Piezoresistive Analysis of pressure sensor

[emily126]

HI all~

I am doing a piezoresistive pressure sensor with 4 resistors above the diaphragm so that a Wheatstone bridge is formed. As I'm only beginner in ANSYS, this job is quite hard to me. I have several questions to ask, I'll be grateful if you can help me.

(1) I would like to compare the voltage calculated by ANSYS and the theoretical voltage, but I lack the formula.
Where can I find it out? ( My model is a 3-D model and only the diaphragm with resistors part is in interest)

(2) Can I get the change of resistance in ANSYS?

(3) I know that for p-type Si used, the resistors should be aligned in <110>, so that maximun value is obtained. But I don't sure how to change the coordinate systm correctly in ANSYS.

Thanks!

 

[srosset]

Hello,

Being myself a beginner in ANSYS in need of help, I can't help you with the ansys related questions, but to answer your first question, and assuming your diaphragm is circular, you would get the following formula linking the applied pressure to the voltage in full wheatstone bridge configuration (with resistor applied along (110) and at the border of the plate)

V=Vo/2*P44*DP*0.75*(R/t)^2*(1-nu)

Vo : applied voltage to the bridge
P44 : piezoelectrical coeff.
DP : Delta P difference of pressure applied on the memebrane
R,t : Radius, thickness
nu : Poisson coefficient

I hope this can get you started...

 

[emily126]

Thanks for your suggestion!

Do you have a formula for square diaphragm?

 

[srosset]

I don't think there is an analytical formula for a square diaphragm. I came across this apporximation though :
V=Vo/2*P44*DP*0.2*(L/t)^2

I haven't checked it, so I don't know why the (1-nu) term is missing. It might be included in the 0.2 factor. I found this in a silicon-related book, so it is possible that they included the nu_silicon in the factor.

What I would recommend you to do : Make the simulation with a circular diaphragm and compare the result with the theory. If this is in accordance, then you can assume that if you change the geometry from circular to square, then your simulated results should still be accurate.

 

[emily126]

If I take the nonlinearity factor into account, does any change in the formula above?