he emperature Compensation of the Silicon iezo-resistive ressure Sensor Using the Half-Bridge echnique K. H. eng*, C. M. Uang Department of Electronic Engineering, I-Shou University, Kaohsiung, aiwan, R.O.C. Y. M. Chang. Department of Mechanical Engineering, Yung-a Institute of echnology & Commerce, ingtung, aiwan, R.O.C. ABSRAC he major factor affecting the high performance applications of the piezoresistive pressure sensor is the temperature dependence of its pressure characteristics. he influence due to temperature variation is manifested as a change in the span, bridge resistance, and offset of the sensor. In order to reduce the thermal drifts of the offset and span of the piezoresistive pressure sensor, a Half-Bridge-Compensating (HBC technique is presented in this paper. here are many advantages such as the temperature compensation of the sensor (typically lower than 1%, and a simple and low cost application circuit. he theoretical analysis and experimental results show that both the put voltage and zero offset drift are much improved by the first-order HBC technique. he experimental results are matched to our theoretical analysis. Keywords: Half bridge technique; piezoresistive; pressure sensor; temperature compensation; constant voltage mode; constant current mode. 1. INRODUCION Micro-sensor has been developed quite a long time and is a pretty mature technique in Micro-Electro-Mechanical Systems (MEMS. Research in micro pressure sensor is the focal point in both academic and industrial areas. he main points of the technique development are minimizing the system to promote system function, quality, and reducing materials usage to lower the product cost. Its application fields include: information, communication, consumer electronics, biotechnology, semiconductor, and other related industries. It can be classified to three types of micro pressure sensor using the silicon material: piezoresistive, piezoelectrical and capacitive pressure sensors. Among them, the widest used type is the piezoresistive pressure sensor. he main reasons are the easy fabrication processes and their small dimensions. he piezoresistive silicon pressure sensor element is based on the fine piezoresistance of silicon itself. When receiving an external pressure, the piezoresistor would change its formation. hese changes would be transformed into the corresponding put voltage according to the Wheatstone Bridge heorem. he piezoresistors are often connected as a bridge circuit in order to increase the sensor s sensitivity and decrease the cross sensitivity. However, the main problem accompanied with the piezoresistive pressure sensor is its innate cross sensitivity to temperature. he effect of temperature existed in the change of the span and offset of the sensor put. Recently, many temperature compensation techniques have been proposed such as double-bridge temperature compensation [1-3], laser-trimming [4], using external resistors [5] and digital compensation [6]. Normally, these techniques are applied within a limited temperature and pressure ranges. In addition, some techniques also involve additional processing steps. he double-bridge temperature compensation technique can effectively handle zero pressure offset and errors caused by the processing variation [1, 7]. he temperature compensation problem due to the different environmental temperatures of the piezoresistive bridge and compensation bridge located on the bulk part of the sensor chip became an important topic [8]. We will propose a novel structure of the piezoresistive pressure sensor with Half- Bridge-Compensation (HBC technique. * b884735@student.nsysu.edu.tw; phone : 886-7-815-6581; fax : 886-7-815-679 9 Reliability, esting, and Characterization of MEMS/MOEMS III, edited by Danelle M. anner, Rajeshuni Ramesham, roceedings of SIE ol. 5343 (SIE, Bellingham, WA, 4 77-786X/4/$15 doi: 1.1117/1.57387 iezoresistive ressure Sensor
Following this short introduction, in section, we will discuss the Wheatstone bridge piezoresistive sensor put behavior and its temperature effect. he HBC technique and design principle will be presented in Section 3. he experimental setup and results are discussed in Section 4. Finally, a conclusion of this technique is summarized in Section 5.. WHEASONE BRIDGE SENSOR WIH EMERAURE EFFEC A general Wheatstone bridge structure is placed as shown in Fig 1 (a or (b, and it is used to detect an unbalance loop put formed by the variation of the temperature or pressure. here are two types of the power excitation modes, Constant oltage mode and Constant Current mode, as applied to the compensation circuit. Fig 1. Half-Bridge compensated pressure sensor. Fig. Structure lay of the piezoresistive pressure sensor with compensation resistors..1. CONSAN OLAGE MODE From Fig 1,, R,, and R4 are the four resistors forming a Wheatstone bridge in counter-clockwise direction on the diaphragm, in means the voltage source applied to the Wheatstone bridge. he configuration lay of these resistors is shown in the center of Fig, in which the two opposite pairs, and, R and R4, are shown. he four resistors are assigned at the directions of parallel and perpendicular to the edges of the membrane or the beams. Under this configuration, the variations of resistors receiving pressure excitation will obtain different polarities and assume the value as R is shown in Fig 1(a. In Fig, C1 and C are located side of the diaphragm. hey act as the temperature compensation factors and will not change when pressure is applied, and also not affect the bridge behavior. All resistors on the chip have almost the same characteristics, and obtain almost the same variations during temperature change. We assume the temperature variation value as R, as shown in figure 1(b. In the static condition, R and R will not show up. he Wheatstone bridge put,, is given by: R R R4 = in = in. (1 ( (.1.1. OFFSE BEHAIOR Consider the dynamic state with no pressure applied. Add the temperature variation, rewritten as: offset in ( R ( R4 4 ( 1 ( 3 (( + ( R (( + ( R4 1 3 4 R, into the equation (1 and n =. ( roc. of SIE ol. 5343 93 iezoresistive ressure Sensor
In an ideal case, assume the resistances of four resistors ( ~ R4 are the same and equal to the value R. he variations of resistors when receiving the temperature change are assumed as R, the equation ( can be rewritten to obtain the put offset as: offset = in ( R ( R ( R ( R ( R + R ( R + R =. (3 It is clearly to be realized that in constant voltage mode in an ideal case, that the offset will not produce a change during temperature variation and the value is zero as described in equation (3. In reality it is often found that resistors in opposite arms of the Wheatstone bridge are equal, but are different from resistors in touching arms, because their lay is slightly different (parallel and perpendicular to the edges of the membrane or the beams [9]. Furthermore, by the IC processing technology we put the resistors into a very small diaphragm will obtain almost the same resistances and the temperature coefficients as shown in Fig 3, which shows a little bit of deviation between the resistors that is caused by the process mismatch, impurity concentration, or some other physical mismatch conditions. hese small differences cause the offset put changes. Assume the resistance of the resistors changes within the range of 1% this will cause the offset deviation from around +5 to 5 m/. If the temperature coefficients deviation is within the range of.1%, that will cause the offset deviation of around.5 m/. hat can be calculated by the equation (, in worst case. Fig 3. Resistance & R % due to temperature variation in the same chip. Fig 4. Equivalent resistance & R % due to temperature variation in different chips. Fig 3 shows the resistance variation of each resistor on the same chip. Fig 4 shows the equivalent resistance variations of bridges (put resistance measured from different chips in our experiments. In Fig 3 and 4, the axis X represents the different parts, the left axis of Y represents the resistance values at 5l and the unit is ohm. he right axis of Y represents the rates of the resistance variations over the resistance at 5l due to different temperature points and the unit is a percentage ratio. he patterns d mark the resistance values at 5l,, d, and mark the rates of the resistance variations at l, 5l, and 75l, respectively. Also, in Fig 5, the axis X represents the different parts, the left axis of Y represents the offset of the sensors at 5l and the unit is m/. he right axis of Y represents the rates of the offset variations over the offset at 5l due to different temperature points and the unit is a percentage ratio. he patterns d mark the offset at 5l,, d, and mark the rates of the offset variations at l, 5l, and 75l, respectively. Actually, the sampled offset range is +3.5 to 1. m/, congregated in the positive area, and the offset variation range is around.5 m/ between ~ 75 l as shown in Fig 5. But these measured data were composed of a lot of physical errors, such as package stress, glass bonding, coating, process mismatch, etc., and were categorized into Calibration errors, as one of the unpredictable sensor parameters [1]. In general, the temperature coefficient of the piezoresistance coefficients is not the major factor of the temperature coefficient of offset (CO. Much more important 94 roc. of SIE ol. 5343 iezoresistive ressure Sensor
factors for the offset of piezoresistive sensors and also for the CO game are the pre-stress condition and its temperature dependence. his refers to the residual stresses on the resistors when no external pressure or force is applied. Origins of stress are typically passivation layers over the resistors and packaging stress. Both can be very dependent on temperature, depending on the materials used. Only careful design and the introduction of stress-releasing packaging configurations can reduce the CO [9]. In general applications, the offset in the same polarity can be achieved by the IC process design. Set the value of R & R4 a little bit bigger then &. Moreover, sensor s offset may have positive or negative temperature coefficient. From the point of view of the meter application, people prefer to select the positive one to help reduce the error reading as the environmental temperature changes. Fig. 5 offset & offset of the different sensors in constant voltage mode. Fig 6. iezoresistance factor (N, as a function of impurity concentration and temperature for p-type silicon..1.. BRIDGE OUU BEHAIOR he piezoresistance factor (N, based on mathematical calculations for p-type silicon is shown in Fig 6 [9]. hey found that the piezoresistance decreased with increasing doping concentration and increasing temperature. he pressure sensitivity and put voltage would be changed in case of the rise of temperature in traditional piezoresistive pressure sensor. Moreover, the electric conductivity of a semi-conductor can be defined as, σ = qn µ + qpµ...(4 n p Where q means elementary charge (magnitude of electronic charge, n is the density of free electrons, p is the density of free holes, µ means electron mobility, and n µ means hole mobility. he resistivity of a semi-conductor is a reciprocal p of defined as, 1 1 ρ = σ q µ ( nµ + p n p. (5 In general, for an extrinsic semi-conductor only one part of it in equation (4 and (5 is important. For p-type semiconductor, the resistivity of resistor, ρ, defined as, 1 ρ =,..(6 qpµ p roc. of SIE ol. 5343 95
p means the doping density of dopant. For lower doping concentration, the mobility decreases with increasing temperature because of the lattice scattering. For higher doping concentration, the mobility increases with increasing temperature because of the impurity scattering [11]. Once we choose the doping concentration, resistors temperature coefficient will follow this rule. According to Fig 1, assume the resistances of the four resistors equal to the value R. he variations of resistors when receiving an external pressure or temperature change are assumed as R and R, respectively. R is the deviation of R due to temperature variation. herefore, the positive put voltage of the Wheatstone bridge can be presented as, o( + = in ( R ( R he negative put voltage is, o( = in ( R + ( R R + ( R + ( R R ( R + ( R ( R Subtract equation (8 from equation (7 and obtain,. (7...(8 = o( + o( = in R R.....(9 As we mentioned, piezoresistance decreases with increasing temperature, which means R with negative value when temperature is increased. Also, the electric conductivity of a semi-conductor will be changed by the change of temperature, lighting, the magnetic field, and minor impurities [11]. Refer to the equation (9, the bridge put will be changed, since R and R appeared due to the temperature variation... CONSAN CURREN MODE According to Fig 1(a, in constant current mode, Wheatstone bridge put is given by, = I R I 3, (1 1 34 R and I = I1 + I 34 following Kirchhoff s circuit law. Given as, I I 1 34 = I, (11 + = I...(1 + I means the current through and R, 1 I means the current through and R4, 34 I is the constant current source we applied to the Wheatstone bridge. ut the equations (11 & (1 into (1, we have, = I R I + + R RR4 = I..(13 + 3 96 roc. of SIE ol. 5343
..1. OFFSE BEHAIOR Consider the dynamic state and no pressure applied, the same assumption we mentioned in constant voltage mode is also used in constant current mode. If the temperature varies and causes a resistance variation named R, put it into n equation (13 and rewrite as, ( R ( R4 4 ( 1 ( 3 ( + ( R + ( + ( R4 = I. (14 1 3 Also let the resistance of resistors be equal to the value R. he variations of resistors when receiving the temperature changes are assumed as R. he equation (14 can be rewritten to obtain the put offset as below, offset ( R ( R ( R ( R ( R + ( R + ( R + ( R 4 = I =. (15 Refer to the equation (15, we found that the offset in an ideal mode is also equal to zero. Consider the real world case, compare the equation ( and (14 in a bounded condition. Once the difference between the four resistors was introduced, we can find that the offset variation of constant voltage mode due to temperature change will be less than the constant current mode.... BRIDGE OUU BEHAIOR Again, assume the resistance of the four resistors is equal to the value R. he variations of resistors when receiving an external pressure or temperature change are assumed as R and R, respectively. R is the difference of R due to temperature variation. herefore, the constant current mode put voltage shown in equation (14 can be rewritten as: = I = I ( R + ( R + R ( R4 + ( R 4 4 4 ( ( R 1 1 1 ( ( R 3 3 3 ( ( R + ( R + ( R + ( ( R + ( R4 + ( R 1 1 1 ( R + ( R ( R + ( R + R ( R ( R ( R ( R ( R ( R + ( R + ( R + ( R ( R + ( R + ( R ( R ( R 4 ( R = I = I ( R 4...(16 Comparing the equations (9 and (16, we found that the term, R, of the put voltage due to the applied pressure in constant current mode can never be canceled, no matter what the change is due to temperature variation. But the term, R, of the put voltage in constant current mode was neutralized during the calculation. hat is the most important reason why the compensated sensor usually prefers to be used in constant current mode instead of constant voltage mode. By the constant current mode, it provides a possibility for the simpler temperature compensation [1]. Both constant voltage mode and constant current mode during the discussion are assumed to be the ideal case, many parameters to be ignored. If we want to know the real activity of the bridge put due to the pressure and temperature variation, we have to put at least 16 coefficients into the equation (1 or (13, that would make the discussion too complex to analyze. 3 3 3 4 4 4 roc. of SIE ol. 5343 97
.3. MEMBRANE-YE SENSORS A piezoresistive membrane sensor consists of a thin silicon membrane, which is supported by a thicker silicon rim, and is fabricated by etching away the bulk silicon on a defined region until the required thickness range is reached. iezoresistors are integrated on the membrane, typically close to the edge. he membrane is used to receive external pressure. Four piezoresistors would gain signals from the change of the membrane. Figure 7 presents the schematic cross-section of a piezoresistive pressure sensor combined with temperature compensation resistors. he membrane sensor is finally bonded with the yrex 774 glass, and serves to be a substratum to minimize the mechanical stress, by the silicon-to-glass bond. Fig 7. he cross-section of piezoresistive pressure sensor combined with temperature compensation resistors. Fig 8. Basic configuration of the pressure sensor using Half- Bridge Compensation echnique. 3. HBC ECHNIQUE AND HE DESIGN RINCILE he novel lay and the structure of the HBC technique pressure sensor are shown in Fig. wo dummied resistors (C1 & C are non-sensitive to pressure but they have the same electrical and thermal characteristics as those of pressure sensitive resistors. hese two resistors are allocated nearby the pressure sensitive resistors with the same directions around 15 ~m side of the diaphragm. C1 and C are used to drain the auto-gain-circuit (AGC factors shown in Fig 8. Because all resistors are put on the same chip and in a very small area, they should have the similar thermal and mechanical characteristics. he bridge put drift due to the temperature variation is minimized by AGC to automatically adjust the supplied voltage source. he gain-factor of AGC-1 (G1 directly comes from C1 with almost the same temperature factor as the piezoresistors and serves to do the first order compensation neutralize the effect from R. he gain-factor of AGC- (G comes from C not the same curve as R and serves to do the second order compensation only used to minimize the remaining total errors, including the physical un-match error. hese two AGCs can easily be structured by appropriate Operation Amplifier (O-Amp and resistors. According to Fig 8, let AGC-1 be a constant current source through C1 and the current is I. Assume the resistances of C1, C and four piezoresistors are equal and the value is R. he variations of all resistors when receiving an external temperature change are assumed as R. and G1 mean the put of AGC-1 and AGC-, respectively. hus, G the bridge voltage ( bridge which we applied to the sensor equal to can be represented as: G ( R G G1 G = I G =. (17 Refer to the equation (9 and with the same assumption, the put of the pressure sensor is given by, 98 roc. of SIE ol. 5343
R = ( R = G I G R ( + R R = I G R R....(18 Assume G is 1 and put it into equation (18, we find that the sensor put will obtain the same result as the constant current mode and get the primary compensation. As we mentioned before, there will be some small differences in the real world case. After the first order compensation, the remaining total errors with negative temperature coefficient mostly come from the piezoresistance factor and non-linearity, and assume to be total. he equation (18 can be rewritten and represent as: ( = I G R 1. (19 total Also, the resistance change of C with the positive temperature factor but not the same curve of remaining error. After we tested two temperature points in first order HBC, we can measure the bridge put change and the resistance variation of C and calculate the gain factor of G. Let G = 1 +. hrough the careful calculation we can set the G value of equal to G and assume the value is. Rewrite the equation (19 and obtain, total ( 1 + R ( 1 = I R ( = I 1..( Generally, the sensitivity loss from the first order HBC to be compensated would be around 1.5%. his assumption will be proved by our experimentation shown in the next section. We can say 1 >>, and ( 1 1. he AGC- serves to minimize the remaining errors. Rewrite equation (, we obtain the sensor put = I R. It s clearly found that the sensor put is almost fully compensated. his new compensation method was proved. As mentioned before, for the constant voltage mode with the minimum offset variation, and the constant current mode, this provides a possibility for the simpler temperature compensation. his new compensation technique is the combination of constant current mode and constant voltage mode, and takes both advantages. By using AGC we can drain the resistor s temperature variation from C1 and transfer the resistance variation into voltage source variation. We call the aforesaid power source Adaptive oltage Source. Basically it s not a really constant voltage source but with the voltage variation correlated with the sensitivity loss we can almost fully compensate the sensitivity loss. his new compensation method we call Half-Bridge compensation technique. 4. EXERIMENAL SEU AND RESULS In our experiments, we set four different temperature points ( / 5 / 5 / 75 l and five different pressure points ( / 5 / 5 / 75 /1 SI. he Unit-Under-est (UU was randomly selected from lots. he related instruments that we used are listed as bellow: 1. Oven : With controlled environment temperature within. l.. ressure Source : Using nitrogen and controlled by DRUCK DI-515 with.1% FSO accuracy. 3. ower Source : Agilent E3633A DC ower Supplies. 4. Measuring Instrument : XI system with c-size mainframe, configured with one Command Module (E146A, one 6.5 Digital Multi-meter (E141A, DMM and two Switch Boxes (E846A. A EE-6. environment was used to program the testing procedures and to control the instruments via GIB connections, except the oven. he computer can access all the measured data automatically. Switch boxes served to wire the UU to DMM to avoid the wiring error. We also put some judgments during the software loop to make sure the roc. of SIE ol. 5343 99
setting temperature and pressure were stable. In order to show the performance differences to the other techniques, we also took the experimental data from the direct parallel compensation technique shown in Fig 9, the simple voltage follower compensation technique shown in Fig 1, the constant current mode and the constant voltage mode. he average sensitivity variations are shown in Fig 11, and the average offset variations are shown in 1. In these two figures, the five curves represent the results of C.. (constant voltage technique, C.I. (constant current technique, M-1 (direct parallel compensation technique, M- (simple voltage follower compensation technique, and M-3 (using first order HBC technique, respectively. Fig 9. Direct parallel compensation. Fig 1. Simple voltage follower compensation. he bridge voltages (s for the different circuits were set to around 5. For the direct parallel circuit we can get the simpler compensation circuit configuration and a limited compensation ratio due to the loading effect of the sensor. While using the voltage follower circuit we can avoid the loading effect of the sensor but still can t get the full ratio of R. he constant current mode provides a possibility for the simpler temperature compensation but with the worst offset variation. he first order HBC obtained a better result on both offset and sensitivity compensation. From Fig 11, we find that the sensitivity loss was compensated to around 1.5% in average during ~ 75l, it also proved the assumption which we mentioned in section 3. he offset variation rate to be compensated to around.3% in average during ~ 75l which can be found in Fig 1. hat because the calibration errors is the same as the sensitivity variation, and the effect of R is almost neutralized by using adaptive voltage source of AGC-1. Fig 11. Average sensitivity variations among different compensation circuits. Fig 1. Average offset variations among different compensation circuits. 3 roc. of SIE ol. 5343
5. SUMMARY Since the pressure sensors are the most widely used for pressure, measuring, and controlling, the foremost things to do now are not only to reduce its costs, but also to increase its accuracy. he key factor in curtailing the costs of these devices is the state of the art design and fabrication. he new HBC technique has been described in detail in this paper. he experimental results show that the span of the sensor is minimized to the average value around 1.5% over ~ 75l by using the first order HBC technique. Furthermore, the remaining total errors can be minimized to less than 1% via the second order compensation circuit AGC-. We conclude that the HBC technique can be practically applied to the pressure sensor design. he contributions provide the low cost and better performance pressure sensor. 6. REFERENCE 1. M. Akbar and M. A. Shanblatt, emperature compensation of piezoresistive pressure sensors, Sensors and Actuators, ol.33, No.3, pp.155-16, 199.. W. H. Ko, J. Hynecek, and S. F. Boettcher, Development of a miniature pressure transducer for biomedical applications, IEEE rans. Electron Devices, ED-6, pp.1896-195, 1979. 3... Hsieh, Y. M. Chang, J. M. Xu, and C. M. Uang. Double bridge technique for temperature compensation of piezoresistive pressure sensor, SIE, Smart Structures and Integrated Systems, ol.471, pp.67-633,. 4. G. Kowalaski, Miniature pressure sensors and their temperature compensation, Sensors and Actuators, 11, pp.367-376, 1987. 5. H. anigawa,. Ishihara, M. Hirata, and K. Suzuki, MOS integrated silicon pressure sensor, IEEE rans, Electron Devices. ED-3, pp.1191-1195, 1985. 6. Mark arsons, ony Allen, and Alec M. Makdessian, MAX145 Reference Manual, MAXIM Integrated roducts, Inc. Sunnyvale, CA,. 7. M. Akbar and M. A. Shanblatt, A fully integrated temperature compensation technique for piezoresistive pressure sensors, IEEE rans. On Instrum. Meas. ol.4, No.3, pp.771-775, 1993. 8. C. G.Hou, A pressure sensor made of two piezoresistive bridges, IEEE Instrum. and Meas. echnology Conference, pp.56-51, 1996. 9. S. M. Sze, Semiconductor Sensors, chapter 4, Wiley-Interscience, New York, 1994. 1. Dr. Janusz Brysek, Dr. Kurt etersen, Mr. Joseph R. Mallon, Jr., Dr. Lee Christel and Dr. Farzad ourahmadi, Silicon Sensors and Microstructures, chapter 8, Silicon alley, 1991. 11. S.M. Sze, Semiconductor Devices hysics and echnology, chapter, Wiley-Interscience, New York, 1985. roc. of SIE ol. 5343 31