Sensors and Actuarors A, 24 (1990) 175-179

Experimental Determination of Silicon Pressure Sensor Diaphragm Deflection

ZORAN DJURIC, MILAN MATIf?, JOVAN MATOVIC, RADOMIR PETROWe and NEVENKA SIMIt?Ic

IHTM-Deparrment, Institute of Microelectronic Technologies, Njegoseva 12, I loo0 Belgrade (Yugoslavia)

(Received November 14, 1989; in revised form March 20, 1990; accepted April 5, 1990)

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Abstract

A method is presented for the accurate deter- mination of the deflection of diaphragms com- monly used for miniature piezoresistive and capacitive pressure sensors. The method utilizes a well-known apparatus for thin-film thickness mea- surements (Talystep), an instrument for accurate pressure measurement and control (Mensor) and a sample holder for simultaneous pressure appli- cation and diaphragm deflection measurement. The deflection measurements for a stiffened and a square diaphragm are presented and compared to analytically calculated results from the literature. High-precision deflection measurements reveal the existence of build-in stresses.

Introduction

Silicon pressure sensors with diaphragms have been used for more than 25 years [ 11. Due to the up-grading of silicon micromachining technology during the last couple of years, miniaturization has progressed and these sensors are becoming more and more reliable and accurate [2-lo]. For example, it is possible to batch fabricate I pm diaphragms using either the boron etch-stop tech- nique or electrochemical silicon etching [8]. The requirements for high accuracy, especially in small pressure measurements, led to the use of stiffened diaphragms with a rigid central area [9] instead of the conventional circular or square plane di- aphragms.

The design of pressure sensors is based on the small-deflection plate theory [ 111. The fact that silicon is an anisotropic material and that the diaphragm edges cannot be ideally clamped [2] complicates the theory somewhat.

In practical cases, so-called intrinsic stress of the sensor chip may occur during manufacture (e.g., thermal oxidation of silicon, boron diffu- sion, etching etc.). Additional stress may also occur later on, during sensor mounting in the housing (electrostatic silicon bonding to glass, eutectic bonding etc.).

The deflection of silicon pressure sensor di- aphragms is often comparable with or larger than

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the diaphragm thickness. In these cases the above- mentioned small-deflection plate theory is not ap- plicable. It is then necessary to use large-deflection theory [ 111, which complicates the analysis even more.

There are various useful methods for silicon pressure sensor modelling [2, 3,7,9], based mainly on the finite-difference or the finite- element method, but it is very difficult to take into consideration all relevant factors influencing di- aphragm behaviour.

Due to the above-mentioned facts, only a de- tailed experimental characterization of thin di- aphragms can determine the characteristics of these sensors accurately [8].

It is interesting to note that only a few papers deal with the problem of the experimental deter- mination of diaphragm deflection. Tufte et al. [ 1] gave a direct comparison between interferometri- tally measured diaphragm deflection and the deflection calculated by the isotropic theory of Tinioshenko and Wonsowsky-Krieger [ 111. Also, Lee and Wise [2] compared the numerical simula- tion using the SENSIM program to the interfero- metric picture of a deflected diaphragm.

Experimental Set-up

The experimental set-up for the direct measure- ment of silicon diaphragm deflection is shown in Fig. 1. The sensor chip, electrostatically bonded to a glass substrate, is fixed on a sample holder which enables the desired pressure to be applied

1 I

Fig. I. Scheme of the experimental set-up for deflection mea- surement of silicon pressure sensor diaphragm.

0 Elsevier Sequoia/Printed in The Netherlands

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and the diaphragm deflection to be measured simultaneously.

The pressure is controlled and measured by a precision pressure controller. The deflection of a diaphragm for a chosen pressure is measured as a function of x and y coordinates by a stylus instru- ment for profile measurement (profilometer). The outputs from both instruments are fed to a com- puter, which displays the functional dependence of the diaphragm deflection w =f(x,y). In our case the instruments used were as follows: a Men- sor (Mensor Corporation) pressure controller, model 12275, with a declared total accuracy of 0.04% full scale, and a Talystep (Rank-Taylor Hobson Ltd.) profilometer. After careful calibra- tion, the accuracy of the profilometer is of the order of + 1% of full scale of the range used. The stylus force can be adjusted in the range lo- 100 PN. For the measurement of deflection, the greatest available range of the instrument was used. The measured deflections were a few mi- crons. The electrical signal from the profilometer was measured by a digital voltmeter. The resolu- tions of the voltmeter and pressure controller were matched. The measured deflections during one measurement ranged over three orders of magnitude, while the repeatability was almost per- fect and the hysteresis negligible. The maximum amplification of the profilometer was lo6 in the nine ranges, which means that a displacement of 10e9 m should have been observable. However, at large amplification the limiting factor would be the thermal and overall stability of the instru- ment. The measurements of the maximum deflec- tion w =f(p) were more reliable, as lateral movement of the stylus was avoided, and were limited practically by the instrument’s accuracy and resolution only.

The method is convenient for all diaphragms where the stylus force can be neglected. This is easily confirmed experimentally by measurements of deflection in the linear response region, by applying first positive and then negative pressure of the same absolute value. The same diaphragm deflection in both the positive and negative direc- tions shows that the stylus force (as well as the influence of gravity) is negligible.

The sensor chips were made of (100) orienta- tion n-type silicon with a resisitivity of 3-5 R cm. The diaphragms were micromachined by standard anisotropic silicon etching in a KOH/n-propanol/ water solution (l/1/4). The etching rate was 1 pm/ min at a solution temperature of 80 “C. An SiOz layer, produced by high-temperature oxidation in steam and approximately 1 pm thick, was used as an etching mask.

The chips were electrostatically bonded to a substrate of borosilicate glass, DURAN (Schott 8330), with a thermal expansion coefficient of Q,,~,,,, = 3.25 x 10W6 K-‘, close to the coefficient of silicon.

To demonstrate the measurement method, two types of diaphragms were used: a stiffened square diaphragm with a rigid central area and a conven- tional square diaphragm (Fig. 2(a) and (b)). Their planar dimensions were defined by standard photolithography and measured by an infrared microscope. In the case of thin diaphragms ( c 10 pm), these dimensions were measured on a standard transmission microscope. The di- aphragm thickness was measured on a Talystep.

Experimental Results

As an illustration of the possibilities of the proposed method, Fig. 3 depicts the measured deflection profile of a stiffened square diaphragm with a rigid centre. The dimensions of the di- aphragm are given in Fig. 2(a), h = 22 pm.

To compare our measurements to published numerical and analytical results [2,3, 5, 8, 10, Ill, we performed measurements on two conventional plane square diaphragms (Fig. 2(b)), 24 pm and 8.8 pm thick respectively.

The results of the thicker diaphragm deflection measurements (h = 24 pm, 2a = 1840 pm, chip di- mensions 2.8 mm x 2.8 mm) are shown in Fig. 4. The applied pressure was 1000 mbar. Figure 4 depicts the qualitative comparison of our experi- ment and the calculated results from a recent study [3].

In order to compare our experiment to theoret- ical calculations performed for dimensionless

Fig. 2. (a) Stiffened square diaphragm with a rigid centre part; (b) conventional plane square diaphragm.

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the dimensionless pressure pa4/Dh, where D = Eh3/12( 1 - u2). For comparison, theoretical curves are also shown. Curve 3 is calculated using the equation [8]

p = Eh4/( 1 - v2)[4.2w,/h + 1.58(w,/h)3] (1) where h is the diaphragm thickness, w, the maxi- mum deflection, E = 1.698 x 10” N/m2 and v = 0.062 [3, 51.

Curve 4 is obtained by a similar calculation method presented in ref. 11.

The maximum deflection of the thicker di- aphragm is almost linear and is in very good agreement with both theoretical curves in the pressure range 0 to 2 bar.

The large-deflection measurements, i.e., w,/ h > 0.3, are especially important and are pre- sented as curve 1 for the thinner diaphragm. Curve 1 is much below the theoretical curves in the whole pressure range. The investigated di- aphragm was only partially clamped and this can be clearly seen in Fig. 5. Therefore an increase of maximum deflection may be expected, which is obviously in contradiction with our experimental results. There are several possible causes for this. As we mentioned above, a reasonable assumption is that the intrinsic built-in stresses along the diaphragm edges cause a lower diaphragm deflec- tion [6-8, 121.

Bonding was performed at 300 “C, followed by quick cooling to room temperature. In spite of the fact that the chosen temperature was expected to result in the lowest residual stresses [ 121, some stresses are evidently present. They are probably induced during some other stage of manufacture. A rough estimate of the built-in stresses in this case can be obtained on the basis of the analysis made in ref. 8 for a circular diaphragm with clamped edges. If the ratio of the theoretical and measured deflections is 0.8, a simple calculation based on the results from ref. 8 reveals residual tensile stresses of the order of 50 bar.

Discussion

A method for the experimental determination of silicon pressure sensor diaphragm deflection is presented here. The data obtained for two differ- ent thicknesses of square diaphragms are com- pared to the calculations of other authors.

More detailed measurements would contribute to the design of pressure sensors with the desired characteristics. For example, the mechanical stress distribution may be obtained from experimental data via the second- and higher-order derivatives of w(x, y). The discussed method may prove itself useful for the determination of the optimum posi-

tion of piezoresistors, when high sensitivity and linearity are desired. The diaphragm areas where partial compensation of the non-linearity caused by both the deflection and piezoresistive co- efficients occurs may also be determined by this method. It is well known that the piezoresistance of the resistors exhibits a certain non-linearity. This non-linearity may be partially compensated for by a minor displacement of the piezoresistor to the side where the non-linearity of the stresses tends to compensate for the piezoresistor non- linearity [ 131.

Our future investigations will consider some interesting phenomena connected with the stress distribution for various diaphragm shapes.

High-precision deflection measurements may also be used in the investigation of the following phenomena: piezoresistive or capacitive sensor output as a function of the diaphragm deflection and pressure, the variation of radial and tangen- tial piezoresistivity as a function of pressure and deflection on the resistor position, the deflection changes along the piezoresistor, the influence of the electrostatic driving force of capacitive sensors etc. They could also bc useful in the design of various other micromachined devices.

References

1 0. N. Tufte, P. W. Chapman and D. Long, Silicon diffused-element piezoresistive diaphragms, J. Appl. Phys., 33 (1962) 3322-3327.

2 K. W. Lee and K. D. Wise, SENSIM: a simulation pro- gram for solid-state pressure sensors, IEEE Trans. Electron Devices., ED-29 ( 1982) 34-41.

3 T. Y. Bin and R. S. Huang, CAPS: a thin diaphragm capacitive pressure sensor stimulator, Sensors and Acruu- tom, I1 (1987) l-22.

4 K. Peterson, The silicon micromechanics foundry, Proc. IEEE Micro Robots and Teleoperators Workshop, Hyannis, MA, U.S.A., Nov. 9-11, 1987.

5 S. K. Clark and K. D. Wise, Pressure sensitivity in an- isotropically etched thin-diaphragm pressure sensors, IEEE Trans. Electron Devices, ED-26 (1979) 1887-1896.

6 J. A. Voortthnyzen and P. Bergveld, The influence of tensile forces on the deflection of circular diaphragms in pressure sensors, Sensors and Actuators. 6 (1984) 201-213.

7 A. Yusakawa, S. Shimada, Y. Matsuoka ‘and Y. Kanda, Design considerations for silicon circular diaphragm pres- sure sensors, Jpn. .I. Appl. Phys., 21 (1982) 1049- 1052.

8 H. L. Chan and K. D. Wise, Scaling limits in batch-fabri- cated silicon pressure sensors, IEEE Trans. Electron Devices, ED-34 (1987) 850-858.

9 A. Yasukawa, M. Shimazoe and Y. Matsuoa, Simulation of circular silicon pressure sensors with center boss for very low pressure measurement, IEEE Trans. Elecrron Devices, ED-36 (1989) 129% 1302.

10 M. Poppinger, Silicon diaphragm pressure sensors, in P. Balk and 0. G. Folberth (eds.), Solid State Deoices 1985, Elsevier, Amsterdam. 1986. DD. 53-70.

11 S. Timoshenko and S. Wonsowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1959, §102.

12 W. H. Ko, J. T. Sumito and G. J. Yeh, Bonding techniques for microsensors, in C. D. Fung, P. W. Cheung, W. H. Ko

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and D. G. Fleming (eds.), Micromachining and Micropock- aging of Transducers, Elsevier, Amsterdam, 1985, pp. 41- 61. K. Suzuki, T. Ishikara, M. Hirata and H. Tanigawa, Nonlinear analysis of a CMOS integrated silicon pressure sensor. IEEE Trans. Electron Devices, ED-34 (1987) 136& 1367.

Biographies

Zoran Djuric received B.S., M.S. and Ph.D. degrees in electrical engineering from the Univer- sity of Belgrade, Yugoslavia, in 1964, 1968 and 1972 respectively. In 1964 he joined IHTM, Insti- tute of Microelectronic Technologies and Single Crystals (IMTM), Belgrade. He is currently engaged in the field of physics and technology of semiconductor devices. Presently Dr Djuric is head of the IMTM, and at the same time he lectures as a professor at the Faculty of Electrical Engineering, University of Belgrade.

Milan MatiC received his Ph.D. degree in physics from the University of Belgrade, Yugoslavia, in 1978. Until 1983 he worked in the Atomic Physics Laboratory of the Institute of

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Nuclear Sciences on the research of atomic colli- sion processes. In 1983 he joined IMTM, Bel- grade, Yugoslavia. His current interests include vacuum technologies and sensor technologies and measurements.

Jovan Matovit received his B.S. in mechanical engineering from the University of Belgrade, Yugoslavia, in 1976. He is currently working at IMTM, Belgrade, as a research engineer. His cur- rent interests include semiconductor sensor tech- nologies and measurements.

Radomir PetroviC is a research engineer at IMTM, Belgrade, Yugoslavia. He received a B.S. (1971) and M.S. (1982) in electrical engineering from the University of Belgrade. His current re- search interests include surface and thin-film tech- nology.

Nevenka SimiEii received her B.S. in chemical engineering from the University of Belgrade in 1985. She is currently working at IMTM, Bel- grade, Yugoslavia, where she is engaged in semi- conductor sensor technologies.