Step by step: Positioning of the resistors to maximize sensitivity

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Hands-on design training for MultiMEMS
D. Lapadatu and P. Ohlckers

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| 5.2 Step by step: Positioning of the resistors to maximize sensitivity

Instantiate four resistors in the cell 'PRESSURE_SENSOR' file saved in Step by step: Thin circular membrane

- Instantiate four copies of the 'Resistor 8 k' cell you designed in Assignment 1:Piezoresistor

Align the centre of the resistors at the location of maximum stress | In principle the location of the maximum stress for a flat membrane is at the edge of the membrane. However for our circular membrane with a soft transition stemming from the diffusion of the deep n- well, the maximum stress is not located at the very edge, but slightly inwards from it. This can be seen in the results from a FEM analysis

| Using an axisymmetric model and with 0.8 bar pressure difference over the membrane, the maximum deflection is found to be about 25 microns. The maximum von Mieses stress is found to be about 379 MPa and located about 740 microns from the centre of the membrane.

Whetstone bridges, piezoresistance and resistor orientation

Unfortunately it is not just adding the piezoresistors to any position 740 microns from the centre of the membrane. The piezoresistance varies with crystal orientation as documented by Smith in 1954. We must therefore align our resistors along the <110> directions. In addition we must orient the resistors normal and horizontal to the stress field to maximize the output from the Whetstone bride.
This can easily bee seen if we consider a Whetstone bride and the expression for the output voltage
If we imaging that R1=R2=R3=R4=R in an unstressed state, the output will be half of Vin. If we now introduce an equal change DeltaR in resistance to all resistors, and knowing that transversal stress gives a negative DeltaR and longitudinal stress a positive DeltaR, how must we configure our resistors to maximize the output?
If R1 and R4 decrease their resistance and R2 and R3 increase an equal amount, the denominators of the fractions in the expression are unchanged, and the output is governed by the difference between the R3 and R4.
This means that R1 and R4 must be configured opposite of R2 and R3. Placing R1 and R4 along to the stress field, meaning normal to the membrane edge, and R2 and R3 parallel to the membrane edge, that is normal to the stress field, the output will be maximized.

Your design should now look like this |

Sub assignment finished

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Last updated: June. 2009 24.06.2009