Cantilever beam sensors

• Piezoresistor is built on the surface of the beam
• Placed near its support in order to utilise stress concentration
  

• Maximum bending stress at the surface occurs right at the beam fixed end
  If the beam support can be considered as rigid in comparison to the beam
  
• Numerical modelling is required to determine the location of maximum stress
  If the beam flexural stiffness became comparable to the substrate stiffness
  
• Beam made by a bulk micromachining of (100) silicon wafer
  • Its orientation will be along a [110] direction
  • In the same direction will appear the stress when the beam is bent
    
    
    
• Two possible orientations of piezoresistors are shown in top view in the following figure:
  

Longitudinal and transversal piezoresistive coefficients of silicon

With the aid of the values from preceding two tables

• p-type piezoresistors
  • Larger sensitivity
  • Longitudinal and transversal coefficients have opposite signs and almost equal magnitudes
  • Well suited for bridge applications
    
• Choice between two orientations of piezoresistors may be done based on system requirements
• Final position of the piezoresistor on the membrane must take into account expected fabrication reproducibility
  
• Transversely oriented piezoresistor
  • Potential for largest response
    Can be placed exactly at the place of maximal bending stress - will be experienced by the entire resistor
  • Disadvantage: very susceptible to manufacturing variations
• Longitudinaly oriented piezoresistor
  • Must extend over some length along the cantilever and may also extend onto the support
    This results to some loss of sensitivity because of the fact that not every part of the resistor experiences the maximum stress
  • Requires less costly manufacturing procedure
  • Several segments used in order to achieve more uniform stress distribution over the length
    Required resistance value is obtained by the choice of number of segments

Piezoresistor composed of several segments, a) top view b) cross section.

• Mixed solution, using two gauges of both orientations
• Opposite sign of piezoresistive coefficients will give higher voltage at the output of the Wheatstone bridge arrangement