matlab 关于数值积分的问题(定积分但是数值很大且式子复杂)X=0.31;d=2*10^-6;E0=8.85*10^-12;T=77;e=1.6*10^-19;k=1.38*10^23;kb=8.625*10^-5;ND=5*10^20;NA=100*10^20;E=E0*(14*(1-X)+7.05*X)Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T
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![matlab 关于数值积分的问题(定积分但是数值很大且式子复杂)X=0.31;d=2*10^-6;E0=8.85*10^-12;T=77;e=1.6*10^-19;k=1.38*10^23;kb=8.625*10^-5;ND=5*10^20;NA=100*10^20;E=E0*(14*(1-X)+7.05*X)Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T](/uploads/image/z/10195431-15-1.jpg?t=matlab+%E5%85%B3%E4%BA%8E%E6%95%B0%E5%80%BC%E7%A7%AF%E5%88%86%E7%9A%84%E9%97%AE%E9%A2%98%28%E5%AE%9A%E7%A7%AF%E5%88%86%E4%BD%86%E6%98%AF%E6%95%B0%E5%80%BC%E5%BE%88%E5%A4%A7%E4%B8%94%E5%BC%8F%E5%AD%90%E5%A4%8D%E6%9D%82%29X%3D0.31%3Bd%3D2%2A10%5E-6%3BE0%3D8.85%2A10%5E-12%3BT%3D77%3Be%3D1.6%2A10%5E-19%3Bk%3D1.38%2A10%5E23%3Bkb%3D8.625%2A10%5E-5%3BND%3D5%2A10%5E20%3BNA%3D100%2A10%5E20%3BE%3DE0%2A%2814%2A%281-X%29%2B7.05%2AX%29Eg%3D-0.295%2B1.87%2AX-0.28%2AX%5E2%2B%286-14%2AX%2B3%2AX%5E2%29%2A10%5E-4%2AT)
matlab 关于数值积分的问题(定积分但是数值很大且式子复杂)X=0.31;d=2*10^-6;E0=8.85*10^-12;T=77;e=1.6*10^-19;k=1.38*10^23;kb=8.625*10^-5;ND=5*10^20;NA=100*10^20;E=E0*(14*(1-X)+7.05*X)Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T
matlab 关于数值积分的问题(定积分但是数值很大且式子复杂)
X=0.31;
d=2*10^-6;
E0=8.85*10^-12;
T=77;
e=1.6*10^-19;
k=1.38*10^23;
kb=8.625*10^-5;
ND=5*10^20;
NA=100*10^20;
E=E0*(14*(1-X)+7.05*X)
Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T+0.35*X^4
nl=(1+3.25*kb*T/Eg)*9.56*10^14*Eg.^(3/2)*T.^(3/2)*10^6/(1+1.9*Eg.^(3/4)*exp(Eg/2/kb/T))
pn0=(-ND+(ND^2+4*nl^2)^(1/2))/2
nn0=(ND+(ND^2+4*nl^2)^(1/2))/2
pp0=(NA+(NA^2+4*nl^2)^(1/2))/2
np0=(NA+(NA^2+4*nl^2)^(1/2))/2
Vpn=kb*T*log(ND*NA/nl^2)/e
V0=(nn0+pn0-np0-pp0-ND*e*Vpn/k/T)*kb/e/(NA-ND)
E=-(2*kb*T*(-e*x*ND/kb/T+np0*exp(e*x/kb/T)+pp0*exp(e*x/kb/T)-nn0-pn0+ND*e*Vpn/k/T)/E).^(1/2);
对1/E求积分,上限是V0,下限是Vpn;
matlab 关于数值积分的问题(定积分但是数值很大且式子复杂)X=0.31;d=2*10^-6;E0=8.85*10^-12;T=77;e=1.6*10^-19;k=1.38*10^23;kb=8.625*10^-5;ND=5*10^20;NA=100*10^20;E=E0*(14*(1-X)+7.05*X)Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T
clear;clc
syms x
X=0.31;
d=2*10^-6;
E0=8.85*10^-12;
T=77;
e=1.6*10^-19;
k=1.38*10^23;
kb=8.625*10^-5;
ND=5*10^20;
NA=100*10^20;
E=E0*(14*(1-X)+7.05*X);
Eg=-0.295+1.87*X-0.28*X^2+(6-14*X+3*X^2)*10^-4*T+0.35*X^4;
nl=(1+3.25*kb*T/Eg)*9.56*10^14*Eg.^(3/2)*T.^(3/2)*10^6/(1+1.9*Eg.^(3/4)*exp(Eg/2/kb/T));
pn0=(-ND+(ND^2+4*nl^2)^(1/2))/2;
nn0=(ND+(ND^2+4*nl^2)^(1/2))/2;
pp0=(NA+(NA^2+4*nl^2)^(1/2))/2;
np0=(NA+(NA^2+4*nl^2)^(1/2))/2;
Vpn=kb*T*log(ND*NA/nl^2)/e;
V0=(nn0+pn0-np0-pp0-ND*e*Vpn/k/T)*kb/e/(NA-ND);
E=-(2*kb*T*(-e*x*ND/kb/T+np0*exp(e*x/kb/T)+pp0*exp(e*x/kb/T)-nn0-pn0+ND*e*Vpn/k/T)/E).^(1/2);
U=double(int(1/E,Vpn,V0))