phần 2

Silicon micromachined infrared sensor with tunable wavelength
selectivity for application in infrared spectroscopy

D. Rossberg

Lehrstuhl für Technische Elektronik, Technische Universität München, Arcisstraße 21, D-80333 Munich, Germany

Abstract

The techniques of silicon micromaching have been used to develop a miniature infrared sensor with tunable wavelength selectivity for application in infrared spectroscopy. The infrared sensor consists of a tunable interference filter in front of a wide-band detector. The applicable spectral bandwidth ranges from 1.5 to 7.5 qjn. The resolution is better than 25 nm over the whole range. The wavelength tuning and parallelism control of the mirrors is carried out by electrostatic forces, varying the voltage at the integrated disk capacitors. The transmitted infrared radiation is absorbed in a black gold layer, the rising temperature being measured by a thermopile consisting of 80 Si-Ni thermocouples. This device is expected to find application as an emission monitor for liquids and gases.

Keywords: Infrared sensors; Silicon micromachining

1.    Introduction

Spectral analysis in the infrared region is a well- known, common and powerful method in physics and chemistry for analysing the composition of many sub­stances [1]. For this application a silicon-based infrared sensor would be a reasonable and handy alternative to conventional infrared spectrometers, which normally tend to be large expensive devices that are difficult to tune electronically. It could be used in portable equip­ment for outdoor chemical analyses.

In the last few years, many powerful miniaturized spectrometers have been developed for the spectral range 300-1100 nm where silicon CCD lines can be used as detectors. The infrared sensor presented in this paper works in the spectral range where silicon is transparent. Therefore this device extends the range of handy and reasonable miniaturized spectrometers into the infrared region, which is a very interesting one for chemical analyses [1].

2.     Structure and device fabrication

2,1. Tunable interference filter

A Fabry-Perot interferometer (FPI) is an optical element made up of two partially reflective mirrors

0924-4247/95/S09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0924-4247194100932-8
separated by a distance d_m. They have to be adjusted in such a way that they are parallel to a very high degree of accuracy. The parallelism is normally achieved by a spacer ring between the mirrors separating them at the desired distance. Such an arrangement of two plane mirrors and a ring as spacer is named a Fabry- Perot etalon. The outer surfaces of the mirrors are usually coated with antireflection layers. The mirror itself is often built up by dielectric layers to obtain high reflectance and to minimize absorbance.

Such a set-up transmits radiation according to the following equation:

T^z

(i-R²) where I = transmitted intensity, R = reflection coefficient of the reflecting layer, T=transmission coefficient of the reflecting layer, ifi=change of phase on reflection at the reflecting layer, /3 = angle of incidence of the beam, n = refractive index of the spacer, d_m = thickness of the space and A=wavelength of radiation.

The reflecting layers are assumed to be identical on both mirrors. This transmission characteristic consists of a number of very sharp transmission peaks, which are caused by multiple reflections of the radiation in the Fabry-Perot etalon [3].

Whenever a multiple number of half wavelengths matches between the two mirrors, radiation will pass through:

d_m = iy (/ = 1,2,3...)                                               (2)

=>A₀ = 2^ (/ = 1,2,3...)                                           (3)

The distance between two transmission peaks, AA₀, is therefore

-1+?)

+!>■) ⁼                                          W

The half-width HW of a transmission peak is given by (¿ = 1,2,3...) (5)

The finesse Q can be calculated by

A₀ _ iirR^m HW~,₀ ⁼ I

(see Fig. 1).

Using highly reflecting mirrors, a small variation of the mirror separation d_m causes a significant change of the transmission characteristic. Therefore the re­alization of a miniaturized Fabry-Perot interferometer is possible [4].

The integrated Fabry-Perot interferometer consists of two silicon parts placed on each other. A cross

^-0 Fig. 1. Optical characteristics at the transmission curve of a Fabry- Perot interferometer.

section of the whole infrared sensor is shown in Fig. 2. The overall dimensions are 20 mmX20 mm X 0.8 mm. On both parts high reflective mirrors are applied by sputtering processes. The reflective index of the mirrors is about 0.92. To reduce substantial Fresnel reflection losses at the outer silicon surface (rz_Si = 3.4) antireflection coatings have been applied.

The first part has a thin membrane with the di­mensions 10 mmXlO mmXl3 ¡im at its centre, which is fabricated by anisotropic wet etching. In the second part a hollow is structured through dry etching methods. The depth of the hollow determines the distance be­tween the two Fabry-Perot mirrors. The roughness of the hollow surface is less than 5 nm. Around the mirror on the membrane four capacitor plates are placed electrically isolated from each other. On the other part a metallic layer of the same size is applied. The two wafers are bonded together to form the optical etalon. So there are four disk capacitors to control the wave­length selectivity by applying a voltage to them. The electrostatic forces thus produced pull the membrane forward to the opposite surface, reducing the distance between the two mirrors. The reaction force is given by the elastic restoring force of the silicon membrane. With four disk capacitors it is not only possible to control the mirror spacing but also the mirror parallelism to achieve maximum finesse of the system. The capacity is given by

C=^-<f₀e_r                                                             (7)

Therefore the value of the capacity changes by variation of the mirror distance. This effect is used to stabilize the mirror distance in an active feedback loop, to

Fig. 2. Cross section of the tunable infrared sensor.

minimize environmental stimulation (microphonia) [2] and to balance manufacturing irregularities. The sche­matic layout is shown in Fig. 3. It consists of an oscillator generating frequency steps with fixed (but adjustable) distances. The distance will determine the resolution and the absolute frequency will determine the wave­length. This frequency is the reference for the automatic control system, consisting of four phase-lock loops (PLLs).

The capacities C_1A3A sensor ^are the frequency-deter­mining elements of four LC oscillators. On changing the value of the capacitors, the related frequency changes according to the equation

^/à-⁴       2tt(LC₁_₄)^1/2 (see Fig. 4). Using the PLL principle for each capacitor, it is possible to regulate the mirror distance d_m( = plate distance of the capacitors) in such a way that no influence of microphonia can be determined. fjd_m ranges from about 4 to about 15 kHz nm'¹.

2.2. Wide-band infrared detector

This part of the infrared sensor consists of two functional groups: an infrared absorber and a thermal detector.

The infrared absorber is placed at the backside of the silicon membrane upon the wet etched surface. It consists of black gold deposited in a rather poor vacuum with high evaporation power. It converts the transmitted radiation wavelength unselectively into heat, which can be measured with a thermal detector [5]. The thermal detector is a thermopile composed of 80 Si—Ni ther­mocouples in series. The hot ends of the thermocouples are arranged under the capacitor plates and around the mirror, whereas the cold junctions are placed at the bulk material. The surfaces of the bond pads of the thermopile are of the same material and set so closely together that no further thermovoltage occurs. The resulting thermovoltage is about 37 mV K^_1 at room temperature and the time constant is about 30 ms. The estimated noise equivalent power is about

^FThe^cpne^l^XlO^WHz-^²

and the responsivity is about

^Thermopi.e=H0 VW^_1

3.     System set-up for infrared spectroscopy

A conventional set-up for infrared spectroscopy is shown in Fig. 5. It consists of an infrared source (e.g., a silicon planar pellistor), the medium of the investigated and the infrared sensor. The significant advantage of this infrared sensor is the outer dimensions, which are very small compared to those of conventional infrared spectrometers. To achieve a small and compact set-up it is useful to have short absorption lengths. Because of their high absorption coefficients, fluid and more concentrated gases need only a short length for high

IR-source                                      medium                                     IR-senso^p

absorption. Therefore the main application area will be the control of fluids and the emission control of gas outlets. In such a set-up it is possible to have no lenses or mirrors. The cuvette for the medium to be investigated is a simple infrared transmitting tube. But it is also possible to use multipass infrared cuvettes to detect low-concentration gases or solvents by giving up the advantage of having a small measurement set-up.

4.     Conclusions

A new silicon micromachined infrared sensor has been presented for use in infrared spectroscopy with tunable wavelength selectivity. Using a Fabry-Perot interformeter offers the unique advantage of having a linewidth which can be applied to the measurement requirements by using a suitable mirror spacing and finesse. The big advantages of this new device are its small dimensions and low cost compared with standard infrared spectrometers. This allows reasonable and handy infrared spectrometers to be built for outdoor use. The limit in wavelength of 1100 nm for miniaturized spectrometers could be extended up to about 7.5 pm. It might be of interest that the structure of the min­iaturized Fabry-Pdrot interferometer can also be used as a voltage-controlled oscillator with a high tunable range.

Acknowledgement

The author wishes to thank Deutsche Forschungs­gemeinschaft (DFG) for financial support.

References

[1]     B.P.Straughan,Specfroicc/jy, Vol. 2, Chapman and Hall, London, 1976, pp. 138-265.

[2]     W. Albertshofcr, A tunable ‘spcctrometerdiode’ with a spectral resolution of 3 nm in the 660-900 nm range, Sensors and Actuators A, 25-27 (1991) 443-447.

[3]     J.M. Vaughan, The Fabry-Tirol Interferometer, Adam Hilger, Bristol, 1989, pp. 89-177.

[4]     P. Hariharan, Optical Interferometry, Academic Press, Sydney, 1985, pp. 79-93.

[5]     R.H. Kingston, Detection of Optical and Infrared Radiation, Springer, Berlin, 1978, pp. 83-100.

A Low Cost Monolithic Accelerometer

S. J. Sherman, W. K. Tsang, T. A. Core, D. E. Quinn
Analog Devices Semiconductor
Wilmington, MA 01887

1,    INTRODUCTION

The ADXL50 is a complete scaled and temperature compensated surface micro-machined accelerometer with an output voltage proportional to acceleration. Full scale measurement range is ±50g, with unpowered shock survival at 2000g. Ultimately, signal span accuracy of 5% should be possible for a temperature range of -55°C to +125°C and a supply range of 5V ±0.25 V. Bandwidth up to 1.5KHz is programmable with a single external capacitor.

A digitally activated self-test will electrostatically deflect a functional beam so that a -50g acceleration is indicated.

An uncommitted amplifier, with rail-to-rail output range, and a reference allow re-scaling and offsetting of the raw output signal (1.8V ±1.0V at ±50g). Capacitors can be introduced in the gain network surrounding the uncommitted amp so that 2 poles of low pass filtering are possible without the addition of off-chip active circuitry.

The ADXL50's objective specifications were crafted for crash detection in second generation automotive air bag systems which rely on single point sensing and per model programmable crash signature analysis for dramatic system cost reduction.

2.       TECHNOLOGY BASE

The sensor's low cost objective, ultimately S5 in automotive volumes, dictates a technology base that includes;

1.    a monolithic approach, with integrated sensor and BiMOS interface circuitry

2.    small chip size, 120x120 mil²

3.    utilization of familiar materials and production processes

4.    the simplest possible mechanical structure, a single layer of self-supporting patterned polysilicon above the substrate surface

5.    standard packaging

6.    exploitation of established technique, laser wafer trimmed (LWT) thin film resistors, for achieving performance objectives

3.       SENSOR GEOMETRY

Figure 1. is a depiction of the sensor's essential functional elements, which are formed from a single layer of patterned polysilicon (processed on a layer of sacrificial oxide 1.6 um thick). The elements stand on the substrate at "anchor" points, a result of pre-pattemed holes in the sacrificial oxide. The sensor, a differential capacitor, exists in a "moat” area, roughly 600um x 400um, with interconnections from the beam elements to points external to the moat accomplished by N-i- emitter diffusions.

The large (by IC standards) nominal lateral capacitor

34          #1992 Symposium on VLSI Circuits Digest of Technical Papers
gaps, 1.3um, between the outer plates and the common center plate, and the low permittivity of dry nitrogen, necessitate the paralleling of 42 unit cells to achieve 0.1 pf for each side of the differential capacitor. At that sensor source impedance level adequate signal-to-noise performance is possible.

4.        SYSTEM BLOCK DIAGRAM AND SENSITIVITY EQUATION

The sensor beam is electrostatically force-balanced so that the inertial force, Fi =ma, is primarily balanced by a net electrostatic force, F_E, created by a change in the beam voltage. As will be explained, this beam voltage change, AV₀, is linearly related to acceleration, a, with the sensitivity being

A V₀ _ md*

a 2Ap6oVr(1 + 1/T)                         (i)

where do = capacitor gap m = beam mass A_P = plate area T = loop gain Eq = permittivty of nitrogen V_R = 1/2 DC voltage difference between the outer plates

Figure 2. is a simplified system diagram representing the essential elements in a forced-balanced scheme. Complementary 1MHz square waves, centered around V_R and -V_R are applied to the outer plates of the sensor. The low input capacitance buffer is to prevent loading of the sensor. The synchronous demodulator detects and amplifies the 1MHz beam node signal proportional to beam deflection. The low pass filter removes 2MHz spiking, a result of the demodulation process, and sets a dominant loop pole for overall frequency compensation.

Two concurrent processes exist at the beam node;

1.   position sensing, at 1MHz. For a translating center plate and fixed outer plates, an ideal parallel plate treatment reveals that output per unit deflection is first order linear, i.e.

V^ = V_P x/do                            (2)

where V_P is peak carrier amplitude and x is deflection from center,

2.   force projection on the beam, accomplished by a non­zero value of V₀ applied to the beam through the 3 meg­ohm resistor (R). The large value of resistance prevents the 1MHz signal, sourced by only the 0.2pf, from being reduced through loading.

The 1MHz beam node signal is a classical error signal which is driven to zero by the global negative feedback

92CH3173-2/92/0000-0034$3.00© 1992 IEEE

loop, which adjusts V₀ to create the net electrostatic force balancing the inertial force, with equilibrium at x = 0, For a two parallel plates, the attractive electrostatic force is

F = e₀ A_PV²/2d²                                     (3)

For the beam, the net force is the sum of attractive forces to each of the outer plates,

F_e = 2A_P£₀V_RV₀/d₀²                               (4)

If the outer plates are biased at V_R and - V_R, the center plate (beam)is biased at V₀, and the beam remains centered, X = 0. Then

F, = F_e

ma = 2Ap£_oV_RV₀/d_o²

Vo/a = mdo^ApCoVR                           (5)

Variables appearing in equation (5) are temperature stable in a 5% accuracy context. (V_R is slaved from a 10ppm/°C reference.)

For finite loop gain, T, the sensitivity takes the form of equation (1), with a 1 + 1/T term in the denominator. The DC loop gain, T₀, is, in fact, trimmed to a value of 10, yielding a predictable bandwidth and adequate temperature desensitization of factors in the expression for T₀, such as carrier amplitude.

Figure 3, is a more detailed block diagram representative of the chip organization.

The carrier generator, a resistively loaded differential pair of bipolars, provides complementary 1MHz square waves which are AC coupled through 50pf capacitors to the inputs of the sensor. DC plate voltages (3.4V and 0.2V)

are set with 200K resistors. The pre-amp is a low accuracy space efficient instrumentation amplifier. The self-test current, I_sx, is routed into R_ST. In the absence of acceleration the loop output V₀ will adjust so the beam node is at 1.8V, F_E = 0, and x = 0. At that condition

V₀ a 1st R-st/O + 1/T)                           (6)

Loop gain is trimmed at R_P1. A wafer level full scale acceleration trim technique under development leads to a calculated change in beam voltage required to force balance 50g full scale acceleration. With this calculated value, Rp2 can be trimmed so that a IV change is observed at V₀ for a 50g input.

5.        EXPERIMENTAL RESULTS

Typical measured performance for the ADXL50, observed at the pre-amp output,follows. (Full scale output, F.S.O., is defined as lOOg, or ±50g, with a corresponding 2V change.)

sensitivity drift, 3.0% sensitivity PSRR, 60dB zero - g drift, lOOmV zero - g PSRR, 48dB noise, p-p, 1% F.S.O. transverse sensitivity, 2% shock survival

2000g, lOOpsec >1600g, 500psec

Photo 1 is a comparison of outputs from a shaker reference accelerometer (top) and the ADXL50 (bottom) for 20g, 100Hz excitation.

				YR-fui •vfr[nr ! *vp DEM0°H^i:
			na 2. SMPUFtCD BLOCK DtAORAM
	PHOTO 1 REF ACCEL (TOP) ADXL50 (BOTTOM)

1992 Symposium on VLSI Circuits Digest of Technical Papers •             35

Accelerometer Systems with Self-testable Features

HENRY V. ALLEN, STEPHEN C. TERRY and DIEDERIK W. DE BRUIN

IC Sensors, 1701 McCarthy Boulevard, Milpitas, CA 95035 (U.S.A.)

Abstract

In recent years, substantial effort has been devoted to the design and fabrication of a new class of silicon sensors, the accelerometer. A num­ber of companies have been working in the area to produce, for the first time, an accelerometer that is substantially more cost effective and with higher performance than previously possible. Careful electromechanical design and micromachining process development has allowed silicon accelero­meters to be fabricated in volume.

Two questions that arise in ultra-high reliabil­ity applications, such as safe-and-arming, are whether the accelerometer is free and working and whether the device is broken. A unique solution to these questions has been designed and imple­mented in a piezoresistive accelerometer; this ap­proach allows the device to be tested by elec­trostatic deflection of the mass. A number of key advantages result from this configuration. Even though the spring constants of the device may vary from unit to unit or over temperature, and even though the piezoresistive coefficients vary over temperature, as long as the voltage and initial separation gap are held constant, the out­put will be proportional to a given acceleration. Applications for the self-testing technique are in temperature compensation, testability and uni­directional force-balance applications.

This approach of building testability into the sensor bridges the gap between the open-loop sensors now in production and the much more complex closed-loop force-balance devices.

Introduction

Historically, silicon accelerometers were thought of as fragile devices, which were more a laboratory curiosity than a viable part that could be manufactured in volume. This belief was based on the early work by Roylance [1] at Stanford University and further reinforced by problems encountered by companies trying to improve on the device [2]. Many of the problems in fabricat­ing these devices were related to the mechanical
structure, not the electrical transduction. Issues such as damping, cross-axis sensitivity, over-load protection and in-process survivability have hin­dered the acceptance of these types of sensors. These issues have led to a desirability to ensure that any accelerometer built using silicon micro­machining is as reliable or more reliable than a common silicon-based pressure sensor.

In a number of applications, it is imperative that failures of sensors are known as quickly as possible. Mechanical failures may be due to device destruction or obstruction of the motion of the deflectable structure in the sensor. By careful de­sign of the sensor, most of these problems can be eliminated. However, there are cases when a test­ing mode in the sensor is desirable, even with an optimally designed device. Field verification of the response over temperature extremes is one such case. It is not uncommon, for instance, in geophysical exploration to chain larger numbers of sensors together. Verification of functionality is useful in that drop-outs in the arrays, due to non-functional sensors, degrade resolution. Fur­ther, the installation and operating environment are extremely hostile and tend to contribute to sensor failure. Another area where operation of an acceleration sensor is extremely critical is in safe-and-arming applications, whether it be for fusing projectiles or activating an airbag in an automobile. Failure of the sensor may mean either unexpected detonation or failure to detonate when required.

Using electrostatic forces within an accelerome­ter housing to deflect the mass allows operation to be verified. Reproducibility and reliability of the structure is set by the overall specific design of the accelerometer.

Accelerometer Design

A number of parameters come into play in the design of an accelerometer. Unlike pressure trans­ducers, which are specified to survive routinely three to five times over-force, accelerometers may have to be built to survive over-shocks hundreds of times their normal operating range. Thus,

(b) Fig. 1. (a) Cross-section and internal view of the quad- supported cantilever accelerometer, (b) SEM view of the cross­section of the quad-supported cantilever accelerometer.

deflection stops must be built into the structures to prevent damage. Accelerometers made in single­crystal silicon exhibit very Iqw mechanical loss; Q values of the spring-mass resonances in excess of 200 000 have been observed when the device is operated with no damping [3, 4] and, with minimal damping, it is not uncommon to measure Q s greater than 200 [1,2], Because of this, the struc­ture needs to have controlled damping in order to ensure a high-fidelity transduction of the accelera­tion.

These requirements have been addressed in the design shown in Fig. 1(a). In this case, the device is a double cantilever structure, where the mass is supported through silicon springs from both ends and moves as a piston. Resistors diffused into the springs detect strain in the supports of the mass and thus deflection that is a result of external acceleration. An SEM view of the cross-section of the structure is shown in Fig. 1(b).

Top and bottom silicon caps are provided and have several applications. First, the caps can be etched to form mesas above and below the mass to limit its motion when it is subjected to over­acceleration. Secondly, a well can be fabricated in the cap to provide a precisely defined cavity to provide ‘squeeze-film’ damping. Squeeze-film damping is an effect whereby air, when squeezed between two large plates, tends to resist displace­ment. For small changes in separation, this fluid- flow resistance, or damping, is linear. The fact that the caps are of the same material as the accelerometer mass and frame simplifies mounting and minimizes the introduction of temperature- dependent stresses.

In addition to provide mechanical stops and controlled damping, the caps also prevent particu­late contamination in the vicinity of the seismic mass. Because the device moves only a few mi­crons for full-scale deflection and has stops built in to limit the maximum deflection to 5 to 10 /im, it becomes critically important that the moving portion of the accelerometer be protected from particulates. Placing uncapped devices in a her­metic package will reduce the probability of fail­ure due to particulate contamination but will not eliminate it. The fully capped devices, sealed at the wafer level of fabrication in a clean-room environ­ment, offer a better opportunity of remaining particulate free during the final fabrication steps such as sawing and die attachment, testing and operation.

The motion of the device in various accelera­tion fields has been carefully modeled to make sure that it has a very low probability of breaking due to off-axis acceleration, while at the same time minimizing the sensitivity to off-axis forces.

Figure 2 shows the motion of the mass when subject to acceleration loads in the three principal axes. Note that in each case, the device will have a tendency for at least one corner of the mass to deflect upwards. When this happens in the struc­ture shown in Fig. 1, the mass will hit one of the build-in over-force stops, which prevent further motion.

From classical plate and beam theory, the mo­tion of the seismic mass shown in Fig. 2(b) will result in a resonant mode that is exactly twice the frequency of the fundamental mode (Fig. 2(a)). This is shown in Fig. 3 for a special test configura­tion of a nominal 2 g full-scale accelerometer. The Mode II resonance, which corresponds to the motion shown in Fig. 2(b), is at 1525 Hz and the peak for Mode I (normal vertical motion) is at 762 Hz.

The Mode III motion (Fig. 2(c)) is more com­plex. By design, the resonance corresponding to this motion can be moved independently of the first two. As the separation between the two beams on each side becomes larger, the motion is
more difficult to initiate and hence the sensitivity in that direction decreases and the resonance frequency increases. As the beam% are brought successively closer, the resonance decreases and this mode can actually coincide with the Mode I resonance. The stiffer structure is desirable in order to minimize phase errors in the normal operating mode. Note that the normal resistor

Fig. 3. Measured frequency ranges of the undamped ac­celerometer structure.

interconnection scheme used in this accelerometer is such that off-axis signals are cancelled and, hence, even with undamped accelerometers, it is difficult to observe the Mode II and Mode III resonances using amplitude data alone.

Damping

One of the earliest identifiable problems with silicon accelerometers was that of Q. Roylance [5] discussed this problem in detail and investigated a number of options to achieve the correct damp­ing. An accelerometer with a Q of 10 will, when driven at resonance, deflect ten times more than it will when driven by the same force at lower frequencies; under such conditions, the chances of breaking the device increase. Further, even with stops to prevent over-travel, excitation of this mode can produce harmonic and inter­modulation distortion because the desired signal is being mixed with the wide travel resonant mode or clipped when the seismic mass hits the stops.

A simple alternative that is sometimes used to mask the problem is to connect an electrical filter across the output of the accelerometer to provide additional attenuation near and above the reso­nance frequency. While this gives the appearance of a critically damped device for small-signal ap­plications, for large-signal measurements, the dis­tortion and non-linearity noted above will affect the performance of the accelerometer adversely. Additionally, the electrical pole will introduce an additional frequency-dependent phase shift. As noted above, the accelerometer design incorpo­rates squeeze-film damping [6,7] to achieve a highly controlled damping coefficient.

In any mechanical system with multiple springs and a mass, such as this accelerometer, each reso­nance contributes a term to the transfer function in the form:            ^v

H{s)=------------ ¹      , ,₂                                                                      (1)

¹ H—+ (~\

Q V'hJ

Measurements on this structure indicate that the damping coefficients associated with the three modes are comparable. Using this assumption and the resonance frequencies of Fig. 3, an electrical model with three poles of the form shown in eqn. (1) yields the expected frequency response of the device. Figure 4 shows this theoretical re­sponse for the three poles with critical damping (Q = 0.707), and for over-damping and under­damping. The depth of the etched cavity in the cap is used to tailor the damping factor for

Fig. 4. Response variations due to a change in cavity depth. Typical variation in depth is +1 /mi.

accelerometers in a particular resonance (or sensi­tivity) range.

The utilization of air instead of oil, for in­stance, to achieve viscous damping is attractive because the viscosity of oil, and thus the damping, changes substantially with temperature. Oil spe­cifically and liquids in general have been found to be a poor choice for operation over a wide tem­perature range. Air, on the other hand, has a relative constant viscosity over temperature and over pressures near normal atmospheric ranges. The temperature dependence of viscosity for air is less than 0.2% per °C, or only a ±15% change from —30 to +75 °C [8]. This corresponds to only a ± 1.2 db change in sensitivity at resonance for a part that is critically damped.

The ability to achieve the desired damping is shown for two typical accelerometers in Fig. 5. The top trace is the response of a 3.3 mV/V/g device and the bottom trace is the response of a 0.5 mV/V/g device. Neither device exhibits peaking. Note that this peaking is intrinsically undersirable. Both are critically damped with Q » 0.707.

Fig. 5. Frequency response of two accelerometers with differ­ent full-scale ranges but with the same control on damping.

Over-force Protection

One of the desirable features of any sensor is its ability to survive the normal environment to which it is exposed. For the accelerometer, this environment includes accidental or intentional droppage. Typically, a three foot drop test onto a concrete floor will expose the part to a force in excess of 300 g. Thus, a desirable target would be a design that was insensitive to overloading in any axis. The quad suspension offers such a structure. Loading in any axis, as shown in Fig. 2, will tend to drive at least one edge of the mass out of the plane of the frame. The stops, provided by the caps, will then tend to protect the structure.

The ultimate proof of the design is in the survivability of the accelerometer under adverse conditions. Figure 6 shows the output of a 5g accelerometer when subjected to a 115 g accelera­tion in its sensing direction (Fig. 2(a)). The device hits the stops at 35 g. A more telling response is seen in Figure 7. The same 5 g accelerometer is shown to survive a 2100 g overload in the nor­mal direction without damage. This accelerome­ter also survived 2000 g shocks in the other two principal axes. The ringing shown by the two

Fig. 6. Impulse response of the accelerometer with built-in damping and over-stop protection for a 115g shock.

Time (milliseconds) Fig. 7. Impulse response of a 5 g accelerometer for a 2100 g shock.

accelerometers is due to mechanical resonances in the block to which the accelerometers are at­tached. The phase lag of the 5 g accelerometer in the Figure is due to the built-in damping. In general, the higher the full-scale g range that an accelerometer has, the wider is its useful band­width. Thus a 10 000 g accelerometer built for recording shock waves and a 5 g accelerometer designed for low-g applications will show major differences in their respective phase responses. Note that these trade-offs are depicted in Fig. 5 for the 3 and 20 g accelerometers.

Self-testing feature

The self-testing feature provides two benefits. The first is that the user can confirm that the mass is free to respond in critical operating conditions. Secondly, the self-test is a force applied to the mass, which cannot be differentiated from an acceleration force. Hence, using a known electro­static force, the accelerometer can be calibrated over temperature or over time. The basic design trade-offs in adapting the accelerometer described above for self testing are presented below.

(a)      Electrostatic Deflection

The accelerometer’s operation is based on sim­ple deflection equations. The sum of all forces acting on a proof mass is zero:

0 = mg9.8 — F_electro — k_s(x₀ — x)                                (2)

where mg is the gravitational or acceleration force (acceleration in g), k_s(x₀ — x) = k_s Ax is the restoring force provided by the springs and F_electro is the electrostatic force, given by

^electro OC 0.5fi^(F/x)²                                                     (3)

where V is the applied voltage between the elec­trodes, A is the electrode area and e is the dielec­tric constant of the damping media.

If the electrostatical force is set equal to zero, then the displacement, Ax, is proportional to accel­eration with the proportionality constant being m/k_s. Because the piezoresistors transduce stress in the springs, and stress and strain are directly related by Young’s modulus, the displacement can be derived by measuring the change in output voltage of the Wheatstone bridge. If an electro­static force is applied, eqn. (2) becomes non-linear:

V²

0 = mg9.8 — 0.5sA ----- ------ ——r — k_sAx                    (4)

(x₀- Axfl

For small deflections (Ax/x < 5%), Ax can be neglected compared with x₀. Typically, for a 50 g device with a 5 /rm gap between the mass and
electrode, the deflection is around 3%. Note that for very sensitive devices (for instance, 5 g full- scale parts), the deflection can be made large and therefore some decreases in the electrostatic voltage drive to maintain the same ratio of elec­trostatic to g forces is needed for low-g devices.

Applying a voltage V to the electrode corre­sponds to subjecting the mass to an acceleration of:

_ eAV²

^gelectro I9.6mx₀²                                                                     ’

assuming small deflections. This force depends only on the applied voltage and the geometry, and is essentially independent of temperature and sen­sitivity of the device, making it suitable for cali­bration purposes.

(b)      Modifications to the Basic Accelerometer for Self Testing

Two simple modifications are needed to con­vert the standard accelerometer for self testing. First, the stop area is increased to make the electrode area as large as possible, while keeping the damping factor constant. The second modifi­cation is in the design of the cap electrode. To make the device simple to fabricate and to pack­age, it is desirable to bring the cap electrode out onto the same surface as the other bond pads for the Wheatstone bridge. Metal is run from the top cap surface onto the top of the middle silicon substrate. The bonding pads are then all on the middle silicon piece. The electrode spacing can be tailored to better than 2% by controlling the depth of the cap etch. Combined with the non­linearity term due to large-scale deflection, the self-testing function can be reproducible from part to part with about a 5 to 7% uncertainty. Time- dependent variations in the response of a single sensor can be substantially less because the gap is fixed and, even for large deflections, the response to an electrostatic force does n<5t change over time.

(c)      Test Results

Based on the equations given above, the ex­pected curve for output versus applied electro­static voltage should be parabolic. This is shown

Fig. 8. Electrostatic attraction normalized by sensitivity vs. applied voltage for devices with different sensitivities.

to be the case in Fig. 8 for parts with a three to one variation in sensitivity. A voltage was applied between the cap electrode and the silicon seismic mass; the voltage was varied from — 20 to + 20 V and the output of the sensor was measured. The electrostatic force was determined by dividing the change in output for a step in electrode voltage by the sensitivity of the device. Note that a 20 V drive is preferable to the 5 V drive in that the effective force is 16 times greater. A more practical voltage of between 10 and 15 V still supplies sufficient deflection and measurable output.

Several devices of various acceleration ranges have been tested. As expected, the electrostatic force for a given electrode voltage is independent of the sensitivity of the device. Small variations in the curves in Fig. 8 are caused by the non-lineari­ties associated with the deflection of the mass and by variations in the gap spacing. Another feature of this device structure is that the part can be checked over a large temperature range to allow it to be calibrated. Figure 9 shows electrostatic g force versus applied electrode voltage for one device when measured at three different tempera­tures, — 25, 25 and 85 °C. While the sensitivity was measured to be linearly decreasing by 12% over a 50 °C range, the effective reproducibility of the self-test feature is within 2% for applied elec­trode voltages of 10 V or higher.

Using this approach, the data in Table 1 were obtained on a second accelerometer with built-in self test. The raw sensitivity of the accelerometer

Fig. 9. Electrostatic attraction normalized by sensitivity vs. applied voltage at different temperatures.

over temperature (—25 to + 100°C) was mea­sured and the output due to the electrostatic force was tabulated for a fixed applied electrode voltage. A normalized sensitivity was computed, as was the relative error from 25 °C. The normal­ized sensitivity is defined as:

(sensitivity per g at temperature/sensitivity per electrode force at temperature)

(sensitivity per g at 25 °C/sensitivity

per electrode force at 25 °C)

The total error was less than 1.6% for an ac­celerometer with an uncompensated temperature error of +28% to —17%. Figure 10 depicts the data for the g sensitivity, the electrostatic sensitiv­ity and the normalized sensitivity when each plot has been normalized to 1.00 at 25 °C. Improve­ment in temperature performance by at least a factor of ten can be achieved using the self-test design. The circuitry that would allow the normal­ization used in Table 1 to be done is described below.

(d)      Application of the Self-testable Accelerometer The self-testable option is a highly desirable feature. The device can be designed to allow auto­matic or manual recalibration to be performed. In

the manual mode, a voltage would be applied to a fully temperature-compensated accelerometer and the change in output would be used to confirm correct operation. A more practical approach would be for a test system to recompute the sensitivity periodically, the advantage being that long-term changes in sensitivity are eliminated and the system can accept non-linear temperature dependencies.

One approach to providing an output that is normalized over temperature is to use the A/D circuit shown in Fig. 11. In this case, the output of the accelerometer is fed through a demulti­plexer, which is synchronized with the self-test electrode control voltage. When the electrode voltage is off, the accelerometer output is passed through the first-stage amplifier and through the multiplexer to the normal input to the A/D con­verter. When the device is in a self-test mode, the voltage is applied to the self-test electrode and the signal path is changed to allow the self-test signal to be acquired. Because the self-test signal will be superimposed on whatever signal the ac­celerometer is currently sensing, it is necessary to take the difference between the output voltages immediately before and during self testing. The difference is simply the force exerted on the ac­celerometer due to the self test. This is done with the 1 x difference amplifier shown in the Figure. This signal is in turn fed through a sample-and- hold circuit and then to the reference input of the A/D converter.

The operation of the A/D converter is based on computing a digital word that is the binary representation of a number from 0 to 1. The analog number which the A/D converter approx­imates is set by the ratio of the applied voltage to a reference voltage. Typically, the reference is a fixed voltage, which can be used to drive a piezoresistive bridge so that the output is nor­malized for variations in the reference voltage. In the self-test case, the opposite approach is used. In this case, the self-test signal becomes the

reference and the normal accelerometer output becomes the normal input to the A/D converter. The division operation required to compensate the unit over time or temperature is performed explic­itly in the operation of the A/D converter. An analog representation of the normalized signal could then be recreated by passing the digital word from the A/D through a D/A converter with a fixed reference voltage.

In practice, there are two modes in which the device may need to operate. One is a continuous, relatively high-frequency sampling mode. In this case, the self test would be sampled at over twice the highest frequency of interest to provide a ‘real-time’ normalization. The other case would be where an update every few minutes, or at power- up, would be acceptable; this mode might be useful in a safe-and-arming application where it is desirable to check the calibration once for a rela­tively short flight. In this case, the circuit in Fig. 11 would be modified to use a D/A converter, instead of the analog sample-and-hold, to hold the reference signal. The principle, however, is the same whether the device is being over- or under­sampled.

Conclusions

The design of a rugged silicon accelerometer has been described. The device has been shown to provide built-in damping to minimize problems due to peaking arising from mechanical reso­nances. The design includes built-in over-stops to protect the device from excessive forces; the device has been shown to survive a 400 x over-force. In addition, integral caps designed into the ac­celerometer minimize the probability that small particles will jam the motion of the device after long periods of use. Because of these features, it has also been possible to adapt this accelerometer for use in a self-testable mode. This allows it to be proved that the device is functional; further, data on temperature-dependent sensitivity changes al­lows the sensitivity over temperature to be com­pensated. The reliability feature has been added with no increase in the process complexity of the basic accelerometer.

Acknowledgements

The authors would like to thank IC Sensors’ Advanced Product group and particularly H. Jerman, A. Crabill, and J. Crawford for design assistance and processing of these and other ac­celerometer structures.

References

1    L. M. Roylance and J. B. Angell, A batch-fabricated silicon accelerometer, IEEE Trans. Electron Devices, ED-26( 1979) 1911.

2     R. E. Suloff and K. O. Warren, Solid-State Silicon Ac­celerometer, Air Force Armament Laboratories, United States Air Force, Eglin Air Force Base, FL, Apr. 1985.

3     H. Guckel, personal communication.

4     R. Buser and N. F. de Rooij, Tuning forks in silicon, Proc. IEEE Micro Electro Mechanical Systems Workshop, Salt Lake City, UT, U.S.A, Feb. 1989, p. 94.

5     L. M. Roylance, A miniature integrated circuit accelerome­ter for biomedical applications, Ph.D. Thesis, Stanford Uni­versity, Nov. 1977.

6     W. S. Griffin, H. H. Richardson and S. Yamanami, A study of fluid squeeze-applications, J. Basic Eng., Trans. ASME, (June) (1966) 451.

7     J. J. Blech, On isothermal squeeze films, J. Lubrication Technol., Trans. ASME, 105 (Oct.) (1983) 615.

8     CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 63rd edn., 1982, p. F-47.

Biographies

Henry V. Allen is vice president of engineering at IC Sensors. Dr Allen received his A.B. and B.E. degrees from Dartmouth College and an MSEE from Stanford University. In 1977, he was awarded the Ph.D. from Stanford University. Be­tween 1975 and 1982, Dr Allen worked as a research associate and then a senior research asso­ciate at Stanford’s Center for Integrated Electron­ics in Medicine, developing advanced, low-power implantable sensors and telemetry systems. In 1982, he was one of the founders of Transensory Devices, Inc. where he held the position of vice president of engineering, in charge of advanced sensor designs. Upon the merger of Transensory Devices with IC Sensors in January 1987, Dr Allen assumed his current position, where he has overall responsibility for the design and intro­duction of advanced sensors and silicon micro­structures.

Stephen c. Terry received his B.s. degree in electrical engineering from the Massachusetts In­stitute of Technology in 1970 and his M.s. and Ph.D. from Stanford University in 1971 and 1975. He continued his work on silicon micromachining in the Integrated Circuits Laboratory at Stanford as a senior research associate until 1980, at which time he founded Microsensor Technology. As R&D manager at Microsensor, he led the team developing a portable gas analyzer, which was based upon a gas chromatograph fabricated on a silicon wafer. In 1985 he joined Transensory Devices, which subsequently merged with IC Sensors, As R&D manager, he currently leads the development of advanced micromachined silicon structures.

Diederik W. de Bruin, a project engineer for IC Sensors, received an M.S. in electrical engi­neering in 1985 from Delft University of Technol­ogy, where he graduated in the sensor group of

Professor Middlehoek. From December 1983 until August 1984 and from October 1985 until January 1987, he worked for Transensory Devices, Inc. on flow sensors and pressure switches. Since January 1987, he has worked for IC Sensors on silicon accelerometers and accelerometer test systems.

WIDE DYNAMIC RANGE DIRECT DIGITAL ACCELEROMETER

Widge Henrion, Len DiSanza, Matthew Ip[1]
Stephen Terry and Hal Jerman**

Triton Technolgies, Inc.* and 1C Sensors, Inc.**

ABSTRACT

Silicon micromachining techniques have been used to fabricate a high-precision, micro-g accelerometer. Operat­ing in a closed loop configuration, the accelerometer utilizes electrostatic field sensing and electrostatic force feedback. The sensor assembly consists of an assembly of three silicon chips, bonded together at the wafer level. The center layer is comprised of the proof mass, springs and supporting struc­ture. Electrochemical etching from both sides of the wafer is utilized to form a double-sided symmetrical structure which minimizes orthogonal sensitivity and harmonic distortion. The springs which support the mass are formed with a composite material to obtain near-zero net stress over the operating tem­perature range. The two outside silicon caps form a cavity for the mass and provide accurately spaced electrodes as well as over-force protection.

The micromachined sensor is operated in a vacuum to eliminate non-linear viscous damping and to provide a high-Q second-order mechanical resonant circuit. Near criti­cal damping is provided by the closed loop control system. The control system is a highly over-sampled sigma-delta modulator, which produces a wide dynamic range and a direct digital output. The second-order spring-mass system with a high mechanical Q provides the integration for the sigma-delta modulator. Noise shaping of the modulator allows for a dy­namic range from micro g's to the g-range, while producing extremely low total harmonic distortion. The single-bit output is decimated by an 8,000-gate, two-stage digital filter de­signed specifically for the accelerometer and fabricated using 1.5 micron CMOS technology.

The paper will describe the micromachined 3.5 x 4.0 mm sensor chip, the "acceleration input-digital output” sigma-delta modulator and the finite element analysis of the mechanical structure. The performance obtained from proto­type units will be presented.

INTRODUCTION

The design of a micro-g accelerometer with a full scale input of 0.1 g, a dynamic range of 120 dB and total harmonic distortion of less than 0.1%, required a different de­sign approach. To achieve the 120 dB dynamic range, it was assumed that a digital output would be required. Initial at­tempts at converting the output of a capacitive accelerometer to an analog frequency, and then converting the frequency to a digital signal, did not yield results that would meet the above specifications. The capacitive sensor, when operated at at­mospheric pressure with the required narrow gaps, has non­linear viscous damping, over damping, and electrostatic force problems. To solve the viscous damping problems, a sensor operating in a vacuum was considered and eventually se­lected. Operation of the sensor in a vacuum results in a high Q resonant peak, which creates its own set of problems. All attempts to passively damp the sensor, without introducing dis­tortion, failed. It was then decided that the high Q second-or­der spring-mass system could be substituted for the second- order transfer function which is required in a second-order feedback system. The electrostatic forces on the mass, rather than being a problem, are used as the feedback force. The sensing, rather than being capacitive, is accomplished by electrostatic field sensing. A sigma-delta modulator system was selected because of its wide dynamic range possibilities. The use of a digital sigma-delta modulator results in an all digital closed loop, force balance sensor.

Numerous problems associated with an open loop
sensor are solved by the closed loop approach. The digital nature of the system begins at the sensor itself. The sigma- delta modulator's only concern is whether the position of the proof mass is above or below its at-rest position, and not by how much. Therefore, this closed loop system has a digital form from the mechanical spring mass on through all of the electronics. Using the sensor in a closed loop feedback con­figuration constrains the proof mass to a position very near its at-rest position. The proof mass’s total excursion is reduced by a factor equal to the open loop gain (in the case of a sigma-delta control system, the gain is signal dependent). The amount the mass position differs from it’s at-rest position at the end of a sample period is carried forward to the next sample period.

The output of the sigma-delta modulator is a high speed serial bit stream. This serial bit stream is then con­verted to a binarily weighted sampled word by use of a digital decimation filter.

Once the sigma-delta system configuration was se­lected, the next step was to select a sensor design to meet the modulator requirements and specifications. The decima­tion filter, as well as the sensor and the sigma-delta modulator will be described in the following sections.

SENSOR DESIGN

The accelerometer consists of a 500 micron thick, <100> lightly doped single crystalline silicon (SCS) spring- mass layer, sandwiched between two identical material and thickness SCS layers. Except for the seal interlevel bond ar­eas, a gap of 1.7 microns separates the top cover layer and the middle mass layer. The same gap also appears between the bottom layer and the middle mass layer. In order to allow for the sag of the proof mass due to the earth's gravity, a depression is etched into the bottom layer and a mesa on the bottom of the top cap is necessary. The small gap is essential for a low-g, high sensitivity electrostatic acceleration sensor. Because of the closed loop environment, the full scale travel of the proof mass is limited to only a small fraction of the gap. A cross sectional view of the sensor construction is illustrated in Figure 1.

Figure 1: Sensor Cross Sectional View

The proof mass is suspended evenly by 8 spring sections; four of the spring sections are attached to the top four corners of the mass and the remainder to the matching bottom corners. A picture of the spring mass layout can be seen in Figure 2. Each spring section, as shown in Figure 3, is equivalent to having a pair of double cantilever beams, joined together by a stiffener. The stiffener is used to prevent

any torsional components of the spring from creating non- linearities. Each spring is composed of 200 micron long, 50 micron wide, and 1.3 micron thick undoped fine-grain polysilicon, silicon oxide, barrier metal, and gold. The present spring materials and their thickness and width ratios, were se­lected only after extensive research in processing techniques and finite element simulations. This is necessary in order to manufacture a flat spring using materials with different coeffi­cients of thermal expansion. Flat springs are extremely impor­tant to ensure good open loop linearity and the correct stiff­ness. An SEM picture of the spring section can be seen in Figure 3. The proof mass is basically a 1000 micron square x 500 micron thick prism with the corners etched back slightly. The <111> plane etch slope from the surface to the middle of the mass increases the volume by 40%, producing a silicon mass of approximately 1.63 mg. ^*

sense electrodes, guards and substrates are brought out through diffused tunnels underneath the seal rings, and on to the external bond pads. The tunnels are P-diffusions in N- tanks. Internal inter-layer electrical connections are made through bump bonds. All the bump bonds possess the same elevation as the seal such that the electrical connections are made at the same time as the seal bonds.

The open loop fundamental resonant frequency of the accelerometer design is 266 Hz. The closed loop cut-off frequency is in the kilohertz range. However, the low pass decimation filter has a cut-off of 200 Hz. Other vibratory modes of the sensor are much higher in frequency than the fundamental. Figure 4 shows the resonant frequencies of the first 3 modes of the sensor.

The 8 spring sections on both the top and bottom of the proof mass not only provide the most balanced and linear spring-mass system, they also provide the rigidity to resist cross axis excitation and rotation from the horizontal axis. Finite element analysis showed that the cross axis motion is less than .001% of the sensing axis sensitivity. The acceler­ometer is also thermally stable, there is no air present inside the sensor to affect the damping due to temperature fluctua­tions. Both static and dynamic temperature analysis were per­formed to ensure no thermal mismatches would cause buck­ling in the springs. Since the composite cantilever springs themselves are free to change length, slight mismatch in their coefficients of thermal expansion with the surrounding material will not create any unwanted thermal stresses due to tempera­ture fluctuations.

The overall sensor dimension is about 3.5 mm x 4.0 mm, it is mounted on to a ceramic substrate inside a 24-pin hybrid package. The units built for testing have the sensing and control loop circuitry and the decimation filter chip mounted externally.

SENSOR PROCESSING

One of the unique features of this accelerometer structure is the complete front-to-back symmetry of the etched silicon proof mass and springs. This symmetry is achieved by performing each process step, including lithogra­phies, implants, diffusions, metalizations, and silicon etches,
simultaneously on both surfaces. Including all of the cap and mass processing, there are 27 photolithography steps per­formed on 5 of 6 wafer surfaces in the 3-wafer assembly.

The center wafer is processed by first Implanting (on both sides) and diffusing n-type tanks into the lightly doped p-type wafer. Into the tanks, p-type resistors are dif­fused to form tunnels and guard regions under the seals. These diffusions are followed by the deposition and patterning of low-stress polysilicon regions which serve as part of the springs. After the passivation of the poly, the metal electrodes and interconnects are deposited and patterned. Following the metalization steps, regions for the silicon etch are opened on both sides of the wafer. Note that since the etch proceeds from both sides of the wafer simultaneously, the metal must survive the entire length of the silicon etch. An anisotropic electrochemical etch is employed to undercut the springs and their supporting structure. The potential of the n-tanks and the p-substrate are controlled separately during the etch. The complex geometry of this device, as opposed to simple dia­phragm structures employing electrochemical etch stops, re­quired that the applied voltages be carefully controlled and optimized to result in the proper etched shapes. After etching half-way through the wafer, the etches meet, freeing the proof mass. After some residual passivation oxide Is removed to insure flat and stress-free supports, the caps are aligned and bonded to the center wafer. The device is then sawn apart Into individual die and the two levels of bonding pads exposed.

The fabrication of the cap wafers is somewhat sim­pler. The top cap is nominally flat, thermal grown silicon oxide is employed to adjust the gap between the top cap electrode and the proof mass with the 1-g sag. A vent hole is first etched through the cap to the central region of each device to provide a means by which the air surrounding the mass can be pumped out before use. The metal electrodes are then deposited and patterned. The bottom cap must allow for the 1-g sag of the mass, so a shallow depression, is formed be­fore the electrode metal is deposited. A schematic cross sec­tion of the device is shown in Figure 1.

The accelerometer die are assembled onto ceramic substrates which are in turn mounted in metal packages. To reduce the number of connections to the outside, the sense and drive electrodes and the guards on the upper and lower surfaces of the mass are connected together on the ceramic substrate. The metal package is then welded to a metal cover in a high vacuum welder.

SYSTEM

The major component blocks of the accelerometer system are shown in Figure 5. These components are: 1) the sensor, 2) the buffer amplifier and associated housekeeping circuitry, 3) the lead-lag network, 4) the quantizer, 5) the sampler, 6) the level shifter, and 7) the decimation filter.

SENSOR         LEAD-LAG     SAMPLER

BUFFER        QUANTIZER                      ^FILTER™

Figure 5: Accelerometer Block Diagram

The first block is the sensor and has been previ­ously described. The second block is a buffer amplifier which provides the necessary loop gain and isolation between the sense electrodes and the rest of the circuitry. It also provides a low output impedance unity gain drive for the guard elec­trodes. The lead-lag network following the amplifier provides the compensation necessary to stabilize the loop. The next block, which is the quantizer, utilizes a comparator to deter­mine if the input signal is above or below a reference level. It provides an asynchronous digital output. The sampler con­verts the output of the quantizer to a synchronous digital sig­nal. The level shifter in the feedback converts the digital pulses from the sampler to extremely accurate (in amplitude and time) pulses. These feedback pulses generate the force which is applied to the proof mass.

Finally, there is the decimation filter which is a cus­tom digital signal processor. The purpose is to produce a 24 bit digital output word and to act as a brick wall low pass filter. This stage has many requirements, and some of them are: that it be able to run at the desired sample clock speed (up to 1 MHz), that it have programmable decimation ratios, and that it produce output levels and format suitable for use with other processors.

SENSOR

Force Feedback:

The closed loop sigma-delta converter requires a single bit digital to analog conversion of plus or minus one full scale feedback unit (shown as the level shifter in Figure 5). A unit in this case is a fixed amount of force which is equal to a multiple (generally about 2) of the full scale “g” range. The mechanical sensor converts either a fixed charge applied to the center mass electrode, or a fixed voltage applied between the top or bottom force electrodes and the center mass, to a plus or minus unit of force. The purpose of the feedback from the closed loop system is to always move the proof mass back to a position in the center of device. If a voltage feedback method is employed, then the center electrodes on the mass are grounded and a voltage is applied to either the top or bot­tom cap electrode while the other is grounded. The mass will always move toward the ungrounded electrode. The equation for the feedback force in terms of the physical parameters of the device and the terminal voltages is given by:

F = -eAv*/2x*

where e is the permittivity of free space, A is the area of the force electrodes, x is the distance of the mass to the fixed electrode on the cap and V is the applied feedback voltage. This is of course non-linear with respect to x for any given fixed V. The distortion produced by this non-linearity however can be made small in a closed loop feedback system where the change of x is very small compared to the gap.

An alternative where extremely low distortion is re­quired is to use constant charge feedback. The expression for the force in this case is:

F = Q/(2eA)

where Q is a fixed packet of charge. The equation is linear and the force is not a function of the displacement x. The implementation of charge feedback is more difficult than volt­age feedback, which has proven to be satisfactory for the re­quired specifications.

Sense:

In order to sense the position of the proof mass, three sense electrodes are employed. Two of the electrodes are fixed and are on the top and bottom caps. The third elec­trode (which is actually two electrodes) is located on the mass and moves with it. A voltage V is applied between the cap electrodes. The mass or "center” electrode is connected through a switching arrangement to a high input impedance amplifier. The amplifier is essentially "floating” electrically for at least 50% of the time during a single control cycle (which is on the order of 2 microseconds for 512 kHz system clock). The total distance from the top cap electrode to the bottom cap electrode is fixed, and hence the electric field is fixed and uniform. If the proof mass is assumed to be conductive, then the equation for the electric field is given as:

E = V/(2.gap)

Then by definition, the voltage on the center electrode with respect to ground at any position x (defined as zero at the bottom electrode and twice the gap at the top electrode) in the uniform field is given by:

Vsense = Ex

This simple relationship implies that the position of the mass can be found by monitoring the voltage on the sense elec­trode. In reality, the input impedance of the amplifier used to buffer the signal is finite, and hence, the signal will always be smaller than expected. This error is very small however and relatively static. A more serious problem with real devices, however, is that they will always accumulate charge over time. The concern here is that this charge build up will cause a time varying (non-static) error voltage. To address this issue, a “housekeeping" cycle is required. This cycle is performed as often as possible to prevent charge accumulation on the elec­trodes, switch, and amplifier. This step is also needed to pre­vent the center sense electrode from acquiring a charge and producing a force error. An added side benefit of this cycle however is that it actually helps to reduce sensor noise. The noise reduction is possible because most of the sensor noise is resistive in nature. This noise source resistance forms an RC time constant with the electrode capacitance, and thus the noise is reduced by the ratio of the housekeeping frequency to the RC product.

Guards:

As with any small signal level, high impedance transducer, good shielding and layout is mandatory. To this end great care has been exercised in the physical placement of all lines and electrostatic shields. Guard rings and diffused regions have been used throughout. The guards are actively driven wherever possible to help reduce stray capacitance and any adverse loading or coupling effects the stray capaci­tance might produce. In addition, charge injection compen­sated MOS switches have also been used to minimize errors.

SIGMA-DELTA

The electrostatic spring-mass sensor is a mechani­cal low pass filter. The cut-off frequency (limit of the pass band) or resonance is given by:

0>n = V(K/M)

where K is the spring constant and M is the mass, con is the natural resonant frequency in radians. The transfer function of the sensor is of the form:

H(S) = C/[S^z+S(0n/Q+(0n²]

where C is a gain constant and Q is the quality or the recipro­cal of the damping the mass encounters (quite small in a high vacuum).

This low pass characteristic of the sensor is used advantageously by the closed loop system. The sigma-delta converter produces a digital signal which is a representation of the analog acceleration input. The advantage of using a closed loop system is reduction of the non-linearities, resonant peaks, and unwanted electrostatic effects which would other­wise be produced by the device. The advantage of using a sigma-delta converter as the feedback method is that the out­put as well as internal signals are all digital.

In all analog to digital (A/D) converters, the analog signal (in this case acceleration) being represented has been “quantized”, and can be no more accurate than one half the least significant bit (Isb) that the converter produces. Obvi­ously then, the smaller the value of the Isb available, the finer is the resolution or accuracy (this determines the smallest ana­log signal which the converter can represent). Since it is also desirable to accurately represent large signals, these convert­ers should work over as wide a dynamic range as possible. What this really means is that the converter should produce as large a digital word as is meaningful to the technique involved.

Another figure of merit of A/D’s is their linearity, which, simply stated, means how the accuracy or scale factor of the A/D conversion varies throughout the dynamic range. Sigma-delta converters are extremely linear and can offer very large dy­namic range with relatively simple circuitry. It is for all of these reasons that this method has been employed for use with the sensor.

A sigma-delta converter uses two techniques to re­duce the quantization noise and thus decrease the minimum detectable signal. The first assumes that the total noise power is constant and that it has a flat spectral distribution. In this case, the signal plus the noise are sampled at a rate much higher than the signal frequency, and by doing so, the noise is spread over a larger bandwidth. Since the noise power is constant and the noise bandwidth is increased, the magnitude of the noise in the baseband is reduced. Each doubling of the sampling frequency further reduces the noise by 3 dB (this is equivalent to 1/2 of a binary bit). The quantization noise of the sigma-delta modulator is much more aggresively reduced by the noise shaping characteristics of the system. Here the noise power is once again assumed to be constant but now it is spectrally shaped. If the frequencies of interest are below a cutoff frequency wn, then the noise shaping is used to push the baseband noise down for all frequencies below u)n, and it rises at frequencies above o>n. The converted output signal is digi­tal, and so digital filter techniques are employed to strip off the unwanted high frequency components, and hence most of the noise. The noise shaping results from the signal and the quantization noise having different transfer functions (see Fig­ure 6). A low pass filter is used to perform the noise shaping.

Figure 6: Signal and Noise Transfer Functions

The order of the filter (n) along with the sampling ratio deter­mine the extent to which the in-band noise is reduced. The combined noise reduction in dB obtained by oversampling and noise shaping is (3+6n) times the number of octaves of over- sampling. (See Figure 7 for a typical sigma-delta output spec­trum.)

Since the sensor is a second order low pass filter and is the noise shaping transfer function, the theoretical reso­lution of the converter will be 3+(6»2)=15 dB times the over- sampling ratio. Therefore for eight octaves of oversampling the resolution will be 120 dB.

Figure 7: Sigma-Delta Spectrum Plot

DECIMATION FILTER

The decimation filter block diagram is shown in Fig­ure 8. It is a custom digital signal processor (DSP) which is

used to reduce the long length, high rate serial bit stream that comes from the sigma-delta into a “decimated” 24 bit digital word. It is also used to strip off the high frequency noise by employing a brick wall low pass filter. The filter is realized in two programmable sections and allows for numerous decima­tion ratios of up to 1024. The output word is "burst” at a high rate along with a frame synchronization signal so that up to 32 accelerometers can be time division multiplexed on a single line. The output format and levels are directly compatible with most DSP chips and also easily interfaced to most computers including PC’s. In a typical application, the computer or DSP chip would perform a Fast Fourier Transform (FFT), which would yield complete amplitude and frequency information of the acceleration being analyzed.

RESULTS

Some experimental units were specially constructed to measure the electrostatic control of mass displacement by varying the amount of voltage on the bottom electrode. These units have a large etch hole on the top layer, so the vertical movement of the proof mass can be monitored through inter­ference microscopy. In addition, the force and the sense electrodes were shorted together at the mass layer and the bottom layer, so a bigger electrostatic force can be produced when a voltage is applied. The top layer only served as a protective layer with no force or sense electrodes. When a DC voltage is applied at the bottom electrode, the mass will move according to the following relationship:

V = >/(2 Kx*/Ae)(d-x)

where K is spring constant, d is the original at-rest gap dis­tance, x is the displaced distance between the two electrodes, and e is permittivity of free space. A series of different volt­ages was applied to the bottom electrodes during the test and the displacement of the mass measured. The results of the experiment can be seen in Figure 9. The results show that the 6

0

Figure 9: Proof Mass Displacement vs. Voltage

empirical data matches very well with the analytical formula with the gap approximately equal to 3.7 microns. The figure also shows that when the mass displacement reaches a point at which the rate of change of the electrostatic force exceeds the spring restoring force, the system becomes unstable. The
unstable point was experimentally observed when the mass displacement exceeded 1 micron.

A variety of different experimental sensor configura­tions have been examined. All were designed to be 0.1 g devices with a resonance of about 266 Hz. The sensors’ characteristics were verified using a B&K 4809 shaker mounted on a double isolation table in an anechoic chamber (measured noise floor of less than -160dBg/%/Rz). Electrical outputs were observed on an HP 3561 dynamic signal analyzer and an HP 3585A spectrum analyzer. The average resonance was about 350 Hz, the noise floor was well below -100 dBg- /x/Hz (no housekeeping or noise reduction techniques were used during these tests), the dynamic range was approaching 100 dBg, and all sensors had low pass characteristics for both mechanical and electrical drive. Sensitivity was hampered by stray wiring capacitance, but when corrected for the strays, the sensitivity approached 0 dBv/g.

SUMMARY

A 0.1g full scale accelerometer designed to operate over a 120 dB dynamic range has been described. It is a direct digital sensor in the truest sense. The device was de­signed to withstand severe shock of over 700g's in any direc­tion. New accelerometers are under development to comple­ment the 0.1g unit. One of the new accelerometers will oper­ate over a range of 10 micro-g’s to 10g’s. A low range unit is in development with a minimum detectable signals of -160 dBg (or 10 nano-g’s).

For extremely low signal levels, quantization noise floors, circuit noises and mechanical noise (Browning noise) must all be considered in the design of accelerometers. Test­ing at these low levels of accelerations require anechoic chambers specially designed for low frequency noise rejec­tion, with massive gas isolated tables supported on geologi­cally stable bedrock.

Micromachined silicon accelerometers can be built to serve widely diverse markets at a reasonable cost. Fre­quency ranges from DC to thousands of hertz, accelerations from nano g's to hundred of g's, and dynamic ranges in ex­cess of 120 dB can all be accommodated in small rugged silicon accelerometers.

REFERENCES

[1]      B.E. Boser and B.A. Wooley, "The Design of Sigma-Delta Modulation Analog-to-Digital Converters”, IEEE Journal of Solid State Circuits, Vol. 23, No. 6, Dec. 1988.

[2]      J.c. Candy, “A Use of Double Integration in Sigma-Delta Modulation”, IEEE Trans. Commun., Vd. COM-33, pp. 249-258, Mar. 1985

[3]      J.c. Candy, "Decimation for Sigma-Delta Modulation”, IEEE Trans. Commun., Vol. Com-34, pp! 72-76, Jan. 1986.

[4]      H. Inose, Y. Yasuda, and J. Marakami, "A Telemetering System by Code Modulation”, IRE Trans, on Space Electron­ics and Telemetry, pp. 204-209, Sept 1962.

[5]      Martin A. Plonus, Applied Electro-Magnetics. McGraw- Hill, Inc., pp. 186-189, 1978.

[6]      L M Roylance, J.B. Angelí, "A Batch-Fabricated Silicon Accelerometer", IEEE Trans, on Electron Devices, Vol. Ed-26 No. 12, pp. 1911-1917, 1979.

[7]      Felix Rudolf, Alain Jornod, Philip Bencze,”Silicon Microac­celerometer”, Transducers '87, pp. 395-398, 1987.

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[1]386_______ 28k V____________ »0008

Figure 3: SEM of Accelerometer Spring

The displacement of the proof mass is controlled by a pair of concentric hexagonal-shape force and sense elec­trodes, located at the top and bottom surfaces of the mass. Identical patterns of the force and sense electrodes are lo­cated on the top and bottom covers, opposite their corre­sponding force and sense electrodes on the proof mass sur­faces. The force and sense electrodes are thin metalized lay­ers of gold, with leads connected to the gold of the composite springs and to the bonding pads outside the accelerometer. The areas of the sense and force electrodes are 548,000 and 127,000 square microns respectively. Surrounding the force and sense electrodes on the mass are guard rings and dif­fused guard plates.

The top and bottom covers are sealed to the middle spring-mass layer through a metal seal ring along the periph­ery of the sensor. Electrical conductors from the force and