Question

Problem #4 (MATLAB) Band gap EG versus T As the temperature increases, the crystal lattice expands, which leads to a weakening of the inter-atomic bonds and an associated decrease in the band gap energy (why?). For many semiconductors the cited variation of the band gap energy with temperature can be modeled by the empirical relationship: aT2 a and B are constants chosen to obtain the best fit to experimental data and E (0) is the limiting where (greatest) value of the band gap at 0 K. As far as Si is concerned, an accurate fit is obtained by employing: EG(O) = 1.1 70 eV, α=4.730 × 10-4-, β-636K (a) In MATLAB, write a script to make a plot of EG versus T for Si spanning the temperature range eV from T-0 K to T 600 K. Make sure to include the codes. (b) What is the value of Ec at 300 K?

Answer 1

close all,
clear all,
clc,

EG_0 = 1.170;
Alpha = 4.73*power(10,-4);
Beta = 636;

EG=[];
for T=0:600
EG(T+1) = EG_0 - ((Alpha*T*T)/(T+Beta));
end
EG(301)
plot(EG); title('EG Vs T Plot');
str = strcat('EG at 300 K = ',num2str(EG(301)));
text(5,1,str);

MatlabOutput

ans = EG(300) =   1.1245

>>

EG Vs T Plot 1.18 1,16 1.14 1.12 1.08 1.06 1.04 1.02 100 400 200 300 500 600 700 EG at 300 K=1 1245