%-------Quantitative evolution of chemisorption Processes on
%Metal oxide Semiconductor--------------
% ----------Discreption of the Programme-----
% This Matlab program calculate the relation between the total surface
% coverage area and the surface potential of the metal oxide
% semiconductors.The surface potential depends upon the gas pressure and
% temperature during the chemnisorption process.This program uses the
% Wolkienstien's theory of adsorption which is more adequate than the
% conventional Langmuir model.
% Variable used-----
% P- Pressure of the gas
% T-Temperature
% q0= Energy released during the weak adsorption
% nunegative= frequency of oscillation of the adions
% nunuetral= frequency of oscillation of the nuetral adsorbates
% M= Molecular mass of the oxygen atom
% Eg= Energy band gap of the semiconductor
% Ga= degeneracy factor for the chemisorption induces states
% Ni= Intrinsic carrier concentration
% K= Boltazmann constant
% Vs= Surface potential
% Nd= Dopant concentration
% Nb= Bulk electron concentration
% Pb= Bulk hole concentration
% Ld= Debye length
% Qs= Surface charge density
% Qsc= Space charge density
%
p= 10^-6T=300;K=1.3807*10^-23;Nd=10^24;q0=0.1*1.6*10^-19;M=32*1.67*10^-27;Ga=2;Nstar=10^19es=5.4*8.85*10^-14;e=1.6*10^-19;x=0.21*1.6*10^-19 %(Ecb-Ef)=x
y=0.8*1.6*10^(-19) %(Ecs-Eas)=y
Nc=2.5*10^25;Nv=1.04*10^25;Eg=2.42*1.6*10^-19;M=32*1.67*10^-27;k1=4.14*10^-21k=1;Vs=0.2S0=10^-19;M=32*1.67*10^-27;nstar=10^25;nunegative=10^13;nunuetral=10^13Ni=sqrt(Nc*Nv*exp(-Eg/(k1)))Nb=Nd/2+sqrt(Nd^2/2+Ni^2)Pb=Ni^2/Nbub=(k1)*log(Ni^2/Nb)Ld=sqrt(es*(k1)/(e^2*Nd))a=(1 + (1/Ga)*exp(y/k1)*exp(-(x/k1))*exp((e*Vs)/k1))b=((k*S0)/(sqrt(2*pi*M*k1)*nunuetral))*exp(q0/k1)c=(1 + (1/Ga)*(nunegative/nunuetral)*exp(-(x/k1))*exp((e*Vs)/k1))Beta =(b/c)*aTheta=(Beta*p)/(1+Beta*p)Qs=-e/(1+(Ga*exp(-y/k1))*(exp(x/k1)*exp(-(e*Vs)/k1)))*Theta*nstar;Qsc=sqrt(2)*(Nb+Pb)*e*Ld*sqrt((cosh(ub+(e*Vs)/k1))/cosh(ub)-(e*Vs)/k1*tanh(ub)-1);syms Vs Ga y k1 e x Theta nstar Nb Pb Ld ubeqns=-e/(1+(Ga*exp(-y/k1))*(exp(x/k1)*exp(-(e*Vs(1)/k1))*Theta*nstar==sqrt(2)*(Nb+Pb)*e*Ld*sqrt((cosh(ub+(e*Vs))/k1))/(cosh(ub-(e*Vs)))/(k1)*tanh(ub)-1))Vs= solve(eqns, Vs)
I want to calculate the Value of Vs from the following code. but I am getting
Warning: Explicit solution could not be found.
and
Vs =[ empty sym ]
I am new to Matlab seeks help in this!!
Thank You
Best Answer