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Asked by Siva Malla
on 21 Dec 2012

I wrote a program to solve 3 variables from 3 equations. For that I used syms command. but unfortunately I got the answers are empty. means matlab doesn't solve these 3 equations. I run this program in matlab 2008a. So please help me to solve these equations, or please suggest alternate command to solve this program: here I posted my program, please give a solution for my problem.

Program:

clc clear all g=4; L=0.5*1e-4; a=0.12*1e-4; W=200*1e-4; q=1.6*1e-19; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NT1=3.8*1e15; NT2=2*1e13; NT3=2.6*1e15; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CCp1=3*1e-14 CCn1=2*1e-14 CCp2=1*1e-15 CCn2=2.4*1e-15 CCp3=1*1e-15 CCn3=5*1e-15 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Eg=3.2*q; Ef=2.268*q; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Et1=Eg-0.67*q; Et2=Eg-1.65*q; Et3=Eg-0.93*q; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ev=0; Es=85.845*1e-14; K=8.62*1e-5; T=300; KTev=K*T; KT=0.0259*q; m0=9.1*1e-31; mp=0.77*m0; Vpth=(3*KT/mp)^0.5; mn=0.351*m0; Vnth=(3*KT/mn)^0.5; mc=0.76*m0; mv=1.2*m0; h=6.626*1e-34; Nc=2*((2*pi*mc*KT/h^2)^1.5)*1e-6; Nv=2*((2*pi*mv*KT/h^2)^1.5)*1e-6; Nd=8*1e17; Nref=2*1e17; Umin=40; Umax=950; r=0.76; vsat=2.07*1e7; y=(Eg/(2*KT)); ni=((Nc*Nv)^0.5)*exp(-y); Vbi=1.3-((KT/q)*log(Nc/Nd)) U0= Umin + ((Umax - Umin)/(1+ ((Nd/Nref)^r))); d1=0.98 Ec=(vsat/U0)*(d1/(1-d1)); Nsam=3*1e15; Nsdp=5*1e15; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ep1=CCp1*Vpth*Nv*exp(-((Et1-Ev)/KT)) En1=CCn1*Vnth*Nc*exp(-((Eg-Et1)/KT)) Ep2=CCp2*Vpth*Nv*exp(-((Et2-Ev)/KT)) En2=CCn2*Vnth*Nc*exp(-((Eg-Et2)/KT)) Ep3=CCp3*Vpth*Nv*exp(-((Et3-Ev)/KT)) En3=CCn3*Vnth*Nc*exp(-((Eg-Et3)/KT))

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NT1mnoneql=NT1*(Ep1/(Ep1+En1)) NT1meql=NT1/(1+((1/g)*exp((Et1-Ef)/KT)))

NT2mnoneql=NT2*(En2/(En2+Ep2)) NT2meql=NT2/(1+((1/g)*exp((Et2-Ef)/KT)))

NT3mnoneql=NT3*(En3/(Ep3+En3)) NT3meql=NT3/(1+((1/g)*exp((Et3-Ef)/KT))) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% N1subm=NT1mnoneql-NT1meql; N2subm=NT2mnoneql-NT2meql; N3subm=NT3mnoneql-NT3meql; Nsubm=(N1subm+N2subm+N3subm) Ubi=(KT/q)* log((Nd/Nsubm)) Ndepp=Nd-Nsam+Nsdp+(NT1*(En1/(Ep1+En1)))+(NT2*(En2/(Ep2+En2)))+(NT1*(En3/(Ep3+En3))) k11=((Nsubm/(Nsubm+Ndepp)))^0.5 Vp=(q*Ndepp*a^2)/(2*Es) k1=q*(Nd-Nsubm)*vsat*W*a*d1; Z=(q*Ndepp*a^2*U0)/(2*Es*L*vsat); VG=-2; Rs=47.03; VD=0:1:10; for i=1:11 syms VDsat ID L1 Rd2(i)=50; hL1=((Vbi-VG+VDsat-ID*Rd2(i))/Vp)^0.5; Y1=q*W*U0*vsat*(Nd-Nsubm)/(vsat*L1+U0*(VDsat-ID*(Rd2(i)+Rs))); hs=((Vbi-VG+ID*Rs)/Vp)^0.5 h1L1=((Ubi+VDsat-ID*Rd2(i))/Vp)^0.5 h1s=((Ubi+ID*Rs)/Vp)^0.5; eq1=VD(i)-VDsat-2*hL1*Ec*a/pi*sinh(pi*(L-L1)/(2*hL1*a)); eq2=ID-Y1*a*Vp*(((VDsat-ID*Rd2(i)-ID*Rs)/Vp)-2/3*(hL1^3-hs^3)-2/3*k11*(h1L1^3-h1s^3)); eq3=ID-q*(Nd-Nsubm)*W*d1*vsat*a*(1-hL1-k11*h1L1); [ID, L1, VDsat]=solve(eq1, eq2, eq3,ID, L1, VDsat) end

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