Membrane sensors

• Possible disposition of piezoresistors on the membrane:
  • Configuration of four p-type piezoresistors
    • Positions on the membrane
    • Membrane orientation relatively to the plane of the wafer

Piezoresistors on a membrane, a) cross section, b) top view

• Usually designed as thin single crystal silicon plates supported on the borders by a thick mass of silicon substrate
• Several piezoresistors connected in a bridge circuit - in order to maximize sensitivity
• Usually a piezoresistor is built in the proximity of the edge of the membrane to utilize stress concentration due to the deformation by externally applied load
• Stresses in two perpendicular directions are experienced - unlike cantilever beam where only one stress direction can be detected
• If one of piezoresistors experience a longitudinal stress T_L, then it must simultaneously experience a transverse stress T_T = n T_L
• Total change in resistance, assuming uniform stress over the entire resistor, would be:

• Another form of the preceding relation:
  Taking into account the Hooke?s relation between stress and strain

where K is the gauge factor.

• Values of piezoresistive coefficients and of Poisson ratio and thus of gauge factor depend on
  • Material
  • Given orientation
    
• p-type piezoresistors often used - high values of piezoresistive coefficients
• It must be remembered that to use a p-type piezoresistor, one must diffuse it into an n-type substrate to achieve junction isolation
• Alternatively, to isolate piezoresistors from each other and from substrate, polycrystalline silicon surface-micromachined structures can be used