Evaluation of Pressure Sensor Performance Dr. Lynn Fuller

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1 ROCHESTER INSTITUTE OF TECHNOLOGY MICROELECTRONIC ENGINEERING Evaluation of Pressure Sensor Performance Dr. Lynn Fuller Webpage: 82 Lomb Memorial Drive Rochester, NY Tel (585) Fax (585) Department webpage: Pressure_Sensor_Evaluation.ppt Page 1

2 OUTLINE Introduction Theory SEM Pictures Basics Response Offset, Span, Linearity, etc. Compensation Temperature Dependence and Compensation Frequency Response References Page 2

3 INTRODUCTION In this lab we will test piezoresistive pressure sensors made at Rit and compare them with sensors made by Freescale Semiconductor, see Page 3

4 CALCULATION OF EXPECTED OUTPUT VOLTAGE +5 Volts R1 R3 R2 R4 Vo2 The equation for stress at the center edge of a square diaphragm (S.K. Clark and K.Wise, 1979) Stress = 0.3 P(L/H) 2 where P is pressure, L is length of diaphragm edge, H is diaphragm thickness Vo1 Gnd For a 3000µm opening on the back of the wafer the diaphragm edge length L is (500/Tan 54 ) = 2246 µm Page 4

5 CALCULATION OF EXPECTED OUTPUT VOLTAGE (Cont.) Stress = 0.3 P (L/H) 2 If we apply vacuum to the back of the wafer that is equivalent to and applied pressure of 14.7 psi or 103 N/m 2 P = 103 N/m 2 L= 2246 µm Stress = 2.49E8 N/m H= 25 µm 2 Hooke s Law: Stress = E Strain where E is Young s Modulus σ = E ε Young s Modulus ofr silicon is 1.9E11 N/m 2 Thus the strain = 1.31E-3 or.131% Page 5

6 CALCULATION OF EXPECTED OUTPUT VOLTAGE (Cont.) The sheet resistance (Rhos) from 4 point probe is 61 ohms/sq The resistance is R = Rhos L/W For a resistor R3 of L=350 µm and W=50 µm we find: R3 = 61 (350/50) = ohms R3 and R2 decrease as W increases due to the strain assume L is does not change, W becomes 50+50x0.131% W = µm R3 = Rhos L/W = 61 (350/ ) = ohms R1 and R4 increase as L increases due to the strain assume W does not change, L becomes x0.131% R1 = Rhos L /W = 61 ( /50) = ohms Page 6

7 CALCULATION OF EXPECTED OUTPUT VOLTAGE (Cont.) 5 Volts R1=427 R3=427 Vo1=2.5v R2=427 Gnd Vo2=2.5v R4=427 No stress Vo2-Vo1 = 0 With stress Vo2-Vo1 = 0.007v =7 mv R1=427.6 Vo1=2.4965v R2= Volts Gnd R3=426.4 Vo2=2.5035v R4=427.6 Page 7

8 Pressure Sensor SEM OF RIT PRESSURE SENSOR Front Back March 10, 2008 Dr. Lynn Fuller Page 8

9 BASICS 5 Volts Vo2=2.5035v R1 R3 R2 R4 Vo1=2.4965v Gnd Check that vo1 and Vo2 are near Vsupply/2 and Vo ~ 0 Apply and release chuck vacuum to observe change in output voltage Page 9

10 PRESSURE SENSOR TEST SETUP Apply pressure, measure and compare with other pressure gages. Collect data. Page 10

11 OUTPUT VOLTAGE VERSUS PRESSURE MEMS Pressure Sensor Output Output Voltage (mv) y = x x psi mv Pressure (psi) Page 11

12 ZERO AND SPAN COMPENSATION Vo- Rzt R1 R2 Rzb Vs Rst R3 R4 Rsb Gnd Vo+ Dr. Lynn Fuller 4/18/2007 Bridge_Balance.xls This spread sheet can be used to find resistor values used to compensate a wheatstone bridge resistor pressure sensor for output offset voltage and span. If we assume that the resistors are TaN thin film resistors that are adjusted by laser trimming then the trimmed value has to be higher than the nominal value. First adjust the value of Rzt and Rzb to set Vout trimmed to zero. Then set Rst and Rsb to make the trimmed stressed value equal to the specified output voltage at maximum applied pressure. Vout Vout Vout Vout Vsupply 10 volts no trim no trim trimmed trimmed nominal stressed nominal stressed nominal stressed R Vo volts R Vo volts R Vout mv R %change 0.5 when maximum pressure is applied (stressed) nominal Rst ohms Vo+ = Itotal * Rsb + Iright * R4 Rsb ohms Vo- = Itotal * Rsb + Ileft * R2//Rzb Vout = Vo+ - Vo- Rzt ohms Rzb ohms no trim no trim trimmed trimmed nominal stressed nominal stressed Rleft (Rzt//R1) +(Rzb//R2) Rright R3+R4 Rtotal Rleft//Rritght + Rst + Rsb Itotal Vs/Rtotal Vbridge Vs- Itotal (Rst+Rsb) Ileft Vbridge/Rleft Iright Vbridge/Rright Page 12

13 TEST SETUP FOR FREQUENCY MEASUREMENT Page 13

14 BALLOON ABOUT TO POP Page 14

15 MEASURED STEP RESPONSE Page 15

16 Dr. Lynn Fuller step to frequency.xls 7-Apr-07 This spread sheet finds the frequency response from the measured step response. The measured step response is converted into a series of 128 data points. The derivitive is found to get the impulse response. The fourier transform of the impulse response is found to get the frequency response. The frequency response is the real part of the fourier transform of the impulse response for positive frequencies. Assume the step responsem (Rn) has the general form shown in the figure below, enter times to, tmid, tend to = sec, where Rn = 0 tmid = sec, where Rn = 0.5 tend = sec, where Rn =1.0 normalized response, Rn to = time at start time increment = Measured Step Response tmid = time at midpoint tend = time at end Number of Samples N = 128 Normalized n t Step Impulse fourier transform freq = (n-n/2)/dt/n sample time Response response dt = number sec Rn dv/dt Real Imag freq 20Log Real E E E E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E E E E i E E E E E E E E E E E E E E E E E E E E E E E E E E E E i E E E E i E E E E E E E E E E E E E E E E E E E E E i E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E i E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E E E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E i E+03 #NUM! E E E+03 time Pressure Sensor 4.50E E E E E E E E E E E+01 Normalized Step Response versus time 1.20E E E E E E E E-01 time (seconds) Real part of Fourier transform versus frequency E E E E E E E E E E E Impulse Response time (seconds) -45 Frequency (hz) 20 log (Real Part of Fourier Transform) versus frequency E E E E E E E+03 frequency (Hz) Measured Step Response from Oscilloscope 60 Hz noise filtered STEP TO IMPULSE TO FREQUENCY RESPONSE Excel Spreadsheet Data Filtered Normalized Step Response Derivative gives Impulse Response Fourier Transform Gives frequency response Real Part in db Page 16

17 STEP TO FREQUENCY.XLS Dr. Lynn Fuller step to frequency.xls 7-Apr-07 This spread sheet finds the frequency response from the measured step response. The measured step response is converted into a series of 128 data points. The derivitive is found to get the impulse response. The fourier transform of the impulse response is found to get the frequency response. The frequency response is the real part of the fourier transform of the impulse response for positive frequencies. Assume the step responsem (Rn) has the general form shown in the figure below, enter times to, tmid, tend to = sec, where Rn = 0 tmid = sec, where Rn = 0.5 tend = sec, where Rn =1.0 Measured Step Response normalized response, Rn time to = time at start tmid = time at midpoint tend = time at end time increment = Page 17

18 MEASURED STEP RESPONSE Measured Step Response from Oscilloscope 60 Hz noise filtered Page 18

19 FILTERED NORMALIZED STEP RESPONSE 1.20E+00 Normalized Step Response versus time 1.00E E E E E E E time (seconds) Page 19

20 IMPULSE RESPONSE 4.50E+02 Impulse Response 4.00E E E E E E E E E E time (seconds) Page 20

21 FOURIER TRANSFORM Real part of Fourier transform versus frequency E E E E E E E E E E E Frequency (hz) Page 21

22 FREQUENCY RESPONSE 0 20 log (Real Part of Fourier Transform) versus frequency E E E E E E E frequency (Hz) Page 22

23 REFERENCES Microsystem Design, Stephen D, Senturia, Lluwer Academic Publishers, 2000, pg Micromachined Transducers, McGraw Hill, 1998,Kovacs, pg 253 Page 23