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I have got a set with experimental data of the voltage drop on a diode an its corresponding current. The general model of a diode is $$ I = I_s \left( e^{V/nV_T} - 1 \right)\ , $$ and I want to estimate parameters $I_s$ and $\beta = 1/nV_T$ to fit the model with my data.

My first attempt was making a least squared error approximation by defining an error function with my set of data $\{V_i,I_i\}$, $$ E(I_s,\beta) = \sum_i \left[ I_i - I_s \left( e^{V_i/nV_T} - 1 \right) \right]^2\ , $$ such that solving the system of equations $\partial E / \partial I_s = 0$ and $\partial E / \partial \beta = 0$. This approach leads to two non-linear equations that I tried to solve numerically with the Newton-Raphson method, but the system and its jacobian seems to not have a ''good behaviour'', and the solutions blow up.

I thought about doing the same but using a logarithmic scale to make a kind of linear regression, but if I try to remove the exponential term I get the following, $$ \ln(I+I_s) = \ln I_s + \beta V\ , $$ being not possible to isolate $I_s$ in a way that I can do a simple linear regression.

What could be a correct approach for fitting the diode model?

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  • $\begingroup$ Can you share the data? $\endgroup$ May 7, 2021 at 17:38
  • $\begingroup$ @Jan I would like to but I'm not allowed to share it for the moment. Sorry $\endgroup$
    – SrJaimito
    May 7, 2021 at 17:40

2 Answers 2

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If you have enough points with large voltages ($V\gg \beta^{-1}$), you can use the asymptote $\log I =\log I_s + \beta V$ to get (usually) a very good estimation of the parameters:

enter image description here

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Well, you can use the following Mathematica-code to do it:

Clear["Global`*"];
q = ((1602176634/(10^9)))*10^(-19);
k = ((1380649/(10^6)))*10^(-23);
Normal[NonlinearModelFit[{{}, {}, {}, {}}, 
  Is*(Exp[(q*V)/(\[Eta]*k*T)] - 1), {Is, \[Eta], T}, V]]

And the {{},{},{},{}} is the data.

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