Summation of series with two index m,n

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NILESH PANDEY 2018-12-16

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https://ww2.mathworks.cn/matlabcentral/answers/435977-summation-of-series-with-two-index-m-n

编辑： per isakson 2018-12-16

equation.pdf

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Hi,

I'm trying to simulate the following math equation( please see attached file name as equation).

There is term name is d1 which is my main concern it has two index in a single summation m and n

I want to verify that I have written right code or not

Please have a look on the attached file name as equation and in that, d1 is given which has a summation over m and in that summation it has a different index n

I put d1=0 after each calucaltion of phi for each n is it right?

In short d1 is given in equation file and I want to know that have I written the correct code of phi1 (as given in equation file) ?

Code is:

q=1.602e-19;
h=8.85e-12;
Eox=7.8*h;
Esi=11.8*h;
Ni=1.1e16;
Na=1e16;
%for Vgs=0:0.1:0.5
Vgs=0.1;
L=45e-9;
tox=3e-9;
tsi=10e-9;
Vds=1;
Q=-q*Na;
V=Vgs;
t1=0.02586;%thermal voltage in V%
Vbi=1.11/2;%source side potential%
phi=0;
d1=0;
phi_1=0;
%syms x y;
y=tox+tsi/2;
x=0:1e-10:L;
for n=1:1:20
    kn=n*pi/L;
    X1=((cosh(kn*(tox+tsi-y)))+(cosh(kn*(tox-y))))/(sinh(kn*tsi));
    %X_1=((cosh(kn*(tox+tsi-y_1)))+(cosh(kn*(tox-y_1))))/(sinh(kn*tsi));
    d2=L*(V*(1-(-1)^n))/((cosh(kn*tox))*pi*n);
    d4=1/(kn*Esi*tanh(kn*tsi))+1/(kn*Esi*sinh(kn*tsi))+tanh(kn*tox)/(kn*Eox) ;
    d3=Vbi*(1-(- 1)^n)/kn+(Vds*(-1)^(n+1))/kn+Q*(1-(-1)^n)/(Esi*kn*kn*kn);;
    for m=1:1:10
        k1=(2*m-1)*pi/(2*tox);
        A1=V/k1+(sin(k1*tox)*(Vbi-Vgs))/(tox*k1^2);
        A2=(V)/k1+(sin(k1*tox)*(Vbi+Vds-Vgs))/(tox*k1^2);
        d1=d1+(2*(sin(k1*(tox)))*kn*(A1+A2*((-1)^(n+1)))/(tox*(kn^2+k1^2)));
    end
    Dsf=((d1+d2-d3))/d4;
    phi=phi+2*((sin(kn*x))*X1*Dsf)/(kn*Esi*L);
    d1=0;
end
hold on
phi1=phi+Vbi+(x/L)*Vds+(Q*(x*L-(power(x,2))))/(2*Esi);
plot(x,phi1, 'b')