Huge inaccuracies in plotting diode IV characteristic in Matlab

I currently have a lab for my microelectronics class where I have to plot measured data against the diode model equation using parameters extracted from the measured data: the ideality factor (n) of the diode and the saturation current (Is).

The diode model used in my class is: Id = Is*[exp(Vd/nVt)-1]

where Vt is thermal voltage, Vd is diode voltage, and Id is diode current.

However, when I plot the diode equation with logscale on the y-axis I have huge discrepancies between the data points on the plot, and the values that the diode equation model should actually assume. The only way I have gotten the models to plot even remotely accurately was by adjusting the saturation currents to absurd values on the order of 10^-51.

This is what my plots look like without the absurd correction in the saturation current. Notice the huge gap between the green and blue lines; that shouldn't be there.

This is what my plots look like with the absurd correction in the saturation current.

Why is this happening? I've already double checked all of my units and everything is definitely in mA, so what am I missing here? Also, as a sanity check I quickly plugged the diode equation with specific values into my TI-84 graphing calculator, and for individual plot points the discrepancy between MATLAB and my TI-84 is on the order of 10 orders of magnitude.

I've attached my MATLAB code to this post. Any explanations and or solutions to this issue would be much appreciated!

Answer 1

[William Rose]

@Nicholas,

It is clear that your model does not fit your data. So there has been an error in the data collection, or the mdoel is just wrong. If you adjust the model parameters, I'm sure you could get a much better fit.

For example, if I change nzm from your value, nzm=1.199 to nzm=0.82, I get a decent fit to the zener data. I'm sure you can do likewise with the LED data, and you can do even better if you also tweak other adjustable parameters in the model.

I recommend comparing your I-V data to the data sheets for the diodes you used, to see if your data looks reasonable.

It can be useful to view the data on a linear-linear plot, which is what I did below. NOte the fit to the zener data when I changerd nzm.

[William Rose]

@Nicholas, in case you are wondering how I came up with nzm=0.82, I looked at the equation then made a few guesses: nzm=2,3 (dumb guesses, in retrospect), then nzm=0.8, 0.6 (0.8 was close), then nzm=0.82, 0.85 (0.82 was better). In other words, I did not use any fancy fitting routines. I'm sure you can do better.

[Nicholas]

Thank you so much for the quick response, William!

The iv characteristic data was collected using a peak atlas DCA pro, which is a tool used for characterizing various two and three terminal semiconducting devices, so I’m fairly certain the measured data should be free of any significant errors. I should also note I collected data twice with two different DCA pro devices, and the data collected from both devices was essentially the same.

Additionally, the original saturation currents and ideality factors that I extracted from the data was done so using an exponential regression model in Microsoft excel, and the coefficient of determination for both regression models was around 0.99, so the models should fit the measured data fairly well, as confirmed by my hand calculations with the regression models which yield comparable values to what was measured.

I believe it may have something to do with my code, or maybe even possibly how MATLAB does floating-point arithmetic; however, I’m only a journeyman so these are only guesses on my part.

I’ve tried using the symbolic math packages for MATLAB, specifically the vpa() function to try and extend the precision of the calculated models in MATLAB, but that didn’t seem to fix any issues.

Do you have any further suggestions for how I might go about plotting these models legitimately in MATLAB?

[William Rose]

@Nicholas,

[edit: fix spelling errors]

You say you are confident that the I-V data are correct. I would still compare the I-V data to the relevant datasheets, but that's up to you.

I suspect Matlab's floating point arithmetic is plenty accurate for a simple model like this. Therefore I am not surprised that trying to extend the precision did not help.

You fitted the model in Excel. I suspect that is where the problem happened. What model parameters did you adjust?

It is nice to separate the code from the data. To do this for you, after running your code, I did

save('ECE302data','Vled','Iled','Vzd','Izd')

This saves the I-V data in file ECE302data.mat.

The you can remove all the lines in your script that specify the data. Replace them with

load('ECE302data');

If you have the I-V data in a 4-column text file, such as ECE302data.txt, you do something similar.

By the way, your model is

Izdm = Iszdm * (exp(Vzdm ./ Vt*nzm) - 1);

This equivalent to

Izdm = Iszdm * (exp(Vzdm*nzm/Vt) - 1);

Is that your intention?

[William Rose]

@Nicholas, Actually, that last thing I mentioned is your problem.

You forgot parentheses. Add those, and your model and your fitted parameters work pretty well.

[William Rose]

@Nicholas,

[edit: fix error in a comment; code is not changed]

Adding the parentheses fixes the problem you had.

But the fit is still not great with the paremeters you got from Excel. I suspect you can do better than the Excel fit. Let's try, with the zener data.

load 'ECE302data'  % load the data

Predict the current with the Excel model parameters

Vt= 300*1.38e-23/1.602e-19;             %=0.0258 Volts
Iszx = 2e-10;                           % from Excel 
nzx = 1.199;                            % from Excel
Izx = Iszx * (exp(Vzd/(Vt*nzx)) - 1);   % predict with Excel params

Compute the root mean square error between measured and predicted current:

RMSErrx=sqrt(sum((Izd-Izx).^2)/length(Izd));
fprintf('Excel prediction RMS error=%.3f mA\n',RMSErrx)

Excel prediction RMS error=0.922 mA

Find the best-fit parameters Isz and nz with Matlab:

fun= @(p,V)p(1)*(exp(V/(0.0258*p(2)))-1);  % model to fit
p0=[1e-10,1];               % initial guess for [Isz, nz]
p=lsqcurvefit(fun,p0,Vzd,Izd);

Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.

Iszm=p(1); nzm=p(2);
fprintf('Matlab fit: Iszm=%.3e, nzm=%.3f.\n',Iszm,nzm)

Matlab fit: Iszm=1.329e-12, nzm=1.003.

Predict the current with Matlab's parameters.

Izm = Iszm * (exp(Vzd/(Vt*nzm)) - 1);   % predict with Matlab params

Compute the root mean square error between measured and Matlab-predicted current:

RMSErrm=sqrt(sum((Izd-Izm).^2)/length(Izd));
fprintf('Matlab prediction RMS error=%.3f mA\n',RMSErrm)

Matlab prediction RMS error=0.312 mA

The RMS error with Matlab's fit is better by a factor of three.

Plot results:

figure;
plot(Vzd,Izd,'k*',Vzd,Izx,'r.',Vzd,Izm,'g.');
xlabel('Voltage (V)'); ylabel('Current (mA)'); 
grid on; title('Zener Diode')
legend('Data','Excel prediction','Matlab prediction','location','northwest')

The Matlab fit looks better than the Excel fit. I don't know how the Excel fit was done, or if it could have been done better.

[Nicholas]

Holy cow. Thank you so much, William! You are a real life-saver. You were absolutely correct about the lack of parentheses in the denominator of the exponetial. That small change made the modeled equations fit like a dream!

I also really appreciate your suggestions for cleaning up my MATLAB code, too. As I mentioned I'm only a journeyman, and haven't had extensive exposure to MATLAB.

[William Rose]

@Nicholas, you're welcome, and good luck with your studies. Do you by any chance use the textbook The Art of Electronics, by Horowitz and Hill?

[Nicholas]

@William Rose my class textbook is not "The Art of Electronics" By Horowitz and Hill its "Microelectronic Circuit Design" by Jaegar; however, I'm aware that it is the gold standard of microelectronic texts. I've come across a few copies here and there, but have never had the fortune of owning a copy myself. Why do you ask?

Out of curiousity, what discipline do you work in?

[William Rose]

I'm a retired anatomy and physiology teacher.

I ask about the book because my 1979 electronics class was taught by Paul Horowitz, the author of The Art of Electronics. Our class notes were the galley proofs for the book. I bought the book when it came out a year later, and it was extremely useful. Prof. Horowitz has a very good sense of humor, which comes across in the book.

The book Numerical Recpies for Scientific Computing ("NR") came out a few years after Art of Electronics. Like Art of Electronics, NR was very well-received. One of my other professors, Bill Vetterling, co-authored NR. I wrote to Prof. Vetterling to say I liked it, and it reminded me of Horowitz's book, and I pointed out a few errors I had noticed. He replied that the resemblance was not a coincidence: they set out to make a book for programming that would be like Horowitz's book was for electronics. They asked Horowitz to be a co-author on NR, since he is good at everything, but he was too busy searching for extraterrestrial intelligence. (Horowitz and Vetterling were in the same department.) And Prof. Vetterling gave me a list of all the errors in NR (long since corrected) which I had failed to notice. Like Horowitz, he has a good sense of humor, and I was on the receiving end of it sometimes.

[Nicholas]

That’s absolutely incredible. It must have been quite the experience to study under such a brilliant person like Horowitz. What was the experience like working in a classroom moving at that pace and level of rigor?

You taught physiology and anatomy, but took an electronics course? What’s the correlation there? Or did you take the course for your own personal pleasure?

Thank you for the textbook resource! Free, quality knowledge is always appreciated! I quickly glanced over the contents and I’m very keen on starting my journey through “NR.”

[William Rose]

It was a privilege to have excellent teachers like Prof. Horowotitz and others. And classmates who made me realize I wasn't as smart as I thought! I majored in physics but went in a different direction. NR was published before there were resources like Matlab and NumPy. Therefore you had to write your own code for spectrum estimation, etc. Now, most of us don't need to know the nitty-gritty coding details that are in NR. But the explanations in NR are still good. For example, the descriptions of optimization and minimization methods, ODE solvers, PDE solvers, etc., are clear and informative.

[Nicholas]

I can only imagine how much of humbling experience that was for you. What I would give to be a fly on the wall in that room. You said that you used to teach; what do you find yourself doing these days? Also, you've had some phenomenal recommendations for me so far. Do you have any other resources I should try to get my hands on? I'm in an electrical engineering program at NC State, and I plan on specializing in some form of signal processing/telecommunications.

[William Rose]

@Nicholas, please email me by clicking on the envelope icon which appears in the window that pops up when you click the "WR" icon next to my posts. We can conitinue the discussion offline.