the semiconductor is behind two more mechanisms.


285

The first, proposed by S. Morrison,6 describes an adsorption of oxygen at the metal’s surface accompanied by electronic transfer. The second, proposed by N. Yamazoe8, 9 takes into consideration the formation of an oxide film at the surface of the metal. – Case proposed by S. Morrison The chemisorption of the oxygen is illustrated in Figure 8.6.

Figure 8.6. Electronic effect mechanism, according to S. Morrison

In this case the oxygen takes the electron to the metal according to the equation: O2 ( gas ) 2 sM 2eM 2(O sM )

eM and sM respectively indicate an electron stemming from the metal and an adsorption site on the metal. The oxygen remains adsorbed on the metal. This negatively charged adsorbed phase is the cause of an electric perturbation at the SnO2-metal interface. This perturbation amounts to an electron exchange between the two materials. Again, this loss of an electron implies a modification in the space-charge layer. In the presence of a reducing gas RH2, we witness its oxidation at the surface of the catalyst according to the equation: RH 2 ( gas ) 2(O sM ) RO ( gas ) H 2O ( gas ) 2eM

Subsequently, an electron is given back to the oxide according to the equation: eOx eM

286


Although this model clearly indicates the presence of a space-charge layer in the semiconductor, its exact location with regards to the metal and the oxide is not accurately determined. – Case proposed by N. Yamazoe In this case, we witness a chemical reaction between the metal and the oxygen. This reaction leads to the formation of oxide. We will note that such a reaction does not imply any modification of the electric properties of SnO2.

Figure 8.7. Schematization of the electronic effect mechanism with oxide formation

The presence of an oxide film at the surface of the metal implies a perturbation at the metallic oxide-SnO2 interface. Yamazoe positions the space-charge layer on top of the metal, as indicated in Figure 8.7. In these two propositions dealing with the electronic effect mechanism, the apparition of a new phase at the surface of metal (an adsorbed phase or metallic oxide) is the cause of an electron transfer from the semiconductor towards the metal. Given the thinness of the space-charge layer, which is about several angstroms at most at the gas-metal interface, it is difficult to imagine that such a perturbation could create new equilibriums at the SnO2-metal interface, which could themselves induce a space-charge layer located on top of the metal. Therefore, Yamazoe’s proposition is called into question. Morrison’s proposition seems more likely and will be used as a working hypothesis for the case of a physico-chemical model in Chapter 10, in which a localization of the space-charge layer will be proposed. 8.2.3.4. Influence of the metal nature on the involved mechanism We are going to see how the authors have tried to predict the kind of mechanism (spill-over or electronic effect) as a function of the added metal nature. The main studies focus on the three most used metals, that is, silver, platinum and palladium.


287

Knowing the oxidation stages of the metallic aggregates is the first step that we must take in order to clearly understand the reaction process. In the case of palladium and silver, it is generally admitted that these elements form stable oxides (Ag2O and PdO) at the functioning temperatures of the sensors, whereas the platinum is less oxidizable. Initially, we considered that Pd and Ag would suit sensitization by electronic effect, while platinum would favor spill-over. These observations have only been partially confirmed by investigations performed using a XPS9, 10 method. This technology allows us to measure the energy of a Sn-O bond and oxidation degree of the metal simultaneously. If a correlation exists between these values, we conclude that the mechanism is an electronic effect. Such studies have been performed under different oxidizing (O2) or reducing (H2) atmospheres. Thus, Yamazoe notes an energy variation in the bond between metal and oxygen for SnO2 doped with silver. There is also a variation of the oxidation degree of the metal during the oxidation of Ag in a Ag2O compound. Though we also observe a variation of this degree with palladium and platinum, there is no variation of the bonding energy with these metals. This initial study proposes an electronic effect for Ag, whereas the spill-over mechanism dominates for Pt and Pd. Using the same kind of study Matsuhima shows the energy of the Sn-O bond is sensitive to the palladium concentration dispersed in SnO2. For low concentrations of palladium ( O @ ȕ , at the į

surface of the beta-alumina, T1, the coverage degree of the species (O s) , noted ªO į º and T the coverage degree of the species (O s) , noted ªO - º at the 2, T ¬ ¼T ¬« ¼»

three boundary point, the equilibrium relations will be written: K1

TE

1 T E

K2

Po2

T1 1 T E

T E 1 T1 T 2

and: K3

T2 T1

The expression of the coverage degree T1 will then be:

T1

K 2 K1 Po2 1 K 2 K1 Po2 (1 K 3 )

[10.10]

Compared with the previous case, this expression relies on another equilibrium constant K3, which necessarily possesses an exothermic character. This expression allows us to express the coverage degree as a function of oxygen pressure and temperature. It should be noted that compared with the energy in Figure 10.19, it is the new į variety of species ªO º T which takes the place of the species ª¬O - º¼ . As far as the T ¬« ¼» species ª¬O - º¼ of the new model is concerned, it is located, because of a much T stronger bond than before, below the energy of the species O2. The influence of oxygen pressure is expressed by a homographic law.

394


As for temperature, its influences depend of the expression of the different equilibrium constants, which are expressed by an expression of the following type: K

§ 'H f · K 0 exp ¨ ¸ © RT ¹

We then note that the formation enthalpy ǻHf of the different species considered will be a necessary factor to express the coverage degree of the species, which is responsible for the electric response. 10.3.2.3. Expression of the theoretical potential difference at the poles of the device We now have to express the theoretical potential obtained at the poles of two electrodes elaborated with two different metallic elements. To simplify the calculations, we will note: ª 'H f ([O ]E ) 'H f ([OG ]T ) º » K10 K 20 exp « RT «¬ »¼

KD

K1 K 2

Thus: ª 'H D ([OG ]T ) º KD0 exp « » RT ¬« ¼»

KD

with: G

G

'HD ([O ]T ) = 'H f ([O]E ) 'H f ([O ]T

We will note that the value of ǻH f >O @ ȕ must be considered as independent from the electrodes because it is caused by a mere interaction between the gas and the solid electrolyte; therefore:

T1

KD Po2 1 KD Po2 (1 K 3 )

Remembering that:

'V V1 V2

DG 2

ªT12 T22 º¼ J ª¬T12 T22 º¼ R ¬

[10.11]

Models and Interpretation of Experimental Results

395

we can write: 'V

2 º¼ J ª¬ T Pt2 T Au

'V

2º 2 ª · § · » KDPt Po2 KDAu Po2 «¨§ ¸ ¨ ¸ » J« Pt Pt Au Au ¨ ¸ ¨ ¸ 1 K Po (1 K ) 1 K Po (1 K ) D D 2 2 «© 3 3 ¹ © ¹ » ¬ ¼

[10.12]

K Pt and K Au are equilibrium constants for platinum and gold respectively.

In order to validate such an expression, it is important to compare the experimental results to the shape of the theoretical curves obtained by varying ǻV as a function of temperature and pressure. In such a case, it is impossible to perform a simple mathematical analysis, which would not even allow us to determine the shape of the curves. We can then conduct a simulation using a spreadsheet, which will calculate the expression of ǻV for different values of the parameters concerned, and which will compare the calculated values to those obtained experimentally; these calculations are performed using the least squares method. 10.3.3. Simulation of the results obtained with oxygen

10.3.3.1. Behavior as a function of temperature and pressure In the present case, we have to take four different parameters for each metal, that is: 'H D , 'H f , K Į0 and K 3 . To avoid certain aberrant values peculiar to this device, and to shorten the calculations, we can impose these conditions: į

į

ǻH ĮAu ([O - ]T ) ! ǻH ĮPt ([O - ]T ) ! 0 (K Į0 )Au and (K Į0 )Pt ! 0 (K 3 )Au and (K 3 )Pt ! 0

The first two conditions stem from the fact that the positive pole of the device is gold, and we can admit that, in general, the species fixed at the three boundary point are more active and, subsequently, less bonded with gold than with platinum.

396


The third condition is linked to the fact that here, 'H 3 is negative. The adopted calculation process allows us to reproduce, with accuracy, the complex behavior of the sensor as a function of temperature and pressure; the difficulty involves the simulation of a peak on the curves displaying the signal as a function of temperature and the simulation at the intersections of curves displaying the influence of the pressure on the signal. The best results obtained for the parameters’ value are displayed in Table 10.2.17, 18

Table 10.2. Values of the different parameters exploited for the simulation

The comparison between the simulation and the experimental results are displayed in Figure 10.20.

Figure 10.20. Results of simulations (dotted lines) as a function of temperature and oxygen pressure


397

The values given to the different parameters are not necessarily the only ones compatible with such a system; nevertheless we can assert that the magnitude of the values has to be respected to obtain satisfying results. Furthermore, the calculation process has convinced us that the formation enthalpy value ǻH Į

([O į ]T ) of the activated specie [O į ]T must be positive

on gold and on platinum. Conversely, the formation enthalpy ǻH Į ([O - ] T ) of the activated species [O - ] T must be negative on gold and on platinum. If not, it would be impossible to obtain a peak for the curves displaying the signal as a function of the temperature. It is also interesting to note that the mathematical solution imposes the existence of endothermic species. Using these results, we will see that it is possible to check certain electric behaviors peculiar to this device, with regards to the size of the electrodes and the information recorded by the surface potential method. 10.3.3.2. Behavior as a function of electrode size The previous simulation has allowed us to determine the variation of the coverage degree T at the level of the electrodes as a function of the experimental conditions and the nature of the metal. This simulation has been conducted with the results observed on the sensors whose electrodes are of the same size but different natures. As was seen in Chapter 8, the use of two electrodes which have the same nature but different sizes can cause a potential difference between these electrodes. This potential difference is expressed by:

'V

V1 V 2

ª 1 1 º 2» 2 R R 2 ¼ ¬ 1

D G 2T 2 «

Knowing T, at different temperatures and different pressures, then allows us to express the potential difference as a function of the radius of the two electrodes and to check the validity of the previous relation by comparing the corresponding experimental results. Before displaying the simulation results of such a phenomenon, we recall that the potential of each electrode is inversely proportional to its size: thus, the electrode which has the greatest size has the lowest potential. Connected to the positive pole of the measuring device, the response will be negative. Finally, the potential difference 'V between the electrodes will be all the greater if the difference in size is substantial.

398


Knowing șAu and șPt, at different temperatures and different pressures, allows us to calculate ǻV for two identical electrodes, either in gold or platinum, and thus as a function of the ratio E R1 / R2 1 . ǻV is then proportional to ș2. The results, displayed in Figures 10.21 and 10.22 enable us to compare the experimental results and the results stemming from calculations. These results are the electric response of the sensors comprising two electrodes of the same size (the surface ratio is 1/10) and the results of the simulation. Results acquired at 300°C for different values of the oxygen pressure (see Figure 10.21) and results acquired under 10 Pa and different temperatures (see Figure 10.22). Given the shape of the curves obtained by the simulation we can consider that the behavior of the device, as a function of temperature and pressure is perfectly in accord with the previous expression, and that the adopted model is not put in check by this series of experiments.

Figure 10.21. Electric responses of sensors composed of two electrodes of the same nature (gold or platinum) with an area ratio equal to 1/10 (1 mbar = 100 Pa): a) experimental results; b) results of the simulation T = 300°C

Figure 10.22. Electric responses of sensors composed of two electrodes of same nature (gold or platinum) with an area ratio equal to 1/10 (1mbar = 100 Pa): a) experimental results; b) results of the simulation PO2 = 10 Pa


399

It appears these results all confirm the validity of the proposed model, and the values given to the different parameters as well. In order to confirm this, we are going to compare the results obtained by this model with the results obtained by measuring the surface potential. 10.3.3.3. Evolution of the surface potential The information recorded by the surface potential measurement (Chapter 6) naturally stems from the presence of charges located at the surface of the device. The previous model has allowed us to clarify their nature, their location and their concentration. The total charge: QTotal, which is proportional to the surface potential, can be expressed by an equation of the following type: Qtotal

q(n1T1 n2T 2 nM T M )

where q is the elemental charge of the electron, șM is the coverage degree on the metal and ni stems from the ionization degree of the species i considered. To simplify, we can consider that șM is negligible compared to ș1 and ș2. This hypothesis is justified by the fact this species, as noted before, is not detected by surface potential measurements conducted on the metal alone. For the other two species, we have admitted that the charge stemming from the į species ª O º T was of dipolar origin. To explain this difference, we have admitted «¬ »¼ į į that the species ª O º T has a greater charge effect than the species ª O º . Thus, ¬« ¼» ¬« ¼» T an arbitrary relation has been adopted: Qtotal

D q (T1 2T 2 )

If we note that the surface potential is proportional to QTotal, and if we remember that T2 = K3T1, it is possible to recalculate to the nearest factor this potential for different temperatures and different pressures. These results are displayed in Figures 10.23, 10.24, 10.25 and 10.26. Figures 10.23 and 10.24 deal with the results obtained with beta-alumina covered with gold; Figures 10.25 and 10.26 deal with the results obtained for beta-alumina covered with platinum. It is interesting to note that the simulation results obtained with gold are especially representative of the experimental results, both for the influence of the temperature as well as the influence of the pressure. With regards to the results

400


obtained with platinum, they are as satisfactory, at least as far as the influence of the temperature is concerned.

Figure 10.23. Variation of the surface potential, observed on beta-alumina powder covered with gold as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)

Figure 10.24. Evolution of the theoretical charge of the gold electrode as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)

Figure 10.25. Evolution of the theoretical charge of the electrode covered with platinum as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)


401

Figure 10.26. Evolution of the theoretical charge of the golden electrode as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)

Nevertheless, given the complex and peculiar shapes of the experimental curves, we can conclude there again that the proposed model is performing well even when many suppositions have been taken into account to simplify the problem. 10.3.4. Simulation of the phenomenon in the presence of CO

We have just seen that the previous model allows us to interpret with accuracy the results obtained with a sensor submitted to different conditions (temperature and pressure). Using such a tool, it is interesting to interpret and simulate the results obtained with the same device submitted to the action or carbon monoxide. 10.3.4.1. Description of the mechanisms considered After analysis of the experimental results concerning the action of carbon monoxide, it appears that oxygen has an essential role in the response of the sensor. Inspired by the model proposed in heterogenous catalysis, we have decided to suppose that the carbon monoxide reacts with the oxygen species present at the surface of the device to form carbon dioxide. This reaction will consume part of these oxygen species, and thus alter the electric response of the device. The potential difference produced will be all the greater if the catalytic activity of the two metals, constituting the electrodes, differs from the oxidation reaction of the carbon monoxide. For this application, platinum appears a better catalyst than gold.19, 20 The functioning principle of the sensor remains unaltered by the action of oxygen, whose concentration in adsorbed species is here controlled by the carbon monoxide concentration.

402


The role of carbon monoxide is then limited to a mere consumption of the adsorbed oxygen species. Such consumption must be explained by a kinetic model in an open system. Before proposing such a model, we are going to try and determine which oxygen species is most concerned by this reaction, then study the different conceivable oxidation mechanisms. We have seen that there are at least four different oxygen species adsorbed at the surface of the device materials. Among these four species, only two are in relation with the three boundary point, but in the hypothesis of a supported catalyst, only the species fixed to the three boundary point characterize such a catalyst.4, 21, 22, 23 Finally, among the two different į species fixed to the three boundary point, only the species ªO º T displays an «¬ »¼ endothermic character and, subsequently, a weak bond. Thus, it is this species, the most reactive, which appears as the best applicant to interact with carbon monoxide. The kinetic model will therefore be developed on the basis of this hypothesis. 10.3.4.2. Oxidation mechanisms of carbon monoxide24, 25, 26, 27 Two kinds of oxidation mechanism for the carbon monoxide at the surface of the solids are frequently acknowledged by scientists. The first, proposed by Eley and Rideal ( Eley-Ridea lmodel) admits that the gaseous carbon monoxide directly reacts with the oxygen species adsorbed to form carbon dioxide, given: [CO] Oadsorbed [CO2 ]

The second, proposed by Langmuir and Hinshelwood (Langmuir-Hinshelwood model), relies on a much more complex reaction. In this reaction the carbon monoxide is in adsorbed form. The equation of the reaction is then written: [CO] COadsorbed COadsorbed Oadsorbed [CO2 ]

An oxidation mechanism of the carbon monoxide following the Eley-Rideal model is realistic if we consider the existence of a weakly bonded oxygen species and, subsequently, extremely reactive oxygen species. Nevertheless, it seems that


403

this model is valid only when the carbon monoxide partial pressure is low compared with oxygen partial pressure. The two mechanisms could both fit with our system, so both cases can be considered. To explain the electric results obtained, it is important to express the į concentration of the reactive species ªO º T , from which stem the potential of the ¬« ¼» electrodes, because they react with carbon monoxide; the hypothesis of a stationary state implies that the speed rate of the reaction is constant and, subsequently, a potentiometric signal that is not a function of time at a given carbon monoxide pressure. – Eley-Rideal model This model is represented by the following reactions: O2 2 ȕ 2[O] ȕ

[O] ȕ s metal [O į ] T ȕ į

[O ] T e [O - ] T CO [O

į

] T CO2 s

This model is treated as the hypothesis for a pure kinetic case or limiting step. This choice, which necessarily implies the hypothesis of a stationary state, allows us to deal with a simpler mathematical system. In fact, it is easy to demonstrate that whatever the chosen limiting step, this model appears incompatible with the experimental results. The expression of the coverage degree, from which stems the electric signal, is either independent of the oxygen pressure (case of the limiting reaction process 1 or 2), or independent of the carbon monoxide partial pressure (limiting reaction process 4), or even independent of the pressure of two gases (limiting reaction process 3). – Langmuir-Hinshelwood model In the case of the Langmuir-Hinshelwood model, the basic steps taken into account are the following: O2 2 ȕ 2[O] ȕ

404


[O] ȕ s metal [O į ] T ȕ į

[O ] T e [O - ] T CO s CO s CO s [O

į

] T CO2

2s

We consider here that carbon monoxide can be directly adsorbed on site s of the three boundary point. If, firstly, we consider that the slowest step of the process is the adsorbed carbon į

monoxide oxidation reaction with the species [O ] T (step 5), we only have to express the fact that all the other steps have reached equilibrium, then we obtain the relation:

TE

T2 T CO

K1 Po2 1 K1 Po2 K 3T1 K 4 PCO >1 T1 (1 K 3 ) @ 1 K 4 PCO

and:

T E K 2 >1 T1 (1 K 3 ) T CO @ T1 (1 T E ) The resolution of this system comprising four equations and four unknown parameters allows us to express ș1 as follows:

T1

K 2 K1 Po2 1 K 2 K1 Po2 (1 K 3 ) K 4 Pco

This expression will allow us to express ǻV and to confirm that its variation as a function of temperature, the oxygen partial pressure, and of course the carbon monoxide partial pressure is compatible with the results obtained by the sensor.


405

For this, it is necessary to calculate the new potential difference that appears between two electrodes of different natures. If we note KD

K1 K 2 , the potential difference obtained between these two

electrodes of same size, which comprise one made of platinum and one made of gold, is expressed as follows: 'V

2 º¼ J ª¬ T Pt2 T Au

'V

2º 2 ª · § · » KDPt Po2 KDAu Po2 «¨§ ¸ ¨ ¸ J« Pt Pt ¨ 1 KDAu Po2 (1 K Au ) ¸ »» «¨© 1 KD Po2 (1 K 3 ) ¸¹ 3 © ¹ ¬ ¼

By comparison with the expression relative to oxygen alone, we still have to define two more constants K 40 and 'H4 to completely define this potential. 10.3.4.3. Results of the simulation The method used to determine the value of these constants is identical to the one used for the simulation of the experimental results obtained with oxygen. The comparison between the experimental results and those obtained by simulation are displayed in Figures 10.27 and 10.32. They allow to us check that, whatever the chosen evolution parameter, the model acts correctly. Figures 10.27, 10.28 and 10.29 display the influence of the carbon monoxide pressure on the potential difference recorded between the electrodes as a function of the oxygen pressure, and for different temperatures. We can note that whatever the oxygen pressure, the simulation, displayed as a dotted line, allows us to explain the complex variations observed, and especially the “toppling” of the response observed at high and low pressures. Figures 10.30, 10.31 and 10.32 concern the influence of the carbon monoxide pressure on the electric response at different oxygen pressures. Once more, and regardless of the temperature, the simulation is in accordance with the experimental results.

406


We also confirm that there is a peak at 10 Pa, and a “toppling” of the response at low temperatures. The values of K 04 and ǻH4, which give the most satisfying results are displayed in Table 10.3.

Table 10.3. Values of the parameters used for the simulation

The value determined for platinum (-14.3 kJ/mole) can be compared with several values provided by publications. Thus, Li, Tan and Zeng28 have determined an adsorption enthalpy of -13.8 kJ/mole with CO on platinum supported by zirconium.

Figure 10.27. Comparison between experimental results (dotted lines) and simulation at different temperatures, PO2 = 1,000 Pa


Figure 10.28. Comparison between experimental results (dotted lines) and simulation at different temperatures, PO2 = 100 Pa

Figure 10.29. Comparison between experimental results (dotted lines) and simulation at different temperatures

407

408


Figure 10.30. Comparison between experimental results (dotted lines) and simulation for different partial oxygen pressures at 500°C (1 mbar = 10 Pa)



409


Given the extreme complexity of the experimental results obtained, such an accordance appears to be an excellent argument in favor of this model. These results allow us to reinforce the thermodynamic model, which makes weakly bound oxygen species react, and furthermore to validate the kinetic model, at least as far as the consumption of these species by a reducing gas, like CO, is concerned. 10.4. Tin dioxide29, 30 10.4.1. Introduction

The results obtained on tin dioxide in interaction with different gases have allowed us to record information that is sufficiently significant and original to make us investigate the nature of the phenomena observed. To do this, we will recall two important results. The first is relative to the experiments described in Chapter 8 and which concerns the alteration of the electric effects observed when a metal is deposited at the surface of the sensitive material. The second is relative to the evolution of the sensitivity of the SnO2 thick films as a function of the thickness. The presence of a peak, whose location depends on the nature of the gas considered, generates interpretive problems that we will attempt to solve.

410


To model such behaviors, we will, firstly, exploit the information obtained with the calorimetric, catalytic and electric tests As in the case of beta-alumina, this procedure will allow us to propose a physicochemical model relative to oxygen adsorption, with the consequences this entails on the depletion layers concerned by this phenomenon and on the electric response of the sensor. Secondly, this physico-chemical model, likened to a physical model of electric conduction in the material, will allow us to interpret the effects linked to the thickness of the sensitive film. 10.4.2. Proposition for a physico-chemical model

We have here to assess the physical and chemical behaviors of the three elements constituting the device, that is, the oxide, the metal and the oxide associated with the metal. In general, these three elements are active from a catalytic point of view, at least as far as the oxidation of carbon monoxide is concerned, the performance of platinum being superior to that of gold. This result led us to suppose the presence of oxygen species catalytically active at the surface of the different materials. The calorimetric tests which confirm the presence of adsorbed species on the oxide and on the oxide associated with the metal furthermore allow us to confirm that the bond between the oxygen and the material is greater with the oxide associated with the metal than with the oxide alone (see Figure 10.33).

Figure 10.33. Quantity of heat exchanged (-Q in mJ) with the different kind of sample during oxygen pressure variations contained between 10 and 5 x 103 Pa at 400°C


411

Finally, these species are electrically charged, as is demonstrated by the electric conduction measurements realized in the cell especially set up to separate the effects linked to the oxide and the effects linked to the oxide/metal association (Chapter 8). Again, these results confirm that in the presence of oxygen, the oxide associated with the metal displays a much greater sensitivity than the oxide alone. Adsorbed oxygen has not been detected on the metal. Nevertheless, several works using the thermodesorption31 or the colorimetric titration32 confirm the presence of chemisorbed oxygen species at the surface of the gold or platinum. These results, displayed in Table 10.4, allow us to imagine the existence of three different species (see Figure 10.34).

Table 10.4. Assessment of the catalytic, electric and adsorption properties of the different parts of the sensor (the number of crosses reflect the intensity of the phenomenon observed)

– The species O1 In the current case, and conversely with the case of beta-alumina, this species fixed on an oxide with a semiconductor character will exchange one or more electrons with the tin dioxide following this kind of reaction: O2 ( gaseous ) 2neox 2 sD 2(O n sD ) with (O n sD )

O1

The surface of the tin dioxide is characterized by the sites sD . – The species O2 Chemisorbed on the element oxide/metal, for which the adsorption site is noted sJ , this species can be likened as in the case of beta-alumina to the three boundary point.20, 33

412


Here again, it is important to explain the physico-chemical contribution of such a site, which can appear more reactive than a site owned by oxide alone. To explain the fact that this species is responsible for an important electric effect on the conductivity of SnO2, we have to imagine that its presence is able to induce an important depletion layer in the semiconductor. This can be explained by a greater degree of coverage for the species O2 than for the species O1 and/or by a greater degree of ionization for the species O2 than for the species O1. To explain a greater degree of ionization, we can imagine that O1 fixed on the oxide is analogous to a species O- - sD , and that the species O2 can be likened to a species of type O2- - sJ. The conversion of one species into another will then be favored by the presence of the metal. To explain the catalytic role of the metal, we will write: O sD eM sJ O 2 sJ sD eox eM

_____________________________ O sD eox sJ O 2 sJ sD

This reaction resembles that induced by S. Morrison34; nevertheless, it is here located at the three boundary point as in the case of certain potentiometric sensors.35 eM and eOX are the electrons present in the metal and the oxide respectively.

– The species O3 The catalytic activity being bigger or smaller than for the metal alone, let us now suppose that at the surface of this material there are oxygen chemisorbed species. These locations are sites and the reaction can be written: O2 ( gaseous ) 2neM 2 sD 2(O n sD )

n is the number of electrons of the metal involved in this chemisorption and its value is a function of oxygen degree of oxidation.


413

The coverage degree and the thermodynamic constant associated with this equilibrium will be noted TE and KE respectively. In the case of gold, which possesses a catalytic activity lower than that of platinum, we can suppose that the coverage degree in chemisorbed TE will be lower than the coverage degree obtained with platinum.

Figure 10.34. Reaction scheme of the transformation of CO into CO2 on the surface of: (a) tin dioxide, (b) tin dioxide on which a metallic film has been deposited, (c) the metal

For the energy plan, we can propose a diagram like the one displayed in Figure 10.35.

Figure 10.35. Energetic diagram of the different oxygen species taken into account

414


Because the reaction involved in this model describes the formation of the species O3, we can simultaneously invoke the mechanisms of spill-over and reverse spill-over, mentioned in Chapter 8. Indeed, mechanism (A) is an approach of reverse spill-over type,36 insofar as certain “oxygen” species are initially adsorbed on the oxide, whereas the type (B) mechanism resembles the spill-over, if we consider that other “oxygen” species are initially adsorbed on the metal. Besides, our model allows a depletion layer to appear, linked to an electron transfer which, contrary to the electronic mechanism described by Yamazoe,37 is not located perpendicularly to the metal, but at the three boundary points. As in Figure 10.36, the intensity of the induced depletion is greater than the depletion provoked by the adsorption of oxygen on the oxide alone. Such a model is in perfect accord, firstly, with that of U. Weimar32 which indicates the presence of an important depletion layer at the three boundary point, and secondly with the model of K. Vargehse38 which explains the presence of an important depletion layer in the extension of a metallic electrode. These models were commented on in Chapter 8.

Figure 10.36. Mechanism proposed to explain the action of oxygen

We will retain from this physico-chemical model the fact that the synergy effects between the gas, the metal and the oxide are especially located at the inter-phase metal/oxide/gas, called the three boundary point, and that these effects are explained by a large space-charge layer, which is itself located in the oxide at the level of this very inter-phase. This configuration is compatible with the notion of the three boundary point, which involves, firstly, an electron transfer from the metal towards the gas and then


415

from the oxide towards the metal. Strictly speaking, the sensitive film elaborated with pulverulent oxide can display a natural and non-negligible porosity that enables metallic elements to diffuse. In these conditions, the inter-phase metal/oxide/gas and, subsequently, the space-charge layer, is localized in the zone of the oxide contaminated by the metal. We can thus imagine that in a real structure, there is a space-charge layer located perpendicularly to the surface of the metallic film. Such a configuration closely resembles the one proposed by K. Vargehse.38 The model, as displayed in Figure 10.36, appears as a limited and simplified case that we will be able to use in kinetic and mathematical plans. We imagine that in such a model, the vastness of the barrier effect must be considered caused by its amplitude compared to the thickness of the material. It remains to be seen whether the thickness of such a zone and, consequently, the value of its resistance is able to control the conductance of the whole device. It is based on these results, obtained on oxide alone as a function of the thickness of the deposited films, that we are going to develop a physical model of conduction able to justify the role of the space-charge layer generated by the presence of electrodes. 10.4.3. Phenomenon at the electrodes and role of the thickness of the sensitive film

The purpose of the present physical model is to demonstrate how the depletion layer at the level of the three boundary point, is able to modulate and control the electrical properties of the device according to the thickness of the material. This model is developed for thick film materials. The diagram of such a device, with two electrodes deposited on the outer surface of the material, is presented in Figure 10.37.

Figure 10.37. Space-charge layers present at the level of the electrodes for a thick film device

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10.4.3.1. Calculation of the conductance G as a function of the thickness of the film – Geometric aspects In the present case, both electrodes are located on the same face of the material. The assessment of the global resistance is not easy because it needs the integration of many current lines whose paths are not linear between the two electrodes. To simplify the problem, our sample will be likened to a sensitive film shaped like a square parallelepiped, of length D (4 mm), of width L (2 mm) and of thickness e. The electrodes deposited at the surface of the sample are also of rectangular shape, of width d (1 mm) and of length L (2 cm). The space-charge layer, as indicated by Figure 10.38, can be decomposed into two zones: – D1, which corresponds to the action of oxygen on tin dioxide alone. This depletion layer can be likened to a square parallelepiped of length D-2d+h, of height y and of width L; – D2, relative to the action of oxygen at the three boundary point. This depletion layer can be represented by a square parallelepiped of height x, of width l and of length L, with x>> y.

Figure 10.38. Space-charge layers present at the level of the electrodes for a thick film device

Given the slight thickness supposed for y, we will consider that zone D1 is homogenous from an electric point of view, and that the resistivity US will have a constant value in all its thickness.


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As far as D2 is concerned and given the greater value supposed for x, we will consider that this depletion layer is not necessarily homogenous from an electric point of view, and that there will be a linear resistivity gradient:

U ( x)

U S ax

The parameter “a”, which characterizes the amplitude of the gradient, will naturally be a function of the physico-chemical perturbation amplitude, that is, a function of the coverage degree at the three boundary point and of the nature of the reducing gases reacting with oxygen. Figure 10.39 displays the schematic representation of such a gradient. To respect the conditions relative to D1 and D2, we will indeed admit that for 0 < x

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