Piezoresistive Sensors

Outline Piezoresistivity of metal and semiconductor Gauge factor Piezoresistors Metal, silicon and polysilicon Close view of the piezoresistivity of single crystal silicon Considerations in the design of piezoresistive sensors Stress analysis of micro cantilevers and membranes (a second pass) Examples

Piezoresistivity of Metal and Semiconductor Piezoresistivity: resistance change due to internal stress or strain R = rl/a Internal stress or strain causes changes in either r, L or A, and then the resistance R. Piezoresistors can be made of metal or semiconductors. Metal Resistance changes mainly due to the deformation in L and A. Semiconductor Resistance changes mainly due to the change of r. Internal stress and strain change the mobility of charge carriers (holes and electrons).

R Gauge Factor R General Definition DR/R = G DL/L = G e (strain) Longitudinal gauge factor (resistance in the same direction of strain) G l = (DR/R) / e l Transverse gauge factor (resistance perpendicular to the direction of strain) G t = (DR/R) / e t Total piezoresistance always consists of two portions DR R = Ł DR R ł l + Ł DR R ł r = G l e + G l t e t

Piezoresistors DR DL = Dr DA el = Dr DA L Metallic strain gauges Gauge factor of 0.8~3.0. Metal deposition and patterning Single crystal silicon piezoresistors Require reasonable amount of resistance through doping (10 15 ~10 18 ). Gauge factor depends on the orientation of the piezoresistor with respect to the crystal direction. Polysilicon piezoresistors Can be deposited and patterned on different surfaces. Require reasonable amount of resistance through doping (10 15 ~10 18 ). Gauge factor depends on deposition condition and is lower than that of SCS.

Fabrication of SCS Piezoresistors

z Piezoresistivity of SCS y x [ p ] T = [ p ][ e Dr / r = E] Dr / r = e [ p ][ E ] = [ G] Gauge factor = Piezoresistive Co. E See Reference 10

Piezoresistivity of SCS

Stress Analysis in Micro Cantilever Beams The stress through the thickness of the cantilever changes from tensile stress to compressive stress. The maximum stress (strain) occurs at the top and bottom surfaces of the cantilever. Through the length of the cantilever, the maximum stress (strain) occurs at the fixed end. If the cantilever is made of homogeneous material with symmetrical geometry, the maximum tensile stress (strain) and the maximum compressive stress (strain) have the same magnitude. e Mt 2EI max = = Flt 2EI

Stress Analysis in Rectangular Membranes b1 pb s max = 2 t b pb s = center 2 t 2 apb w center = 3 Et 4 2 2

Optimal Location of the Piezoresistors on Micro Cantilevers and Membranes

Considerations for the Design of Piezoresistive Sensors Material Metal v.s. Si and polysilicon The resistivity and nominal resistance (R) The gauge factor (G) Temperature sensitivity Minimize the TCR Use circuit for compensation The location of the piezoresistor Should be at the place with maximum stress or strain (e) Function of doping concentration DR = DR piezo + DR thermal = R G e + R TCR DT

DR Wheatstone Bridge Circuit = DR piezo + DR thermal = R G e + R TCR DT Piezoresistors are often also thermal resistors. Resistance change due to temperature variation can be reduced or eliminated using Wheatstone bridge circuit configuration. All the resistors encounter the same temperature variation

Application Piezoresistive accelerometer Piezoresistive pressure sensor Piezoresistive tactile sensor Artificial hair cell sensor

Piezoresistive Accelerometer l L DR 1 1 Sensitivity : R m ( l ) 2 a w t Big mass, soft beam m k f R f resonance 1 1 3 3 1-2 3 k 1 Ewt - 2 2 2 = = m ( w t l 3 2p m 4p l m Small mass, rigid beam )

Piezoresistive Accelerometer

<110> Piezoresistive Pressure Sensor Si bulk etching Membrane thickness: 25µm 1 pb s max = DR/R = G e (strain) = G s/e 2 t b 2

Piezoresistive Pressure Sensor (II) SiN Reference resistors Poly-Si piezoresistors R1 R5 R7 R3 Reference 5-21: Liu, Caltech thesis, 1994

Piezoresistive Pressure Sensor (II) R1 R5 R7 R3 Half bridge circuit V0 VI R 1 R 5 Reference 5-21: Liu, Caltech thesis, 1994

Piezoresistive Pressure Sensor (II) Vacuum SiO (sacrificial layer) SiN (structural layer) Polysilcion (piezoresistor)

Piezoresistive Tactile Sensor An array of 4096 elements. Reference 5-3: Kane, et al, JMEMS, 2000

Piezoresistive Tactile Sensor R 4 R 4 Half bridge circuit DV=V-V0 R 4 R 4 Normal stress causes the bending of all four guided beams. Shear stress causes the stretching of two beam on one side and the compression of another two beams on the other side.

Artificial Haircell Sensor Polyimide as the cilium Ni-Cr as the piezoresistor Use Wheatstone bridge to cancel the relatively high thermal resistance Chen, et al., 2003

Artificial Haircell Sensor

Piezoresistive Accelerometer with Inplane Sensitive Axis Reference 5-20: Patridge, et al, JMEMS, 2000