Piezoresistive Effect Research Paper

The piezoresistive effect is given by
 


 (1 2 )



R
R
(1) where  is the resistivity of the piezoresistor,  depends on the doping concentration of the piezoresistors, ν is the Poisson’s ratio and  is the mechanical strain induced in the diaphragm.
The first part of the left hand side of equation 1 describes the piezoresistive effect and the second part defines the geometric effect. For piezoresistive materials like polysilicon, the piezoresistive effect dominates over geometric effect, so the second part of Equation 1 is neglected and the linear piezoresistive effect is stated by the superposition of the longitudinal and the transverse piezoresistive effect with the stress components l in longitudinal and  t in transverse direction.
_T_a_b_le_ _3_. _C_o_e_ff_i_c_ie_n_t_s _o_f _α_,_ β_ _fo_r_ v_a_r_y_in_g_ _b_/a_ _ra_t_io_s_ _ a/b 1.0 1.2 1.4 1.6 1.8 ∞ α 0.00126 0.00172 0.00207 0.00230 0.00245 0.0026 β1 0.0513 0.0639 0.0726 0.0780 0.0812 0.0833
_β2_ _ _0_.0_5_1_3_ __ _0_.0_5_5_4_ _ __0_.0_5_6_8_ _ _0_._0_5_7_1_ _ _0_._0_5_7_1_ _ _0_._0_5_7_1_
The maximum induced stress on the square diaphragm is given by
 
2
max max 6 h M x or y
  (17)
Therefore, considering the Parallel–Normal
Combination of Piezoresistors, according to the specific diaphragm, the equation for differential output voltage has been changed to
 
  2 max
(1 )
1
2
  l  t  r r
V
V
 


 (18)
Sensitivity ‘S’ of the sensor is given by,
P
V
S

