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Piezoresistive Coefficent of n-type Silicon- sigma0 function of N or nd?

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Hi!

I am trying to simulate resistivity change in n-type doped Si given some mechanical stress. My Comsol results for resistivity change are 10E-5 smaller than my theoretical math.

Can anyone please help me understand where the "sigma0" analytic function for n-type piezoresistive Silicon conductivity comes from?

I don't understand the sigma0 equation in terms of 'N'. Is 'N' number density which is equal to dopant concentration or total number of particles? When I define number density nd= dopant conc[1/m^3] my Comsol resistivity change is 10e-5 times smaller than my hand calculations. So I am guessing my definition of nd[1/m3] should not be dopant conc.

This is the comsol eq: (Ne_const0.1400/sqrt(1+N/(N/350 +3e22)))

Thank you so much!


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