35.Microelectromechanical Systems

35• Microelectromechanical Systems

35• Microelectromechanical Systems Laser Beam Machining Abstract | Full Text: PDF (167K) Micromechanical Resonators Abstract | Full Text: PDF (278K)

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Wiley Encyclopedia of Electrical and Electronics Engineering Laser Beam Machining Standard Article Martyn R. H. Knowles1, Gideon Foster–Turner2, Keith Errey3, Andrew J. Kearsley4 1Oxford Lasers Inc.., Abingdon, UK 2Oxford Lasers Inc.., Abingdon, UK 3Oxford Lasers Inc.., Abingdon, UK 4Oxford Lasers Inc.., Abingdon, UK Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4601 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (167K)

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Abstract The sections in this article are Generalized Laser Beam Machining Laser Micromachining Laser Beam Characteristics and Manipulation Applications of Laser Beam Machining Process Monitoring About Wiley InterScience | About Wiley | Privacy | Terms & Conditions Copyright © 1999-2008John Wiley & Sons, Inc. All Rights Reserved.

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234

LASER BEAM MACHINING

LASER BEAM MACHINING Laser beam machining involves the practical harnessing and manipulating of laser radiation to have some effect on a material. The advantage of the laser over other light sources is that the light is produced in a well-defined beam which is easily manipulated and focused to produce the high intensities required to machine materials. The first laser was operated in 1960 by Maiman (1) and for a little while, at least, the cliche´ that it was an invention looking for an application had some truth to it. However, it was soon realized that the properly developed laser could be used in a wide range of scientific and industrial applications. It is ironic that in these early days before dedicated power and energy meters had been developed, the unit of measure of ‘‘power’’ of the laser was the number of razor blades drilled with a single pulse. Today, one large application of lasers is spot welding the flexible blades of a modern ‘‘high tech’’ razor blade to its support. Throughout the ages, humankind has advanced by using its intelligence to harness and manipulate energy. Early civilizations developed tools, first made of stone but later of metal. These tools were used to direct their energies in a more efficient way. More recently we have mastered chemical, electrical, and nuclear energy. As our mastery of these energy forms has advanced, so has our technology, and this is reflected in the precision to which we can manufacture components and our ability to miniaturize them. Examples of this are abundant. The computing power which once occupied several large rooms is now built into a device the size of a wrist watch through the replacement of valve technology with transistors and then integrated circuits (ICs). Automobile body panels, once made to a tolerance of a millimeter or so, are now manufactured to within a few tens of microns. The fuel injection orifices in a diesel engine are drilled to within a few microns. Lasers have contributed greatly to our ability to manufacture and miniaturize and continue to do so. By 1966 the first commercial 100 W power carbon dioxide (CO2) laser was commercially available. Since then the power available has increased a hundredfold and there are many laser types available offering a choice of power, wavelength, and pulse format. This proliferation has widened the scope of laser applications which today range from heavy industry, such as welding in shipyards, to microelectronics, where the laser photolithographic process is used to manufacture ICs and memory chips. A laser beam for welding has a number of advantages over conventional techniques. A laser beam is an almost parallel beam of light. It is focused to a small diameter, it is easily directed via optical components, and its power is accurately controlled. This allows the user to exert precise control over the position and extent of the weld which, in turn, improves the quality of the weld and reduces thermal damage to the component.

GENERALIZED LASER BEAM MACHINING Laser beam machining is the interaction of the laser beam with a material resulting in some change to the material. This is in the form of material removal (drilling and cutting), material addition (alloying and cladding), chemical changes (marking), structural changes (hardening or annealing), or joining (welding and soldering). The interaction results from J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.

LASER BEAM MACHINING

the absorption of laser radiation by the workpiece. A certain fraction of the incident laser power is absorbed over the absorption depth and the remainder is reflected. Transmission of the beam occurs only when the absorption depth is greater than the material thickness but this is not the case for most materials of interest. Generally the absorbed energy or power is converted into heat in the material. Then the nature of the induced effect depends on the amount of energy absorbed, the time over which it is absorbed, and the thermal transport and thermodynamic properties of the material (2,3,4). In some cases, the energy of individual laser photons is important because, when high enough, it breaks chemical bonds which change the chemical nature of the material or even removes individual atoms or molecules from the structure. This is often called ‘‘cold ablation’’ because there is little or no thermal input to the material. The absorption of the incident light intensity I0, is given by the following equation: I(x) = I0 e−αx

Heats

Melts

Boils

(1)

where I(x) is the intensity at depth x and 움 is the absorption coefficient. The absorption coefficient is a material property that also depends on the wavelength of the light and its intensity (at high intensities nonlinear effects occur). Light is an electromagnetic wave which, as it passes through a medium, interacts with the electrons of the medium whether they are bound or free. The electric field forces the electron to vibrate at the frequency of the wave. As the electron vibrates, it reradiates (transmits light), or, if it is restrained by lattice forces, it couples energy into the lattice via phonons. The phonons cause the lattice to vibrate which is manifested as heat. If sufficient heat is absorbed, then the material melts or is vaporized. Figure 1 shows the sequence of events as the absorbed power increases. Beyond heating the material, the process in Fig. 1 assumes that the flow of heat away from the irradiated zone is less than the absorbed power. However, in some cases, a point is reached where the heat loss equals the absorbed power, and, therefore, the process may reach only the melting stage, for example. Heat flow in a material is proportional to its thermal conductivity k and the rate of change of temperature depends upon the specific heat C. The heating rate is inversely proportional to the specific heat per unit volume, which is equal to ␳C, where ␳ is the density. A thermal diffusivity ␬ may therefore be defined as k/ ␳C which is the change in temperature produced in a unit volume by the quantity of heat which flows in unit time through a unit area of a layer of unit thickness with a unit temperature difference between its faces. Thermal diffusivity is involved in all nonsteady-state heat flow processes and is therefore of great significance for pulsed-laser machining. The depth of heat penetration D over time t is given in Eq. 2 (see 2,3,4): D = (4κt)1/2

235

(2)

Typical values of ␬ for metals range from 0.05 to 1.0 cm2s⫺1. Taking carbon steel as an example (␬ ⫽ 0.12 cm2s⫺1), the penetration depths for laser-pulse durations of 10 ns, 100 애s and 10 ms are 0.7, 70, and 700 애m, respectively. A short laser pulse (10 ns) ablates material and so the heat penetration

;;;; ;;;;

Plasma formation

Figure 1. The sequence of events as the absorbed power increases. First the material is heated, then it melts, increasing power absorbed boils the melt, and finally very high absorbed power leads to plasma formation.

depth characterizes the extent of the heat damage to the remaining material, and submicron values are typically observed. Medium-length laser pulses (100 애s) are often used in laser drilling applications, and the heat penetration depth is typical of the drill depth per pulse. A long-pulse laser (10 ms) is often used for welding sections approximately 1 mm thick. Thus an appreciation of the laser beam energy, pulse duration, material absorption coefficient (which is wavelength-dependent) and the thermal diffusivity give a good indication of the type of interaction and effects possible.

LASER MICROMACHINING Laser micromachining is the use of lasers to produce features or components with micron precision and is widely used in the electronics, automotive, and precision engineering industries (5). Typical applications include drilling blind and via holes in printed circuit boards (6), dicing chemical vapor deposition (CVD) diamond wafers into miniature heat spreaders for high-power semiconductor devices (7), drilling precision fluid orifices for fuel injection (8) and aerosol components, etching silicon in the photolithographic process (9,10), manufacture of micro sensors and micro devices for surgical use, drilling orifice plates for inkjet printer heads (11), and manufacturing micromolds (12). For the feature size and precision required in micromachining, low- to medium-power lasers are used which control material removal more accurately. In addition the laser beam must produce small, well-defined, irra-

236

LASER BEAM MACHINING

diation zones on the workpiece to make the hole or pattern desired. The material removal must be precise and must not produce significant amounts of debris or heat damage or induce mechanical stress in the component. These results are usually most easily achieved with a short-pulse laser operating in the visible or ultraviolet part of the spectrum where absorption is greater. Lasers which fall into these categories are the copper vapor laser, the Q-switched Nd : YAG laser, and the excimer laser.

Stable resonator Totally reflecting mirror

Active medium

Partially reflecting mirror

Unstable resonator

LASER BEAM CHARACTERISTICS AND MANIPULATION Laser Beam Characteristics

Totally reflecting mirror M1

Active medium

Totally reflecting mirror M2

A laser beam is characterized by describing its spatial properties (beam profile and divergence), spectral properties (the range of wavelengths which it contains) and temporal properties (pulse duration and pulse repetition frequency). An excellent review of these subjects is in (13,14). A detailed treatise on these subjects and lasers in general can be found in Ref. 14a.

Figure 2. Diagram of a stable resonator showing the containment of the paraxial ray and output coupling via a partially reflecting mirror. The lower diagram shows an unstable resonator illustrating the output coupling by geometrical loss.

Laser Beam Divergence and Profile. Laser beam divergence is the spreading of the beam as it propagates by diffraction. It should not be confused with the spread or convergence of a beam caused by a lens or some such device which may be canceled by using an appropriate optical element. The divergence ␪ of the beam determines the minimum diameter w to which the beam is focused by a lens of focal length f and is given approximately by Eq. (3) [see (13), (14)].

diffraction presents a limit to minimum divergence. This minimum divergence (often called diffraction-limited) is realized only with certain lasers and when conditions are optimum. The diffraction-limited divergence, which also depends on the near-field beam profile, is given in Eq. (4) for a Gaussian beam and in Eq. (5) for a plane wave (as produced by an unstable resonator with high magnification):

w = fθ

(3)

The beam profile is the spatial distribution of cross-sectional intensity at a given point along the axis of beam propagation. The ‘‘near-field beam profile’’ (near the output of the laser) and ‘‘far-field beam profile’’ (at a great distance from the laser or at the focus of the beam) are the profiles most often quoted. The beam divergence and profiles are determined by the laser resonator of which there are two principal types known, somewhat misleadingly, as stable and unstable resonators. Their descriptive names do not refer to the power or beam stability of the laser but rather to the type of output coupling. A stable resonator has mirrors which contain the paraxial rays over multiple reflections within the resonator. The beam is coupled out of the resonator by making one of the mirrors partially reflecting. In an unstable resonator, paraxial rays leave the resonator after a few reflections by being coupled past the perimeter of one of the mirrors. These resonators are illustrated in Fig. 2. The beam profile of the stable resonator is Gaussian or Gaussian-like in both the near and far field. The beam profile of the unstable resonator is more complex; it is annular in the near field, and forms a central disc with lower intensity rings outside it in the far field. When the magnification of the resonator (defined as the ratio of the radius of curvature of mirror M1 to M2) is high, the near field is a plane wave and, in the far field, 84% of the power defines the central disc. The far-field intensity distribution is described mathematically by the Airy pattern. From Eq. (3) it can be seen that, for applications requiring a very small focused beam diameter, the beam divergence should be as small as possible tending to zero. Unfortunately

θDL = 4λ/πd = 1.27λ/d

(4)

θDL = 2.44λ/d

(5)

where ␪DL is the full-angle, diffraction-limited divergence, ␭ is the radiation wavelength and d is the near-field beam diameter. These equations show that the divergence is inversely proportional to the beam diameter. Therefore, it is meaningless to compare beam divergences without stating the nearfield beam diameter or the ratio of the divergence relative to the diffraction limit. Using Eqs. (3), (4), and (5), the minimum focused beam diameter for a diffraction-limited beam is calculated by the expression w = f θDL = f βλ/d = ( f #)βλ

(6)

where 웁 is 1.27 for a Gaussian beam and 2.44 for a plane wave, and f# is the f-number of the focusing system used, that is, the focal length divided by the beam diameter at the lens. For a copper vapor laser, ␭ ⫽ 511 nm and with f1 focusing the minimum spot size is 1.24 애m. The spot size for a Gaussian beam is defined as that diameter which contains 86.5% of the power, and, for an unstable resonator, it is the diameter which contains 84% of the power. Although the laser spot size is a good indicator of the minimum size feature, such as a hole, that can be produced, it is possible to produce features larger and smaller than the spot size. For example, if the intensity of the beam at the spot diameter is in excess of the ablation or machining threshold intensity, then the feature size will be larger than the beam spot. Likewise, if the machining threshold is much higher than the intensity of the beam at the spot diameter, then the

LASER BEAM MACHINING

feature size will be smaller than the spot. This is illustrated in Fig. 3. The optical quality of the laser beam differentiates it from any other light source and significantly affects the machining process in many complex ways. The laser beams described in this section are those that are achieved under ideal conditions. In practice these ideal conditions are not always achievable, titled and it is not possible to describe the interaction of the laser beam with the material by simple algebraic equations. However, some qualitative observations can be made. As described in this section and the section titled ‘‘Focusing,’’ the focused laser spot size is proportional to the divergence of the laser beam. Therefore a low divergence laser beam enables the beam to be focused to a smaller spot size, which permits the drilling of smaller holes, the cutting of narrower kerfs and welding, soldering, or heat treating smaller areas. A smaller focused spot size also increases the focused intensity of the laser beam. Higher intensities generally produce higher temperatures in the workpiece and therefore tend to increase or change the machining effect (for example, increasing the evaporation rate of the material or change the machining effect from melting to evaporation). The depth of focus (DOF) of a laser beam is given in Eq. (6a) and is defined as the distance over which the laser beam is within a factor of 兹2 of its minimum diameter. For a given beam diameter and required focused spot size, a lower divergence beam enables a longer focal length lens to be used which increases the depth of focus. Therefore a lower divergence beam (closer to the diffraction limit) can enable deeper holes or cuts to be made or can be used to relax the tolerance to which the lens position has to be held relative to the workpiece. DOF = 2πw2 /λ = 2π f 2 θ 2 /λ = 2π ( f #)2 β 2 λ

(6a)

While the divergence of the beam plays an important part in the machining process, so does the intensity distribution of the laser beam at the workpiece. For example, most hole drilling applications require round holes and a nonround intensity distribution at focus can produce nonround holes. Uniform intensity distribution is very important when the laser beam is used to illuminate a mask which is then imaged onto the workpiece.

237

For further details and examples of how the optical quality of the laser beam affects the machining process the reader is referred to Refs. 14b, 14c, 14d in the bibliography. Laser Beam Spectral Bandwidth. The laser spectral bandwidth is the range of wavelengths or frequencies emitted by the laser. The bandwidth or spread of wavelengths depends on the type of laser and how it is configured. Some lasers, such as dye lasers, have large bandwidths of 20 THz (approximately equivalent to a 20 nm spread at a central wavelength of 600 nm) whereas others, such as the frequency-stabilized HeNe laser, are essentially monochromatic with bandwidths of 1 MHz. The gross bandwidth is determined by the bandwidth of the atomic or molecular transition that produces the laser photons. The laser cavity itself has resonant modes (14) whose width and bandwidth are determined by the cavity length and mirror reflectivity. Resonant longitudinal modes occur when a laser photon has the same phase after one complete transit through the laser cavity. Equation (7) gives the frequency separation ⌬␯ of the longitudinal modes where c is the speed of light and 2L is the complete round-trip distance. ν = c/2L

(7)

The bandwidth 웃␯ of each mode depends on the reflectivity of the cavity mirrors and is given by Eq. (8). δν = {c[1 − (R1 )1/2 ]}/[2Lπ (R1 )1/2 ]

(8)

In this equation it is assumed that the reflectivity of one mirror is R1 and the second mirror has 100% reflectivity as in Fig. 2. The bandwidth of a longitudinal mode is typically a few megahertz. Therefore the spectral output of the laser is made up of a series of longitudinal modes, each with a very narrow spectral bandwidth and whose intensity envelope follows the gain profile of the laser. The practical bandwidth of the laser is reduced by configuring the laser cavity so that optical losses are incurred over all but part of the bandwidth. These losses reduce the effective gain over most of the bandwidth to levels below the threshold required for laser action. Consequently laser action then occurs at longitudinal modes which fall within the part of the bandwidth above threshold.

Intensity

Intensity to machine highthreshold material

Intensity which includes 84% of the laser power (spot diameter definition). Hole diameter for highthreshold material Hole diameter for moderatethreshold materia = spot radius Hole diameter for highthreshold material

Radius

Intensity to machine highthreshold material

Figure 3. Laser beam with a simple beam profile, illustrating how the feature size depends on the machining threshold relative to the laser intensity.

238

LASER BEAM MACHINING

This technique is used to narrow the bandwidth and is also used to tune the laser frequency. In most machining applications, the laser wavelength significantly affects the machining process because of the wavelength-dependent nature of the workpiece material’s absorption coefficient. However the bandwidth does not greatly affect the process because the absorption bands in most materials are relatively broad. Spectral bandwidth is important when the ultimate performance is required and when focusing or imaging a laser beam and chromatic aberrations must be minimized. The focal length of a simple singlet lens depends on the curvature of its surfaces and its refractive index. Because the refractive index is wavelength-dependent, the lens focal length is also wavelength-dependent. Photolithographic production of integrated circuits employs excimer lasers because their ultraviolet wavelengths permit higher resolution imaging. To attain the highest resolution, however, the laser bandwidth is narrowed from typically 1 nm down to a few picometers. Laser Beam Temporal Characteristics. Lasers produce continuous output or pulsed output. The pulse widths range from milliseconds to femtoseconds although usually a given laser or configuration is limited to a much narrower range of pulse widths. A laser is operated in one of four basic ways: continuous wave (CW), pump-pulsed or quasi-CW, Q-switched, or mode-locked (14). CW operation is possible with most but not all lasers. CW operation requires that the lifetime of the lower level of the laser transition is shorter than the lifetime of the upper laser level. If this is so, then electrons are quickly recycled to the upper laser level to maintain output with continuous energizing or pumping of the laser. Quasi-CW operation occurs when the laser is capable of CW operation but the pumping of the laser is pulsed. Typically this produces pulses of millisecond or microsecond length. The pulse repetition rate for such a device is usually in the range 1 Hz to 1000 Hz. Q-switching employs an intracavity shutter (often an electro-optic or acousto-optic device, rather than a mechanical device) to produce nanosecond length pulses. The laser is either pump-pulsed or continuously pumped. Initially the shutter is closed and, while the laser is pumped, the electron population inversion of the laser medium is built-up to a population resulting in a gain which greatly exceeds the laser threshold value. When the shutter is opened, the intracavity optical intensity increases very rapidly because of the high gain of the laser medium. The rapid increase in intensity quickly depopulates the upper laser level and, at some point, the gain is driven below the threshold value terminating the laser pulse. The resulting output pulse is usually very short, ranging from 1 to 1000 ns depending on the laser gain and cavity length. The pulse repetition rate is usually in the range of 1 Hz to 50,000 Hz. Certain lasers, such as the copper vapor laser and excimer laser, are inherently pulsed and produce pulse widths in the range of 10 to 100 ns. The inherent pulsed nature of these lasers greatly simplifies their design compared to Q-switched lasers. Modelocking is a technique in which an intracavity shutter is operated at the cavity round-trip frequency for laser radiation. This phase-locks the longitudinal modes, and the pulse width of the laser is then the Fourier transform of the longitudinal mode spectrum’s bandwidth. For a broad bandwidth la-

ser, such as titanium sapphire, the pulse widths are as short as 5 fs with a pulse repetition rate in the megahertz range. The pulse width and pulse repetition rate, along with other characteristics, such as laser wavelength and workpiece material characteristics, significantly influence the type of material interaction that occurs. Laser Beam Manipulation The output beam from most lasers is a collimated beam of several millimeter diameter, usually in the range of 2 mm to 20 mm for a machining laser. The intensity of the collimated beam is usually too low for most applications. The intensity at the workpiece is increased by focusing or imaging the beam with a lens or mirror. Although it is possible to machine small features directly with the laser beam, in many cases and especially for larger features, it is necessary to manipulate the laser beam or the workpiece or both. Beam manipulation techniques include focusing, imaging, and scanning. The beam is scanned by a variety of means including mirrors (galvo or piezo-driven), moving refractive optics (lenses and prisms), acousto-optic modulators, articulated mirror beam delivery systems, and fiber beam delivery. Practical examples of beam manipulation can be found in Refs. 2, 3. Focusing. The diameter w of a focused laser beam was given in Eq. (3). The equation assumes that the lens is aberration-free, that the lens is in the near field of the beam, and that the f-number of the lens is much less then the inverse of the divergence (1/ ␪). The general equation for the diameter of a beam at the focus of a lens (13) is given in Eq. (9) where the beam diameter at the lens is wL: w = (λ/π ){θ 2 + (wL / f )2 − (2λ/ f )[(πwθ )2 − 1]1/2 }−1/2

(9)

When the lens is in the near field of the beam, this equation simplifies to Eq. (10): w = f θ[1 + ( f θ/wL )2 ]1/2

(10)

When the f-number is much less than 1/ ␪, then Eq. (10) reduces to Eq. (3), and the focused beam is located at a distance f from the lens. Finally when the lens is placed in the far field of the beam, then Eq. (9) reduces to Eq. (11): w = (λ/π )[(wL / f ) − θ]1/2

(11)

Assuming that the lens f-number is small compared to 1/ ␪, then Eq. (11) simplifies to Eq. (12). w = λ f /πwL

(12)

Lens Aberration. Equations (9)–(12) assume an aberrationfree lens. If there is significant aberration, it is not usually possible to calculate the spot size exactly without using a raytracing software program. The common aberrations include spherical, astigmatism, coma, field curvature, distortion, and chromatic and are discussed in detail in Ref. 14e. Spherical aberration is caused by rays distant from the optical axis focused at a different distance from the lens than those closer to the axis. For a positive lens, the distant rays are focused closer, and, for a negative lens, the distant rays

LASER BEAM MACHINING

are focused further. Combining a positive lens made from a low refractive index glass and a negative lens made from a high index glass produces a combination in which the spherical aberration cancels but the focusing power does not. Astigmatism occurs when a lens effectively has two different focal lengths leading to a cylindrical component to the spherical lens. It is caused by a nonspherical curvature of the lens or because the lens is nonorthogonal to the optical axis. Coma results from different parts of a spherical lens surface exhibiting different degrees of magnification. This causes an off-axis imaged point to appear as a flare rather than a point. Field curvature is the tendency of optical systems to form an image on a curved surface rather than a flat plane. The field curvature varies with the square of the field angle or square of the image height. It is reduced by reducing the field angle. It is corrected to some extent by combining positive and negative lenses. Distortion occurs when a point in the object plane is focused to a point in the image plane but not to the correct axial position. Distortion usually increases with image height. It does not reduce the resolution of the optical system but does distort the shape of the image. Chromatic aberration results from the wavelength dependence of the focal length. This is only significant for a laser with broadband wavelength output. Optimum Focal Position. When optimizing the focusing of a laser beam, the first task is to choose the appropriate lens for the desired machined feature. In addition to this, it is necessary to choose or experimentally determine the optimum position of the focus relative to the surface of the workpiece. This position depends very much on what type of laser is being used, the workpiece material, and the desired effect. When the laser beam is focused on the surface of the workpiece, then the minimum surface spot size is achieved. At focus, the beam is collimated, that is, it is neither diverging or converging, as shown in Fig. 4. It can be seen from Fig. 4 that if the beam is not focused on the surface then as it enters the material it is diverging or converging. This affects the machining as the beam propagates further into the material. Except for very thin workpieces (typically less than 0.2 mm thick), then the workpiece is thicker than the distance over which the focused beam is approximately collimated (depth of focus). Therefore the user must consider the effect that the out-of focus beam has on the workpiece. For example, if the focus is placed at the surface to drill a hole, then, as the beam propagates into the workpiece (as material is removed by the laser beam), the laser beam expands. This initially causes the di-

Distance over which the laser beam is nominally collimated Figure 4. Propagation of a laser beam through focus. The distance over which the laser beam is nominally collimated is defined as the distance by which the diameter has increased by a factor 兹2 苵. This distance is known as the confocal parameter.

239

Laser

Beam conditioner

Mask Lens

Image

Figure 5. Typical optical configuration for a laser mask imaging system. Note that the image is inverted.

ameter of the hole below the surface to increase. However, for a typical Gaussian profiled beam, a point is reached at which the intensity of the beam near its outer diameter is reduced to a value below the machining threshold (see Fig. 3). At this stage the diameter of the hole starts to reduce. This continues until the hole breaks through the lower surface or machining ceases. In some cases, the user finds that it is possible to drill a parallel-sided hole whose depth is much greater than the depth of focus of the beam. The reasons for this behavior are complex, but it is most likely to occur by guiding the beam through the material by reflection and scatter from the hole wall or by balancing the beam expansion and machining threshold. Experimental evidence suggests that both mechanisms occur and can be used to advantage. For example, take a laser beam focused on the surface of a material where the laser is removing material in an ablative mode. If the laser power is high enough, it is possible to drill a hole whose diameter increases into the material, creating a hole with a negative taper (15). Now if the laser power is reduced a little, then it is possible to balance the beam expansion with the lower intensity and losses to produce a parallel-sided hole. Mask Imaging. Mask imaging is a technique whereby a laser beam illuminates a mask and an image of the mask is projected onto the workpiece. A typical mask imaging configuration is shown in Fig. 5. Through appropriate optical design, magnified or demagnified images are created. In most cases the image is demagnified. One advantage that mask imaging has over conventional focusing of beams is that the user easily chooses and adapts the shape of the beam to the workpiece. With conventional focusing, the beam at the workpiece is the Fourier transform of the beam at the lens, and therefore it is typically circular with a Gaussian profile. Although this is suitable for many applications, mask imaging opens a wider range of possibilities to the user. To get the best results and maximum benefit from mask imaging, however, the material must be removed only where the workpiece is exposed, that is, it must be a ‘‘cold’’ process in which material is removed through vaporization, ablation, or chemical means. If there is a large degree of melting the edges of the interaction

240

LASER BEAM MACHINING

zone blur. Thus the laser beam must be strongly absorbed by the workpiece and in most cases this requires a UV laser source. The most common type of UV machining laser is the excimer. These lasers use a rare gas-halide mixture as the gain medium. The usual gas mixes are XeCl, KrF, and ArF, which generate 308, 248, and 193 nm wavelengths, respectively. These short UV wavelengths are strongly absorbed by most materials including plastics, polymers, ceramics, diamond, and metals. In many materials the photon energy (inversely proportional to the laser wavelength) is high enough to break the atomic and molecular bonds of the workpiece material. Therefore the material is removed by photochemical dissociation. If the energy density greatly exceeds the machining threshold, then the excess energy introduces thermal input to the workpiece which leads to a loss in image definition. To achieve a uniformly machined depth, the mask must be uniformly illuminated. Most laser beams are not uniformly intense across their beam area. For example, many have a Gaussian intensity beam profile. Even lasers with a nominally uniform beam profile, such as the excimer, are not uniform enough. Therefore optical beam homogenizers are employed. In addition the laser beam area may need to be compressed or expanded to use the mask efficienctly. In Fig. 5, these units are represented by the beam conditioner module. The beam then illuminates the mask, an inverted triangle in this case. The mask is usually formed in a metal sheet or by etching/depositing a metal film on a silica substrate. The lens is placed some distance after the mask. This distance is called the ‘‘object distance’’ represented by the symbol s in Eq. (13). The distance from the lens to the image is the ‘‘image distance,’’ s⬙ in Eq. 13, and f is the focal length of the lens. 1/ f = 1/s + 1/s



(13)

The ratio of the image size h⬙ to the object size h, called the magnification, is given by Eq. (14): m = h

/h = s

/s

etched simultaneously is limited by the laser pulse energy and the energy density required for machining. A simple CNC program is then used to repeat this pattern over a larger area. If a direct-writing technique is used, then the CNC programming required to etch the feature and repeat it is more complex, although the optical set-up is more straightforward. When the laser wavelength is UV, then strong absorption means that the depth of absorption is shallow, typically in the range of 0.1 애m to 1 애m. Then it is possible to control the depth of the etch by using a fixed energy density and counting the number of laser pulses. In addition this technique is used to create 3-D structures in materials by overlapping images or changing the image as the depth of etch increases. Take, for example, a simple slit mask. If the workpiece is moved across the image plane, then, by programming the number of pulses per CNC position and the overlap of the image of the workpiece, the width of the etch as a function of depth is varied. An example is shown in Fig. 6. With some imaginative use of the mask and programming, complex shapes are generated. Some practical examples of mask imaging as applied to the marking of products can be found in Ref. 3. Diffractive Optics for Beam Shaping. Diffractive optics are a new class of optics that replace conventional optics or produce effects not readily achievable with conventional optics (16). The structure and propagation of a laser beam is determined by the spatial distribution of its amplitude, phase, and polarization. Diffractive optics modify the spatial amplitude and phase of a beam to effect some change. The modification to the amplitude and phase is produced by etching the surface of an optic with micron resolution. The beam shape after the beam has propagated a great distance is called the ‘‘far-field’’ beam profile or beam shape. This condition is also achieved at the focus of a lens. Diffractive optics usually produce farfield beam shapes. Because the beam shape in the far field is the Fourier transform of the near field, then, for a desired farfield pattern, computational techniques are used to calculate the near-field pattern. Then an optic is manufactured which

(14)

Typical values for m range from 0.05 to 1. The lens focal length is usually in the range 0.05 m to 0.2 m and so object distances are usually of the order 1 m. Because magnification values are often much less than unity, the mask is made without resorting to high precision micromachining techniques. Chemical etching and standard laser cutting techniques are often used to fabricate the mask. The depth of focus of a lens is the distance over which the image is acceptably sharp and within certain dimensional tolerances. These criteria are set by the user and depend very much on the application. Depth of focus increases with increasing f-number, where the f-number is the effective focal length divided by the system clear aperature. In many cases the depth of focus is just a few tens of microns or less and therefore mask imaging techniques are best suited to surface structuring or cutting/drilling very thin layers. Mask imaging techniques, when applicable, simplify the processing procedure and increase production rates. For example, if the workpiece requires reproducing a certain etched shape over the surface, this is achieved by using a mask with this shape repeated in it. The number of features that are

Mask

Lens

Workpiece Controlled depth machining by varying pulse number Figure 6. An example of 3-D machining by a mask imaging technique with step indexing of the workplace.

LASER BEAM MACHINING

produces the required near-field pattern. In addition to custom optics, a wide range of standard diffractive optics are available. These include transformation from Gaussian to tophat (super-Gaussian) and vice versa, transformation from Gaussian to an annulus or line or cross or square or arrays of dots. The efficiency of these devices is usually ⬎70% and is as high as 95%. This is much higher than is often achieved with a mask, and so diffractive optics are being adopted in certain applications. Adaptive Optics. Adaptive optics are optics, usually mirrors, that are deformed to modify the wave front (spatial phase distribution) of the beam. The mirror is usually deformed to a prescribed curvature with an array of piezo-actuators attached to the back face of the mirror. The advantages of this technique over diffractive optics are that the phase and hence far field of the beam is controlled from a PC in real time. Also the efficiency of the mirror should be ⬎99%. The disadvantage is that the technique cannot modify the amplitude of the wave front, and this limits the range of shapes and their definition. A description of an adaptive optic mirror can be found in Ref. 16a. Beam Scanning. The inertia of the workpiece and CNC tables limit the accelerations and velocities possible, especially for small movements. Optical deflection and scanning techniques achieve very high accelerations and velocities and are widely used in laser beam machining applications. The three techniques used conventionally are galvanometer-driven mirrors (galvo-mirrors), piezo-driven mirrors, and acousto-optic deflection. Galvo-mirrors are standard optical equipment widely used in industrial applications of lasers. The optical configuration usually includes two independent galvo-mirrors, one to scan the beam in the X direction and the other in the Y direction. The beam is then focused onto the workpiece with a flat field lens which maintains the focus over a scanned area up to 300 ⫻ 300 mm for laser machining applications, although the highest precision is achieved only over smaller areas. The most common use is in laser marking systems in which the galvo-mirrors scan the beam over an area of material to etch text or graphics (3). Typically such a system writes at 300 dpi over an area of a few cm2 in a few seconds. Very high accelerations and velocities (2 ms⫺1) are achieved while maintaining positional accuracy to within 5 애m. The step response time for a step change of a few degrees (equivalent to a few mm movement on the workpiece) is approximately 5 ms. This should be compared to a response time of 50 ms to 150 ms for a typical linear translational stage. The controls and programming of the galvo-mirror drivers are integrated with the host controller of the production machine. Galvo-mirrors are also used in drilling, cutting, welding, and soldering applications. After deflection by the mirror, the beam passes through the focusing lens. The angular deflection imparted to the beam becomes a positional change or displacement at the focus of the beam. The displacement is approximately equal to the product of the angular change and the focal length of the lens. This holds exactly when the angle is small and the beam

241

Lens D = F.A

A

Ray through center of lens at an angle A to the optic axis

F Focal plane

Figure 7. Rays passing through the center of a lens are not refracted.

passes through the center of the lens (Fig. 7) because elementary optics says that a ray traveling through the center of a lens is not refracted. Piezo-Driven Mirrors. The principle of operation is similar to that of the galvo-mirror system, that is, the beam is deflected by a mirror and then focused by a lens. For the piezodriven mirror, two piezo-actuators tilt the mirror in the X and Y directions, so that only a single mirror is required. The acceleration and velocities are similar to that of the galvo-mirror systems. However, the range of deflection is smaller but more precise. Therefore these systems are sometimes preferred for micromachining applications (16b). Acousto-Optic Deflection. Acousto-optic deflectors operate by producing a dynamic acoustic standing wave in an optically transmissive crystal via the piezo-electric effect (16c). The compression/decompression of the crystal generates a standing wave that produces a periodic variation in optical density which behaves as a diffraction grating. By varying the drive amplitude and frequency, the dynamic diffraction grating deflects the laser beam. Again this angular deflection is converted to a displacement at the focus of the lens. This is an attractive solution because there are no moving parts and the response is very fast. The disadvantages are the lower efficiency (typically 80%) compared to a mirror (⬎99% efficiency) and the restricted range of deflections achieved at certain wavelengths where the choice of appropriate crystals is limited. Beam Splitting. Beam splitting is used in laser beam machining to increase process speeds or spread the heat input into a component over a larger area. It is accomplished spatially or by amplitude. Spatial splitting is the simplest and is illustrated in Fig. 8(a). A mirror is inserted into the side of a beam and that part of the original beam is split off. The fraction split off is determined by the area of mirror presented to the beam relative to the original beam area. The disadvantages of this technique are that it is difficult to set the power in each beamlet exactly, the space occupied by the optics becomes large if more than a two-way split is required, and the change in dimensions of the beam changes the size and shape of the focused beam. Amplitude splitting of the beam is achieved with partially reflecting mirrors [Fig. 8(b)] or diffractive optics [Fig. 8(c)]. Although the concept of the partially reflecting mirror is simple, in practice it is difficult to attain the exact reflectivity

242

LASER BEAM MACHINING

Mirror (a)

Partially reflecting mirror

(b)

(c) Diffractive optic beam splitter Figure 8. (a) A mirror is partially inserted into the beam to split off a fraction of it. (b) Amplitude splitting using a partially reflecting mirror. (c) Schematic of a diffractive optic producing three beamlets.

required, especially when a larger number of beamlets is needed. For example, a four-way split requires three mirrors with reflectivities of 25, 33, and 50%, respectively. In addition it is difficult to fabricate a compact system. Diffractive beam splitting uses a custom-made optic which has a diffraction grating type pattern etched onto it. The pattern is optimized to create a finite number of orders (beamlets) with equal power in each order. The emerging beamlets are identical in size to the incoming beam and have an angular separation determined by the wavelength of the beam and the diffractive optic. The angular differences between the beamlets are converted to displacements in the focal plane of the focusing lens thereby creating a number of focused beams of equal intensity on a fixed pitch. The advantages of the diffractive optic are that it is extremely robust and simple to use. The disadvantages are the low efficiency (50% to 90%) and the high cost for custom designs. APPLICATIONS OF LASER BEAM MACHINING Surface Micromachining Surface micromachining is the etching, texturing, or milling of a surface with micron-scale resolution. Applications of these techniques are used in a wide range of industries. For example, etching creates channels and reservoirs for fluids.

Such features are used to aid lubricant delivery to specific components inside combustion engines. Another application is in the medical industry where microchannels and reservoirs are used in drug delivery systems (12). Similarly, excimer lasers are used to pattern and etch polyimides for use in desktop inkjet printers (11). Nd : YAG lasers (7) and copper vapor lasers are used to manufacture photovoltaic panels by scribing the large substrates into smaller panels. Isolation and connections between different layers are achieved through selective laser scribing steps. Lasers alter the topography of a surface removing material by ablation or reshaping it via melting. Surface texturing alters the appearance of a component (for cosmetic reasons) or modifies its characteristics. Texturing increases surface area for catalytic or voltaic reasons and modifies the flow of a fluid over the surface (as is done conventionally on a macroscopic scale on golf balls). Milling is an extension of the etching/scribing process whereby the small focal laser spot is scanned over the surface of a material to remove ‘‘bulk’’ material on a micron scale. This creates complex 3-D structures and could be used to take existing planar microelectronic fabrication technologies into a new dimension. Another use of laser milling is to replace a number of primary steps in the laser LIGA process by a single laser operation. LIGA is a German acronym for Lithographie Galvanoforming Abforming which translates as photoablation, metal deposition, and molding (12). An excimer laser ablates a master mold form in a polymer. This has a thin conductive coating applied using vapor deposition. Then electroforming makes a metal (nickel cobalt) mold which replicates the part in PMMA or polystyrene. Using a copper vapor laser or Nd : YAG laser and a milling technique, the master form is created directly in a metal substrate by laser ablation. Photolithography. Photolithography is used to fabricate integrated circuits on silicon. One of the drivers of this technology is the market demand for dynamic RAM (DRAM). Each year the manufacturers increase the memory capabilities of these chips by etching smaller and smaller features onto the wafer (9,10). In the photolithographic process, a light source illuminates a mask which is imaged onto a photoresist for subsequent chemical etching. The feature size produced is primarily governed by the lithographic resolution although a great deal of technology is also involved in optimizing the rest of the process such as the chemical etch. The lithographic resolution is proportional to the exposing wavelength and the numerical aperture of the projection lens. Consequently the illumination sources have changed from mercury g-line lamps (436 nm) to the i-line (365 nm) to deep UV sources (248 nm excimer laser) and even to X-ray sources. Although the X-ray source has significant advantages in terms of resolution by virtue of its wavelength, the excimer laser has a number of practical advantages for production use. The 250 nm features needed for 64 Mbit DRAM fabrication is resolved using i-line lithography but 248 nm excimer lasers are required for the 250 nm resolution for the 256 Mbit generation. The design of the projection lens is so critical that although chromatic aberrations could be compensated, to do so would be at the expense of some other parameter. Therefore the illuminating source must have a narrow bandwidth. In the case of the excimer laser this is possible but involves the use of additional

LASER BEAM MACHINING

intracavity components and is at the expense of output power. However, modern excimer lasers produce adequate power for this application, and this is anticipated to be a major application for these lasers. Microhole Drilling The requirement for microhole drilling is increasing in many industrial sectors (5,6,8,11,15). For example, in the electronics interconnect industry, the sizes of via holes in printed circuit boards are limiting the packing density of components on the boards and are currently the factor limiting miniaturization. Although high speed twist drills drill holes down to 100 애m, the cost of the drills is high, their lifetime is short, and the reliability in the process is poor. International legislation is forcing automotive manufacturers to produce cleaner burning engines. Lower emissions are achieved when the fuel is injected at higher pressure and this in turn demands smaller injection orifices. The orifice sizes (⬍140 애m) are now going beyond the limit of conventional drilling techniques (mechanical twist drill and wire electric discharge machining). Laser drilled holes are increasingly used in the aerospace industry as cooling holes in turbine blades, vanes, and combustion chamber liners. Designers are examining the use of small holes over the aerofoil to improve the laminar flow and hence improve the lift efficiency. The size (typically ⬍100 애m diameter) and number require high speed precision drilling for which the laser is the best solution. Laser drilling involves the removal of material by vaporization or melt expulsion. The simplest mechanism to model is vaporization. When the laser beam strikes the surface of the workpiece a fraction of the incident power is absorbed. This heats the workpiece and if the laser beam intensity is high enough, typically greater than 105 Wcm⫺2, vaporization occurs. Initially the workpiece surface reaches the vaporization temperature; if the laser continues to deliver more energy to the surface then the excess energy overcomes the latent heat of vaporization and material is removed as a vapor. The maximum depth that can be vaporized dmax using this model is expressed in Eq. (15). dmax = [(1 − R)E/Aρ][c p (Tv − T0 ) + Lv + L f ]

(15)

Equation (15) is a heat balance equation where R is the reflectivity of the workpiece surface, E is the laser pulse energy, A is the area of the laser beam on the workpiece, ␳ is the density, cp is the specific heat, Tv is the boiling temperature, T0 is the ambient temperature, Lv is the latent heat of vaporization per unit mass, and Lf is the latent heat of fusion per unit mass. Applying the above equation to nickel and using a 10J pulse from an Nd : YAG laser (wavelength of 1064 nm) focused to a spot of 10⫺3cm2, then the maximum hole depth is 1.4 mm. This value is in broad agreement with that observed experimentally. There are three basic laser drilling techniques; single-shot drilling, percussion drilling, and trepanning. As implied, single-shot drilling uses a single laser pulse to pierce the material and form the hole. Typically a Nd : YAG laser is used with a pulse energy of a few joules and a pulse width in the 0.1 ms to 5 ms range. The hole size is largely determined by the laser beam diameter when it hits the surface. The hole quality is quite poor but is adequate for some applications. The advan-

243

tage is that the drilling rate is high and is often performed ‘‘on-the-fly’’ because only a single pulse is used. Percussion drilling is similar except that several pulses are used. One or more may be required to pierce the material, and then an additional pulse is fired to remove debris from the hole and give it its final shape. The hole quality is better than with single-pulse drilling but the drilling rate is lower. The best hole quality is usually achieved by a trepanning technique in which the laser beam is used to cut out the hole. The laser beam is focused to a spot size much smaller than the hole diameter required and then the beam is moved relative to the workpiece to form the hole. Generally a large number of laser pulses is used. The hole quality and precision are greatly enhanced because of the large number of pulses used (a lower pulse energy is used and a smaller amount of material is removed per pulse). In addition the size and shape of the hole are now controlled by the relative movement of the beam and workpiece and this is effected more easily and precisely than manipulating the beam focal spot size. The copper vapor laser is ideal for precise drilling of microholes because of its deal laser parameters for this application (high beam quality, high peak power, high average power, low pulse energy, high pulse repetition rate, short pulse length, and visible wavelength). Micro Soldering Higher integration density of electronic circuits demands improved mounting technology. Because of the reduced contact area of surface-mount packages, sophisticated soldering systems are required to ensure product quality and yield. Standard reflow soldering techniques thermally damage sensitive devices and mechanical tension occurs in the solder joints. These problems are avoided with a laser because the amount of energy delivered is precisely controlled and accurately directed, so that the heat input to the component is minimized. The laser also offers the possibility of controlling the heat flow to each individual solder joint (17). Using a fiber optic beam delivery or scanning galvo-mirror system, the Nd : YAG laser is well suited to this task and similar tasks such as microspot welding. Laser soldering occurs when the laser energy absorbed by the solder surface melts the surface, and the melt front propagates inwards until the energy of the pulse is dissipated in the melt process. The melt process then stops and a resolidification from moves back towards the surface. For simplicity this model ignores energy which is dissipated into the components to be soldered. Assuming that the laser pulse has a square temporal profile of length t0, so that the incident power is either P0 or zero, then the temperature T of the materials at a depth z and time t is given by Eqs. (16,17), where ierfc is the integral of the complimentary error function.

T (z, t) = (1 − R){[2P0 (κt)]/K}ierfc(z/(2 (κt))

for t ≤ t0 (16)


√ √ T (z, t) =(1 − R)[[2P0 κ ]/K]{ t .ierfc[z/(2 (κt)]}

− (t − t0 ).ierfc{z/[2 κ (t − t0 )]} for t > t0

(17)

The energy required to melt an area of material A to depth d is given by Eq. (18). E = [c p (T f − T0 ) + L f ]ρπA2 d/[4(1 − R)]

(18)

244

LASER BEAM MACHINING

Further information on thermal modeling of these processes can be found in texts such as Refs. 17a and 17b.

Incoming laser beam

Welding As with laser soldering, welding benefits from the laser’s ability to precisely heat a certain area or volume of material. Lasers are used extensively for welding in the automotive industry because of their flexibility, precision and cost effectiveness (18). Laser welding is used in one of two ways, either conduction welding or keyhole welding. In conduction welding, the laser beam melts the surface of the metal to a depth determined by the heat input and conduction properties of the metal. This technique is limited to shallow welds because of the limited conduction depth. Keyhole welding is used for deep, high penetration welds. The impinging laser energy is concentrated by focusing the beam, and this heats the metal above its boiling point, forming a hole in the metal. The vaporized cavity is full of ionized metallic gas (plasma), trapping some 95% of the laser power in a cylindrical volume called a keyhole. Heat is transferred from the keyhole region outward rather than from the surface down, forming a molten region around the vapor. As the laser beam moves relative to the workpiece, the molten metals fills in behind the hole and solidifies, forming the weld. The process happens very rapidly so that welding speeds of several meters per minute are obtainable with minimal heating, a small heat affected zone, minimal thermal distortion, and limited residual stress. The keyhole enables high aspect ratio welds. In addition keyholing induces a stirring motion within the weld puddle. This allows gases to escape and provides low-porosity welds. The intense heat also lowers the impurity content and provides very rapid cooling rates, so that the resultant weld nugget has average tensile strengths equivalent to or greater than the parent material. Detailed discussions of the theory and practice of laser welding can be found in Refs. 2, 3, and 18a. The ability of high power CO2 lasers (1 to 20 kW) and high power Nd : YAG lasers (1 kW to 5 kW) to produce high integrity, deep welds at high speeds has enabled their uptake by automotive industry, replacing electron beam welding, which must operate in a vacuum and is sensitive to magnetic fields. Laser welders are used extensively in welding transmission gear assemblies, body panels, and other automotive components. They are used in the electronics industry to seal hermetic packages, spot-weld TV guns, and other structural components. An example of laser welding on a household item is the spot welds on the Gillette Sensor razor which attach the flexible blade to its support. Cutting Laser cutting is the largest application for industrial lasers accounting for about 40% of the industrial laser market. High speed cutting is usually performed by high-power CO2 or Nd : YAG lasers. The copper vapor laser is emerging as the leading candidate for precision cutting in micromachining applications on metals, ceramics, and diamond. High-speed laser cutting (using either CO2 or Nd : YAG lasers) is similar to laser welding except that a high-pressure (2 bar to 20 bar) assist gas removes the melted material, thereby forming a cut (2,19). The gas is delivered coaxially to the laser beam and removes the melt material by virtue of the gas pressure, blowing the material out of the bottom of the cut, or a

Assist gas inlet

Cutting direction Cut edge Molten layer

Gas delivery nozzle Cross section of workpiece Liquid material ejected from molten layer

Figure 9. Illustration of the coaxial-assist gas nozzle and laser-melt cutting process.

reactive gas, such as oxygen, is used which chemically reacts with the melt to aid decomposition. Figure 9 shows the gas nozzle for coaxial delivery of the gas and illustrates the cutting mechanism. Gas-assisted laser cutting uses a lens to focus the laser beam on the surface of a workpiece. The assist gas, introduced coaxially with the focused laser beam, blows the heated material away. When the cutting head or workpiece is moved, a kerf or cut is formed. This type of cutting is most often applied to metals and cuts thicknesses from 0.1 mm to 20 mm. With high-power lasers, cutting speeds of several meters per minute are achieved in moderate thicknesses (0.5 mm to 2 mm). However, this process does not lend itself to high precision cutting which is best accomplished by ablative material removal. Laser ablation usually refers to the direct removal of material through vaporization or the removal of molten material via an explosive ejection of the molten zone. The explosive ejection results from a very rapid rise in the temperature of the zone during irradiation and the consequent rapid rise in pressure which ejects the melt. This ablative process therefore requires a short laser pulse and high pulse repetition frequency produced by the copper vapor laser and some Nd : YAG lasers. PROCESS MONITORING Process monitoring keeps track of key parameters or influences in a machining operation to maintain the reproducibility of the production process. Although modern lasers are very reliable and their performance is reproducible, laser machining is complex and the results are subject to many influences including the laser, the environment, the workpiece material, the workpiece handling (CNC), and the skill of the operator. The process monitor is used to warn the operator of a problem or is part of a feedback system to actively control the process. One of the key laser parameters to control is the focus position of the laser beam relative to the workpiece surface. Nonuniformities in the flatness of the workpiece, CNC errors, or complex workpiece shapes all lead to focus errors. This in turn changes the laser spot size on the workpiece resulting in either too large a spot which does not have the required intensity for the process and is too large or too small a spot whose higher intensity damages the component or pro-

LASER BEAM MACHINING

duces too small a feature. The position of the workpiece relative to the focus is determined by various metrological means (height monitors) or by observing the effect that the focused intensity has on the laser-induced plasma or the acoustic noise generated. Some other examples of process monitoring and control can be found in Ref. 2. Height Monitors Many different height monitors have been developed and often it is necessary to tailor the device to the application. For example, in machining flat metal sheets, a capacitative monitor is used. The capacitance between a probe (which is attached to the assist gas nozzle) and the workpiece is measured. A calibration of the capacitance relative to the focus position is determined and used to monitor the process. This technique is simple and benefits from being noncontact. Commercial devices are readily available. Simple mechanical probes are also used but are not appropriate for thin, flexible, or soft materials. A range of optical techniques have also been developed. The most common uses a low-power pointing laser, such as a helium neon laser or semiconductor laser. This is directed at an angle onto the workpiece at or near the point to be machined by the main laser. The pointing beam is reflected off the surface of the workpiece onto a linear array detector. As the height of the workpiece changes, the position of the beam on the linear array changes. This technique is used on materials that are nonconductive and therefore cannot use the capacitative technique. However, a direct line of sight is required for the pointing laser and linear array onto the workpiece, and changes in the slope of the workpiece surface produce erroneous measurements. Laser-Induced Plasma Characteristics When a focused laser beam impinges on a workpiece, the high beam intensity and subsequent high temperatures induced in the workpiece produce an ion plasma above the workpiece surface. These ions emit electromagnetic radiation, usually in the UV, visible, and IR parts of the spectrum. Greater intensities generate higher plasma temperatures and therefore the plasma becomes more highly ionized or excited. This is observed as an increase in intensity of the shorter wavelengths emitted and an additional contribution of spectral lines from more highly ionized species. For example, at a given (moderate) intensity, blackbody radiation occurs and superimposed upon that are spectral lines of the neutral and singly ionized species of the workpiece. At higher intensities, additional lines from doubly ionized species are expected. For a fixed laser power, then, the intensity is a measure of the beam diameter and hence focal position. Acoustic Monitoring The acoustic noise generated by laser machining is also related to laser intensity at the workpiece. A low-intensity beam does not strongly interact with the material except to warm it. As the intensity increases and material is removed, then the acoustic noise increases. To the experienced operator, the sound of the machining is a useful diagnostic. However, a simple microphone and spectrum analyzer characterizes the acoustic emission as a function of laser intensity (focal position) and can be developed into a useful diagnostic.

245

Beam Profile Control The laser beam profile (spatial intensity distribution) is also an important parameter especially in micromachining applications where the beam shape is important in defining the machined feature. Laser beam profiles are readily measured by amplitude sampling the beam on-line via the leakage through a mirror or by the reflection off an appropriately coated optic. The sampled beam is focused or imaged onto a CCD which is coupled to a PC with image analysis software. This displays the beam profile in section, as an intensity map or isometric 3-D plot. Comparison of the beam profile against a standard is used to indicate alignment errors in the laser or beam delivery system. Alternatively the data could be fed to an adaptive optic to correct the laser beam profile in real time. BIBLIOGRAPHY 1. T. H. Maiman, Stimulated optical radiation in ruby. Nature, 187: 493–494, 1960. 2. W. M. Steen, Laser Material Processing, London: Springer-Verlag, 1991. 3. S. S. Charscham, Guide to Laser Materials Processing, Orlando: Laser Institute of America, 1993. 4. G. Chryssolouris, Laser Machining, Theory, and Practice, New York: Springer-Verlag, 1991. 5. S. A. Weiss, Think small: lasers complete in micromachining, Photonics Spectra, 29 (10): 108–114, 1995. 6. J. A. Morrison, Lasers and the fabrication of PWB vias, Industrial Laser Rev., 10 (11): 9–14, 1995. 7. J. Golden, Green lasers score good marks in semiconductor material processing. Laser Focus World, 28 (6): 75–88, 1992. 8. M. R. H. Knowles et al., Visualization of small hole drilling using a copper laser, Proc. ICALEO’94, Orlando, October 17–24, 79: 352–361, 1994. 9. H. Ito, Deep-UV resists: evolution and status, Solid State Technol., 39 (7): 164–173, 1996. 10. S. Wittekoeket al., New developments in wafer stepper technology for submicron devices, Proc. Optical Microlithography Metrology Microcircuit Fabrication, 1138: 2–13, 1989. 11. C. Rowan, Excimer lasers drill precise holes with higher yields, Laser Focus World, 31 (8): 81–83, 1995. 12. T. Lizotte, T. O’Keeffe, and J. Bruere, Micromachining with excimer lasers, Industrial Laser Rev., 12 (5): 11–14, 1997. 13. D. R. Hall and P. E. Jackson (eds.), The physics and technology of laser resonators, Bristol: Adam Hilger, 1989. 14. W. Koechner, Solid State Laser Engineering, Berlin: SpringerVerlag, 1988. 14a. A. E. Siegman, Lasers, University Science, Mill Valley, California, 1986. 14b. W. P. Latham and A. Kar, Laser optical quality, Proc. ICALEO 97, San Diego, Nov. 17–20, 82: A197–A206, 1997. 14c. A. Kar, J. E. Scott, and W. P. Latham, Effects of mode structure on three-dimensional laser heating due to single or multiple rectangular laser beams, J. Appl. Phys., 80: 667–674, 1996. 14d. J. Xie et al., Temperature dependent absorptivity and cutting capability of CO2, Nd : YAG and chemical oxygen-iodine lasers, J. Laser Applications, 9: 77–85, 1997. 14e. E. Hecht, Optics, Addison-Wesley, Reading, MA, 1987. 15. M. R. H. Knowles et al., Drilling of shallow angled holes in aerospace alloys using a copper laser, Proc. ICALEO’95, San Diego, November 13–16, 80: 321–330, 1995.

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16. M. R. Feldman and A. E. Erlich, Diffractive optics improve product design, Photonics Spectra, 29 (9): 115–120, 1995. 16a. R. Q. Fugate, The use of copper vapor lasers in guide-star applications, Proc. of the NATO Advanced Workshop on Pulsed Metal Vapour Lasers, St. Andrews August 6–10 1995, Kluwer Academic, Boston, MA, 1996. 16b. R. E. Warner et al., Industrial applications of high power copper vapour lasers, Proc. of the NATO Advanced Workshop on Pulsed Metal Vapour Lasers, St. Andrews, August 6–10 1995, Kluwer Academic, Boston, MA, 1996. 16c. M. Gottlieb, C. L. M. Ireland, and J. M. Ley, Electro-optic and acousto-optic scanning and deflection, Marcel Dekker, New York, 1983. 17. M. Hartmann, H. W. Bergmann, and R. Kupfer, Experimental investigations in laser microsoldering, Proc. Lasers Microelectronic Manufacturing, SPIE, 1598: 175–185, 1991. 17a. M. Bass (ed.), Laser Materials Processing, North Holland, Amsterdam, 1983. 17b. A. M. Prokhorov et al., Laser heating of metals, Adam Hilger, IOP Publishing, New York, 1990. 18. D. Havrilla and T. Webber, Laser welding takes the lead, Lasers Optronics, 10 (3): 30–40, 1991. 18a. N. Rykalin, A. Uglov, and A. Kokora, Laser machining and welding (English edition), MIR Publishers, Moscow, 1978. 19. J. Powell, CO2 Laser Cutting, London: Springer-Verlag, 1993.

MARTYN R. H. KNOWLES GIDEON FOSTER–TURNER KEITH ERREY ANDREW J. KEARSLEY Oxford Lasers Ltd.

LASER CAVITY RESONATORS. See LASER BEAM MACHINING.

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Wiley Encyclopedia of Electrical and Electronics Engineering Micromechanical Resonators Standard Article S. P. Beeby1 and M. J. Tudor1 1School of Electronics and Computer Science, University of Southampton, England Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4603 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (278K)

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Abstract The sections in this article are Introduction Micromechanical Resonators Micromechanical Resonator Materials Resonant Silicon Sensors Comparison of Silicon Sensing Technologies Vibration Excitation and Detection Mechanisms Theory of Resonance Quality Factor Non Linear Behavior Hysteresis

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MICROMECHANICAL RESONATORS RESONANT SENSORS SILICON SENSORS

INTRODUCTION Micromechanical resonators have been used for several years as a timebase in electronic and mechanical systems and as a sensing element for a wide range of applications such as pressure sensing and rotation (gyroscope). This article details the basic principles of resonant sensing and reviews the fundamentals involved in designing a micromechanical resonator. The various materials previously used to realize miniature resonant transducers are discussed after which the article concentrates on micromachined silicon resonators. As explained in the article, the fact single crystal silicon is not piezoelectric means alternative methods of exciting and detecting the resonator’s vibrations must be fabricated as an integral part of the device. Various mechanisms can be used and these are reviewed in detail. The quality factor of a micromechanical resonator is a figure of merit describing its resonance. The importance of the quality factor and the damping effects that limit it are discussed enabling the reader to gain an in depth knowledge of the design principles involved. Other important resonator behavioral characteristics such as non linear behavior are also included. The references present a survey of key resonant silicon sensors developed to date enabling the reader to access a full background to the technology. MICROMECHANICAL RESONATORS A resonator is a mechanical structure designed to vibrate at its resonant frequency. Micromechanical resonators are miniature structures with dimensions typically varying from submicron to a few hundred microns. The structure can be as simple as a cantilever beam, a fixed-fixed beam clamped at each end or a tuning fork. The frequency of the vibrations of the structure at resonance are extremely stable enabling the resonator to be used as a time base (the quartz tuning fork in watches for example), or as the sensing element of a resonant sensor. In each application the behavior of the resonator is of fundamental importance to the performance of the device. A resonant sensor is designed such that the resonator’s natural frequency is a function of the measurand (1, 2). The measurand typically alters the stiffness, mass or shape of the resonator hence causing a change in its resonant frequency. The other major components of a resonant sensor are the vibration drive and detection mechanisms. The drive mechanism excites the vibrations in the structure whilst the detection mechanism “picks up” these vibrations. The frequency of the detected vibration forms the output of the sensor and this signal is also fed back to the

drive mechanism via an amplifier maintaining the structure at resonance over the entire measurand range. A typical resonant sensor is shown diagrammatically in Figure 1. The most common coupling mechanism is for the resonator to be stressed in some manner by the action of the measurand. The applied stress effectively increases the stiffness of the structure which results in an increase in the resonator’s natural frequency. This principle is commonly applied in force sensors (3), pressure transducers (4) and accelerometers (5). Coupling the measurand to the mass of the resonator can be achieved by surrounding the structure by a liquid or gas, or by contact with small solid masses. The presence of the surrounding media increases the effective inertia of the resonator and lowers its resonant frequency. Densitometers and level sensors are examples of mass coupled resonant sensors (1). One example of coupling to the resonator via the shape effect is a micromachined silicon pressure sensor which uses a hollow, square diaphragm supported at the midpoints of each edge as the resonator (6). The internal cavity within the diaphragm allows each side to be squeezed as applied pressure increases which alters the curvature of the diaphragm in turn altering its resonant frequency. MICROMECHANICAL RESONATOR MATERIALS Since the design and behavior of the resonator is a major influence on the performance of the sensor, the properties of the material from which it is constructed are of fundamental importance. This section discusses the suitability of some common materials used to fabricate micromechanical resonators: silicon, polysilicon and quartz and gallium arsenide. The material properties of these materials are given in Table 1. Single crystal silicon Silicon is a single crystal material possessing a face centered diamond cubic structure. Silicon atoms are covalently bonded with 4 atoms bonded together forming a tetrahedron. As these tetrahedra combine they form a large cube or unit cell as shown in Figure 2. It is an anisotropic material with many of its physical properties, such as Young’s Modulus, varying with the crystalline direction. Directions and planes within silicon are identified using the Miller Indices. The indices use the principle axes within the crystal and the form of bracket to denote each feature. For example (111) denotes a particular plane that bisects the x, y and z axes at 1, as shown in Figure 2. An important feature of silicon is that it remains elastic up to fracture exhibiting no plastic behavior and therefore no hysteresis. This is an ideal material characteristic for resonant structures, since any plastic deformation would permanently alter the shape, and therefore resonant frequency, of the structure. Single crystal silicon is also intrinsically very strong. Given the fact it is elastic to fracture, the practical strength of silicon is however extremely dependent upon the number and size of crystalline defects, and the quality of the surface. Given silicon wafers with a low level of defects, sensible structural design, careful han-

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright © 2007 John Wiley & Sons, Inc.

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Figure 1. Block diagram of resonant sensor layout Table 1. Material properties for common resonator materials

Silicon Quartz1 Stainless Steel GaAs

a

Young’s Modulus (N/m2 ) 1.9 × 1011 9.7 × 1010 2 × 1011 8.53 × 1010

Fracture Strength (N/m2 ) 7 × 109

Density (kg/m3 ) 2330

Thermal Expansion (10−6 /◦ C) 2.33

Thermal Conductivity (W/cm ◦ C) 1.57

8.4 × 109

2650

0.55

0.014

2.1 × 109 2.7 × 109

7900 5360

17.3 6.4

0.329 0.44

Values given for Z cut quartz

Figure 2. Diamond cubic unit cell and the (111) plane

dling and processing, strengths close to intrinsic and far in excess of alloyed steels can be obtained. The mechanical fatigue characteristics of silicon are also excellent. Fatigue can result in structures fracturing at applied stresses much lower than should otherwise cause such failure. Fatigue failure begins at a microscopic level with a minute defect or crack in the material which propagates due to fluctuating applied stresses. The varying stresses caused by the flexural vibrations of a resonating structure would be a typical environment for such fatigue to occur.

Other important favorable considerations include the low temperature cross sensitivity of resonant frequency, being measured at -29ppm/◦ C (7). The long term stability of silicon resonators have also been tested in numerous applications, and these results show no significant frequency shift over long periods of time (8). Silicon wafers are readily available in a variety of sizes, currently from 50 mm to 300 mm in diameter. Wafers are relatively cheap in their basic form, especially considering that hundreds of devices can be realized on each wafer. Standard wafers are avail-

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Figure 3. Quartz tuning fork resonator vibrating in a torsional mode

able in two forms distinguished by the crystal plane from which the wafer is cut, the most common wafer orientation being (100). More expensive wafers are available that include buried layers of silicon dioxide and these are useful for the fabrication of many types of micromachined devices, including resonant sensors. A drawback associated with silicon with regard to its application as a resonator material is that it is not piezoelectric. When as voltage is applied to a piezoelectric material it deforms, and when it is forced to deform a potential gradient is generated. Piezoelectric behavior is ideal for exciting and detecting vibrations. In order to excite and detect vibrations in silicon resonators, alternative mechanisms such as electrostatic forces or thermal effects have to be employed. Whilst their use is well established, it does however complicate the fabrication of the resonator in comparison to similar structures fabricated from a piezoelectric material such as quartz. Polysilicon Polysilicon is an alternative material suitable for resonator fabrication and, as with single crystal silicon, much of the process development for polysilicon has been carried out by the semiconductor industry. It is often used where electronics are being integrated on the sensor chip due to the compatibility of the fabrication processes. In many applications, however, the material properties required for polysilicon micromechanical devices are different to those required in the fabrication of microelectronic devices. This is especially true in the case of resonant sensing where the mechanical properties of the polysilicon will play a vital role in sensor performance. Also reproducibility and repeatability of these properties is essential. Polysilicon is a film of silicon atoms deposited upon the top surface of a substrate typically using chemical vapor deposition (CVD) processes. The film either has a granular or amorphous structure depending upon the process parameter. In the case of resonator applications, the film is typically deposited on a sacrificial layer of silicon dioxide. The polysilicon layer is then patterned and the sacrificial layer removed to leave the freestanding resonant structure. This is called surface micromachining. The deposition process is of prime importance in determining the resulting mechanical properties of the deposited film. Process parameters such as substrate temper-

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ature, gas flow rate, deposition rate, deposition pressure and reactor design all affect the structure and behavior of the film. Another key factor affecting the performance of a resonator fabricated from polysilicon is the amount of residual stress built into in the layer during deposition. Residual stresses result from thermal expansion coefficient mismatches between the film and substrate, and also from the grain growth process which can trap atoms in positions that induce stress in the lattice. For resonant structures such stresses will naturally alter the performance of the device and will make prior modeling inaccurate. Residual stresses can be controlled and reduced by annealing the deposited films. The mechanical properties of polysilicon will vary depending upon the process parameters, but general values have been reported for Poisson’s ratio, Young’s Modulus and tensile strength of 0.226, 1.75 ± 0.21 × 1011 Nm−2 and 1 × 109 Nm−2 respectively (9). The long term stability of the material is reported to be good, with resonators fabricated in polysilicon being tested over 7000 hours of temperature cycling showing no detectable change in resonant frequency. Also, no signs of fatigue failure have been reported. Such polysilicon films are well suited to resonant sensor design as long as residual stresses are controlled. The repeatability of the film’s properties will also be an important consideration when attempting to mass produce a resonant silicon sensor. Like single crystal silicon, polysilicon is not piezoelectric and vibration excitation and detection mechanisms must be fabricated at wafer level. Quartz The application of quartz as a resonant sensor material has evolved from its use as a crystal control for oscillating circuits. Quartz crystals were first used in radio communications equipment and now can be widely found in many applications, most noticeably as the timebase in clocks and watches (10). An important quality of quartz is its piezoelectric behavior. Piezoelectric materials deform when an electric field is applied and conversely generate a potential field when forced to deform. Quartz is a piezoelectric material because it possesses groups of atoms with an unbalanced charge, these being known as dipoles. These dipoles are permanently orientated in the same direction and quartz is therefore permanently polarized. When external stress is applied to the material its crystal structure is deformed. This deformation shifts the dipoles changing the polarization of the material and inducing a voltage in the process. Conversely, if an external voltage is applied to the crystal the orientation of the dipoles is changed deforming the crystal structure. Silicon is not piezoelectric because it possesses a covalently bonded symmetrical structure and therefore has no dipoles. Quartz resonators employ the piezoelectric effect to excite the vibrations of the resonant structure. An applied alternating electric field will produce strain in alternating directions and this is a very simple way of exciting vibrations. A quartz resonator consists of a precisely dimensioned resonant structure with electrodes patterned on its surface. The nature of the vibration excited by the applied field depends upon the geometry of the resonator, its crystalline

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orientation and the electrode pattern (11). Resonators can be designed so that torsional vibrations can also be simply excited. Torsional vibrations are advantageous since they suffer less damping effects within the material. Quartz possesses many other attractive features. It has excellent stability and long term aging characteristics. It possesses excellent material properties and resonators can be to batch fabricated using photolithographic techniques similar to those used in silicon. It also benefits from very low temperature cross sensitivity in certain crystal orientations. The main drawbacks of quartz when compared to silicon revolve around its fabrication technology and the fact integrated circuitry cannot be formed on the sensor chip. Also quartz wafers are more expensive than silicon wafers. Nevertheless, quartz in an excellent resonator material and a wide range of quartz resonant sensors exist. Applications include sensing temperature, thin film thickness, force, pressure and fluid density.

Figure 4. Resonant pressure sensor configuration

Gallium Arsenide

RESONANT SILICON SENSORS

Gallium arsenide (GaAs) is used in the semiconductor industry for high frequency, high temperature (>125 ◦ C) electronic and opto-electronic applications. As with silicon, the development of the material for these applications has benefited the microengineering community. It is especially well suited to resonant sensing applications since it is piezoelectric and electronic circuitry can also be integrated onto the sensor chip. It may therefore be considered to combine the benefits of quartz and silicon as a resonator material. GaAs atoms are arranged in a zincblende crystal structure and are held in place by ionic bonds. The presence of the arsenide atoms in the lattice draws the electrons and this results in dipoles orientated along the directions (12). These dipoles result in the piezoelectric nature of GaAs. As with quartz, longitudinal, flexural, torsional and shear vibrations can be excited piezoelectrically and this makes it well suited for resonant applications. GaAs is a brittle material and, as with silicon, its mechanical strength will ultimately depend the presence of stress concentrating defects. GaAs wafers contain more crystalline defects than single crystal silicon wafers, and structures will therefore not be as strong as their silicon counterparts. Tests have been carried out on GaAs cantilever beams which failed at 2.7 GNm−2 (13), whilst this is well below the values obtained for silicon structures it is nevertheless stronger than steel. There are a wide range of micromachining techniques available including various wet and dry etches, bonding, and selective etch stops. Structures can also be fabricated on GaAs substrates using thin films of aluminum gallium arsenide (AlGaAs) and sacrificial layers as described in the case of polysilicon structures (14). Internal stresses mainly due to thermal mismatches are however a problem with this technique. There are certainly many more micromachining options available for GaAs resonant sensors than for their quartz counterparts. The main drawbacks associated with GaAs as a microresonator material result from the increased costs involved in its use. GaAs wafers are more expensive than silicon

The mechanical properties of the pure silicon wafers used in the fabrication of integrated circuits and the ability to form microstructures using some of the processes developed by the semiconductor industry, has enabled silicon to be used in a variety of microengineered devices. At the forefront of such microengineered devices are silicon sensors, including resonant silicon sensors. In the case of micromachined silicon resonant sensors, the resonator can be fabricated from silicon and the vibration drive and detection mechanisms fabricated on, or adjacent to, the resonator. The resonator is then located in a silicon structure specifically designed for the sensing application. This is illustrated by the approach used in the design of the majority of resonant silicon pressure sensors where the resonator is fabricated on the top surface of a silicon diaphragm (see figure 4). In such a case the resonator is being used as a strain gauge sensing the strain induced due to the deformation of the diaphragm caused by an applied pressure (15). The use of silicon overcomes the major disadvantage of traditional resonant sensors, namely the manual fabrication of individual resonating elements. Fabricating the sensor in silicon enables the resonator to be batch fabricated and hundreds of devices can be realized on each silicon wafer simultaneously. The wafers themselves can also be processed simultaneously in the majority of the fabrication steps.

wafers and processing costs are also higher than for the equivalent silicon operation. Silicon also possesses a much wider range of processes. Silicon and Quartz are also well characterized materials and their use as resonator materials is long-standing and fully documented. The use of gallium arsenide in MEMS applications is still relatively uncommon.

COMPARISON OF SILICON SENSING TECHNOLOGIES Silicon strain sensors monitoring deflections in the sensor structure can employ piezoresistive, capacitive or resonant sensing techniques. Of these, resonant sensing is inherently the more complex approach. This is highlighted by the fact the vibration excitation and detection mechanisms are commonly based upon piezoresistive or capacitive techniques. However, the typical performance figures for the three strain sensing techniques listed in

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Table 2. Performance features of resonant, piezoresistive and capacitive sensing Feature Output Form Resolution Accuracy Power consumption Temperature cross sensitivity

Resonant Frequency 1 part in 108 100–1000 ppm 0.1–10 mW −30 × 10−6 /◦ C

Piezoresistive Voltage 1 part in 105 500–10000 ppm ≈ 10 mW −1600 × 10−6 /◦ C

table 2 clearly show the advantages resonant sensing offers.

VIBRATION EXCITATION AND DETECTION MECHANISMS There are many potential vibration excitation and detection mechanisms possible in silicon. Many of the mechanisms listed below can be used to both excite and detect a resonator’s vibrations, either simultaneously or in conjunction with another mechanism. Devices where a single element combines the excitation and detection of the vibrations in the structure are termed one-port resonators. Devices which use separate elements are termed two-port resonators. The choice of mechanism for driving or detecting a resonator’s vibrations depends upon several important factors. These factors include the magnitude of the drive forces generated, the coupling factor (or drive efficiency), sensitivity of the detection mechanism, the effects of the chosen mechanism upon the performance and behavior of the resonator and practical considerations pertaining to the fabrication of the resonator and the sensor’s final environment.

Capacitive Voltage 1 part in 104 –105 100–10000 ppm < 0.1 mW 4 × 10−6 /◦ C

Piezoelectric excitation and detection This approach uses a deposited layer of piezoelectric material to both excite and detect the resonator’s vibrations (20). The piezoelectric material, typically zinc oxide (ZnO), is formed in a sandwich between two electrodes creating a piezoelectric bimorph. Applying an oscillating voltage to the bimorph causes periodic deformation thereby exciting the resonator. Detection is provided by the corresponding potential generated by the deformation in the bimorph. The piezoelectric bimorph is formed and patterned on the resonator surface in a manner similar to the dielectric electrostatic mechanism. Magnetic excitation and detection This technique places a current carrying resonator in a permanent magnetic field, the excitation being due to Lorenz forces acting upon the resonator. Applying an alternating current to the resonator results in alternating forces and hence vibrations are induced in the resonator. The associated detection mechanism utilizes the change in magnetic flux caused by the resonator moving in the magnetic field (21). Electrothermal excitation

Electrostatic excitation and detection The electrostatic excitation of a resonator relies upon electrostatic forces between two plates. These plates may be separated either by an air gap with one plate being located upon the resonator and the other located on the surrounding structure. Alternatively a three layer sandwich can be formed on resonator’s surface consisting of two electrodes separated by a dielectric layer. The associated vibration detection mechanism relies upon the change of capacitance between the electrodes as the resonator deflects. One drawback to be considered when using the dielectric sandwich on the resonator surface is the increase in the temperature cross-sensitivity of the resonator. Lateral vibrations in the plane of the wafer have also been excited using the electrostatic mechanism combined with a comb structure (16). The resonator must be designed with suitable comb fingers that align with comb fingers fabricated adjacent to the resonator. The resonator is typically fabricated from polysilicon on the top surface of the wafer. One port resonators using the same pair of electrodes to both excite and detect vibrations (17), or two port configurations using separate electrode pairs (18) have both been achieved. Electrostatic excitation is also commonly used alongside alternative vibration detection techniques e.g. piezoresistive (19).

This approach relies upon the heating effect caused by passing a current through a patterned resistor located on the surface of the resonator. The heat energy generated causes a thermal gradient across the resonator’s thickness, with the top surface at a higher temperature than the bottom. The induced thermal expansion of the material results in a bending moment on the resonator thereby deforming the structure. Vibrations can simply be excited by modulating the current through the resistor. Electrothermal excitation is widely used and can be found on many resonant devices. Optothermal excitation The thermal drive technique described above can also achieved using the heating effect resulting from a light source incident on the resonator. Modulating the light source will result in periodic thermal expansion on the surface of the resonator and hence induce vibrations in the structure (22). The light source is commonly aligned over the resonator using an optical fiber and this method can be conveniently used in conjunction with optical vibration detection techniques. Optical methods can also be used to obtain self oscillation of the resonator using unmodulated light (23). The unmodulated light source is directed on to the resonator via an optical fiber, the end of which forms a Fabry Perot

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interferometer with the reflective surface of the silicon resonator. The interferometer output varies as a function of the resonator’s displacement and this has the effect of modulating the incident light as the resonator vibrates. It is however difficult to sustain these vibrations and it requires critical and stable alignment of the fiber. Optical excitation techniques are attractive since they enable a passive resonant structure with no on chip excitation mechanisms required. The use of optical fibres is compatible with miniature nature of micromachined silicon devices they are immune to electromagnetic interference can allow resonant silicon sensors to be used in harsh, high temperature environments. However the accurate integration and alignment of the optical fiber onto the sensor chip is difficult to achieve, especially in mass produced sensors. Optical detection There are several optical detection techniques suitable for monitoring the vibrations of a resonator. This approach was developed using optical fibre to couple the light to the resonator which enabled it to be readily combined with the optical drive mechanisms. More recently, advances in onchip waveguides offer the potential for incorporating optical detection mechanisms at wafer level, albeit light still has to be coupled in from an external source in the devices demonstrated (24). Interferometric techniques rely upon two interfering reflections, one from a fixed reference and the other from the vibrating resonator. The combination of the reflected light results in interference fringes the number of which gives a direct measure of the amplitude of displacement. Intensity modulation techniques use changes in the intensity of the reflected light to monitor the amplitude of the resonator vibrations. The reflections can be modulated for example by the angular displacement of the resonator as it vibrates. Piezoresistive Detection This uses the inherent piezoresistive nature of silicon to detect the vibrations of the resonator. Resistors can be fabricated by diffusing or implanting them into the silicon, or by depositing polysilicon resistors on the top surface of the resonator. The resistor can simply be connected in a Wheatstone bridge circuit, the value of the resistor varying as the resonator vibrates. The frequency of the changing resistance forms the output of the sensor and hence the actual value of the resistance and the behavior of the resistor becomes largely unimportant. This approach is simple to achieve being widely used in many resonant sensors (25), is compatible with integrated circuit fabrication techniques, and can be readily used either with electrothermal excitation or an alternative drive excitation mechanism such as electrostatic. THEORY OF RESONANCE In order to understand resonance the propagation of mechanical waves within a solid must be understood. A mechanical wave may be defined as the propagation of a physi-

cal quantity (e.g. energy or strain) through a medium (solid or fluid) without the net movement of the medium. As the wave travels through the medium particles are displaced from their equilibrium position thereby distorting the medium. The form of the wave will depend upon the nature of its source and the material through which it travels. The speed of a wave in a solid is dependent upon the mechanical properties of the material, and its wavelength is a function of the frequency of the wave source. As the wave travels through a solid it can meet boundaries or regions of non-uniformity of material or geometrical form. Upon meeting such discontinuities the nature of the wave will be changed due to phenomena known as refraction, diffraction, reflection and scattering. When considering the phenomena of natural frequencies and resonance, reflection of a mechanical wave at a system boundary becomes important. Reflection is the reversal in direction of the wave back along its original path. If the reflected wave exactly coincides with the incoming wave then a standing wave is created. The superposition of these waves results in the amplitude of each wave combining to become twice that of the initial wave. Taking a string fixed at each end as an example, a mechanical wave will be reflected back from the fixed boundary at each end. The standing wave phenomena will occur at specific frequencies known as the natural, or modal, frequencies of the fixed-fixed string. For each natural frequency, the string will have a characteristic distorted form, or mode shape as shown in figure 5. These are the modes of vibration of the string and also the mode shapes associated with a fixedfixed beam. Points of zero displacement are called nodes whilst the points of maximum displacement are known as antinodes. The amplitude of the standing waves will decline with time due to damping effects in the system. The amplitude will be maintained however if the wave source, for example a harmonic driving force, at that frequency is maintained. If a harmonic driving force is applied to a system and a mode of vibration is excited, then the system is in resonance. Resonance will occur when the frequency of the driving force matches the natural frequency of the system. Resonance is a phenomena associated with forced vibrations whilst natural frequencies are associated with free vibrations. The motion of the oscillating body will not usually be in phase with the driving force. When resonance has occurred the motion of the oscillating body will lag the driving force by a phase angle of π/2. QUALITY FACTOR As a structure approaches resonance the amplitude of its vibration will increase, its resonant frequency being defined as the point of maximum amplitude. The magnitude of this amplitude will ultimately be limited by the damping effects acting on the system. The level of damping present in a system can be defined by its Quality Factor (Q-factor). The Q-factor is a ratio of the total energy stored in the system to the energy lost per cycle due to the damping effects present: Q = 2π(maximum stored energy/energy lost per cycle) (1)

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From equation (1) it is clear the Q-factor is limited by the various mechanisms by which energy is lost from the resonator. These damping mechanisms arise from a number of sources identified in the equation below: Q=(

1 1 1 1 1 −1 + + + + ) Qm Qt Qc Qsu Qf

(3)

where: 1/Qm is the dissipation arising from the material loss, 1/Qt is the dissipation arising from the thermoelastic loss, 1/Qc is the dissipation arising from the clamping loss, 1/Qsu is the dissipation arising from the surface loss, 1/Qf is the dissipation arising from the surrounding fluid, Minimizing these effects will maximize the Q-factor.

Figure 5. First 4 modes of vibration of a fixed-fixed string

In addition: 1 1 1 1 = + + Qf Qv Qa Qs f

(4)

where: 1/Qv is the dissipation arising from the viscous or molecular region loss, 1/Qa is the dissipation arising from the acoustic radiation loss, 1/Qsf is the dissipation arising from the squeeze film loss. These various damping effect in resonators are now discussed in turn. Figure 6. Typical amplitude frequency relationship

Material derived losses A high Q factor indicates a pronounced resonance easily distinguishable from non resonant vibrations, as illustrated in Figure 6. Increasing the sharpness of the resonance enables the resonant frequency to be more clearly defined and will improve the performance and resolution of the resonator. It will also simplify the operating electronics since the magnitude of the signal from the vibration detection mechanism will be greater than that of a low Q system. A high Q means little energy is required to maintain the resonance at constant amplitude thereby broadening the range of possible drive mechanisms to include weaker techniques. A high Q factor also implies the resonant structure is well isolated from its surroundings and therefore the influence of external factors, e.g. vibrations, will be minimized. The Q-factor can also be calculated from: Q=

f0 f

(2)

Where resonant frequency fo corresponds with amax , the maximum amplitude, and f is the difference between frequencies f1 and f2 . Frequencies f1 and f2 correspond to amplitudes of vibration 3dB lower than amax .

Movement of dislocations and scattering by impurities. A dislocation is an imperfection within the crystal lattice and these fall into two categories, edge or screw dislocations. Attenuation of the resonator vibrations can occur due to movement of these dislocations. The magnitude of such losses depends upon the number of dislocations, the resonator’s frequency and temperature. Only at higher temperatures (>150 ◦ C) is there sufficient energy present to move the dislocations. Also silicon is available in a very pure form and typical wafers contain a very low number of dislocations. Given likely operating temperature ranges and the low dislocation density this form of internal damping can effectively be ignored in silicon resonators. Impurities are foreign atoms either inadvertently trapped in the lattice during crystal growth or intentionally added during the fabrication process. The presence of these impurities can result in point defects within the lattice introducing regions of inelastic scattering of the structural wave within the solid and thus causing energy to be lost within the material. The levels of impurities present within silicon are low and they have been shown to have negligible effect below 200 ◦ C (26). This effect can therefore also be ignored for typical device operating conditions.

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Phonon interaction. Each atom contained within the crystal lattice vibrates, due to thermal energy, about a mean position. When determining the heat capacity and thermal conductivity of the solid, these atomic vibrations are viewed collectively as a series of traveling lattice waves known as phonons (27). These phonons are subject to the scattering effect of, and they can also be similarly scattered by, variations in the lattice strain field due to the presence of other phonons. This is known as phonon-phonon interaction. The mechanical wave forming the structure’s resonance can hence interact with variations in the strain field due to the presence of phonons. This results in the acoustic energy being converted to thermal energy, i.e. phonons are created. Akheiser loss (28, 29). At lower frequencies Akheiser theory must be used to analyze the damping effects of phonons upon the mechanical wave. The thermal phonons within the material are analyzed as a gas described by a number of macroscopic parameters. The energy loss mechanism arises from the influence of the structural wave of the resonator on the phonon gas. The structural wave of the resonator will introduce fluctuations in the strain field of the material causing a modulation of the phonons. The modulated phonons collide with each other, and with impurities, and this has the effect of throwing the phonon gas out of equilibrium. This is an irreversible process and therefore energy is lost from the resonator’s vibrations. Thermoelastic effect Flexural vibrations of a resonator lead to cyclic stressing of its top and bottom surfaces. The majority of the energy employed in displacing the beam is stored elasticity but some of the work is also converted into thermal energy. Material on the surface in compression will rise in temperature whilst the surface in tension falls in temperature. Hence a temperature gradient is formed across the thickness of the beam. If the deformation is maintained for a sufficient length of time, heat energy will flow across the gradient in order to equilibrate the system. Any thermal energy transferred in this manner is lost to entropy and the resonator’s vibrations are attenuated. The magnitude of this effect is dependent upon the mechanical properties of the resonator material, temperature and the resonant frequency. The damping fraction (δ=1/2Q) can be expressed as a product of two different functions, (T) and (F) (30): δ = (T )(F )

(5)

a TE 4ρC

(6)

(T ) = (F ) = 2[

2

Fo F ] + F2

Fo2

where α is the thermal expansion coefficient T is beam temperature E is Young’s Modulus ρ is material density

(7)

Figure 7. Formation of transverse wave

C is specific heat capacity F is resonant frequency Fo is the characteristic damping frequency given by: Fo =

πK 2ρCt 2

(8)

where t represents the beam thickness K is the thermal conductivity of the resonator material This form of damping can be reduced by designing a structure with a resonant frequency removed from Fo . Shear deformation, associated with torsional modes, does not suffer from thermoelastic damping. Clamping friction or support loss (1/Qc ) Clamping friction for the beam results from radiation of acoustic energy through the resonator’s supports into the bulk of material surrounding the resonator. At resonance the vibrations set up a standing-wave pattern within the resonator. However, at the supports or ends of the resonator, some energy is lost outside the resonator decreasing the Q. This is caused by the shear force and moment on the clamped end. The shear force and moment act as vibration sources for launching elastic waves into the support. To avoid this, the motion of the supports should be minimised. This is achieved for tuning forks or double ended tuning forks in some particular balanced vibrational modes, in which the two beams vibrate in antiphase. Finite element analyses (31) have provided the optimum DETF geometry to minimise this source of losses. An analytical model has been derived for the support loss in micromachined beam resonators for clamped-free and clamped-clamped geometries (32) for in plane flexural vibrations. The coupling mechanism between the resonator and its support can be illustrated by observing a fixed-fixed beam vibrating in its fundamental mode. Following Newton’s second law, every action has an equal and opposite reaction, the reaction to the beam’s vibrations is provided by its supports. The reaction causes the supports to deflect and as a result energy is lost from the resonator. This is shown in Figure 8. The degree of coupling of a fixed-fixed beam can be reduced by operating it in a higher order mode. For example the second mode in the plane of vibrations shown above

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Figure 8. Support reactions a) Fundamental mode b) Second mode

will possess a node half way along the length of the beam. The beam will vibrate in antiphase either side of the node and the reactions from each half of the beam will cancel out at the node. There will inevitably still be a reaction at each support, but the magnitude of each reaction will be less than for mode 1. The use of such higher order modes is limited by their reduced sensitivity to applied stresses and the fact there will always be a certain degree of coupling. Balanced resonator designs operate on the principle of providing the reaction to the structure’s vibrations within the resonator. Multiple beam style resonators for example incorporate this inherent dynamic moment cancellation when operated in the balanced mode. Examples of such structures are the Double Ended Tuning Fork (DETF) which consists of two beams aligned alongside each other and the Triple Beam Tuning Fork (TBTF) which consists of three beams aligned alongside each other, the center tine being twice the width of the outer tines. Figure 9 shows these structures and their optimum modes of operation. 1/QC is of fundamental importance since it not only affects the Q-factor of the resonator, but provides a key determinant of resonator performance. A dynamically balanced resonator design that minimizes 1/Qc provides many benefits:


High resonator Q-factor and therefore good resolution of frequency.


A high degree of immunity to environmental vibrations.


Immunity to interference from surrounding structure resonances.


Improved long term performance since the influence of the surrounding structure on the resonator is minimized.

Figure 9. DETF and TBTF resonators

Surface loss (1/Qsu ) Surface loss is particularly relevant to nanoscale devices since as the surface to volume ratio increases the surface loss become more significant (33). The surface loss is mostly caused by surface stress which can be significantly enhanced by absorbates or surface defects. Air damping resulting from viscous drag or molecular collisions (1/Qv ) A resonator vibrating in a viscous fluid produces movement of the fluid, with fluid velocity components both parallel and perpendicular to its surface and propagating perpendicular to its surface. Both components give rise to loss. The parallel component causes the loss due to viscous drag and produced a frictional force in phase with the resonator velocity (34). An early paper (35) associated the viscous drag with two pressure regions. In region 1, the lower pressure region, the fluid molecules are so far apart they do not interact with each other. The individual air molecules exchange momentum with the resonator at a rate proportional to the difference in velocity between the molecules and the resonator. In the second pressure region the fluid molecules interact like a viscous fluid. The displacement of the fluid particles will also have an effect on the resonator’s natural frequency. This is because the mass of the adjacent fluid particles is effectively added to the mass of the resonator and hence its resonant frequency will be reduced. The order of magnitude of the added mass effect is dependent upon the relative densities of the fluid and resonator material (36), and there is a much smaller dependence upon the fluid pressure and the aspect ratio of the structure (37).

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Air damping resulting from acoustic radiation (1/Qa ) Acoustic radiation occurs when the vibrations of the resonator causes small pressure variation in the fluid in contact with the resonator. These pressure variations effectively form a source of travelling acoustic waves with the same frequency as the vibrations of the resonator. The production of the perpendicular component, corresponding to acoustic radiation is efficient and results in a low Q when the wavelength of the acoustic waves in the resonator is approximately equal to the acoustic wavelength in the fluid at the frequency of vibration. It has been shown (38) that the acoustic radiation loss is zero if the wavelength of flexural waves within the resonator is less than the wavelength of acoustic waves within the fluid. Squeeze film damping (1/Qsf ) Squeeze film damping occurs between two normally oscillating plates separated by a small gap (39). Assuming a fluid within the gap the pressure has two components one in phase with the drive to the oscillating plate and another in phase with the velocity of the oscillating plate. These respectively represent the spring like behaviour of the gas and the damping of the gas. This form of damping often occurs in electrostatically driven resonators where close positioning of the drive and detection electrodes is essential. In such an arrangement it can become the major damping mechanism (40). The magnitude of this effect depends upon the frequency of operation, the pressure of the surrounding fluid and the geometry of the resonator. The frequency dependence arises from the time taken to displace the fluid. At low frequencies the fluid has time to move between the surfaces and energy is lost from the resonator’s vibrations. As the frequency rises however, some of the fluid at the center of the resonator does not have enough time to move and becomes trapped between the surfaces. As the frequency rises further an increasing proportion of the fluid remains trapped. The trapped volume of fluid acts as a spring resulting in a slight increase in resonant frequency. As the frequency continues to rise the spring effect becomes increasingly predominant and the damping effect progressively declines (41). The squeeze film effect can be alleviated to a certain extent by incorporating apertures in the resonator allowing some fluid transport through the resonator. NON LINEAR BEHAVIOR Non linear behavior becomes apparent at higher vibration amplitudes when the resonator’s restoring force becomes a non-linear function of its displacement. This effect is present in all resonant structures. In the case of a flexurally vibrating fixed-fixed beam the transverse deflection results in stretching of its neutral axis (42). A tensile force is effectively applied and the resonant frequency increases. This is known as the hard spring effect. The magnitude of this effect depends upon the boundary conditions of the beam. If the beam is not clamped firmly the non-linear relationship can exhibit the soft spring effect whereby the

resonant frequency falls with increasing amplitude. The nature of the effect and its magnitude also depends upon the geometry of the resonator (43). The equation of motion for an oscillating force applied to an undamped structure is given below: «

my + s(y) = Fo cosωt

(9)

where m is the mass of the system, F the applied driving force, ω the frequency, y the displacement s(y) the non-linear function. In many practical cases s(y) can be represented by: s(y) = s1 y + s3 y3

(10)

the non-linear relationship being represented by the cubic term. Placing equation (10) in equation (9), dividing through by m, and simplifying gives: «

y + s1 /m(y + s3 /s1 y3 ) = Fo Cos ωt

(11)

Where s1 /m equals ωor (ωor representing the resonant frequency for small amplitudes of vibration) and s3 /s1 is denoted β. The restoring force acting on the system is therefore represented by: 2

2 (y + βy3 ) R = −ωor

(12)

If β is equal to zero the restoring force is a linear function of displacement, if β is positive the system experiences the hard spring non-linearity whilst a negative β corresponds to the soft spring effect. The hard and soft non-linear effects are shown in Figure 10. As the amplitude of vibration increases and the non-linear effect becomes apparent, the resonant frequency exhibits a quadratic dependence upon the amplitude, as shown below ωr = ωor (1 +

3 2 βy ) 8 o

(13)

The variable β can be found by applying equation (13) to an experimental analysis of the resonant frequency and maximum amplitude for a range of drive levels. The amplitude of vibration is dependent upon the energy supplied by the resonator’s drive mechanism and the Q-factor of the resonator. Driving the resonator too hard or a high Q-factor that results in excessive amplitudes at minimum practical drive levels can result in undesirable non-linear behavior. Non-linearities are undesirable since it can adversely affect the accuracy of a resonant sensor. If a resonator is driven in a non-linear region then changes in amplitude, due for example to amplifier drift, will cause a shift in the resonant frequency indistinguishable from shifts due to the measurand. The analysis of a resonator’s non-linear characteristics is therefore important when determining a suitable drive mechanism and its associated operating variables.

Silicon Sensors

11

Figure 10. Hard and soft non-linearities

Figure 11. Frequency/amplitude relationship exhibiting hysteresis

HYSTERESIS A non-linear system can exhibit hysteresis if the amplitude of vibration increases beyond a critical value. Hysteresis occurs when the amplitude has three possible values at a given frequency. This critical value can be determined by applying (43). yo2 >

8h 3ωor |β|

is mounted on a diaphragm and used to sense differential pressure (21). The exacting demands required by the oil and gas industry for down hole pressure sensing applications can only be met by resonant sensors. This market is currently dominated by a resonant quartz device supplied by Quartzdyne (44). A purely surface micromachined resonant beam pressure sensor has been demonstrated where the compact diaphragm and resonator design enables its use in catheter pressure sensing applications. The electrostatically operated resonant beam of dimensions 130 × 40 × 1.2 µm was coupled to a 150 × 100 × 2 µm diaphragm and the micromachining process includes on-chip vacuum encapsulation (45). Vacuum sensing has been demonstrated using micromechanical resonators. The resonators are surrounded by the evacuated media and variations in the applied vacuum levels alter the damping effects which change the characteristics of the resonance (46, 47). The applied vacuum not only determines the Q-factor but also influences the resonant frequency of the device. Other applications include strain sensing employing a surface micromachined polysilicon DETF resonator (48) and a bulk micromachined resonant beam accelerometer (49) both of which operate atmospheric pressure and therefore have low Q-factors of 370 and 170 respectively.

(14)

Where h is the damping coefficient and can be found by measuring the Q-factor of the resonator at small amplitudes and applying: ωor Q= (15) 2h MICROMECHANICAL RESONANT SENSORS A wide number of resonant microsensors have been demonstrated in the literature and some of these have been successfully commercialised. This section mentions just a few of the devices which have been reported. The main application of micromechanical resonators are in pressure sensors. These include the Druck resonant ’butterfly’ structure positioned on a pressure sensing diaphragm (4) and the Yokogawa H-shaped resonator which employed a novel wafer level vacuum encapsulation process, again this resonator

MICROMECHANICAL RF RESONATORS A more recent application of micromechanical resonators is as a timebase for radio frequency (1 – 1 GHz) applications. The advance of mechanical resonators into this field has been facilitated by the improvements in fabrication processes enabling ever smaller resonant structures, and therefore higher frequencies, to be realized. Micromechanical resonators are a potential replacement for quartz crystal oscillators which, despite their excellent performance, have the drawbacks of large size and incompatibility with on chip integration. To be successful in this application, the resonator should exhibit a high Q (tens of thousands), excellent stability across a range of temperatures and good signal to noise characteristics. The high Q values are required to meet phase noise standards for communications reference oscillators (e.g. 130 dBc/Hz at 1 kHz offset for a 10 MHz crystal oscillator reference) (50).

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MEMS piezoelectric thin-film bulk acoustic resonators (FBAR’s) consisting of thin films of piezoelectric material sandwiched between metal electrodes and operated in an extensional mode are already commercially successful (51). However, to achieve integration with electronics, nanoscale resonant structures have also been fabricated from polysilicon. These resonators are predominantly electrostatically excited into resonance and the vibrations detected capactively. This approach is non-thermal and noncontact (i.e. doesn’t require dissimilar materials on the resonator structure) which are essential factors necessary to achieve the required levels of stability. A range of structures have been presented in the literature including a 10 MHz fixed-fixed beam (52), a wine glass disk structure resonating at 60 MHz (53), a contour mode disk resonator at 1.5 GHz (54) and a hollow disk structure (55) with a Q of over 15,000 at a frequency of 1.46 GHz.

CONCLUSIONS Micromechanical sensors are miniature structures which can be used in both timebase and sensing applications. When used as a sensor, a variety of sensing principles can be employed to monitor a wide range of measurands such as pressure, acceleration, density and flow. Micromechanical resonator sensors use a micromachined resonator with dimensions in the range of tens of nanometres to hundreds of microns. The micromechanical resonator can be fabricated in batches from silicon, quartz and gallium arsenide wafers. Resonant sensors offer high accuracy, high resolution and high stability and, if designed correctly, should be superior to alternative sensing mechanisms e.g. piezoresistive, capacitive. The frequency of the mechanical resonator typically changes with the measurand and the output of the sensor is thus a change in frequency. Mechanisms to excite the resonator’s vibrations and detect them must be included in the sensor and a wide variety of techniques are available to the sensor designer. A simple method is the use of the piezoelectric effect in quartz.

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S. P. BEEBY M. J. TUDOR School of Electronics and Computer Science, University of Southampton, England