252 ICSE’96 Proc., Nov. 1996, Penang, Malaysia

DESIGN AND CALIBRATION OF A 3-D MICRO-STRAIN GAUGE FOR IN SITU ON CHIP STRESS MEASUREMENTS

Tommy C. P. Lo, Philip C. H. Chan Department of Electrical and Electronic Engineering

Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong

Abstract Silicon piezoresistive stress sensors can be used for in

situ stress measurements during fabrication and encapsulation of the silicon die. These sensors are fabricated in the silicon die using the conventional silicon processing steps. In this paper we describe a stress sensor or a 3-D micro-stain gauge for such applications. We shall describe the design and fabrication of the test chip, experimental results as well as the detailed calibration procedures using a four-point bending (4PB) fixture. The resistance of stress sensors was found to vary linearly to the applied stress. The piezoresistive coefficient was calculated and found to agree with the reported values for silicon. The problems associated with the calibration process was also discussed.

I. THEORY OF PIEZORESISTIVE MEASUREMENT

The piezoresistive coefficients can be determined by [11[21,

where 7c. is the element of sixth order tensor. R, is the resistance of the stress sensor parallel to the uni-axial applied stress. Ry is the resistance of the stress sensor perpendicular to the uni-axial applied stress. However the nl;p + 7 ~ ; ; and a:: can also be determined by using the

stress sensor that is rotated by an angle A€).

The equation are then modified as follows,

11. DESIGN AND FABRICATION OF TEST CHIP

The layout of the stress test die was shown in Figure 1. Two stress sensors were placed orthogonally for the measurement of the parallel and perpendicular components of the applied stress. The crystal orientations of these two resistors were < 1 i o > and < 110 > respectively. Another pair of the stress sensor was rotated 135” with respect to the axis of the applied stress. The crystal orientations of these two resistors were < Too > and < 010 > respectively. Each stress sensor is carefully designed so that all of them have 154 squares. A Van der Pauw structure was used to measure the sheet resistivity.

The size of the resistors must be small in order to measure the local stress applied to the area rather than global stress. The sheet resistivity was about 200Q/O. The typical resistance of the resistor is between 27kQ to 30k Q. The measurable change in resistance due to applied uni-axial stress is about 1.45kQ. The percentage of resistance change is 1 to 7%.

Thermal oxide of thickness 5100a were grown on both n-type and p-type silicon wafers. Next, the locations of resistors were etched. The resistors were implanted using boron on n-type wafers while using phosphorous on p-type wafer. Afterwards, the wafers were subjected to annealing and drive-in diffusion. The expected surface

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ICSE’96 Proc., Nov. 1996, Penang, Malaysia 2.53

concentration of the dopant is about 10’8cm-3 in order to form good ohmic contacts. Diodes were also fabricated on the same wafer as temperature sensor. Next, aluminum and tungsten were sputtered to form the metal layer. Tungsten was used to suppress aluminum hillocks. Finally, a passivation layer (low temperature oxide and silicon nitride) was deposited. The stress sensors are placed at the center of the die to minimize the effect of probe forces on the bonding pads. This reduces the applied stress that could lead to experimental error in the measurement.

III. EXPERIMENTAL RESULTS AND DISCUSSION

The equipment used in applying stress in this study is a four-point bend loading fixture. Such a structure has been used previously by other researchers in the area [11[41[51. The schematic of the four-point bending (4PB) fixture was shown in Figure 2.

The relationship between the applied load and the stress was reported in [l],

3F( L - d ) c T = (5)

t2h This equation was derived using classical strength of

materials beam theory [6] assuming a uniform stress state for points on the top of the specimen and within region specified by the dimensions “d” and “h”. This also assumes that t and h are small when compared to d and L.

Ceramic material is used in points-of-action of the four- point bend fixture. Since the stiffness of the wafer is very high, the sharp point in stainless steel will become obtuse after several measurements. This could induce error in calculation of applied stress.

Resistance was measured using a HP 34401A multimeter, which has a six-and-half digit resolution. The 4-point measurement mode of multimeter was used to measure the sheet resistance. In the four-point measurement, the resistance of lead wires and contact resistance were excluded in the measurement. The measurement error was less than 5x10m5%. A HP 4145A semiconductor parameter analyzer was used to measure the IV characteristics of the stress sensor to assure the contact is ohmic contact.

The main error was due to the four-point bend loading fixture. The source of error was previously documented in paper [ll. The error can be easily calculated by using Equation (5).

3AW( L - d ) ACT = (6)

t2h

In this study, 30g is added in each step. The weights were calibrated to H.01g. Thus the error induced by the weight was 0.03%.

By using Equation (5 ) , the percentage error is given by

A 0 A ( L - d ) %Error = 100- = 100 1 0 1 I L - d I (7)

The Length of L-d is 1 inch. The tolerance of the length error is 0.001 inch. Thus the error due to the length measurement is about 0.1 %

Stress will not be applied parallel or perpendicular to the wafer strip if it was misaligned by an angle 8. According to [l], the error is approximately 1% if wafer strip was rotated within 5”. Thus an aluminum guide was used to assure the rotation misalignment was within 5”.

In addition, there could be measurement error if the stress sensor was not placed at the midpoint of the region defined by dimension “d” and “h”. This is illustrated in Figure 4. Suppose d and S are the dimensions. The distance S+AS is the actual length between the right support and the right applied force. Using the strength of materials beam theory, the percentage error would be,

As (8) ACT

%Error = 100- = 100- I CT I l2Sl For S=0.5 inch and the error in loading from the center

of the region is about 0.02 inch that is indicated by using marks in setup. Therefore, the error due to the loading asymmetry is 2%.

Although, in our study, the measurement is done at room temperature, the resistance versus temperature was also studied. The temperature effect can be expressed in Equation 9 [5]. a is the temperature coefficient of resistance. p is the piezoresistive temperature coefficient.

R = & +(a, +P1)T+(a2 +p2) T 2 + ... (9)

Figure 5 shows that the resistance change was quite linear with the temperature. Thus, the second and higher order terms of the equation can be ignored. The al+P1 is determined to be 2.82H.O2W0C.

V. CHARACTERISTIC OF PARALLEL AND PERPENDICULAR STRESS SENSOR

Figure 6 shows the variation in the resistance of the stress sensor parallel and perpendicular to the applied stress for the n-typed sensors. Thus the x:, + Z& and x:,can be calculated from Equations 1 and 2. The average 7tyl +7tr2 was found to be -548x10- Pa and the 12 -1

254 ICSE’96 Proc., Nov. 1996, Penang, Malaysia

n$ was found to be -1 18x10-12Pa-’. And the?$ + X$ is -484~10”~Pa-~ and X:4 is -136~10-’~Pa’’, the values match the previous work reported[3]. Figure 7 shows the variation in resistance of the stress sensor parallel and perpendicular to the applied stress for the p-typed sensors.

Also, the X{ +Xi and Xi was found to be 60x10-

12Pa-l and 1213x10-’2Pa-’ respectively. Also, they match the previous values reported.[2] Figure 8 shows the change of the rotated stress sensors that can also be used to

calculate the Z r + X i p of silicon. It shows almost the same value with the one calculated using the Equation 1.

VI. CONf2LUSION

We have presented a silicon piezoresistive stress sensor. A four-point bend loading fixture was developed to characterize the sensor. Sources or experiment errors were discussed in detail. The piezoresistive coefficient was found to match previous reported values. We plan to use the sensor to measure thermally induced stress during the plastic encapsulation process for integrated circuits.

ACKNOWLEDGMENT

This research is support by UPGC Research Infra- structure Grant RI 93/94.EG04 and a grant from ASM Pacific Technology Ltd., Hong Kong.

REFERENCE [l] R. E. Beaty, J. C. Suhling, C. A. Moody, D. A. Bittle, R. W. Johnson, R. D. Butler and R. C. Jeager, “Calibration Considerations for Piezoresistive-Based Stress Sensors”, Proceedings of 40th Electronic Components and Technology Conference, pp.797-806.

[2] R. C. Jaeger, J. C. Suhling and R. Ranmani, “Error Associated with the design and calibration of piezoresistive stress sensors in (100) silicon”, Advances in Electronic Packaging ASME 1992, pp. 447-456.

[3] Yozo Kanda, “A Graphical Representation of the Piezoresistance Coefficients in Silicon”, IEEE Transactions on Electron Devices, Vol. Ed-29, No. 1, January 1982, pp. 64-70.

[4] R. E. Beaty, R. C. Jaeger, J. C. Suhling, R. W. Johnson and R. D. Butler, “Evaluation of Piezoresistive Coefficient Variation in Silicon Stress Sensors Using a Four-Point Bending Test Fixture”, IEEE Transactions on Components, Hybrids and Manufacturing Technology, Vol. 15, No. 5, Oct. 1992, pp. 904- 914.

[5] S. A. Gee, V. R. Akylas and W. F. van den Bogert, “The Design and Calibration of a Semiconductor Strain Gauge Array”,

1988 IEEE Proceedings on Microelectronic Test Structures, Vol. 1, No. 1, Feb. 1988, pp. 185-191.

[6] F. P. Beer and E. R. Johnson, Mechanics of Materials, McGraw-Hill, 1981.

Figure 1. The Layout of the Stress Sensor

F F

d

Figure 2. The schematic of a four-point bend loading fixture

Figure 3. The actual setup of four point bend structure

t - S A &s+As+ Figure 4. The schematic of loading symmetry error

ICSE'96 Proc., Nov. 1996, Penang, Malaysia 255

Temperature Characteristic of Stress Sensor

Figure 5 . The Variation of initial resistance against temperature of two stress sensor with error bar

Reslstance of Parallel and Perpendicular n-typed Stress sensor (n)

Applied Stnss (MPa)

Figure 6. Resistance of Parallel and Perpendicular n-type Stress Sensor verse Applied Stress

Reslstance of Panllol and Perpendicular ptyped Stress Sensor (n)

Applied Stress (MPa)

Resistance of Rotated Stress Sensor @)

3 1) 53 110 1% 150 170 19J 210 m M

Applied Stress (MPa)

Figure 8. Resistance of Stress Sensor Rotated 135" verse Applied Stress

Figure 7. Resistance of Parallel and Perpendicular p-type Stress Sensor verse Applied Stress