MOS TRANSSTOR PRESSURE SENSOR Salvador Alcantara. Antonio Cerdeira and Gabriel RomeroParedes Seccion de Elecrronica del Estadu dido. Depto. de lngenieria Elecrrica CNVESTAV PN. Av. PN No. 1508. A.P. 14740, 07300. Mexico D.F. email: salcanta@mvax.red.cinvestav.mx Abstract An expression that describes the behavior of the channel mobility of a Metal Oxide Semiconductor Transistor ( MOST) under pressure. longitudinally oriented with respect to the edge of a silicon square diaphragm. used as a pressure sensor, is derived. * This expression is incorporated into PSPCE. to allow themodeling of transistors under pressure, by means of this conventional simulator. An integrated readout circuit consisting of four active MOST, four dummy MOST and two differential amplifiers is presented. which provides a linear variation dependence between pressure and output voltage, for pressures between 0 and 100 kpa with an output of 250 mv at maximum pressure. This circuit also provides compensation for the output voltage dependence on temperature and channel misalignment with respect to the edge of the diaphragm. Keywords: Microelectromechanical. MOST model. Pressure sensor ntroduction Computers communicate with real world through sensor devices that convert physical or chemical signals into electronically tractable ones. These electronic systems require sensors. compatible with their advanced technology, [ ], giving rise to a new branch in microelectronics called Microelectromechanical (MEM) devices that permits the integration of the sensors with their readout electronics. MEM pressure sensors are now widely used in industry, medicine and research. They are fabricated using Micromachining Techniques to delineate the diaphragm and Planar Technology for the readout circuit. Usually. a square diaphragm is integrated into the silicon die. The conversion of pressure into an electric signal is carried out by means of a capacitive. optic or piezoresistivesensitive device, [2]. Semiconductor pressure sensors commercially available are most frequently based on a difhsed resistor bridge. with resistors appropriately positioned relatively to the square diaphragm. to detect the deflections of the diaphragm by means of the piezoresistive effect of the resistances. High thermal unstability, selfheating and an abrupt decrease in the device sensibility due to the misalignment of the resistors with respect to the diaphragm edges are the principal disadvantages of these piezoresistive sensors. This type of sensors require thermistors in the readout circuit to compensate for temperature variations and laser trimming to precisely balance the resistive bridge [3]. They also require very small size resistances to be located very close to the diaphragm edge. 11. Pressure effects on a MOST When pressure is applied to a square silicon diaphragm formed by selective etching. a stress distribution will appear throughout the membrane. The analysis of the stress distribution present in one quadrant of a square membrane can be found in [4]. The normalized stress acting along axis x. can be expressed as: where: h is the diaphragm thickness, is the length of the diaphragm side: P is the applied pressure and o, isthe srress along axis x. for a given x and y coordinates. where coordinates x and.. can also be normalized and expressed as.t = x / 1 and y= yll. The normalized stress along axis.y for y 4, and y=0.5 calculated in [4] are shown in Fig. b. As can be seen. this stress for y=o varies linearly with.t in the interval 0.435.T 10.5 and can be expressed in this re,' 0ion as: qr = (2317)e.T0.864 (2) t can also be seen from Fig. b. that for y 0.5. the normalized stress along.t, (a, ), varies little with coordinate in the interval 0 F 5 0.066. n addition. interpolating the calculated values of q, for 0.43 y 10.5. and 74. it can be estimated
that the stress in this region will also vary linearly with axis y and can be expressed as: Since this behavior occurs at any of the diaphragm edges. we can consider the whole stress acting at any of them. as the superposition of the stress given by eqn (2) acting perpendicular to the edge. and the stress given by eqn (3) acting parallel to the edge. The regions where the stress can be expressed through eqn 1 and 3 are shown in Fig. la. &m Fig. a) Position of the selected areas on the diaphragm. b) Normalized stress for 7 =O and 7 =0.5 as function of F. From another point of view. when pressure is applied to the channel of a MOST. changes in channel conductance. have been observed and reported by several authors [S 121. From these previous works, it is clear that when a MOST is constructed on a silicon diaphragm as shown in Fig. 2. the pressure applied on the diaphragm will generate a stress that will change the conductance of the MOST channel. f the MOST is operated in saturation region. the constant value of the drain current will change with pressure. n this paper. we derive an expression that relates the channel mobility with the pressure in order to model the behavior of a MOS transistor under pressure. As it is known. the resistivity depends on mobility, and since the piezoresistive effect can be expressed through the relative variation of resistivity [2]. the relative variation of mobility can be expressed as [4]: where q and o, are the longitudinal and transversal components of the stress with respect to the length of the MOST channel: scl and x, are the corresponding piezoresistive coefficients. Both components are function of the diaphragm side size and pressure. Fig. 2 Structure of a PMOS transistor on the edge of a silicon square diaphragm. Substituting eqn (1) and (3) into eqn (4) and averaging the longitudinal and transversal stress components in an area that must be located inside the previously defined regions where eqn. (2) and (3) are valid, KP. for (100) orientation and hll = 100 can be expressed as: Kpl = (5.724 13.75F). 1 o~ P = (a by) P (5) where a=5.724x 10". b= 13.75~ 10. f & is the value of the carrier mobility in the channel under stress. and p,, is the value of the carrier mobility in the channel with no pressure applied. the variation of the carrier mobility due to the applied pressure can be expressed as: AP= Pp C4h where,up is equal to: Pp = w (1&). (6) The general expression for the drain current when pressure is applied to the MOST is: where F involves the pressure independent terms and all the pressure dependence resides in the mobility h. The calculation of the drain current is performed for the case when the transistor channel is parallel to one of the diaphragm edges. and the channel width lies on the diaphragm at a distance of less than (0.07)x(f) from the diaphragm edge toward the center (see Fig. ). Fig. 3 shows the relative position of the MOST with respect to the diaphra. The applied pressure will deform the channel, providing a channel width increment distributed along x axis that is also a function of the x coordinate. This channel width increment produces an increment of the channel current: the new channel current can be calculate by integrating between x, and xl (W = xz x,) the expression for the current differential:
L The total current will be: (9) f the current for the MOST with na pressure applied (P=O) is lo. then An important case occurs when the channel overlaps the frame. f the channel width on the diaphragm is Wl and on the frame is W2. the whole current wiikbe the sum of the current affected by the channel deformation. and the current 12. nonaffected by the deformation. (see Fig. 4). n this case the relative channel current variation can be expressed as:... f om : W the center 4. edge Fig2 Longitudinal MOST placed along the diaphragm edge. When two MOS transistors placed on the opposite sides of a diaphragm are connected in parallel. see Fig. 4. the whole current can be expressed as: where d is the misalignment. due to photolitho,gaphy. For diaphragm dimensions of = 1500 mm and h = 15 mm. and a misalignment d varying from 0 to 5 mm. the current variation, expressed by eqn 12 is shown in Table. Notice that a relative variation of the current of only 0.01 % occurs for a misalignment as big as 5 Crm. ntegrated pressure sensor The analytical expression for the carrier mobility in a MOST channel under pressure given by eqn 5 can be easily introduced into the PSPCE MOST models to provide the possibility of a simultaneous analysis of the behavior of a MOST under pressure. together with other MOST electronic readout circuit integrated with the silicon diaphragm. The readout circuit integrated with the diaphragm type MEM pressure sensor consists of four MOS transistors located on the diaphragm (T T4). overlapping the edge ofthe frame: four identical MOST located on the frame and used as dummy MOST (Dl D4). (see Fig.5). that are connected as a Wheatstone bridge in order to obtain a good thermal stability and Fig. 4 frame. Longitudinal MOST overlapping the tolerance to the misalignment with respect to the frame edge. n order to amplify the differential output of this bridge. two differential amplifier stages are added. The interconnection and the dimensions of the different elements of the circuit are shown in Fig. 6. n order to increase the piezoresistive sensibility to pressure of the MOST channel. P channel transistors and ( 00) orientation substrates are recommended. All the transistors are fabricated with a standard PMOS Planar Technology which simplifies the fabrication process.
Table Current variation due to channel misali, ~nment for 1=1500 pn and h=15 w.n for two MOST placed at opposite sides of the diaphragm and connected in parallel. Fig. 6 MOST pressure sensor bridge and the differential voltage amplifiers. Fig.5 Relative position of the 4 sensitive MOST on the diaphragm and the 4 dummy MOST on the frame. V. Simulation results The circuit shown in Fig. 6. designed for a PMOS technology with oxide thickness of 60 nm. substrate concentration of 1015 cm", and (100) orientation. was electrically simulated with the PSPCE. using level 3 and incorporating eqn 6 to describe the dependence of mobility with pressure. The pressure was varied from 0 to 100 kpa. This circuit has only one voltage source of 5 v. The response of the bridge and the complete circuit as a function of pressure variations is shown in Fig. 7. They present a linear behavior with a sensibility at 27 "C of 0.15 mvkpa and 225 mvkpa respectively. The differential output at 100 kpa is 225 mv. The bridge and the readout circuit were analyzed for thermal stabibility. from 0 to 80 "C at 100 kpa. The results are shown in Table 2. The bridge sensibility.at 80 "C is of 0.05 kpa / OC. which represents a variation of the sensibility referred to its value at 27 "C of 2.6%: the complete circuit sensibility at the same conditions is 0.05 kpa / OC. representing a 2.7% with respect to its value at 27 "C. The bridge and the complete circuit sensibility to variations in the voltage source VD. at a pressure of 100 kpa are shown in Table 3. For a variation of f 10% in V,. the output voltage varies less than 10 %. V. Conclusions An analytical expression for the channel carrier mobility as a function of the pressure applied to the MOST is derived for transistors with their channels located parallel to an edge of the silicon diaphragm. This expression can be incorporated in PSPCE MOST models, so that the simulation of the pressure sensor can be performed together with its readout electronics.
at a maximum pressure of 1 OOkPa, with.a channel misalignment of 5 mm. is lcs than 0.01 96. These results are superior to those found in literature. when readout circuits do ;.. incorporate special electronics for temperature compensation. Acknowledgment The authors acknowledge Cr. Magali Estrada for helpful discussions and suggestions. This work was supported by CONACyT Fig. 7 bridge. A,% P [kpa] ~es~onse of the amplifier, A. and the a fiinction of pressure at 27 OC and 80 C. Table 7 Thermal sensibility of the bridge and the readout circuit at 00 kpa T T BRDGE AMPLFER 1 OUTPUT. mv OUTPUT. mv 0 14.9 217.3 10 15.0 218.6 27 1 5.0 220.6 50 15.2 223.4 80 15.4 297.0 Table 3 Sensibility to voltage variation of Vn for the bridge and readouicircuit at TOO kpa VD, BRDGE AMPLFER 1 V OUTPUT. mv OUTPUT. mv A new MEM pressure integrated sensor consisting of a silicon diaphragm. eight PMOS transistors in a Wheastone bridge configuntion and two simples PMOS differential amplifiers stages that uses only one voltage source. is presented and simulated. This design gives high differential output. improves themil stability and increases the tolerance to the channel misalignment with respect to the edges of the membrane. The simulation results show a lineal output in the full range of 0 to 100 kpa; with a sensibility of 2.2 mv/ kpa at VD= 5 V, and 27 "C. The variation of the differential output with temperature. in the interval from 0 to 80 C. is of 0.05 kpa / "C. The output variation References M. Sze. Semiconductor Sensors, J. Willey (1994) 160171. Kanda Pie:oresistance effect of silicon. Sensors and Actuators A. 28 ( 199 ). E. Petersen. Silicon as mechanical material. Proceedings of the EEE. Vol. 70, No 5. May. 1982. pp 420457. Clark, Pressure Sensitivin in anisotropical!~ Etched ThinDiaphragm Pressure Sensors. EEE Trans Electron Devices. Vol. DE26. No 12 Dec. 1979 1887 1896. Colman. R.T. Bate. J. P. Mize. Mobilih. Anisotropy and Picoresistance in Silicon p Tpe nversion Lqvers, J. of Applied Physics. Vol. 39. NO. 4, (1968), 1923 1930. P. Dorey, T. S. Maddern. The effect of strain on MOS transistors, Solid State Electronics Dorda Piezoresistance in Qtrantijed Conduction Bands in Silicon lnversion Lqvers. Journal of Applied Physics, Vol 42. N 5, April 197 1. pp 20532060. P. Dorey.4 high sensitivity semiconductor strain sensitive circuit. Solid State Electronics. Vol. 18, ( 1975). 295299. Canali. G Ferla. B. Morten and A Taroni. Pie:oresistivip effects in MOSFET tlsefirl for pressure transdtrcers, J. Phys. D Appl. Phys.. Vol. 12. 1979, pp. 1973 1983. [ 101 M ikos hiba. StressSensitive properties of SiliconGate MOS Devices, Solid State Electronics. Vol. 24 pp. 29122 [ ] Neumeister. G. Shuster and W. Von MLlnch. A Silicon Pressure Sensor using MOS Ring Oscilla~ors. Sensors and Actuators, 7 (1985). 167 1776. [21 Wang, J. Suski. D. Collard. E. Dubois. Piezorresistivig effects in nrcosfet devices, Sensors and Actuators A. 34. (1992) 5965.