Help needed for below error

Kindly help with the below error for the below mentioned code. All other values are constant

scale1 = 100;   
T1 = linspace(10, 2000, scale1); 
Ta = rdivide(1,T1);  
ND1 = 1e17;  
NA1 = 1e5;   
%Computing n and p values to be plotted
hole1 = ones(scale1,1)*0;
Eflevel1 = ones(scale1,1)*0;
electron1 = ones(scale1,1)*0;
 NC1 = 2*Mc*(((mde*kb*T1(1:100))/(2*pi*(hbar^2))).^(3/2));  
      NV1 = 2*(((mdh*kb*T1(1:100))/(2*pi*(hbar^2))).^(3/2));   
      kbT1 = (kb*T1(1:100))/e; 
      ev1 = 0;
      ea1 = ev1 + Eai;
      eg1 = 1.17 - (4.73e-4*((T1(1:100)).^2))./(T1(1:100) + 636);
      ec1 = eg1;
      ed1 = ec1 + Edi; 
      x2 = [0 1.73];
for range1 = 1:prod(size(T1))
     
      eq2 = @(EF1) ((NC1(range1))*exp(-(ec1(range1)-EF1)/kbT1(range1))) + ((NA1)/(1+4*exp(-(EF1-ea1(range1))/kbT1(range1)))) -  (((NV1(range1))*exp(-(EF1-ev1(range1))/kbT1(range1))) + ((ND1)/(1+2*exp(-(ed1(range1)-EF1)/kbT1(range1)))));
      Eflevel1(range1) = fsolve(eq2, x2);  
      y1 = Eflevel1(range1);
      x2 = y1.';
      s11 = Eflevel1(:,1,:);
      electron1(range1) = (NC1(range1))*exp(-(ec1(range1)-Eflevel1(range1))/(kbT1(range1)));
      s12 = electron1(:,1,:);
      hole1(range1) = (NV1(range1))*exp(-(Eflevel1(range1)-ev1(range1))/(kbT1(range1)));
      s13 = hole1(:,1,:);
end

[John D'Errico]

https://www.mathworks.com/matlabcentral/answers/29922-why-your-question-is-not-urgent-or-an-emergency

So others do not deserve just as fast attention to their problems?

[Amy Topaz]

Sorry about that, I have modified it. I didn't mean in that sense.

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

The page has now been archived.

Answer 1

[Walter Roberson]

 x2 = [0 1.73];

row vector

Eflevel1(range1) = fsolve(eq2, x2);  

vector is used as the example parameters for fsolve, so eq2 is going to be passed something the same length as x2.

eq2 = @(EF1) ((NC1(range1))*exp(-(ec1(range1)-EF1)/kbT1(range1))) + ((NA1)/(1+4*exp(-(EF1-ea1(range1))/kbT1(range1)))) -  (((NV1(range1))*exp(-(EF1-ev1(range1))/kbT1(range1))) + ((ND1)/(1+2*exp(-(ed1(range1)-EF1)/kbT1(range1)))));

That vector becomes EF1 on input. You use that vector EF1 in several places, including in

/(1+4*exp(-(EF1-ea1(range1))/kbT1(range1)))

so the right hand side of the / is a row vector.

But remember that the / operator is matrix-right-divide, mrdivide, with A/B being similar to A*pinv(B) except with some size constraints. And the size constraints are such that row vector / row vector is not permitted .

[Amy Topaz]

oh got it, thank you for your explanation. Do you know how can I modify it so that it is corrected?

[Walter Roberson]

No... you haven't defined how it should work, so I cannot recommend a correction.

If you switch to element-by-element processing using ./ instead of / then your eq2 would return a vector of two elements. fsolve() can deal with a vector of two elements being returned: it tries to adjust the values so that both values become 0. However, since nothing else in your expression modifies the expression differently for the two elements, it follows that the same value (0) would be returned if you managed to find a 0 for one of the elements and then set the other element to the same value. So at present, the calculations cannot differentiate between the two values passed in to the function.

Notice you are assigning the result of fsolve() to the scalar location Eflevel1(range1), implying that you expect fsolve() to return a scalar. But fsolve() is always going to return a non-scalar whenever the example input (x2) is non-scalar, since fsolve() returns the array of model coefficients that lead the function to have all-zero output.

[Amy Topaz]

oh okay.

Can we use fzero instead of fsolve?

[Amy Topaz]

I basically need all the values of EF for the given range so that I can plot a graphs between Ta and s11

[Walter Roberson]

fzero can only deal with a single variable, not a vector of variables, so it would be an error to use fzero with that x2.

[Amy Topaz]

okay, so how shall I proceed?

Answer 2

[Torsten]

Since it seems that you only solve for a single unknown, change

x2 = [0 1.73];

to

x2 = 1.73;

Then your code should be

for range1 = 1:prod(size(T1))   
   eq2 = @(EF1) NC1(range1)*exp(-(ec1(range1)-EF1)/kbT1(range1)) + NA1/(1+4*exp(-(EF1-ea1(range1))/kbT1(range1))) -  (NV1(range1)*exp(-(EF1-ev1(range1))/kbT1(range1)) + (ND1/(1+2*exp(-(ed1(range1)-EF1)/kbT1(range1)))));
   Eflevel1(range1) = fsolve(eq2, x2);  
   x2 = Eflevel1(range1);
end
y1 = Eflevel1;
x2 = y1.';
s11 = Eflevel1;
electron1 = NC1.*exp(-(ec1-Eflevel1)./kbT1);
s12 = electron1;
hole1= NV1.*exp(-(Eflevel1-ev1)./kbT1);
s13 = hole1;