Terahertz frequency detection and identification of materials and objects: [proceedings of the NATO Advanced Research Workshop on Terahertz Frequency Detection and Identification of Materials and Objects, Spiez, Switzerland, 7 - 11 July 2006]

Terahertz Frequency Detection and Identification of Materials and Objects

NATO Science for Peace and Security Series This Series presents the results of scientific meetings supported under the NATO Programme: Science for Peace and Security (SPS). The NATO SPS Programme supports meetings in the following Key Priority areas: (1) Defence Against Terrorism; (2) Countering other Threats to Security and (3) NATO, Partner and Mediterranean Dialogue Country Priorities. The types of meeting supported are generally "Advanced Study Institutes" and "Advanced Research Workshops". The NATO SPS Series collects together the results of these meetings. The meetings are coorganized by scientists from NATO countries and scientists from NATO's "Partner" or "Mediterranean Dialogue" countries. The observations and recommendations made at the meetings, as well as the contents of the volumes in the Series, reflect those of participants and contributors only; they should not necessarily be regarded as reflecting NATO views or policy. Advanced Study Institutes (ASI) are high-level tutorial courses intended to convey the latest developments in a subject to an advanced-level audience Advanced Research Workshops (ARW) are expert meetings where an intense but informal exchange of views at the frontiers of a subject aims at identifying directions for future action Following a transformation of the programme in 2006 the Series has been re-named and re-organised. Recent volumes on topics not related to security, which result from meetings supported under the programme earlier, may be found in the NATO Science Series. The Series is published by IOS Press, Amsterdam, and Springer, Dordrecht, in conjunction with the NATO Public Diplomacy Division. Sub-Series A. B. C. D. E.

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Terahertz Frequency Detection and Identification of Materials and Objects edited by

R.E. Miles University of Leeds, U.K.

X.-C. Zhang Rensselaer Polytechnic, Troy, U.S.A.

H. Eisele University of Leeds, U.K. and

A. Krotkus Semiconductor Physics Institute, Vilnius, Lithuania

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Research Workshop on Terahertz Frequency Detection and Identification of Materials and Objects Spiez, Switzerland 7 – 11 July 2006

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CONTENTS

Organising Committee

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Sponsors

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Preface xi Theme 1: Devices Terahertz Emission from Semiconductors Excited by Ultrafast Laser Pulses A. Krotkus, R. Adomavičius, and V. L. Malevich

3

Terahertz Generation by Multiplication Jan Stake, Tomas Bryllert, T. Arezoo Emadi, and Josip Vukusic

17

Towards Superlattice Terahertz Amplifiers and Lasers Alvydas Lisauskas, Ernst Mohler, Hartmut G. Roskos, and Nataliya V. Demarina

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Tailoring the Emission of Terahertz Quantum Cascade Lasers Richard Green, Lukas Mahler, Cosimo Mauro, Tonia Losco, Ji-Hua Xu, Alessandro Tredicucci, Fabio Beltram, Harvey Beere, and David Ritchie

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Guided Propagation of Terahertz Pulses on Metal Wires Kanglin Wang and Daniel M. Mittleman

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Superlattice and Other Negative-Differential-Resistance Devices: Current Status Heribert Eisele

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Theme 2: Interactions with Materials Molecular and Organic Interactions A. G. Davies and E. H. Linfield

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91

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CONTENTS

Terahertz Beam Interactions with Amorphous Materials Mira Naftaly and Robert E. Miles Development of Tagless Biosensors for Detecting the Presence of Pathogens Jing–Yin Chen, Joseph R. Knab, Shuji Ye, Yunfen He, and Andrea G. Markelz

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Theme 3: Detection and Sensing Improvements to Electronic Techniques for Terahertz Spectroscopic Detection Daniel W. van der Weide, Alan D. Bettermann, Min K. Choi, and John Grade Terahertz Time-Domain Spectroscopy of Crystalline and Aqueous Systems Peter Uhd Jepsen, Hannes Merbold, Zhengxin Li, Xiaoyu Xing, and Stewart Clark Continuous-Wave Terahertz Photomixer Systems for Real-World Applications Ian S. Gregory, Hideaki Page, and Lee Spencer

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147

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Theme 4: Systems for Security Systems Requirements for A Multi-Channel Terahertz Contraband Scanner William S. Truscott

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Challenges to Terahertz Counter-Terrorism and Security-Related Applications Howard Cummins

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Terahertz Detection of Illegal Objects Roger Appleby, Peter R. Coward, and Gordon N. Sinclair

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Terahertz Rays to Detect Drugs of Abuse Kodo Kawase, Adrian Dobroiu, Masatsugu Yamashita, Yoshiaki Sasaki, and Chiko Otani

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CONTENTS

Terahertz Spectroscopy for Explosive, Pharmaceutical, and Biological Sensing Applications Hai-Bo Liu and Xi-Cheng Zhang Terahertz Communications: A 2020 vision Martin Koch

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Theme 5: Overview Applied Terahertz Science: The Technology of the Future, and Always Will Be? Martyn Chamberlain

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List of speakers

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List of participants

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Group photograph

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Index

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ORGANISING COMMITTEE

Professor X.-C. Zhang (Rensselaer Polytechnic, USA)

Co-director

Professor A. Krotkus (Semiconductor Physics Institute, Vilnius, Lithuania)

Co-director

Professor R. E. Miles (University of Leeds, UK)

Secretary

Dr. H. Eisele (University of Leeds, UK)

Treasurer

ix

We wish to thank the following for their financial contributions which have contributed greatly to the success of the workshop.

NATO US Army International Technology Centre – Atlantic, Research Division US Air Force Office of Scientific Research Teranova (European Union Integrated Project)

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PREFACE This volume contains an account of the third NATO-sponsored meeting on terahertz science and technology. The first, held in 1996, was an Advanced Study Institute (ASI) on “New Directions in Terahertz Technology” which in turn was followed in 2000 by an Advanced Research Workshop (ARW) entitled “Terahertz Sources and Systems”. In these earlier meetings, the difficulties involved in generating THz frequency signals formed a background to most of the presentations and discussions – with frequent mentions of the 0.3 to 3 THz “Terahertz Gap”. This gap is still with us but, with advances in technology, has been reduced to the region between about 1.0 THz and 2.5 THz. In the 2000 ASI, the lack of a complete set of THz electronic devices, in particular an amplifier, was identified as an obstacle to progress. While this is still the case, it became clear from this ASI that THz amplifiers based on semiconductor superlattice structures are very close to being realized. The purpose of this workshop was to explore the potential of THz techniques in the detection of illegal substances, especially for security purposes. The workshop set out to identify the state of the art, to define the scope of the problem and the areas where THz frequency radiation could contribute. Extensive studies have shown that drugs of abuse and explosives can be identified from their THz spectra and prototype systems are already in place in Japan to scan mail online as it passes through the automated systems. From this and other work reported at the ASI it is clear that THz technology has a part to play in security screening but developments are still required to improve the delivery of THz signals to the area of concern and its subsequent detection. One possibility is that THz techniques may not be the first line of detection but could be used for more detailed identification of, say, suspicious packages. Stand-off detection, as is required in the identification of suicide bombers, is a more difficult issue but the delegates concluded that detection at 30 m is possible but effective systems will only result from close cooperation between the THz generation and signal-processing communities. We learned at this meeting that THz radiation can be generated at a distance using air as the transducer. However, this necessitated the use of a powerful laser beam which could not be employed in a public place such as an airport, but could perhaps be implemented in other situations. We trust that the readers of this book will gain a flavour of the excitement of the meeting. However, one thing that is difficult to convey here is the wonderful way in which we were looked after by our hosts Peter and Margit Schlatter for whom nothing was too much trouble.

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Theme 1 DEVICES

TERAHERTZ EMISSION FROM SEMICONDUCTORS EXCITED BY ULTRAFAST LASER PULSES

A. KROTKUS* AND R. ADOMAVIČIUS Semiconductor Physics Institute, A. Gostauto 11, 01108, Vilnius, Lithuania V. L. MALEVICH Institute of Physics, National Academy of Sciences of Belarus, F. Skorina Ave. 68, 220072, Minsk, Belarus

Abstract. Various physical mechanisms leading to terahertz (THz) emission from semiconductor surfaces illuminated by femtosecond laser pulses are analyzed. Results obtained on different materials are described and relative efficiency of these materials as THz emitters is compared.

Keywords: semiconductors, InAs, THz emission, THz emission spectroscopy

1. Introduction Currently, there are two basic approaches for generating THz radiation beams which utilize ultrashort laser pulses: photoconductive technique based on high-speed photodetectors integrated with wideband-radiating antennae and bare semiconductor surfaces illuminated by femtosecond laser beams. In the case of photoconductive antennae that are used both for THz pulse generation and their detection, the main problem remaining is the availability of the proper semiconductor material that should be photosensitive at the laser wavelength and should have other distinctive properties like high resistivity and sub-picosecond carrier lifetimes. For the most popular in THz pulse applications femtosecond laser system – mode-locked

______ *

To whom correspondence should be addressed: Arunas Krotkus, Semiconductor Physics Institute, A. Gostauto 11, 01108, Vilnius, Lithuania; e-mail: [email protected]

3 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 3–16. © 2007 Springer.

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Ti:sapphire laser (laser wavelength of ~800 nm), the material of choice is low-temperature molecular-beam-epitaxy grown GaAs (LTG GaAs) layers [1]; however, the search for the most suitable semiconductor that could be used in THz antennae activated by femtosecond lasers generating at longer wavelengths from 1 to 1.5 µm is still not finished. Ion-implanted InGaAs [2, 3] and LTG GaBiAs [4] are among the possible candidates for ultrafast photodetectors for this spectral range. In the second case, when THz pulses are generated by illuminating semiconductor surfaces with ultrashort laser pulses all mentioned above restrictions on the material properties are less important. The best THz emitters are narrow-gap semiconductors like InAs [5], which have optical absorption edge corresponding to the mid-infrared spectral region. Stronger or weaker THz pulses are emitted from the majority of weakly or moderately doped semiconductors with rather long carrier lifetimes. Besides of the universal occurrence of this effect, emission from the semiconductor surfaces provide much wider and better shaped THz beams than those generated by photoconductive antennae, which could be preferable for some specific applications like THz imaging. In this chapter, we will review the physical mechanisms leading to THz emission from the semiconductor surfaces and will compare the characteristics of this effect in various materials. 2. Physical Mechanisms 2.1. INSTANTANEOUS POLARIZATION EFFECTS

The lowest order nonlinear optical response of a non-centrosymmetric crystal is caused by the second-order susceptibility χ2 that leads to the sum and difference frequency generation. In the case when the optical beam contains nearly the same frequencies (which is typical for femtosecond laser spectra) and interacts nonlinearly with the crystal, the difference frequency is in the dc range and the induced polarization is referred as optical rectification (OR) with the induced charge displacement following the optical pulse envelope. When a built-in dc field Es is present at the semiconductor surface, transient THz polarization can also be induced due to the third-order nonlinear susceptibility χ3; THz pulse magnitude generated due to this electrical-field-induced optical rectification (EFIOR) effect will be proportional to the effective second-order susceptibility χ2 χ 2eff = χ 3 E s .

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As a fingerprint of nonlinear optical THz pulse generation mechanisms is usually considered the dependence of the emitted THz pulse amplitude on the orientation of the optical field with regard to the crystallographic axes. It has been pointed out recently [6] that these so-called azimuthal angle dependences of the THz emission efficiency from zinc-blende semiconductors like GaAs measured at different crystallographic planes can also help in distinguishing OR and EFIOR mechanisms. For (111) plane both effects give similar cos 3ϕ – type azimuthal dependences, whereas for (100) plane THz signal is constant for EFIOR mechanism and depends on the azimuthal angle ϕ proportional to cos 2ϕ – for OR mechanism. THz generation due to nonlinear optical interaction is significantly modified when the energies of the laser quanta become larger than the fundamental energy bandgap of the semiconductor Eg [7]. It has been shown by Sipe and Shkrebtii in [8] that laser-induced nonlinear polarization in this case contains an additional to OR contribution arising from the spatial shift of the charge during excitation leading to the “shift” current. 2.2. PHOTOCURRENT SURGE EFFECTS

2.2.1. Surface field effect If there is a static electric field at the surface of semiconductor illuminated by an ultrashort laser pulse, the free carriers created by this pulse are driven by the static field and accelerate along the field direction, forming a transient photocurrent. The rise time of the photocurrent pulse is comparable to the optical pulse duration; its decay time corresponds to the shorter of two characteristic times: carrier lifetime or their transit across the field region time. This fast changing photocurrent leads to the radiation of the electromagnetic waves with amplitude proportional to the first time derivative of the current, in the far field. Built-in electric fields in the majority of semiconductor surfaces appear due to the band bending imposed by the surface potential different from the energy position of the Fermi level in the bulk of the material. The sign of this field is usually opposite for n-type and p-type crystals, which leads also to the opposite polarities of THz pulses generated from the surfaces of these crystals. 2.2.2. Photo-Dember effect Transient photocurrent surge can appear at the semiconductor surface illuminated by ultrafast laser pulse even in the absence of the surface

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electric field. This situation is typical for narrow-gap semiconductors, which are relatively good THz emitters despite of the small band bending at their surfaces. Electrons and holes excited at the surface are predominantly moving perpendicular to it, towards the bulk of the material. Electron diffusion usually is faster than hole diffusion, therefore a dynamic photovoltage can develop at the illuminated surface that can lead to the THz emission. This effect is especially strong in semiconductors with a narrow energy bandgap, where the electrons are excited with quite large excess energies εex that can exceed 1 eV for the excitation by Ti:sapphire laser quanta ( hν ≈ 1.55 eV). In the majority III–V and IV–VI narrow-gap materials characteristic time of the electron-LO phonon scattering is around 200 fs, the majority of these scattering processes lead only to small changes in electron momentum, therefore, during the first few hundred femtoseconds after the photoexcitation excitation, the electron movement is purely ballistic rather than diffusive. 2.2.3. Optical orientation For III–V semiconductors the ballistic photocurrent can depend on the crystallographic direction and can have a component parallel to the surface, which could explain the azimuthal angle dependencies of the THz emission without involving nonlinear optical interactions. Valence band of III–V semiconductors consists of two subbands of heavy and light holes at the center of the Brillouin zone. Due to the optical selection rules, the momenta of electrons excited from the heavy-hole band by linearly polarized light will mainly lie in the plane perpendicular to the direction of the light electrical field (Figure 1). On the other hand, the momentum distribution for electrons excited from the light-hole band will be stretched out along the direction of the optical field polarization. When the light is falling into air-semiconductor interface at incline angle and is absorbed at a thin surface layer, the electrons moving to the right in Figure 1 will be diffusively scattered by the surface and a lateral photocurrent component will arise. This lateral photocurrent effect has been discovered in GaAs crystals in [9]. In this experiment as well as in the observation of the polarized hot-electron photoluminescence [10], cryogenic temperatures and photon energies leading to the photoelectron energies smaller than the optical phonon energy were used for reducing the electron-scattering rate. However, when the semiconductor is excited by a short light pulse, such lateral surface photocurrent component will be present even at the room temperature also for larger energy quanta during the first few hundreds of femtoseconds when the electrons are still moving ballistically and could

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lead to the THz radiation that will be efficiently outcoupled from the semiconductor. Real iso-energetic surfaces in the valence bands of III–V semiconductors are not spherical but warped as a result of their cubic symmetry; therefore, amplitudes of the lateral and perpendicular to the surface photocurrent components will depend on the orientation of the polarization vector relative to the crystallographic axes.

Figure 1. Illustration of the surface photocurrent appearing due to the optical alignment of the electrons and their diffusive scattering at the surface.

2.3. COLLECTIVE RESPONSE EFFECTS

When THz emission from semiconductor surfaces by ultrashort laser pulses is caused by coherent movement of photoexcited carriers, its intensity and density depends on the basic semiconductor material parameters themselves, especially on its doping level. The fast change of the electric field at the vicinity of the surface can initiate plasma oscillation of the extrinsic carriers that will amplify the THz wave [11]. Pulsed excitation of the semiconductor can also lead to the coherent generation of infrared-active lattice vibrations that would produce oscillations of macroscopic dielectric polarization and emission of electromagnetic waves at the phonon frequency. Such an effect has been observed in Te [12] and several other semiconductors.

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3. Discussion of the Results Obtained on Various Semiconductor Materials 3.1. INDIUM ARSENIDE

THz generation from InAs was investigated more often than from any other narrow-gap semiconductors, because these crystals are most efficient emitters, especially when a strong magnetic field is applied in parallel to their surfaces [5]. This enhanced magnetic field influence (magnetic fields of ~1 T can lead to an increase of the emitted THz power by a factor of 100) had focused the attention of researchers on the photo-Dember effect, although some authors have also pointed out the role of other phenomena like bulk OR [13], magneto-plasma waves [14], or coupled plasmon-phonon modes [15] in THz radiation from InAs surface.

Figure 2. Dependence of the emitted THz field amplitude on the InAs crystal doping level.

Possible influences of the surface electric field to the THz emission were usually written off due to a narrow-bandgap in InAs and potentially smallband bending at the surface of this material. This is not always justifiable because it is known that surface potential in InAs is fixed at fairly high

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(0.18–0.2 eV [16]) values above the conduction band minimum and in a p-doped crystal surface depletion layer can be sufficiently wide and strong. It has been found in [17] that p-type InAs is a better THz emitter than n-type InAs (Figure 2), which was explained by a possible contribution of the EFIOR effect. A similar conclusion was drawn in [6] from the analysis of the symmetry of the azimuthal dependences of THz radiation measured by illuminating different crystal planes of InAs and also from the fact that the surfaces of InAs illuminated by P-polarized optical beams radiate both P and S-polarized THz signals, which is typical to nonlinear optical rather than to the current surge mechanisms of THz generation. Dependences of the THz-radiation efficiency from femtosecond laser illuminated InAs surfaces on the photon quantum energy were measured in [18]. The results of such measurements are presented in Figure 3. THz field amplitude increases with the increasing photon energy, reaches maximum at hν = 1.6 eV, and then decreases. Such a shape of the spectral dependence for THz emission could be expected in the case when free electron contribution to this effect is dominating. When the quantum energy is large

Figure 3. Dependences of the THz emission efficiency in InAs on the femtosecond laser quantum energy.

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enough, the electrons are excited high in the conduction band, where they are efficiently scattered to the subsidiary L valleys with a low mobility. Intervalley separation in the conduction band of InAs determined from the experiments presented on Figure 3 ∆εΓL = 1.08 eV coincides with the previous estimations of this parameter. However, this contradicts with the previously made conclusion on the prevalence of the EFIOR effect that should not be influenced by the electron scattering rate variation. Moreover, it can be seen from Figure 3 that the azimuthal angle anisotropy of THz amplitude at large photon energies is also decreasing. In part, these contradictory experimental facts could be explained by the optical alignment effect, however, the calculation of this contribution using commonly accepted valence band parameters of InAs had shown that the anisotropy of this band can lead to a much weaker azimuthal angle dependence of the radiated THz signal as it is observed experimentally. The situation becomes more transparent, when one remembers that photoexcited electrons can themselves create at the crystal surface a strong electrical field. Electrons are excited by Ti:sapphire laser quanta at excess energies of ~1 eV and move towards the bulk with the velocity greater than 1.5108 cm/s. Their movement is being stopped by an electrical field that is appearing due to the electron and hole separation. Figure 4 shows the results of numerical Monte Carlo simulation of the temporal and spatial dynamics of the surface potential in InAs after its photoexcitation by 150-fs duration laser pulse. It can be seen

Figure 4. Spatio-temporal dynamics of the surface potential in InAs excited by femtosecond laser pulse.

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from Figure 4 that electrical fields as large as 2·105 V/cm are developing during the laser illumination over distances reaching ~0.5 µm. These fields are much stronger than any static, built-in electrical field in InAs, thus they could induce an intense nonlinear optical interaction with the exciting laser pulse, and cause THz generation due to the EFIOR effect. As a test of this mechanism of THz generation from InAs surface an additional pump-and-probe experiment was performed. The laser beam was split into two parts, one of which (the probe beam) was incident on the sample’s surface at 45° angle and generated THz pulses monitored by the detector. The second (the pump beam) part of the laser beam was parallel to the surface normal; it was focused to a rather large spot (diameter of ~0.5 mm) in order to avoid possible interference at the detector of THz pulses generated by both laser beams. Carrier densities of approximately 4·1017 cm−3 and 1018 cm−3 were excited by the probe and pump beams, respecttively. S-polarized component of the THz signal at its maximum was measured as a function of the time delay between the probe and pump pulses. Figure 5 shows the results of the pump-and-probe experiment. THz emission increases at times close to the overlap of both optical pulses and becomes weaker when the pump pulse arrives to the sample before the probe pulse.

Figure 5. Results of the pump-and-probe THz generation experiment on InAs.

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The effect of carriers excited by the pump pulse on the THz signal generated by the probe pulse is twofold. First of all, electron ballistic movement and the charge carrier separation add to the surface electric field and leads to an increase in the generated THz signal. Secondly, when the pump pulse arrives at the surface at much earlier time moment than the probe pulse, carriers excited by the pump pulse have already cooled down and contribute to the relaxation of the surface electrical field and to the reduction of THz generation. The shape of the experimental trace presented on Figure 5 evidences the presence of both effects. The peak of THz emission at time close to the zero delay is due to the enhancement of the EFIOR contribution in the field induced by the pump pulse and the reducetion of this emission at longer delays is, most probably, caused by the screening of the surface electrical field by the photoexcited carriers. The timescale of both contributions coincides with the characteristic times of the surface field nucleation and decay obtained by numerical calculations (Figure 4) and discussed above. 3.2. OTHER NARROW-GAP SEMICONDUCTORS

When the ballistic photocurrent surge effect is dominates the THz emission from semiconductor surfaces, the emission becomes stronger with increasing electron excess energy. This is illustrated in Figure 6 by the THz pulse amplitudes measured at the same experimental conditions on different semiconducting compounds from the InAs/GaAs system. Throughout this system, the energy bandgap varies from 0.35 eV for InAs to 1.4 eV for GaAs, and the electron-excess energies – from 1.05 eV to 0.15 eV (when Ti:sapphire laser pulses are used for the illumination of the samples). Therefore, semiconductors with a narrower bandgap should be more efficient THz emitters. InSb has a band structure similar to that of InAs, but with two times smaller energy bandgap, however, THz power radiated from this semiconductor surface illuminated by femtosecond Ti:sapphire laser pulses is ~100 times weaker. It has been suggested that this reduction of THz emission efficiency is caused by the intervalley scattering of the photoexcited electrons. Spectral dependence of THz radiation from InSb supports this conclusion [18]; intervalley energy separation in the conduction band of InSb evaluated from this dependence is equal to ∆εΓL = 0.53 eV. It should be pointed out that for longer laser wavelengths of around 1.5 µm, InSb is preferred over InAs as a THz-emitting material.

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Figure 6. Amplitudes of THz pulses emitted from the surface of various compounds from the InAs/GaAs system when excited by femtosecond Ti:sapphire laser pulses.

CdxHg1−xTe crystals are also narrow-gap semiconductor compounds widely used in infrared devices. THz emission from these compound semiconductor surfaces illuminated by Ti:sapphire laser pulses was investigated in [19]. The samples investigated were CdxHg1−xTe crystals with x = 0, 0.2, and 0.3. HgTe sample was single-crystalline, whereas thesamples of remaining two alloy compositions were epitaxial layers grown on CdTe substrates. Figure 7 shows the time-domain waveforms measured on three CdxHg1−xTe samples with different alloy composition. As it can be seen from that figure, the largest amplitude has THz transient emitted by the sample with x = 0.2. In contrary to our expectations, HgTe, for which the excess energy of photoexcited electrons should be the largest, radiates the transient with the smallest amplitude.

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Figure 7. THz field transients measured for the samples from different CdxHg1−xTe alloys.

The band structure of CdxHg1−xTe alloy system changes drastically when altering the alloy composition. On substituting Cd for the heavy Hg atom the energy spectrum of the CdxHg1−xTe alloys exhibits a transition from a semimetal behavior in HgTe to a semiconductor behavior in CdTe. The bandgap changes almost linearly with x and becomes equal to εg = 0.35 eV for x = 0.3. Spin-orbital split band Γ7 energetic position relative to the heavy-hole band is changing with the alloy composition slower than the bandgap and, for the alloy compositions investigated in our work, is in the range of ∆0 = 1−1.2 eV. Optical pulses generated by Ti:sapphire laser (hν = 1.51 eV) can excite electrons from all three: light-hole, heavy-hole, and spin-orbital split valence bands. Excess energy of electrons and THz transient magnitude excited by first two of those transitions will decrease with x, which is inconsistent with the experimental observations. Moreover, transitions from the heavy-hole band will excite electrons to very high energies in the conduction band, where possible scattering to the subsidiary, larger effective mass L-valleys (positioned at 1.2–1.4 eV in CdTe/HgTe system [20]) will reduce the photo-Dember voltage and the radiated THz signal.

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Therefore, we suppose that most important are the transitions from the spin-orbital split valence band to Γ6 conduction band valley. 3.3. GERMANIUM

As compared to compound semiconductors, the data on THz emission from the surfaces of elementary semiconductors, such as silicon or germanium, are very scarce. For example, Ge, which is a better THz emitter as Si, excited by Ti:sapphire laser pulses with the duration of ~100 fs radiates THz pulses with an amplitude almost one order of magnitude smaller than InAs [21]. However, some peculiarities of the energy band structure of this material raise a hope that it can find some particular applications in optoelectronic THz range devices. Ge is an indirect bandgap material with the lowest conduction band valleys positioned at L points of the Brillouin zone. Energy bandgap of Ge is rather narrow ( ε g = 0.74 eV), therefore Ti:sapphire laser quanta excite electrons by direct transitions into Γ valley lying 0,12 eV above the Lvalleys. Photoexcited electrons are then rather fast (~50 fs) scattered from the Γ valley to L and X-valleys, where their mobility is quite low. Therefore, in combination with laser pulses longer than 50 fs, Ge emits THz radiation rather poorly – the magnitudes of THz pulses radiated from a Ge surface illuminated by 150-fs duration Ti:sapphire laser pulses are ~3% of that radiated by p-type InAs crystal. However, when shorter laser pulses are used, the effect of the high mobility G valley electrons becomes more important and THz pulse amplitude can increase. Experiments performed with 20-fs duration pulses have shown that relative amplitude of THz pulses emitted from Ge surface increases by more than 4 times as compared with 150-fs pulse excitation. 4. Conclusions Semiconductor surfaces illuminated by femtosecond laser pulses can rather efficiently radiate THz pulses. THz radiation from semiconductor surfaces can be caused by a number of different physical mechanisms involving both bound and free electrons. Most efficient emitters are group III–V narrow-gap semiconducting compounds such as InAs. Relative intensity of THz pulses radiated from laser excited semiconductor surfaces depends on the details of the electron band structure of the material and its doping level as well on the wavelength and the duration of the laser pulses.

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References 1. A. Krotkus and J-L. Coutaz, Semicond. Sci. Technol., 20, S142 (2005). 2. C. Carmody, H. H. Tan, C. Jagadish, A. Gaarder, and S. Marcinkevičius, Appl. Phys. Lett., 82, 3913 (2003). 3. N. Chimot, J. Mangeney, L. Joulaud, H. Bernas, K. Blary, and J. F. Lampin, Appl. Phys. Lett., 87, 193510 (2005). 4. K. Bertulis, A. Krotkus, G. Aleksejenko, V. Pačebutas, R. Adomavičius, G. Molis, and S. Marcinkevičius, Appl. Phys. Lett., 88, 201112 (2006). 5. N. Sarukura, H. Ohtake, S. Izumida, and Z. Liu, J. Appl. Phys., 84, 654 (1998). 6. M. Reid, I. V. Cravetchi, and R. Fedosejevs, Phys. Rev., B 72, 035201 (2005). 7. X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett., 69, 2302 (1992). 8. J. E. Sipe and A. I. Shkrebtii, Phys. Rev., B 61, 5337 (2000). 9. V. L. Alperovich, V. I. Belinicher, V. N. Novikov, and A. S. Terekhov, JETP Pisma, 31, 581 (1980). 10. V. I. Zemskii, B. P. Zakharchenia, and D. N. Mirlin, JETP Pisma, 24, 96 (1976). 11. R. Kersting, K. Ulterrainer, G. Strasser, H. F. Kaufmann, and E. Gornik, Phys. Rev. Lett., 79, 3038 (1997). 12. T. Dekorsy, H. Auer, C. Waschke, H. J. Bakker, H. G. Roskos, H. Kurz, V. Wagner, and P. Grosse, Phys. Rev. Lett., 74, 738 (1995). 13. P. Gu, M. Tani, S. Kono, K. Sakai, and X.-C. Zhang, J. Appl. Phys., 91, 5533 (2002). 14. J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Mueller, and K. Unterrainer, Phys. Rev., B, 64, 085202 (2001). 15. M. P. Hasselbeck, D. Stalnaker, L. A. Schlie, T. J. Rotter, A. Stintz, and M. SheikBahae, Phys. Rev. B, 65, 233203 (2002). 16. C. Affentaugscheggl and H. H. Wieder, Semicond. Sci. Technol., 16, 708 (2001). 17. R. Adomavičius, A. Urbanowicz, G. Molis, A. Krotkus, and E. Šatkovskis, Appl. Phys. Lett., 85, 2463 (2004). 18. R. Adomavičius, G. Molis, A. Krotkus, and V. Sirutkaitis, Appl. Phys. Lett., 87, 261101 (2005). 19. A. Krotkus, R. Adomavičius, G. Molis, A. Urbanowicz, and H. Eusebe, J. Appl. Phys., 96, 4006 (2004). 20. R. Dornhaus, G. Nimtz, and B. Schlicht, Narrow-gap Semiconductors (Springer, Berlin, 1983). 21. A. Urbanowicz, R. Adomavičius, A. Krotkus, and V. L. Malevich, Semicond. Sci. Technol., 20, 1010 (2005).

TERAHERTZ GENERATION BY MULTIPLICATION JAN STAKE*, TOMAS BRYLLERT, T. AREZOO EMADI, AND JOSIP VUKUSIC Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

Abstract. We report on the status of symmetric varactor diode multipliers for signal generation in the terahertz frequency range. The progress and basic principles of heterostructure barrier varactor (HBV) diodes are presented. Furthermore, the design methodology and electro-thermal simulation results of high-power HBV multipliers for signal generation in the millimeter and submillimeter wave region are also presented. Finally, a state-of-the-art HBV tripler with an output power of 0.2 Watt at 113 GHz is presented.

Keywords: frequency multiplier, heterostructure barrier varactor (HBV), varactor diode, submillimeter wave generation, terahertz sources

1. Introduction Terahertz technology, in this chapter defined as technology using frequentcies from about 100 GHz to several THz, is gradually maturing and already used in many applications.1 The main applications today are within science, particularly radio astronomy.2 Applications under development or still at a planning stage are high-speed wireless networks, short-range high-resolution radar sensors, medical and biological imaging, high-speed inter-satellite communication, earth environment monitoring, military applications, and surveillance systems, notably security systems. Most such applications crucially depend on the availability of reasonably inexpensive, lightweight and compact sources and detectors. However, as the frequency approaches 1–2 THz, the output power for both electronic and photonic signal sources drops rapidly. This is commonly referred to as the THz gap. Traditional

______ * To whom correspondence should be addressed. Jan Stake, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden; e-mail:jan.stake@ chalmers.se

17 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 17–30. © 2007 Springer.

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fundamental signal sources are backward-wave oscillators (BWO) that can generate a few milliwatts at 1.5 THz, and optically pumped lasers for spot frequencies between 0.5 and at least 5 THz with output power in the mW range. However, these sources are heavy, bulky, and very expensive. The quantum cascade laser (QCL) is a strong candidate for signal generation above ∼2 THz.3 The major problem is that the present technology requires cryogenic cooling at long wavelengths, which makes QCLs awkward to use. Another approach is photomixing4, which has shown promising results between 100 GHz and 1 THz, but the output power has only been in the µW range in the best case, apart from a recent demonstration of 20 mW at 100 GHz.5,6 Furthermore, Gunn devices are widely used as efficient and low noise sources in the millimeter wave region. State-of-the-art InP Gunn oscillators deliver an output power of about 5 mW around 300 GHz.7 The most promising approach to deliver reasonable power level in the terahertz frequency range, 0.2–2 THz, with a solid-state source is to use a frequency multiplier. Traditionally, this has been accomplished with a nonlinear capacitor such as a reverse-biased Schottky Diode (SD).8–10 However, the power-handling capability of the SD is limited by the device area, which has to be very small at high-operating frequencies. From a circuit point of view, higher harmonic multiplication factors (>×3) become increasingly difficult to implement and, therefore, high-order multipliers are usually realized as a chain of several low-order SD varactor multipliers.11 In order to provide compact solutions and sufficient power levels at terahertz frequencies for future heterodyne imaging systems there is a strong need to develop broadband, highly efficient, multipliers with a high multiplication factor (>3) and improved power-handling capability. The invention of the heterostructure barrier varactor (HBV) diode, at Chalmers,12 offers a very promising alternative to the SD varactor for signal generation in the submillimeter wavelength region. Since the HBV has a symmetric capacitance-voltage (C-V) characteristic, it operates unbiased and will only generate odd harmonics of the low-frequency signal, which simplifies the design of high-order multipliers (×3, ×5). Another important advantage with the HBV diode compared to the SD varactor is that several barriers can be epitaxially stacked, which increases the power-handling capability considerably. At short millimeter wavelengths, corresponding to a frequency of 250 GHz, 10 mW, and at least 10% efficiency have been demonstrated13–16 with HBVs. At high power levels, the effect of selfheating17 must be considered and the thermal resistance of the diode chip geometry should be minimized in order to keep the operating temperature reasonable.16,18,19

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Because of the apparent advantage of symmetric varactors for multiplication, i.e. exclusion of biasing and idler circuitry, another scheme has recently been proposed.20 By Anti-serially connecting two Schottky varactor (ASV) diodes similar I-V and C-V characteristics as for the HBV diode are obtained. Recently, published results for a tripler circuit employing ASVs grown on AlGaAs/GaAs showed an impressive conversion efficiency of 22% at 228 GHz.20 This approach has therefore emerged as very interesting alternative for high-frequency multiplication. This chapter focuses on the principles, progress and status of HBV multipliers. 2. Varactor Frequency Multipliers 2.1. BASIC CONCEPTS

A varactor is a nonlinear reactive device useful for harmonic generation, parametric amplification, mixing, detection, and voltage-variable tuning.21 Varactors normally exhibit a voltage-dependent capacitance and can be fabricated from a variety of semiconductor materials22. A common varactor is the reverse biased Schottky diode. Advantages of varactors are low loss and low noise. The maximum frequency of operation and performance is mainly limited by a parasitic series resistance, see Figure 1.

Figure 1. Equivalent circuit for a pure varactor.23

An important and extensively used figure-of-merit for varactors is the dynamic cutoff frequency, fc, which is defined as

fc =

S max − S min 2πRs

(1)

where Smax and Smin are the maximum and minimum elastances during a pump cycle, respectively, and Rs is the series resistance. The starting point for a varactor design24,25 is, hence, to maximize the elastance swing, Smax – Smin, and minimize any losses, Rs. For semiconductor varactors, the maximum elastance swing is limited by at least one of the following conditions:

J. STAKE ET AL.

20

• • • •

Depletion (modulation) layer punch-through, Large electron conduction from impact ionization, forward conduction current, and self-heating effects, Current saturation.26 The saturated electron velocity in the material determines the maximum length an electron can travel during a quarter of a pump-cycle, Large temperature rise due to dissipated power.

Increasing the pump power beyond any of the above conditions will result in reduced performance and probably introduce extra noise. In general, to analyze a varactor multiplier at high frequencies and drive levels, the conduction current through the device and the effect of device temperature should be included in the model.27

Figure 2. Comparison of HBV (left) and ASV (right) topologies for planar, symmetric diodes. The insets show the corresponding diode orientations.

During the early years of varactor diode development, the diodes were often mounted in a whisker contacted fashion, with waveguides serving as input/output feeds.12 During the last years, however, the majority of the designs are made in a planar28 topology and also fully integrated structures.9 Figure 2 shows a comparison of the planar HBV and ASV topologies. The inset shows the diode orientations for the two cases. 3. Heterostructure Barrier Varactor Multipliers 3.1. GROWTH AND DESIGN OF THE MATERIAL STRUCTURE

An HBV is a symmetric device composed of a high bandgap semiconductor (barrier) that is surrounded by moderately doped low band-gap semiconductors (modulation layers), see Table 1. In this work, the modulation and barrier layers are comprised of In0,53Ga0,47As and In0,52Al0,48As respectively. We also use a pseudomorphic

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21

(3 nm) AlAs layer in the centre of the barrier in order to increase the effective potential barrier, resulting in a very low-leakage current. In Figure 3 (TEM), the AlAs and the In0,52Al0,48As layers of the electron barrier are clearly shown. For this material system, an experimental study shows that the optimum total barrier thickness range is between 10–14 nm in order to minimize any conduction current.29 TABLE 1. A typical two-barrier InGaAs/InAlAs/AlAs HBV layer structure (Chalmers MBE1197)

No.

Layer

Material

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Contact Modulation Spacer Barrier Barrier Barrier Spacer Modulation Spacer Barrier Barrier Barrier Spacer Modulation Contact Substrate

InxGa1−xAs In0.53Ga0.47As In0.53Ga0.47As In0.52Al0.48As AlAs In0.52Al0.48As In0.53Ga0.47As In0.53Ga0.47As In0.53Ga0.47As In0.52Al0.48As AlAs In0.52Al0.48As In0.53Ga0.47As In0.53Ga0.47As In0.53Ga0.47As InP

Thickness [nm] 260 250 5 3,5 3 3,5 5 250 5 3,5 3 3,5 5 250 500

Doping [cm–3] ∼1019 1×1017 undoped undoped undoped undoped undoped 1×1017 undoped undoped undoped undoped undoped 1×1017 ∼1019 SI

Figure 3. TEM picture of the barrier region (Chalmers MBE1197).

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Optimum epi-layer structures for high-power applications have been designed and studied. These multi-barrier structures were grown using the molecular beam epitaxy (EPI 930) at the Nanofabrication laboratory, Chalmers. The optimum doping concentration and layer thicknesses are calculated by optimisation of the dynamic cutoff frequency.25,30 The main goal is a low series resistance and a large elastance (1/C) modulation swing and there is a trade-off with respect to the doping concentration in the modulation layer, pump frequency, and maximum voltage. The barrier structure is designed to minimize conduction current through the structure. Calibration of the growth conditions is crucial since the HBV structure contains relatively thick epi-layers (1–5 µm), heterostructures, as well as strained layers. Top quality of the epi-growth is needed, translating into high electron mobility, high level of symmetry and excellent barrierblocking characteristics. All epi-materials are analyzed during growth and characterized after growth using TEM, x-ray diffractometer (lattice strain) and by fabricating large test diodes (A ≈ 3,000 µm2) for I–V and C-V characterization. Measurements of a three-barrier HBV material (Chalmers MBE995) are shown in Figure 4. The Chalmers MBE995 has a modulation layer thickness of l = 370 nm, buffer layer thickness = 0.5 µm, barrier thickness of b = 15 nm, doping concentration of Nd = 1 × 1017 cm–3.

Figure 4. C-V and I-V measurements for a three-barrier HBV material, Chalmers MBE995.

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3.2. HBV DEVICE MODEL

The parallel plate capacitor model, where the plate separation should be replaced with the sum of the barrier thickness, b, the spacer layer thickness, s, and the length of the depleted region, w, is normally an adequate description of the differential capacitance. The depletion length is bias dependent and the layer structure is symmetric, therefore the elastance is an even function of applied voltage and is given by:

S=

1 N⎛ b s w⎞ = ⎜ + + ⎟ C A ⎝ εb εd εd ⎠

2εd Vd w= qN d

(2)

where Vd is the voltage across the depleted region, Nd is the doping concentration in the modulation layers, b is the barrier thickness, s is the undoped spacer layer thickness, A is the device area, εb and εd are the dielectric constants in the barrier material and modulation layers, respectively. The maximum capacitance or the minimum elastance, Smin, occurs at zero bias. However, due to screening effects, the minimum elastance, Smin, must include the extrinsic Debye length, LD, as:-

Smin = LD ≡

1 N ⎛ b 2s 2L ⎞ = ⎜ + + D⎟ εd ⎠ Cmax A ⎝ εb εd

εd kT

(3)

q2N d

To achieve a high Cmax/Cmin ratio, the screening length can be minimized with a sheet doping, Ns, at the spacer/depletion layer interface. The minimum capacitance, Cmin, is normally obtained for punch-through condition, i.e. w = l, or when the breakdown voltage, Vmax, is reached. An accurate quasi-empirical expression for the C-V characteristic of homogeneously doped HBVs has been derived by Dillner et al.31 The voltage across the nonlinear capacitor is expressed as a function of its charge as: Q ⎛ ⎛ ⎛ ⎞⎞⎞ − bQ sQ Q2 4kT ⎜ 2L D AqN d ⎟⎟⎟ (4) V (Q,T) = N ⎜ +2 + Sign(Q)⎜ + 1− e 2 ⎜ ⎟ ⎜ ⎟ ⎜ εb A ⎟ q ⎝ εd A 2qN d εd A ⎠⎠⎠ ⎝ ⎝

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where T is the device temperature, q is the elementary charge, and Q is the charge stored in the HBV. The series resistance Rs associated with a varactor diode is a quantity, which summarizes the resistive losses that characterize various layers and connections forming the device. The main contributions to the series resistance are the ohmic contact resistance, the resistance in the modulation layers, and the spreading resistance. Given the voltage-charge relationship in (4), the series resistance can be expressed as25

⎛

⎛ − Q ⎞⎞ 2L D AqN d ⎜ ⎟ (5) R(Q,T) = Rs − + 2LD e −1 ⎟ ⎜ ⎟⎟ A ⎜ qN d A ⎝ ⎠⎠ ⎝ where Rs is the zero-bias series resistance and ρd is the resistivity of the

ρd N ⎜ Q

modulation layer,

ρd =

1 . qN d µe (T, N d )

(6)

The conduction current is a mixture of thermionic emission and tunneling through the barrier and hence difficult to model with a physical analytical expression. However, an empirical model based on the Sinh(x) function can often be used to describe the antisymmetrical I–V characteristic of the HBV. A complete electro-thermal model (Chalmers HBV Model) can be found in reference by Ingvarson et al.27 3.3. HBV MULTIPLIER CIRCUITS

3.3.1. Status of HBV multiplier research An HBV quintupler (×5) with a state-of-the-art conversion efficiency of 11% has been demonstrated at 100 GHz.32 HBV triplers (×3) have been shown to provide 200 mW at 114 GHz33 and also recently a state-of-the-art efficiency of more than 21% at an output frequency of 102 GHz has been achieved.34 At short millimeter wavelengths, corresponding to a frequency of 200–300 GHz, 10 mW and at least 10% efficiency have been demonstrated.13–16 In terms of output power, the best results have been achieved using a filter circuit on AlN instead of quartz (see Figure 5). The AlN substrate provides a better heat-sink for the flip-chip mounted diode. According to detailed analysis, there is room for substantial improvements in terms of output power in the millimeter wavelength range 27,35 with a proper electrical and thermal design. Our predictions suggests an output power of >0.5 W at 100 GHz, 50–100 mW around 200 GHz, 10–20 mW around 500 GHz and ∼1mW at 1 THz for high-power single HBV diode

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multipliers. Such power levels have not been demonstrated using Schottky diode (SD) multipliers. This is especially true when compared with SD triplers.36 More important, the overall conversion efficiency, reliability, cost and weight are improved with less number of cascaded modules for a complete terahertz source.

Figure 5. Reported output power for HBV multipliers (September 2006). The red line shows the predicted capability of the HBV technology (single device).

3.3.2. A high-power millimeter wave tripler In this section, we describe the development of a high-power millimetre wave tripler. The design flow can be summarized in a number of steps: • • • •

The diode geometry (area, number of barriers, layer structure, etc.) is chosen based on parameters like input power and operating frequency. The optimum diode-embedding impedances are simulated using harmonic balance techniques, using the electro-thermal HBV device model developed at Chalmers. 27 Embedding circuits, including waveguide probes are designed using a combination of ideal circuit simulations (Agilent ADS) and 3D EM simulations (Ansoft HFSS). The final circuit response is simulated using the nonlinear device model and extracted S-parameters from the completed embedding circuitry including waveguide feeds.

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Figure 6. SEM picture of a 500-µm2 HBV. This 4-mesa, 12-barrier device is fabricated from Chalmers MBE1038 epitaxial material.

Figure 7. 113-GHz high power tripler. AlN microstrip circuit mounted in the waveguide block.

In the current design a 3-barrier epi-material is used, and the diode consists of four series-connected mesas in order to increase the powerhandling capability even further, see Figure 6. A major limitation for highpower multipliers is the self-heating of the devices; this results in lower efficiency and device breakdown. To improve the thermal properties, the microstrip circuit is fabricated on an AlN substrate – AlN is a material with excellent thermal conductivity (~175 W/mK). Both the HBV chip and the AlN substrate were lapped down to 40/100 µm, respectively. The hybrid circuit was then mounted in the waveguide block with a WR-22/WR-10 input and output waveguides respectively. Figure 7 shows the hybrid circuit

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27

mounted in one half of the waveguide block. Note the fixed tuned back shorts, which are part of the matching circuitry. Figure 8 shows the output power and flange-to-flange conversion efficiency versus available input power. The tripler exhibits a maximum output power of 195 mW at 113 GHz. The performance can be improved further with an improved heatsink, e.g. monolithic HBV circuit, and further optimized matching circuit.

Figure 8. Output power and conversion efficiency for a 3×37.7 GHz frequency multiplier. The measurement result is from a 700-µm2, 12-barrier HBV.

4. Discussion The output power around 100 GHz for single HBV diode triplers is comparable to state-of-the-art Schottky doublers.8,37 This statement is true despite large investments during many years in the development of SD and related multiplier circuits. Obviously, concerning the HBV technology large improvements can be gained by optimizing the devices and the circuits. Furthermore, HBV multipliers with output frequencies above 500 GHz have not yet been reported.

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Acknowledgments This work is supported by the European Space Agency (“HBV Devices and MMICs”, No.18164/04/NL/LvH), the Swedish Foundation for Strategic Research (HSEP), and the Swedish Defence Research Agency (FOI). We would like to thank Mahdad Sadeghi at the Nanofabrication laboratory, Chalmers for providing MBE grown HBV materials.

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30. M. Ingvarson, A. Ø. Olsen, and J. Stake, Design and analysis of 500 GHz heterostructure barrier varactor quintuplers, in 14th International Symposium on Space TeraHertz Technology, Tucson, AZ, (2003). 31. L. Dillner, J. Stake, and E. L. Kollberg, Modeling of the heterostructure barrier varactor diode, in International Semiconductor Device Research Symposium (ISDRS), Charlottesville, pp. 179–182 (1997). 32. T. Bryllert, A. Ø. Olsen, J. Vukusic, T. A. Emadi, M. Ingvarson, J. Stake, and D. Lippens, 11% efficiency 100 GHz InP-based heterostructure barrier varactor quintupler, Electron. Lett., 41, 3, 30 (2005). 33. T. Bryllert, J. Vukusic, T. A. Emadi, and J. Stake, A high-power frequency tripler for 100 GHz, in The Joint 31st International Conference on Infrared and Millimeter Waves and 14th International Conference on Terahertz Electronics, Shanghai, China, pp. 30 (2006). 34. J. Vukusic, B. Alderman, T. A. Emadi, M. Sadeghi, A. Ø. Olsen, T. Bryllert, and J. Stake, HBV tripler with 21% efficiency at 102 GHz, Electron. Lett., 42, 6, 355–356 (2006). 35. T. A. Emadi, J. Vukusic, M. Ingvarson, M. Sadeghi, T. Bryllert, A. Ø. Olsen, and J. Stake, Design, fabrication and characterisation of high power HBV diodes, in International Symposium on Space Terahertz Technology, J. Stake and H. Merkel, Eds., Chalmers, Göteborg, Sweden, pp. 285–290 (2005). 36. T. W. Crowe, T. C. Grein, R. Zimmermann, and P. Zimmermann, Progress toward solidstate local oscillators at 1 THz, IEEE Microw. Guided Wave Lett., 6, 5, 207–208 (1996). 37. D. Porterfield, J. Hesler, T. Crowe, W, Bishop, and D. Woolard, Integrated terahertz transmit/receive modules, Proceedings of the 33rd European Microwave Conference, vol. 3, pp. 1319–1322 (2003).

TOWARDS SUPERLATTICE TERAHERTZ AMPLIFIERS AND LASERS ALVYDAS LISAUSKAS†, ERNST MOHLER, AND HARTMUT G. ROSKOS Physikalisches Institut, Johann Wolfgang Goethe-Universita¨t, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany NATALIYA V. DEMARINA Electronics Department, Radiophysics Faculty, Nizhny Novgorod State University, Gagarin Avenue 23, Nizhny Novgorod 603950, Russia

Abstract. We describe our work towards THz sources which employ the “Bloch gain ” , a stimulated-emission mechanism which has been predicted as early as 1971 to exist for semiconductor superlattices but which researchers – in spite of much recent work – have not yet been able to take advantage of for the implementation of THz amplifiers and lasers. From a basic-physics point-of-view, the interest in Bloch gain arises from its dynamical, second-order character, involving simultaneous scattering of an electron and emission of a THz photon. This aspect has the practically important implication that the temperature dependence of the gain is determined to a large degree by the optical-phonon energy scale and not that of the photon energy, with the consequence that there is a rather slow roll-off of the gain with temperature. This feature together with the rather high-gain values which are calculated to be comparable with those of THz quantum cascade lasers at low temperature, fosters the hope that a Bloch THz laser could be the first semiconductor-based THz laser operating at room temperature. Keywords: semiconductor superlattice, terahertz radiation, terahertz lasing

1. Introduction The lack of compact and tunable sources of terahertz (THz) radiation together with the exciting physical properties of semiconductor superlattices have stimulated the experimental search for a novel laser gain mechanism often termed as Bloch gain. Shortly after the proposal of semiconductor superlattices,1 it was predicted that electrons oscillating at the Bloch frequency (ωB ) in the presence of dissipative scattering should provide gain at frequencies 2 †

To whom correspondence should be addressed, Physikalisches Institut, Johann Wolf¨ Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany, e-mail gang Goethe-Universitat, address: (lisauskas @ physik.uni-frankfurt.de) 31 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 31–40. © 2007 Springer.

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ω < ωB . Recently, a series of theoretical investigations either within the semiclassical picture 3−5 or based on quantum-mechanical approaches 6 have provided support for this surprising prediction. A practical interest arises from the fact that the gain of this second-order process is predicted to be tens per centimeter 6at low temperatures thus favorably competing with the gain of THz quantum cascade lasers which, however, exhibit population inversion . 7 − 9 Equally important, theory predicts that the decline of the gain with temperature is significantly slower in the case of the Bloch gain. As we will discuss in more detail later, the gain in optimized superlattice structures should be large enough to permit laser operation at room temperature. 2. The Challenge of Finding Experimental Evidence for Bloch Gain Despite the sizeable number of theoretical investigations, no conclusive experimental proof for inversionless gain has ben produced yet. The key practical challenge is the tendency of superlattices to break away from the homogeneous-field situation which has been the idealized basis of nearly all theoretical treatments of the phenomenon. As this tendency is a result of the same nonlinear current-voltage characteristics associated with a negative differential velocity which also brings forth the Bloch gain itself, and as it becomes more severe as one tries to optimize the structure and the doping concentration of the superlattice with respect to the gain value, one deals indeed with a profound challenge. Researchers have been able to take advantage of the field instability and implemented novel Gunn-type superlattice oscillators for the sub-millimeter wavelength regime.10 − 12 While they were able to reach frequencies as high as 147 GHz directly and 300 GHz with an intrinsic tripling process 13 , the hope to simultaneously gain access to higher frequencies by Bloch gain proved futile. In fact, it has been shown theoretically that Bloch gain is quenched in a Gunn-type operation of a superlattice oscillator 14 . In a different approach, it was attempted to obtain evidence for the existence of Bloch gain by all-optical time-resolved experiments in combination with data evaluation in the framework of semiclassical theory 15, 16 . The authors measured the THz transients emitted from undoped GaAs/AlGaAs superlattices after excitation of exciton wavepackets with femtosecond laser pulses. Analyzing the Fourier spectra of the coherent THz pulses in terms of a frequency-depenent conductivity, the authors found the real part of this quantity to be negative and its spectra to exhibit a shape as predicted by the semiclassical transport theory. This was then interpreted as clear evidence for Bloch gain. In the meantime, we have pointed out that this approach is incorrect . 17,18 The correct quantity because the conductivity has been defined wrongly

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to investigate would have been the small-signal conductivity at the operation bias voltage above the critical voltage (defined by the maximum of the current/voltage curve). This conductivity is, however, not directly accessible in this kind of THz-emission experiments. The quantity studied, in contrast, is a large-signal response function involving a linearization across the entire highly nonlinear current/voltage curve of the superlattice from zero bias up to the operation point. This reponse function cannot be compared with the (small-signal) conductivity from the semiclassical theory as has been done , 15,16 and it is hence not correct to infer Bloch gain by such a comparison. The closest any experiment has come to prove the existence of Bloch gain until now, is a THz-beam amplification experiment performed by Allen et al. at the THz-free-electron-laser facility at UCSB.19 The amplification medium was a waveguide structure containing pillars of electrically pumped stacks of 34 short-length InAs/AlSb superlattices. Each of the latter consisted of only 15 superlattice periods and subsequent superlattices were separated by 100 nm-thick highly doped field-pinning layers. With n+ -InAs contact layers on top and bottom of the stack, each pillar had a thickness of about 10 µm. When the superlattices were biased within the correct voltage range, the structure showed an increased THz transmittance as expected if amplification of the radiation from the free-electron laser in the pillars sets in. Self-starting laser action, however, has not been reported until now. With the stacking of short superlattice segments, the authors seem to have found an effective way to prevent the formation of field domains. In the design, they applied Kroemer’s rule to keep the length L of each superlattice segment below the domain-formation length: nL < 70 Fc /e, with n being the total carrier density in the superlattice,  and 0 denoting the relative dielectric permittivity of the superlattice and the vacuum permittivity, respectively, Fc representing the critical electric field of the superlattice, and e the elementary charge. While their design does not strictly fullfil Kroemer’s condition, it seems to be sufficiently close to keep field inhomogeneities insignificant. 3. Field Dynamics in a Superlattice In order to understand the field dynamics in superlattices better, we have investigated undoped superlattices and traced the spatial distribution of optically excited charge carriers along the superlattice growth direction as a function of time. This is possible, within limits, by pump-probe photocurrent spectroscopy at low temperatures because of the following reason. The carrier densities of interest for an amplifier or laser employing Bloch-gain are low in the 1015− 1016 cm−3 range, just as in the case of the quantum cascade

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laser and for similar reason: to keep space-charge effects and THz-radiation losses limited. As a consequence, the sharp excitonic absorption lines are hardly broadened yet, and allow, with the strong dependence of their peak wavelength on the local electric field, to monitor the temporal evolution of the field, albeit in an integral manner, averaged over the growth direction of the superlattice and weighed there with the distribution of the charge carriers generated by the probe laser radiation. We have then applied the semiclassical transport theory to model and fit the measured data. The calculated data and the measured ones agree well with each other during the time scale of the sweep out of the electrons (nonnegligible deviations show up for longer time scales dominated by sweep-out of the holes, and seem to result from approximations of the model calculations which do not take into account the full complexity of the valence band with its warping and population by heavy and light holes which can also change their character by scattering 20 ). As any practical device would work with electrons and not holes, we seem to capture the relevant part of the field dynamics. Figure 1 shows data of model calculations which were performed to explain experimental results measured with an intrinsic GaAs/Al 0.3 Ga0.7 As superlattice. It consisted of 35 periods of 6.7 nm-wide wells and 1.7 nm-wide barriers and was grown by molecular beam epitaxy. With a width of the first electron miniband (∆) of 33 meV, it is in the intermediate coupling regime. Bloch-gain lasers and amplifiers would be realized with more strongly coupled systems, which would exhibit a considerably faster carrier transport and a correspondingly faster field dynamics. While it would be more difficult to temporally resolve the dynamics with this type of photocurrent spectroscopy, we expect that the results for the electron dynamics would be similarly well explained by the semiclassical model. The spatiotempoal evolution of electron density and electric field plotted in Figure 1 paints the following picture. First, the electrons sweep out of the 350 nm-thick superlattice on a time scale of only 10 ps. It is an important result of our study that experiment and semiclassical transport theory with plausible device parameters are in agreement with each other here which raises the level of confidence with respect to other predictions of the theory. Second, the drift of the charge carriers rapidly leads to a field pattern which can be identified as the onset of domain formation, with a region with a strong field gradient at the left side of the superlattice and a low-field, low-gradient region on the right side where the electrons leave the superlattice. At the carrier density chosen for this example, the domain formation is not complete before the electron density decreases too much. In other words, no region in the superlattice experiences full-field screening yet. This is consistent with an evaluation of Kroemer’s relation which predicts that the domain formation length should

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Figure 1. Results of simulations with parameters adjusted to obtain good agreement with the experimental data. Left panel: Depth profile of the electron density as a function of time in steps of 2 ps. Laser pulse generates electron-hole pairs in the undoped superlattice at t = 0 ps. Right panel: Corresponding depth profile of the electrical field. Model parameters: µe = 1,200 cm2 /Vs, µh = 100 cm2 /Vs, initial carrier density ne = 3.3 · 1015 cm−3 and starting field of 22.8 kV/cm.

slightly exceed the length of the superlattice for the chosen parameters. This result strengthens the confidence in the applicability of Kroemer’s formula. We point out that Bloch gain is fairly robust against field inhomogeneities. This is a consequence of the broadband nature of the gain which spans the frequency range from zero up to nearly the circular Bloch frequency ωB given by ~ωB = eFd, d being the spatial period of the superlattice and F the local field. If F decreases somewhere in a superlattice, then the spectral range over which gain is provided shrinks here, while the gain at low frequencies is enhanced. One must, however, strictly avoid full-domain formation because the gain vanishes in regions where the field drops to zero. 4. Estimates of Gain Values and Their Temperature Dependence Having corroborated that short-period superlattices indeed represent a practical solution of the domain-formation problem, we now estimate absolute values of the gain at specific target frequencies and as a function of temperature. We base these estimates on the following analytical expression for the small-signal gain given by 6 within the framework of a semiclassical single-relaxation-time model: 21 α(ω) =

h 1 − ω2B τ2 − iωτ i τ e2 d2 ∆ I1 (∆/2kB T ) n × Re . 0 nr c 2~2 I0 (∆/2kB T ) 1 + ω2B τ2 ω2B τ2 + (1 − iωτ)2

(1)

Here, kB is Boltzmann’s constant, nr the refractive index, and τ the scattering time constant of the dissipative processes. I1 (∆/2kB T )/I0 (∆/2kB T ) denotes

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Gain, cm-1

100

dd==8.4 8.4nm nm n = 5x101515cm-3-3 n = 5x10 cm t = 200 fs t = 200 fs

1 THz

80

2 THz

60

3 THz

DD = =80 80meV meV

40 2 THz

1 THz = 36 meV D =D36 meV

20

3 THz

0 0

50

100 150 200 Temperature, K

250

300

Figure 2. Temperature dependence of Bloch gain calculated with Willenberg formula for two superlattices of different width ∆ of the first electron miniband. At each data point, the electrical field F across the superlattice has been varied in order to maximize the gain value.

the ratio of Bessel functions of orders one and zero, and describes the temperature dependence of the gain for a nondegenerate electron gas. The electric field strength F enters through the Bloch frequency ωB . While Monte Carlo simulations 22 have clearly identified the emission of longitudinal optical (LO) phonons as the dissipative process which more than any other determines the strength of the Bloch gain, this relaxation process does not enter explicitly into the Willenberg formula. The only parameter which reflects any specific scattering mechanism is the relaxation time τ. For our calculations, we select τ to be 0.2 ps, a nearly temperatureindependent value which is typical for optical-phonon emission in situations when the electrons have enough kinetic energy to emit an LO phonon of energy 36 meV. Figure 2 displays the Bloch gain calculated for two superlattices of different electron miniband width, but for the same superlattice period d = 8.4 nm (hence the ratio of the width of the wells to the width of the barriers changes as ∆ is varied). We assume a fixed electron density of n = 5 · 1015 cm−3 . The temperature dependence of the gain is plotted for three target frequencies, 1 THz, 2 THz, and 3 THz. In the simulations, the electrical field has been treated as an optimization parameter for the Bloch gain and hence, varies even from data point to data point. For any temperature and radiation frequency, the gain value of the superlattice with intermediate coupling strength (∆ = 36 meV) is always lower

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Figure 3. Literature data of the theoretical thermal dependence of the gain in THz quantum cascade lasers. Left panel: Data taken from Williams et al. 2003b, for a radiation frequency of 3.4 THz; the horizontal lines indicate typical losses of metal – metal waveguides and of single-plasmon waveguides. Right panel: Data taken from Callebaut and Hu, 2005, for a radiation frequency of 3.2 THz.

than that of the superlattice with strong coupling (∆ = 80 meV). For stronger coupling, the temperature dependence is also less pronounced. Another interesting aspect is the frequency dependence of the gain. Independently of the coupling strength, lower frequencies find a larger gain. It is worth mentioning that this behavior is opposite to that found in the case of quantum cascade lasers .9 The two decisive questions which decide over the fate of the Bloch gain on the long run, are the following: (i) Is the gain at any temperature large enough to be of practical interest, and (ii) is it large enough at 300K to potentially allow for laser operation at room temperature. In order to give at least a preliminary answer to this question – i.e. one which is only based on the calculations with the Willenberg formula we compare the data of Figure 2 for the Bloch gain in superlattices with gain data of state-of-the-art THz quantum cascade lasers. Figure 3 displays calculated data for the latter from two source .23,24 The left panel displays gain values for a laser operating at 3.4 THz which do not exceed 35 cm−1 at any temperature. The panel also displays typical waveguide losses encountered in such lasers (which are optimized for low losses): 18 –19 cm−1 for the metal – metal waveguide and 30 –31 cm−1 for the single-plasmon waveguide. Given the typical temperature dependence of the gain in THz quantum cascade lasers, the gain equals the losses at 80 – 90K, respectively 160K in the two cases. That the gain values of this panel are not singular in the literature is proven by the data shown in the right panel of Figure 3. Here, two theoretical approaches are compared with each other, a semiclassical one and one based on density-matrix

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Monte Carlo simulations. While the semiclassical calculations predict gain values and a temperature dependence of the gain very similar to the data in the left panel, the more complex density-matrix calculation predict even higher gain up to 53 cm−1 at low temperatures. If we now compare these data with those of Figure 2 for a radiation frequency of 3 THz, we find that the superlattice with intermediate coupling strength exhibits somewhat lower gain values that the quantum cascade lasers. The gain of the strongly coupled superlattice, on the other hand, exceeds that of the quantum cascade lasers for all temperatures. The decrease of the gain with rising temperature is more gradual than in the case of the quantum cascade lasers. At room temperature, the gain still amounts to 35 cm−1 . This answers the first question: The gain compares well with that of the established lasers which implies that it is of practical interest. This holds even more so with respect to the second question: the gain of the strongly coupled superlattice is predicted to be sufficiently high to exceed the waveguide losses even at room temperature. Considering such promising predictions, especially with respect to the temperature dependence of the gain, one has to recall that the Willenberg formula does not treat the relevant scattering process of LO-phonon emission explicitly. Nevertheless, more sophisticated semiclassical theory based on single-particle Monte Carlo simulation of the electron motion in the presence of scattering at optical and acoustic phonons22 also corroborates high values of THz gain. It was shown that for a large amplitude of an applied THz field a superlattice displays larger amplification coefficient at the frequency slightly below the Bloch frequency, i.e. amplification coefficient increases with increasing frequency. It also grows larger with a miniband width. For the superlattice with a miniband width of about 90 meV it reaches about 40 cm−1 for frequency close to 3 THz, the electron density 5 · 1015 cm−3 and lattice temperature of 4K. This value is comparable with the gain number for a quantum cascade laser (Figure 3). It decreases only by 30% for lattice temperature of 300 K. The latter apparently implies that a semiconductor superlattice is a promising candidate for a terahertz emitter operating at room temperature. Such exciting results urge for further more detailed theoretical studies (and certainly experiments) in order to explore the validity of the predictions. 5. Summary We have explored some aspects of the Bloch gain of semiconductor superlattices with respect to the question whether it may provide a viable alternative to the realization of lasers for the terahertz frequency range. Common wis-

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dom leads one to assume that the second-order character of the processes involved limits the attainable gain values. Quite in contrast, estimates of the gain values for optimized superlattice structures let it appear competitive with the first-order gain of terahertz quantum cascade lasers. Furthermore, the temperature dependence is predicted to be more gradual promising laser operation even at room temperature. A third advantage of the second-order nature of the gain (not discussed in detail here) could be its extremely large bandwidth which promises tunability of a laser over a huge terahertz frequency range, provided this large gain bandwidth does not hinder the self-starting of a laser. With all its interesting and auspicious properties, it is striking that the experimental evidence even for the mere existence of the Bloch gain is still extremely scarce. This has to do on one hand with the considerable technological effort needed to explore it, but on the other hand also reflects the fundamental challenges imposed by this strongly nonlinear system. The most obvious one, the tendency to form field domains, however, now appears to get under control by measures such as the implementation of stacked short-period superlattices with a thickness below the finite domain-formation length. The stage seems set for significant experimental progress in the next few years. Acknowledgments Funding by DFG and NATO is acknowledged. We are grateful to K. K¨ohler for providing us top-quality superlattice samples over the many years of cooperation. One of us (NVD) thanks the Russian Agency of Education and CRDF (grant BF5M01) and RFBR for support.

References 1. L. Esaki and R. Tsu, Superlattice and negative conductivity in semiconductors, IBM J. Res. Dev. 14, 61–65 (1970). 2. S. A. Ktitorov, G. S. Simin, and Y. Sindalovski, Bragg reflections and high-frequency conductivity of an electronic solid-state plasma, Sov. Phys. Solid State 13, 1872 (1972). 3. A. A. Ignatov, K. F. Renk, and E. P. Dodin, Esaki-tsu superlattice oscillator – josephson-like dynamics of carriers, Phys. Rev. Lett. 70, 1996 –1999 (1993). 4. E. Schomburg, N. V. Demarina, and K. F. Renk, Amplification of a terahertz field in a semiconductor superlattice via phase-locked k-space bunches of bloch oscillating electrons, Phys. Rev. B 67, 155302 (2003). 5. D. A. Ryndyk, N. V. Demarina, J. Keller, and E. Schomburg, Superlattice with hot electron injection: An approach to a bloch oscillator, Phys. Rev. B 67, 033305 (2003). 6. H. Willenberg, G. H. Dohler, and J. Faist, Intersubband gain in a bloch oscillator and quantum cascade laser, Phys. Rev. B 67, 085315 (2003).

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7. M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, Low-threshold terahertz quantum-cascade lasers, Appl. Phys. Lett. 81, 1381–1383 (2002). 8. B. S. Williams, H. Callebaut, S. K. Q. Hu, and J. L. Reno, 3.4-thz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation, Appl. Phys. Lett. 82, 1015–1017 (2003). 9. R. Sachs and H. G. Roskos, Mode calculations for a terahertz quantum cascade laser, Opt. Express 12, 2062–2069 (2004). 10. J. Kastrup, R. Hey, K. H. Ploog, H. T. Grahn, L. L. Bonilla, M. Kindelan, M. Moscoso, and A. Wacker, J. Galan, Electrically tunable ghz oscillations in doped gaas-alas superlattices, Phys. Rev. B 55, 2476–2488 (1997). 11. E. Schomburg, S. Brandl, K. Hofbeck, T. Blomeier, J. Grenzer, A. A. Ignatov, K. F. Renk, D. G. Pavel’ev, Y. Koschurinov, V. Ustinov, A. Zhukov, A. Kovsch, S. Ivanov, and P. S. Kop’ev, Generation of millimeter waves with a gaas/alas superlattice oscillator, Appl. Phys. Lett. 72, 1498–1500 (1998). 12. E. Schomburg, R. Scheuerer, S. Brandl, K. F. Renk, D. G. Pavel’ev, Y. Koschurinov, V. Ustinov, A. Zhukov, A. Kovsh, and P. Kop’ev, Ingaas/inalas superlattice oscillator at 147 ghz, Electron. Lett. 35, 1491–1492 (1999). 13. K. F. Renk, B. I. Stahl, A. Rogl, T. Janzen, D. G. Pavelev, Y. I. Koshurinov, V. Ustinov, and A. Zhukov, Subterahertz superlattice parametric oscillator, Phys. Rev. Lett. 95, 126801 (2005). 14. N. V. Demarina, to be published. 15. Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, Terahertz conductivity and possible bloch gain in semiconductor superlattices, Phys. Rev. Lett. 90, 046806 (2003). 16. N. Sekine and K. Hirakawa, Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices, Phys. Rev. Lett. 94, 057408 (2005). 17. A. Lisauskas, N. V. Demarina, E. Mohler, and H. G. Roskos, Comment on dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices, condmat/0605651. 18. A. Lisauskas, N. V. Demarina, E. Mohler, and H. G. Roskos, Bloch gain and single-pulse terahertz emission experiments, to be published. 19. P. G. Savvidis, B. Kolasa, G. Lee, and S. J. Allen, Resonant crossover of terahertz loss to the gain of a bloch oscillating inas/alsb superlattice, Phys. Rev. Lett. 92, 196802 (2004). 20. A. Lisauskas, N. V. Demarina, C. Bl¨oser, R. Sachs, H. G. Roskos, A. Juozapavicius, ¨ G. Valusis, and K. Kohler, Time-resolved photocurrent spectroscopy of optically excited superlattices and the prospects for bloch gain, Proceedings SPIE International Society for Optical Engineering 6118, 311 (2006). 21. A. A. Ignatov, and Y. A. Romanov, Nonlinear electromagnetic properties of semiconductors with a superlattice, Physica Status Solidi (b) 73, 327–333 (1976). 22. N. V. Demarina, and K. F. Renk, Bloch gain for terahertz radiation in semiconductor superlattices of different miniband widths mediated by acoustic and optical phonons, Phys. Rev. B 71, 035341 (2005). 23. B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, J. L. Reno, Terahertz quantum-cascade laser operating up to 137 k, Appl. Phys. Lett. 83, 5142–5144 (2003). 24. H. Callebaut, and Q. Hu, Importance of coherence for electron transport in terahertz quantum cascade lasers, J. Appl. Phys. 98, 104505 (2005).

TAILORING THE EMISSION OF TERAHERTZ QUANTUM CASCADE LASERS

RICHARD GREEN, LUKAS MAHLER, COSIMO MAURO, TONIA LOSCO, JI-HUA XU, ALESSANDRO TREDICUCCI,* AND FABIO BELTRAM NEST CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy HARVEY BEERE AND DAVID RITCHIE, Cavendish Laboratory, University of Cambridge, Madingley Rd, Cambridge CB3 0HE, UK

Abstract. For THz quantum cascade lasers to prove useful for applications, certain requirements for their spectral performance will have to be met. Here, we focus on the provision of single mode operation. Distributed feedback devices lasing on a single longitudinal mode are reported using both first and second order gratings. We also report the operation of terahertz master oscillator power amplifier structures with the potential to increase the output power which is available in a single mode.

Keywords: terahertz, quantum cascade laser, intersubband

1. Introduction Quantum cascade lasers (QCLs) operating at terahertz frequencies were first demonstrated in 2002.1 Since then, there been great improvements in their performance, with operation in pulsed mode up to 164-K,2 high-output powers,3 and an operating wavelength range extending from 1.9 THz4 to 4.8 THz5 without the use of an external magnetic field.

______ * To whom correspondence should be addressed. Alessandro Tredicucci, NEST CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy. e-mail: [email protected]

41 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 41–54. © 2007 Springer.

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QCLs differ from conventional semiconductor lasers in several ways. In a conventional semiconductor laser, the emitted light results from the recombination of an electron within the conduction band of the device with a hole in the valence band. Thus, the wavelength of the emitted light is determined by the bandgap of the semiconductor material, together with a relatively small additional energy originating from the quantum confinement present in quantum well and quantum dot lasers. In contrast, in a QCL, the emitted light arises from radiative transitions of electrons between subbands in a system of coupled quantum wells. Hence, the emission energy can be controlled over a wide range by careful choice of the well and barrier thicknesses. Because of the intersubband nature of the transition, an electron will remain in the conduction band even after undergoing a radiative transition. By cascading many identical active regions, it is possible to achieve internal quantum efficiencies of more than one, with each electron responsible for the emission of more than one photon into the lasing mode. The various potential applications for coherent THz light each have different performance requirements. For the use of QCLs in gas spectroscopy, emission on a single longitudinal mode greatly simplifies the analysis of the resulting data.6 In addition, since the absorption lines being studied tend to be narrow, at least at low pressures, some small amount of tunability can ensure sufficient spectral overlap between the laser and the absorption line. High-emission powers are advantageous, since the signal to noise ratio achievable increases linearly with power for experiments involving direct transmission, and as the square of the emission power for photoacoustic spectroscopy. The use of QCLs as local oscillators for astronomical experiments presents very similar performance requirements spectrally, although less stringent in terms of output power. In contrast, for potential applications in free space optical communications the detailed mode structure of the emission line is less critical, as long as the emission line is located in a spectral region with low atmospheric absorption. More important here is the beam profile which must allow convenient coupling of the beam into an optical system and the ability to modulate the output at high rates. To provide direct modulation of the devices, low threshold currents are desirable, together with small device dimensions and convenient packaging to reduce the parasitic capacitance. There are of course some aspects of performance which are advantageous for all applications. Higher powers tend to increase signal to noise ratios, and simplify detection schemes and optical alignment, while increased operating

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temperatures will make the devices simpler to use while reducing the running costs and complication of the setup. In this chapter, we focus first on the spectral purity of THz QCLs. After a discussion of the different techniques by which single mode operation can be obtained, first- and second-order distributed feedback QCLs will be presented, based on novel, surface plasmon gratings. Preliminary results from master oscillator power amplifier structures based on THz QCLs will then be reported, followed by a discussion of possible methods for tuning the emission line of these devices. 2. Single Mode Emission from THz QCLs THz QCLs are usually processed into ridge waveguide devices, with end mirrors formed by cleaved facets, to form a Fabry-Perot (FP) cavity. Cavity lengths are typically in the range of about 1–4 mm, meaning that many modes of the cavity exist within the material gain peak. The consequences of this can be seen in Figure 1, which shows the evolution of the lasing spectrum of a typical FP device as the injection current is increased. The bottom panel of the figure shows the spectrum measured at 450-mA injection current, approximately 10% above threshold. The laser output is concentrated completely within a single longitudinal mode. At 500-mA current, while the spectrum is still largely single mode, a small second mode is emerging on the long wavelength side, with an intensity about 5% that of the main peak. By 550 mA the emission spectrum is strongly multimode, and this situation continues until the maximum output power of the device is reached, at about 750 mA. We see that single-mode operation can be achieved from a FP device, close to threshold. However, the output power available into this single mode is severely limited by the appearance of additional longitudinal modes at increased current levels. To provide true single mode operation over a wider range of conditions a different means of optical feedback needs to be provided. Ways of doing this include the use of coupled cavity lasers,7 an external cavity,8 and the fabrication of frequency selective mirrors,9 but the simplest and most common is the use of a distributed feedback (DFB) grating. This consists of a periodic perturbation introduced into the waveguide, designed to have a period equal to half the lasing wavelength within the material.

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Figure 1. Emission spectrum of a typical FP THz QCL, measured at 7K, for a range of injection currents in pulsed mode. The cavity length is 1.44 mm, with a ridge width of 300 µm. Measured threshold current was 405 mA, corresponding to a threshold current density of 95 A cm−2.

2.1. DFB DEVICES BASED ON ETCHED GRATINGS

Before studying the different methods of introducing a periodic perturbation into the laser waveguide, it is worth considering the structure of the waveguide. Two types of waveguides are used for THz QCLs; the surface plasmon (SP) waveguide,1 which is the one considered here, and the double metal waveguide.10 In the SP case, the waveguide mode consists of a combination of the SP mode arising from the top metallic contact layer evaporated onto the top of the laser ridge, and the SP from a buried heavily doped layer positioned below the stack of active regions. There is also a top contact layer, consisting of about 200 nm of heavily doped GaAs just below the top metallization; this facilitates the provision of electrical contacts to the structure.

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In Reference 11, a grating was etched into this top contact layer before the evaporation of the Cr/Au top metal. Figure 2 shows the calculated optical mode profiles in three situations; with the complete 200-nm top contact layer, with the thickness reduced to 50 nm and with the layer completely removed. All three cases are considered with Cr/Au top metallization. The most prominent difference between the three curves is in the amount of overlap between the optical mode and the active region. This results in a modulation of the modal gain of gth∆Γ = 1.3 cm−1 for a typical waveguide structure emitting at 68 µm (4.4 THz). However it should also be noted that free carrier absorption within the contact layer is responsible for some of the optical losses within the waveguide, and so there is a loss modulation of ∆αw = 1.5 cm−1. These two mechanisms tend to cancel out as parts of the waveguide with the top contact layer removed experience lower losses, but also a reduced modal gain. Overall, this means that the imaginary part of the coupling constant, κ, for a DFB grating fabricated along these lines is very small, and κ is predominantly index coupled, arising from the variation in the real part of the refractive index of the two sections. It is estimated that κ ~2.5 cm−1.

Figure 2. (a) Calculated waveguide mode profile in three situations: with the top contact layer left intact (solid line), etched so that only 50 nm remains (dashed line), and completely removed (dotted line). (b) Solid lines show spectra measured close to the maximum optical power from etched grating DFB devices, 2.8-mm long and with three different grating periods. The dotted lines show the spectra measured from devices where an additional loss modulation had been introduced using an additional annealed contact step. The 9.2-µm grating period device was 3.2-mm long, and the 9.4-µm device 4.4 mm. All laser ridges were 150-µm wide.

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Single mode operation was not observed from these devices. The dotted lines in Figure 2(b) show laser spectra measured from three devices fabricated with this type of DFB, but using slightly different grating periods. For the two longer grating periods, the measured spectra appear broadly similar to a FP laser spectrum, but with the presence of a stopband, corresponding to the suppression of two FP modes. This is typical of an undercoupled DFB device where the product of the coupling constant and the cavity length, κ·L, is much less than one, while there is also strong facet reflectivity. The position of this stopband tunes with grating period at a rate in good agreement with that expected based on the effective refractive index calculated for the device. The absence of a stopband in the spectrum measured from the device with the shortest grating period is attributed to an excessive detuning between the material gain peak and the grating resonance. The solid lines in Figure 2(b) show laser spectra from similar devices, fabricated using a slightly different approach. A grating was etched into the top surface of the ridge as before, but a AuGe/Au annealed contact was deposited onto the unetched parts of the grating. This type of contact results in an increase in the optical losses in these regions, and a complex coupled grating is obtained, where both real and imaginary parts of the coupling constant are significant. Single mode operation was observed from these devices, with the laser mode within the previously observed stop gap. 2.2. DFB DEVICES BASED ON SURFACE PLASMON GRATINGS

2.2.1. First-order gratings We have already noted that the optical mode in the waveguide arises from the SP associated with the Cr/Au top metallization; in regions where this has been removed no waveguide mode is present. To understand the operation of these SP DFB gratings, let us consider the situation of a normal ridge waveguide, containing one small region where a slit has been opened in the top metal. For a photon incident on the slit three processes can take place: it can be reflected, it can tunnel through this region without a guided mode, or it can be scattered up through the slit and lost to the laser mode. By fabricating a periodic array of these slits a DFB grating can be produced.12,13 The above picture is not quite accurate, however. At these long wavelengths, there is also a SP mode associated with the layer of heavily doped GaAs used to facilitate electrical contacts to the device, and even in the regions where the metal has been removed there will still be a waveguide

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mode due to this. True SP gratings can instead be easily obtained by etching away this heavily doped layer in the regions where the metal has been removed. The optimum slit width for the grating is the result of a trade off between the stronger coupling that arises from a wider slit and the increased scattering losses that also occur for wide slits. This is illustrated in Figure 3(b), which shows the calculated grating reflectivity for three different slit widths. The optimum width is found to be 2 µm, which corresponds to a duty cycle of ~10%.

Figure 3. Calculated reflectivity of a first-order surface plasmon grating for three different slit widths.

Figure 4(a) shows emission spectra from three SP DFB devices, emitting around 2.55 THz. Two of these devices (with grating periods of 16.6 and 16.4 µm) showed single mode operation, The multimode operation observed from the 16.2-µm grating period device is attributed to an excessive detuning between the grating mode and the material gain peak. The observed rate of tuning of the emission line with grating period is in good agreement with the expected value using the calculated modal refractive index. Figure 4(b) shows a similar spectrum, measured from the 16.4-µm grating period device, displayed on a logarithmic scale to show the high spectral purity obtained, with a side mode suppression ration (SMSR) >20 dB. For the majority of injection currents measured, single mode behaviour is observed, with a good side mode suppression ration of up to 20 dB. However, for very high injection currents, close to the roll-off in the LI curve, a second mode becomes visible, as shown in Figure 4(c). This is attributed to the presence of a higher-order transverse mode, which can be

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prevented by reducing the width of the top metallization relative to the ridge. Devices fabricated in this way showed single mode emission for all investigated currents and temperatures.

Figure 4. (a) Spectra measured from first-order surface plasmon DFB lasers with three different grating periods. (b) Spectrum measured from a surface plasmon DFB structure with grating period 16.4 µm, shown on a log scale. (c) Spectrum measured from a 16.5-µm DFB structure, close to the maximum optical power. The smaller peak is attributed to the presence of a higher order transverse mode.

2.2.2. Second-order gratings Because of the intersubband nature of QCLs, the radiative transition will not couple to an optical field propagating in the growth direction, and so surface-emitting devices such as the VCSEL cannot be fabricated.14 However, it is possible for light emission from the surface of a device to be based on a scattering mechanism, either in a photonic crystal structure,15 or using a second order DFB grating.16,17 Second-order DFB structures have been produced based on the SP grating concept. The reflectivity of second-order gratings with different slit widths was simulated using a finite element technique. The results are reported in Figure 5(a), showing the optimum slit width to be the same as in the first-order case. Because the period of a second-order grating is twice that of a first order, this now corresponds to a duty cycle of 5%. The primary reason for the reduced reflectivity of the second-order gratings

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compared to the first order is the lower number of grating periods per unit length. Additionally, there will be higher scattering losses, due to the intentional vertical emission.

Figure 5. (a) Reflectivity of second-order surface plasmon gratings with different slit widths, compared with that of a first-order grating with 2-µm slits. (b) Emission spectra measured from two second-order DFB devices, with different grating periods. The measured light was emitted in the vertical direction. (c) Emission spectrum of a second-order DFB device, with 36.2-µm grating period, shown on a log scale. (d) Vertically emitted power from a second-order DFB QCL measured as a function of angle in the directions parallel to (dotted line) and transverse to (solid line) the laser ridge.

Vertical emission spectra measured from two second-order DFB lasers with different grating periods are shown in Figure 5(b). For these devices, the grating did not extend over the full length of the ridge; a 1.5-mm long grating section was fabricated in the centre of a 2-mm long laser ridge. To avoid any possibility of the bond wires affecting the grating properties, these were attached at either end of the ridge, in the regions of unpatterned top metallization. The tuning of the emission wavelength with grating period is again in good agreement with the expected value. This, together with the presence of vertical emission confirms that the grating is the dominant source of optical feedback in the devices.

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For all devices measured, lasing was observed on a single longitudinal mode. However, for some devices a second transverse mode was observed under higher injection currents. This is not surprising for these large ridge widths (250–300 µm), since the waveguide losses for the first and second order transverse modes will be almost equal. Figure 5(c) shows the emission measured from a device emitting on a single transverse mode plotted on a log scale. Again, a very high spectral purity is observed, with a SMSR better than 20 dB. The vertically emitted power was measured as a function of the angle, both along and perpendicular to the direction of the waveguide, as shown in Figure 5(c). As expected the angular divergence in the direction along the ridge is considerably reduced, owing to the increased size of the emitting aperture. Second-order DFB lasers, and particular TM-polarized devices using metallic gratings tend to lase on an asymmetric longitudinal mode, resulting in a double-lobed far-field pattern. There are two possible reasons why this is not observed here. The first is due to insufficient angular resolution of the setup; a simple calculation based on reference 18 suggests that the separation between the two lobes should be less than 1°. It is also possible that the more complex structure of this sample, with facet reflections of arbitrary phase and the ridge sections without grating may generate phase shifts resulting in a more symmetric lasing mode. 2.3. MASTER OSCILLATOR POWER AMPLIFIERS

So far, we have seen that, using distributed optical feedback, it is possible to produce THz QCLs which show good single mode operation. However, the amount of power which it is possible to emit in a single mode is limited by the appearance of higher-order transverse modes at high currents. Although it is possible to avoid these by using narrow ridges to selectively increase the losses in the higher transverse modes, this has the effect of reducing the available output power from the device, and so is not an ideal solution. For lasers emitting at much shorter wavelengths, it has been possible to circumvent this problem by using a master oscillator power amplifier (MOPA) structure. This is a two-section device, with a narrow laser ridge acting as the master oscillator, emitting laser light in a single mode. This emitted light is then amplified in a flared second section of the device. Feedback is usually suppressed from the amplifier section, to ensure that it only has the effect of amplifying the light, without having any influence on its spectral properties. Thus, in an ideal MOPA, the threshold current of the laser section will be independent of the current level in the amplifier section.

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MOPA structures have been fabricated based on THz QCLs. A schematic diagram of the device is shown in the lower part of Figure 6. The two sections are separated by a 20-µm wide slot. The structure was defined using a single etch step, using inductively coupled plasma dry etching based on a Cl2/Ar/HBr chemistry, and a Cr etch mask. The upper part of Figure 6 shows an SEM image of the slot between the two sections of the device. After this processing step, narrow AuGe/Au annealed contacts were deposited at the edge of the device, followed by a Cr/Au top contact layer. Common side contacts were used for the two sections, resulting in a three terminal device. The sample was then thinned, cleaved, and indium soldered onto copper submounts for testing.

Figure 6. Scanning electron micrograph of part of the THz MOPA structure. The laser section (top) is separated from the amplifier section by a 20-µm slot. The lower part of the figure shows a schematic diagram of the structure, not to scale.

Figure 7 shows experimental data measured from a device with a 2.5mm long laser section, and a 780-µm amplifier section. In Figure 7(a) the threshold current of the laser section is shown as a function of the amplifier current. Initially, with cleaved facets on both ends of the device, a very strong dependence was seen. This was attributed to light reflected from the amplifier facet being coupled back into the laser section. With no current passing through the amplifier, this section will have a net absorption, and so the amount of light coupled back after passing through the amplifier will be small. However, as the amplifier current is increased towards transparency, this increases, effectively reducing the mirror losses of the laser section and so reducing the threshold current. Although the amplifier section did not lase on its own, it is likely that, for high current levels through both sections, the device was in fact acting as a coupled cavity laser. At very high amplifier currents, we are operating beyond the current carrying capability of the miniband within the active region, and the device

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no longer shows gain. The threshold current of the laser section then returns to the same value as for an unbiased amplifier. In order to eliminate this problem, the amplifier facet was polished at an angle of 9°, as shown in the schematic diagram of Figure 6. The result of this can be seen in Figure 7(a), where the change in threshold with amplifier current is now very small. Light intensity-current curves were measured at a selection of amplifier currents by sweeping the laser current. These are shown in Figure 7(c). The highest amplification achieved was ~2, limited by the short length of the amplifier section. We estimate the maximum achievable amplification to be ~20, for an amplifier length ~3 mm; gain saturation is expected to prevent further improvement by using even longer amplifiers.

Figure 7. (a) Threshold current of the laser section, plotted against amplifier current for two devices with a cleaved amplifier facet (solid line) and an amplifier facet polished at 9° (dotted line). The threshold currents have been normalized to the value obtained with an unbiased amplifier section. (b) Power output measured from the MOPA structure at different amplifier currents, while keeping the laser current constant close to the maximum power. (c) Plot of the output light intensity against laser current measured at various different amplifier currents.

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The maximum output power measured in the course of the LI measurements is plotted against the amplifier current in Figure 7(b). We can see that this increases up to a current density of ~200 Α cm−2. This current density corresponds to the roll-off in the material gain, as can be seen in Figure 7(c). The reduction in power observed for very high amplifier currents is attributed to heating effects. 3. Conclusions and Acknowledgements THz QCLs emitting on a single mode have been demonstrated using both etched gratings and SP gratings, based on arrays of thin slits in the top metallization of the laser ridge. SP DFB lasers have also been fabricated based on second-order gratings, and vertical emission characterized. Finally, THz master oscillator power amplifiers have been fabricated and characterized. It is predicted that for an amplifier length of 3 mm these can show amplifications of up to 20. This work was funded by the European Commission through the IP project Teranova, the PASR project Terasec and the Marie Curie RTN POISE. Partial financial support from Physical Sciences Inc. is also gratefully acknowledged.

References 1. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, Terahertz semiconductor heterostructure laser, Nature 417, 156 (2002). 2. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, Operation of terahertz quantum cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode, Opt. Express 13, 3331 (2005). 3. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, High power terahertz quantum cascade lasers, Electron. Lett., 42, 89 (2006). 4. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, 1.9 THz quantum-cascade lasers with one-well injector, Appl. Phys. Lett., 88, 121123 (2006). 5. A. Tredicucci, L. Mahler, T. Losco, J. Xu, C. Mauro, R. Köhler, H. E. Beere, D. A. Ritchie, and E. H. Linfield, in Novel In-Plane Semiconductor Lasers IV, C. Mermelstein and D. P. Bour, Eds., Proceedings SPIE 5738, 146–158 (2005). 6. A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Methane concentration and isotopic composition measurements with a mid-infrared quantum-cascade laser, Opt. Lett., 24, 1762 (1999).

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7. L. Hvozdara, A. Lugstein, S. Gianordoli, W. Schrenk, G. Strasser, K. Unterrainer, E. Bertagnolli, and E. Gornik, Self-aligned coupled cavity GaAs/AlGaAs midinrared quantum –cascade laser, Appl. Phys. Lett., 77, 1077 (2000). 8. G. Totschnig, F. Winter, V. Pustogov, J. Faist, and A. Müller, Mid-infrared externalcavity quantum-cascade laser, Opt. Lett., 27, 1788 (2002). 9. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdré, L. Sirigu, G. Scalari, M. Giovannini, M. Hoyler, and J. Faist, Design, fabrication and optical characterisation of quantum cascade lasers at terahertz frequencies using photonic crystal reflectors, Opt. Express 13, 8960 (2005). 10. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, Terahertz quantumcascade laser at λ≈100 µm using metal waveguide for mode confinement, Appl. Phys. Lett., 83, 2124 (2003). 11. L. Mahler, R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, Single-mode operation of terahertz quantum cascade lasers with distributed feedback resonators, Appl. Phys. Lett., 84, 5446 (2004). 12. J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A. L. Baudrion, Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides, Phys. Rev., B 70, 235406 (2004). 13. L. Mahler, A. Tredicucci, R. Köhler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings, Appl. Phys. Lett., 87, 181101 (2005). 14. M. Helm, in Intersubband Transitions in Quantum Wells: Physics and Device Applications I, H. C. Liu, F. Capasso, Eds. (Academic Press, San Diego, 2000). 15. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, Quantum cascade surface emitting photonic crystal laser, Science 302, 1374 (2003). 16. C. Pflügl, M. Austerer, W. Schrenk, S. Golka, G. Strasser, R. P. Green, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Single mode surface emitting quantum cascade lasers, Appl. Phys. Lett., 86, 211102 (2005). 17. O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, J. Xu, A. Tredicucci, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamošiūnas, Opt. Express, 14, 5335 (2006). 18. N. Finger, W. Schrenk, and E. Gornik, Analysis of TM-polarized DFB laser structures with metal surface gratings, IEEE J. Quantum Electron., 36, 780 (2000).

GUIDED PROPAGATION OF TERAHERTZ PULSES ON METAL WIRES KANGLIN WANG AND DANIEL M. MITTLEMAN* Rice University, Department of Electrical and Computer Engineering, MS 366, Houston, TX 77251-1892, USA

Abstract. We demonstrate a new waveguiding structure for terahertz (THz) radiation, in which broadband THz pulses are confined and guided along a bare metal wire. This waveguide exhibits close to the lowest attenuation of any waveguide for broadband THz pulses reported so far. It also supports propagation of broadband radiation with negligible group-velocity dispersion, making it especially suitable for use in pulsed terahertz sensing and diagnostic systems. In addition, the structural simplicity lends itself naturally to the facile manipulation of the guided pulses, including coupling, directing, and beam splitting. These results can be described in terms of a model developed by Sommerfeld, for waves propagating along the surface of a cylindrical conductor.

Keywords: waveguide, surface plasmon polariton, time-domain spectroscopy

1. Introduction Rapid advances in laser technology have enabled various techniques for the generation and detection of electromagnetic radiation in the terahertz region (spanning from ~100 GHz to ~10 THz).1 As a result, numerous uses of terahertz radiation have been explored, including trace gas detection,2 medical diagnosis,3,4 security screening,5 and defect analysis in complex materials such as space shuttle tiles.6 Many of these studies have relied on terahertz time-domain spectroscopy, a technique for generating sub-picosecond pulses with spectral content spanning much of the THz band.7–10

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* To whom correspondence should be addressed: Daniel M Mittleman, Rice University, Department of Electrical and Computer Engineering MS366, Houston, TX77251-1892, USA

55 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 55–68. © 2007 Springer.

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However, progress has been limited by the overwhelming reliance on free-space transport of the terahertz beam, using bulk optical components. In many real-world situations, the sample or region to be studied may not be readily accessible to a line-of-sight beam. Common devices such as optical fiber-based sensors or medical endoscopes rely on the guided wave delivery of light to the remote-sensing location. In order to extend this paradigm to THz applications, the development of optimized guided wave devices is required. Furthermore, the development of practical THz waveguides will dramatically expand the application of THz-TDS in areas such as gas sensing and nanometer thin-film measurements.11,12 The development of THz waveguides has been hindered by the material properties and the application requirements in this spectral range. On the one hand, the characteristics of materials at THz frequencies make it extremely difficult to build a fiber to guide THz beams over a long distance. The most transparent materials for this range are crystalline (e.g. high-resistivity silicon), and thus are costly, fragile, and challenging to form into specific geometries for waveguide configurations. Other materials, such as low-loss polymers or glasses, are more malleable but exhibit prohibitively high-absorption losses for propagation distances of more than a few centimeters. For this reason, THz waveguides generally must rely on propagation in air, rather than via dielectric confinement as in an optical fiber. On the other hand, many THz applications rely on the use of broadband pulses for time-domain analysis and spectroscopic applications. To avoid pulse reshaping during propagation, the significant additional constraint of low dispersion is also required. But for many conventional metal waveguides (e.g. metal tubes), pulse reshaping in propagation is difficult to avoid, due to the extreme dispersion near the waveguide cutoff frequencies. Furthermore, finite conductivity of metals can lead to considerable losses in the wave propagation. Great efforts have been devoted to finding useful THz waveguides within the past few years, and various guides with quasi-optical coupling have been demonstrated. Most of these THz waveguides have been based on conventional guiding structures, such as metal tubes,11,13,14 plastic ribbons,15 or dielectric fibers.16 There have also been reports on the application of the latest technology of photonic crystal fibers to THz radiation.17,18 In all of these cases, the utility for transport of THz pulses is limited by group velocity dispersion of the guided waves. The most promising studies have reported dispersionless propagation in parallel metal plate waveguides.19–21 In this case the reported attenuation (~80 dB/m) is limited by the finite conductivity of the metal components.

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In this paper we show how a metal waveguide with very simple geometry, namely a bare wire, can be used to guide broadband THz pulses with outstanding performance, including low-loss and negligible group velocity dispersion. The guided propagation of THz pulses on a metal wire shows similar behavior to the cylindrical surface guided waves first described by Sommerfeld.22,23 The structural simplicity of the wire waveguide presents great advantages in the manipulation of guided THz radiation.24,25 2. Characterization of the THz Wire Waveguide The propagation of THz radiation along bare metal wires was first observed in the demonstration of apertureless near-field scanning optical microscopy (NSOM) using THz-TDS.26,27 In order to directly observe and characterize the guided THz propagation on metal wires, we use a different configuration, employing fiber-coupled terahertz photoconductive antennas.28 This permits us to change the incident position (the start point of the propagation) and the detection position of the THz pulses, to observe the propagation distance dependance and the spatial profile of the guided mode.24 Scanning Optical Delay Line

Femtosecond Laser

Fiber Coupler

THz transmitter

x Input Coupler

Metal wire waveguide

y

z

Fiber Coupler

THz receiver Guided wave

Movable Stage

Movable Stage

Figure 1. Experimental setup for the direct characterization of the THz wire waveguide.

A schematic of the experimental setup is shown in Figure 1. The horizontally polarized THz pulses are focused onto the waveguide, a stainless steel wire. Another stainless steel wire is placed at the focal spot, oriented perpendicular to the waveguide (the y direction in Figure 1). This second wire serves as an input coupler. Scattering of the input THz radiation at the

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intersection structure helps to excite the radially polarized mode which can propagate along the waveguide. Both the waveguide and the coupler are 0.9 mm in diameter, and the separation between them is 0.5 mm. The receiver is placed at the end of the waveguide and is oriented to detect only the vertically polarized component of the electric field in order to eliminate the possibility of detecting directly scattered radiation which would interfere with the detection of the guided mode. The incident THz beam is modulated by a chopper in front of the transmitter and a lock-in amplifier is used for detecting the induced photocurrent in the receiver. The THz transmitter, the focusing lenses, and the coupler are all mounted on a movable stage so that the incident position along the waveguide can be controlled. The THz receiver is mounted on a three-axis stage for detection at various positions with respect to the end of the waveguide. 2.1. SPATIAL PROFILE

Electric field (arb. units)

As the first step to characterize the propagating mode on the wire waveguide, we measure the spatial profile of the electric field around the waveguide by vertically scanning the THz receiver at the end of the waveguide. Figure 2 shows typical time-domain electric field waveforms, for two different receiver

0

5

10

15

20

25

30

Delay (ps) Figure 2. Time-domain electric field waveforms detected with the receiver 3 mm above (top) and 3 mm below (bottom) the waveguide. The polarity reversal shows the radial nature of the guided mode.

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positions located 3 mm above and 3 mm below the wire waveguide. These waves are vertically (y) polarized, perpendicular to the horizontally (x) polarized input beam. The polarity reversal as the detector scans across the wire clearly shows the radial nature of the guided mode. The peak-to-peak amplitude of the waveform decays with increasing distance from the wire surface, approximately as 1/r where r is the radial distance from the axis of the wire.25 The observed behavior can be understood using Sommerfeld’s description of an electromagnetic wave propagating along the surface of a cylindrical conductor, a so-called Sommerfeld wire wave. In this case, it has been shown that the important propagating solution is an axially symmetric TM wave. Outside the metal, the variation of the radial electric field component (the dominant component) is described by a Hankel function, H1(1)(γr), where γ is defined in terms of the propagation constant k of the field outside the wire according to γ 2 = ω2 c 2 − k 2. For a perfectly conducting wire, γ = 0 and the field propagates with a velocity determined solely by the external medium (in our case, air).22 For large but finite conductivity, γ is small and the approximate form for the Hankel function can be used, appropriate for small argument:

H1( ) ( x ) ≈ −2i π x . 1

(1)

Thus, a Sommerfeld wire wave also exhibits 1/r decay, within a distance r0 > 1 ). At visible and infrared frequencies, the dispersive behavior of an SPP on an Al wire of 25-µm diameter is almost indistinguishable from that of a planar Al surface. But the low-frequency portion of the dispersion curve approaches the light line in a different way from that of a planar surface, which leads to the unique dispersive behavior observed in the THz frequency range. For comparison with the experimental data, we calculate the phase velocity of the SPPs on Al wires of several different diameters. The results are shown as solid curves in Figure 5. The calculated phase velocity agrees qualitatively with the observed results, reproducing in particular the notable feature of decreasing vp with decreasing frequency.36 It is clear from our data and from the calculations that the observed dispersive behavior only appears at THz and lower frequencies. This indicates

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that for frequencies much lower than the surface plasmon frequency, the resonant interaction between the electromagnetic wave and the plasma oscillation is no longer the dominant mechanism for determining the properties of surface waves. Instead, the electromagnetic properties of the metal play an increasingly important role due to the larger skin depth at lower frequencies. This effect is enhanced for SPPs propagating on wires, due to the geometry of the metal surface. Since Sommerfeld waves are single-mode azimuthally symmetric TM waves, the electric field components inside the metal at a given point along the length of the wire are in phase. So, due to the curved nature of the surface, these evanescent field components can constructively interfere inside the metal. As a result, more power is transmitted inside the metal for SPPs on metal wires as compared to SPPs on planar metal surfaces. This enhanced skin effect is more significant for smaller wire diameters, since increased surface curvature leads to a larger overlap of the evanescent waves penetrating into the metal. It is also more significant at lower frequencies, due to the larger skin depth. This unusual dispersive behavior indicates the decreased plasmonic nature of SPPs in the THz frequency range. 3. Conclusions We have demonstrated a new type of THz waveguide with low loss, negligible group velocity dispersion and structural simplicity. This waveguide enables many new THz-sensing applications. It is now possible to direct the THz pulse inside of containers or around corners, where line-ofsight optics is not practical. Besides the waveguide described above, we have also tried many other metal wires as THz waveguides. The materials for these guides include steel, aluminum, copper, zinc, and nichrome. The wire diameter of these guides ranges from 0.5 mm to 6.4 mm. There is no strong difference in the performance of these waveguides, showing that THz pulses can be launched along any thin metal rod structures. In situations where the guided mode could be perturbed by other structures close to the waveguide, we could add a section of outer metallic shield to form a coaxial waveguide, as long as the additional ohmic losses can be tolerated. With a Y-splitter structure used to separate the output wave from the input wave, and a small mirror attached at the end of the waveguide as a 90° output director, we have successfully demonstrated a THz endoscope, by detecting THz pulses reflected from the bottom and the side wall inside a container.24,25 Further improvement could be made by combining an endoscope with an imaging system. This can be accomplished by scanning

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the endoscope along the surface of the detected region, or alternatively, scanning or rotating the sample to obtain an internal THz image. One challenge for this goal is the low power transmitted by the endoscope which strongly limits the data acquisition rate as well as the dynamic range. With optimization of the mode of the input beam and the coupling geometry, the power launched into the endoscope probe can be greatly increased.29,39 It is also interesting to note that this waveguide naturally generates a radially polarized mode. So with a focusing lens mounted at the distal end of the endoscope, a higher resolution can be obtained than in the normal THz imaging system, due to the sub-diffraction-limited focusing of radially polarized beams.40,41 Furthermore, since the radially polarized mode is an ideal input field for a coaxial near-field probe42–44 or an apertureless nearfield optical antenna,26 nanometer-resolved endoscopic THz imaging may be possible.45 This will pave the way for a wide range of new applications for terahertz sensing and imaging. Acknowledgments This work has been funded in part by the R. A. Welch Foundation, the National Science Foundation, and by Advanced Micro Devices.

References 1. D. Mittleman, Ed., Sensing with Terahertz Radiation (Springer, Heidelberg, 2002). 2. R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, Chemical recognition of gases and gas mixtures with terahertz waves, Opt. Lett., 21, 2011–2013 (1996). 3. R. M. Woodward, V. P. Wallace, D. D. Arnone, E. H. Linfield, and M. Pepper, Terahertz pulsed imaging of skin cancer in the time and frequency domain, J. Biol. Phys., 29, 257–261 (2003). 4. D. Crawley, C. Longbottom, V. P. Wallace, B. Cole, D. D. Arnone, and M. Pepper, Three-dimensional terahertz pulse imaging of dental tissue, J. Biomed. Opt., 8, 303–307 (2003). 5. K. Kawase, Y. Ogawa, and Y. Watanabe, Non-destructive terahertz imaging of illicit drugs using spectral fingerprints, Opt. Express 11, 2549–2554 (2003). 6. S. Wang and X.-C. Zhang, Pulsed terahertz tomography, J. Phys. D, 37, R1–R36 (2004). 7. P. R. Smith, D. H. Auston, and M. C. Nuss, Subpicosecond photoconducting dipole antennas, IEEE J. Quant. Elec., 24, 255–260 (1988). 8. M. van Exter and D. Grischkowsky, Characterization of an optoelectronic terahertz beam system, IEEE Trans. Microw. Th. Tech. 38, 1684–1691 (1990).

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9. P. U. Jepsen, R. H. Jacobsen, and S. R. Keiding, Generation and detection of terahertz pulses from biased semiconductor antennas, J. Opt. Soc. Am. B, 13, 11, 2424–2436 (1996). 10. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, T-ray imaging, IEEE J. Sel. Top. Quant. Elec., 2, 679–692 (1996). 11. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, Terahertz waveguides, J. Opt. Soc. Am. B, 17, 851–863 (2000). 12. J. Zhang and D. Grischkowsky, Waveguide terahertz time-domain spectroscopy of nanometer water layers, Opt. Lett., 29, 1617–1619 (2004). 13. R. W. McGowan, G. Gallot, and D. Grischkowsky, Propagation of ultrawideband short pulses of THz radiation through submillimeter-diameter circular waveguides, Opt. Lett., 24, 1431–1433 (1999). 14. J. A. Harrington, R. George, P. Pedersen, and E. Mueller, Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation, Opt. Express 12, 5263–5268 (2004). 15. R. Mendis and D. Grischkowsky, Plastic ribbon THz waveguides, J. Appl. Phys., 88, 4449–4451 (2000). 16. S. P. Jamison, R. W. McGown, and D. Grischkowsky, Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fiber, Appl. Phys. Lett., 76, 1987–1989 (2000). 17. H. Han, H. Park, M. Cho, and J. Kim, Terahertz pulse propagation in a plastic photonic crystal fiber, Appl. Phys. Lett., 80, 2634–2636 (2002). 18. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, Teflon photonic crystal fiber as terahertz waveguide, Jpn. J. Appl. Phys., 43, L317–L319 (2004). 19. R. Mendis and D. Grischkowsky, Undistorted guided-wave propagation of subpicosecond terahertz pulses, Opt. Lett., 26, 846–848 (2001). 20. R. Mendis and D. Grischkowsky, THz interconnect with low loss and low group velocity dispersion, IEEE Microw. Wireless Comp. Lett., 11, 444–446 (2001). 21. S. Coleman and D. Grischkowsky, A THz transverse electromagnetic mode twodimensional interconnect layer incorporating quasi-optics, Appl. Phys. Lett., 83, 3656– 3658 (2003). 22. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941). 23. G. Goubau, Surface waves and their application to transmission lines, J. Appl. Phys., 21, 1119–1128 (1950). 24. K. Wang and D. M. Mittleman, Metal wires for terahertz wave guiding, Nature 432, 376–379 (2004). 25. K. Wang and D. Mittleman, Guided propagation of terahertz pulses on metal wires, J. Opt. Soc. Am. B, 22, 2001–2008 (2005). 26. K. Wang, A. Barkan, and D. M. Mittleman, Propagation effects in apertureless near-field optical antennas, Appl. Phys. Lett., 84, 305–307 (2004). 27. K. Wang, D. M. Mittleman, N. C. J. van der Valk, and P. C. M. Planken, Antenna effects in terahertz apertureless near-field optical microscopy, Appl. Phys. Lett., 85, 14, 2715–2717 (2004). 28. J. V. Rudd, D. Zimdars, and M. Warmuth, Compact fiber-pigtailed terahertz imaging system, Proc. SPIE 3934, 27–35 (2000). 29. J. Deibel, M. Escarra, and D. M. Mittleman, Photoconductive terahertz antenna with radial symmetry, Elec. Lett., 41, 9–10 (2005).

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30. H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988). 31. G. Schider, J. R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F. R. Aussenegg, W. L. Schaich, I. Puscasu, B. Monacelli, and G. Boreman, Plasmon dispersion relation of Au and Ag nanowires, Phys. Rev. B, 68, 155427 (2003). 32. J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides, Phys. Rev. B, 70, 235406 (2004). 33. J. K. Lim, K. Imura, T. Nagahara, S. K. Kim, and H. Okamoto, Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy, Chem. Phys. Lett., 412, 41 (2005). 34. J. Saxler, J. Gómez Rivas, C. Janke, H. P. M. Pellemans, P. Haring Bolivar, and H. Kurz, Time-domain measurements of surface plasmon polaritons in the terahertz frequency range, Phys. Rev. B, 69, 155427 (2004). 35. D. R. Lide, CRC Handbook of Chemistry and Physics, 85th edn. (CRC Press, Boca Raton, 2004). 36. K. Wang and D. Mittleman, Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range, Phys. Rev. Lett., 96, 157401 (2006). 37. T.-I. Jeon, J. Zhang, and D. Grischkowsky, THz Sommerfeld wave propagation on a single metal wire, Appl. Phys. Lett., 86, 161904 (2005). 38. M. J. King and J. C. Wiltse, Surface-wave propagation on coated or uncoated metal wires at millimeter wavelengths, IRE Trans. Antennas Propag., 10, 246 (1962). 39. J. Deibel, K. Wang, M. Escarra, and D. Mittleman, Enhanced coupling of terahertz radiation to cylindrical wire waveguides, Opt. Express 14, 279–290 (2006). 40. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Focusing light to a tighter spot, Opt. Comm., 179, 1–6 (2000). 41. R. Dorn, S. Quabis, and G. Leuchs, Sharper focus for a radially polarized light beam, Phys. Rev. Lett., 91, 233901 (2003). 42. U. C. Fischer and M. Zapletal, The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation, Ultramicrosc., 42, 393–398 (1992). 43. F. Keilmann, FIR microscopy, Infrared Phys. Technol., 36, 217–224 (1995). 44. C. W. McCutchen, Transmission line probes for scanning photon-tunneling microscopy, Scanning: J. Scan. Microscopies 17, 15–17 (1995). 45. H.-T. Chen, R. Kersting, and G. C. Cho, Terahertz imaging with nanometer resolution, Appl. Phys. Lett., 83, 3009–3011 (2003).

SUPERLATTICE AND OTHER NEGATIVE-DIFFERENTIALRESISTANCE DEVICES: CURRENT STATUS

HERIBERT EISELE* Institute of Microwaves and Photonics, University of Leeds, Leeds, LS2 9JT, UK

Abstract. The paper discusses and compares the concepts, performance potential, and most recent experimental results of both classical and novel active two-terminal devices for low-noise RF power generation at submillimeter-wave frequencies up to 1 THz. These devices use transit-time, transferred-electron, and quantum-mechanical effects (or a combination of them) to create a negative differential resistance at the frequency of interest. Examples of state-of-the-art results are output power levels of more than 70 mW at 62 GHz and more than 10 mW at 132 GHz from GaAs/AlGaAs superlattice electronic devices; more than 9 mW at 280 GHz, 3.7 mW at 300 GHz, 1.6 mW at 329 GHz, and more than 40 µW at 422 GHz from InP Gunn devices; and more than 140 µW at 355 GHz from a GaAs tunnel-injection transit-time diode.

Keywords: Gunn devices, millimeter-wave devices, millimeter-wave generation, millimeter-wave oscillators, negative differential resistance, oscillator noise, phase noise, power combining, submillimeter-wave devices, submillimeter-wave generation, submillimeter-wave oscillators, superlattice, transferred-electron effect, transit-time diodes, tunneling.

1. Introduction Sources of coherent continuous-wave (CW) radiation are a key component in many emerging systems applications at submillimeter-wave frequencies. Wide availability, compactness, reliability, and low power consumption are

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* To whom correspondence should be addressed: Heribert Eisele, School of Electronic and Electrical Engineering, University of Leeds, Leeds, LS2 9JT, UK, e-mail: [email protected]

69 R.E. Miles et al. (eds.), Terahertz Frequency Detection and Identification of Materials and Objects, 69–88. © 2007 Springer.

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much sought-after features of such fundamental sources and they call for an all-solid-state solution1. The first microwave oscillator ever with a semiconductor device, a tunnel diode, exploited the principle of combining a passive resonant circuit with an electronic device that exhibits a negative differential resistance (NDR) around the resonant frequency of the circuit2–4 and thus overcomes the losses in the circuit. Since then, this basic principle has been extended successfully well into the frequency range of submillimeter waves. Tremendous progress in the upper frequency limits5–11 and RF output power levels12,13 of three-terminal devices in amplifiers has been demonstrated within the last decade and has resulted in a rapidly expanding use of such amplifiers in systems applications up to at least W-band (75–110 GHz). In addition, the availability of high-performance monolithic millimeter-wave integrated circuits (MMICs) fostered the development of sufficiently broadband frequency multiplier chains with GaAs Schottky varactor diodes up to at least 2.5 THz14,15. Despite these major technological advances, there have been few practical demonstrations of fundamental oscillators with three-terminal devices above 100 GHz. Furthermore, only low RF power levels of less than 1 mW were reported16–19. In contrast, two representatives of active two-terminal devices, i.e. Gunn or transferred-electron devices (TEDs) and impact avalanche transit-time (IMPATT) diodes, are operated at higher oscillation frequencies and, in oscillators, generate higher RF output power levels than three-terminal devices. Together with electronic vacuum tubes such as backward-wave oscillators (BWOs), these two-terminal devices continue to play an important role in systems applications at high millimeter-wave and submillimeter-wave frequencies. This paper discusses the concepts and compares the performance potential of active two-terminal devices that meet the following criteria: they either exhibit a strong potential of reaching submillimeter-wave frequencies up to at least 1 THz as evidenced by detailed device analysis or simulations or already generated substantial amounts of CW RF output power with excellent noise performance at frequencies above 300 GHz. 2. Technology Issues The dc-to-RF conversion efficiencies of electronic RF sources generally decrease with frequency and, at high millimeter-wave frequencies, rarely exceed 10%3,4. As a consequence, most of the dc input power is dissipated in the devices as heat, and proper heat management becomes as crucial a technological issue as appropriate low-loss circuits in order to extract the

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highest RF power levels from these devices. Selective etching technologies3,4,20 yield substrateless devices with low thermal resistances, particularly on diamond heat sinks, but also help minimize the skin-effect resistance as much as possible. These technologies enabled the recent experimental results above 100 GHz with state-of-the-art performance from Si IMPATT diodes21, GaAs IMPATT diodes20,22, GaAs tunnel-injection transit-time (TUNNETT) diodes20,23–26, and InP Gunn devices20,27–31. The RF properties of these devices are discussed in subsequent sections. The use of diamond heat sinks or heat spreaders becomes mandatory when the highest RF power levels at millimeter- and submillimeter-wave frequencies need to be generated with these devices3,4,20. 3. Fundamental Device Limitations and Potential Solutions Waveguide circuits, commonly used with active two-terminal devices above 60 GHz2,3,31, are limited in how small a positive imaginary part Xres they offer to the active device near the circuit resonance2,28,29. To fulfill the oscillation conditions3,4 the negative imaginary part Xdev of the device, which arises mostly from the “cold” capacitance Ccold, must be matched (Xres + Xdev = 0). As Ccold of the device scales with device area A, the oscillation conditions impose an upper limit on A. Immaterial whether effects from the carrier transit time τ = ldev/vs are exploited to create the NDR or are detrimental (as, for example, in resonant tunneling diodes and three terminal devices), the material-dependent carrier drift velocity vs forces the device length ldev to decrease with frequency. As Ccold = εrε0A/ldev has an upper limit from the aforementioned oscillation conditions, A strongly decreases with frequency. Avalanche breakdown imposes an upper limit, Ebr, on the electric fields in any electronic device. Therefore, the decrease in ldev, Vbias ∝ Ebr × ldev, and A with operating frequency is responsible for the well-known fundamental limits in the power generation capabilities of all electronic devices. Nonetheless, at least two potential solutions exist to overcome the limitations, for example, in active two-terminal devices, and, most importantly, initial promising results have already been obtained experimentally. Most active two-terminal devices have strongly nonlinear properties, and these properties suggest their use as self-oscillating frequency multipliers. This extraction of power at higher harmonic frequencies requires the oscillation condition only to be met at the fundamental frequency and the transit time τ in the device to be chosen in relation to the (longer) RF period of the fundamental frequency. This means that the limits on Ccold and consequently A are less restrictive. In addition, somewhat higher contact resistances ρc are tolerated.

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This principle has been known for decades and has been exploited successfully, in particular, with transferred-electron devices3,28–31. Recently, it has been shown to work equally well with several other types of active twoterminal devices and some examples with resonant tunneling diodes (RTDs), IMPATT diodes, and TUNNETT diodes are given in subsequent sections. Semiconductor material systems with high values of Ebr and vs as well as low values of the dielectric constant εrε0 are particularly well suited to overcome the aforementioned limitations and one example of a novel device structure is discussed in Section 6. Superlattices allow achieving values of vs that are different from the bulk semiconductor materials composing them. Therefore, they are another method to overcome the aforementioned limitations, and initial experimental results as described in Section 5 are highly promising. 4. Resonant Tunneling Diodes Resonant tunneling through discrete energy levels of a so-called quantum well was first described in 197432. Major advances in growth techniques, such as molecular beam epitaxy (MBE) or metalorganic chemical vapor deposition (MOCVD), had to occur in the 1980s before device structures suitable for oscillators could be grown and evaluated. As can be seen from Figure 1, RTDs in the InAs/AlSb material system yielded the highest oscillation frequency of any fundamental solid-state RF source33,34, but RF power levels of, for example, 3 µW at 360 GHz and 0.3 µW at 712 GHz are low34. This makes it very difficult to employ standard phase-locking techniques either for frequency stabilization or in systems applications where the exact oscillation frequency must be known or be tied to a very accurate reference frequency. Recently, higher RF power levels of 23 µW at the fundamental frequency of 342 GHz and 0.6 µW at the third-harmonic frequency of 1.02 THz were measured with RTDs in the GaInAs/AlAs material system, but the RTDs were operated in a “quasi-CW” mode with a pulse length of 0.3 ms and a repetition rate of 300 Hz35. The NDR that is present in RTDs from dc to the highest oscillation frequencies causes such RF sources to be prone to severe instabilities or bias oscillations, which ultimately limit their RF power generating capabilities. Monolithic integration36 and power combining36,37 was shown to alleviate some of these problems. Although an example of an RTD-based local oscillator (LO) for a receiver system was demonstrated38, problems associated with RTDs have so far prevented their use in systems applications. Present measurement equipment offers only limited sensitivity, which degrades significantly at submillimeter-wave frequencies. Therefore, the low RF power levels from

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RTDs also severely restrict how accurately important oscillator characteristics, such as free-running oscillator spectra and oscillation frequency shift vs. temperature or dc bias, can be determined. A record dc-to-RF conversion efficiency of 50% at a microwave frequency of 2 GHz for an RF output power of 20 mW39 was reported from a quantum well injection transit-time (QWITT) diode, which, in this particular case, was an RTD with a very short adjacent drift region. In contrast and as shown in Figure 1, dc-to-RF conversion efficiencies of RTDs at millimeter- and submillimeter-wave frequencies fall well below 1% and may indicate inferior impedance matching and/or significant losses from series resistances in ohmic contacts and RF circuit.

Figure 1. Published state-of-the art results from RTDs and SLEDs in the 30–1,000-GHz frequency range. Numbers next to the symbols denote dc-to-RF conversion efficiencies in percent, where applicable.

5. Superlattice Electronic Devices Recently than RTDs, superlattice electronic devices (SLEDs) in the GaAs/AlAs and InGaAs/InAlAs material systems were demonstrated as millimeter-wave oscillators40–45. SLEDs exploit the Bloch effect, which occurs

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when the barrier layers that separate the quantum wells of the superlattice are thinner than the de Broglie wavelength of electrons in the wells. Instead of discrete energy levels for electrons, as exploited in the aforementioned RTDs, energy minibands form. Electrons are energetically confined within these minibands. In the case of no scattering, they undergo oscillatory motion, the so-called Bloch oscillations, when a dc bias is applied across the superlattice. With ever-present phonon scattering, electrons lose some of their energy as they travel, and then the Bloch effect causes a region of negative differential mobility (NDM) in the average electron drift velocity46. SLEDs exploit this NDM in a mode of operation similar to that of Gunn devices (which are described in Section 7). The NDM, however, arises from a very different physical process, the Bloch effect, with much shorter relevant time constants than those of the transferred electron effect in Gunn devices44. Therefore, SLEDs are expected to reach much higher oscillation frequencies47 than, for example, InP Gunn devices. In addition to the results from RTDs, Figure 1 also summarizes the published results from SLEDs40–45. These SLEDs were typically evaluated as quasi-planar devices, first in standard rectangular metallic waveguides40,41 and then in a configuration with contact pads for a standard coplanar waveguide ground-signal-ground probe to be connected to a spectrum analyzer42–44. Recently, they were mounted and tested in waveguide cavities micromachined in the photosensitive SU-8 epoxy45. SLEDs are not associated with the same severe restrictions3,4,20 that bias instabilities impose on the device areas A of RTDs and, as shown in Figure 1, their RF output power levels and dc-to-RF conversion efficiencies tend to be higher than those of RTDs. The result with the so far best dc-to-RF conversion efficiency of 5% at 64.4 GHz was obtained in the aforementioned micromachined waveguide cavity. These promising results, however, are thought to be limited by heat dissipation issues. As can be seen from Figure 2, first attempts at adopting the same advanced fabrication technologies as for state-of-the-art GaAs TUNNETT diodes3,4,20 resulted in two orders of magnitude higher RF output power levels from GaAs/AlAs SLEDs on integral heat sinks when they were operated in the fundamental mode around 65 GHz. Two similar standard superlattices were employed, one with a nominal n-type doping of 1×1017 cm−3 and 120 periods of 12 monolayers of GaAs and 3 monolayers of AlAs (wafer 1)48, the other with a nominal n-type doping of 1.4×1017 cm−3 and 100 periods of 14 monolayers of GaAs and 3 monolayers of AlAs (wafer 2).

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Figure 2. RF output power levels and corresponding dc-to-RF conversion efficiencies (in percent) of GaAs/AlAs SLEDs on integral heat sinks operating in the fundamental mode around 65 GHz (◄: wafer 1, ►: wafer 2, see text).

Figure 3. Spectrum of a free-running oscillator with a superlattice electronic device in a second-harmonic mode, center frequency: 132.64 GHz, vertical scale: 10 dB/div., horizontal scale: 2 MHz/div., resolution bandwidth: 200 kHz, video bandwidth: 10 kHz.

Devices from the same wafer 1 (and also on integral heat sinks) but operated in a second-harmonic mode yielded RF output power levels of more than 10 mW around 130 GHz with corresponding dc-to-RF conversion efficiencies of up to 0.9%. Figure 3 shows an example of the clean spectra that are achieved using SLEDs in free-running oscillators, in this case operating in a second-harmonic mode at 132.6 GHz. Strong signals were also detected in the waveguide circuit at even higher harmonics,

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for example, the third and fourth harmonic 48, and this observation is in line with previous results 40–45. 6. Transit-Time Diodes Si IMPATT diodes were the first semiconductor devices to generate RF power above 300 GHz and, as shown in Figure 4 (and in conjunction with Figures 1 and 8), yielded the highest RF power levels from any solid-state fundamental RF source up to 300 GHz. Exemplary RF power levels (and corresponding dc-to-RF conversion efficiencies) of 50 mW (