Question

Make a plot of built-in voltage on the y-axis and log (aoping concentration from 1010-1020/cm2) on the x- axis for symmetrical pn junctions (NA = No). Do not just sketch the curve plot it. Make a plot of depletion width on the y-axis and log (doping concentration from 1010-1020/cm3) on the x axis for symmetrical pn junctions. Again plot don't sketch. Be sure to use enough data points to give an accurate doping level for when the curve is a maximum Discuss the two plots

Answer 1

Given that:- Make a plot of bailt-in voltage on the Y-axis and log (doping Concentration from 10.1038/(m3) on the x-axis for gymmetrical on junctions. Soli- It can be derived that the built in potential of Bymmetric Pn juction is given by, Voi = KI in (Math ) If Na=Nd, then the equation becomes Voi = 2 kI in (Na)

The matlab code is developed to plot the graph withVbi vs Na or Nd

%Vbi Computation (Na=Nd symmetric device)
clear all;
clc;
%Constants
EG=1.12;
kT=0.0259;
ni=1.0e10;

%Computation
ND=logspace(10,20);
Vbi=2*kT.*log(ND./ni);

%Plotting
close
semilogx(ND,Vbi); grid
axis([1.0e10 1.0e20 0.05 1.2])
xlabel('NA or ND (cm-3)'); ylabel('Vbi (volts)')
title('Plot of Vbi vs NA or ND');

plooted graph:

Plot of Vbi vs NA or ND Vbi (volts) 0,15 1010) பட்டப் பட்டப் பட்டப்பட்டவர் பபபபபபபபபபபாடடபபபபபபபபபபபா 1011 1012 1013 1014 1016 | 1018 1013 NA or ND (cm-3) 101/ 1020

2.) The written deplation width vs doping Concentration is as, - Na tnd I - Nard , vbi If Nai Nd, then the equation becomes WERE Cata) Ubi

Matlabcode:

%Constants and Parameters
T=300; % Temperature in Kelvin
k=8.617e-5; % Boltzmann constant (eV/K)
e0=8.85e-14; % permittivity of free space (F/cm)
q=1.602e-19; % charge of an electron (coul)
KS=11.8; % dielectric constant of Si at 300K
ni=1e10; % intrinsic carrier conc. in Silicon at 300K (cm^-3)
EG=1.12; % band gap of Silicon (eV)

%Depletion width calculation
ND=logspace(10,20);
Vbi=2*kT.*log(ND./ni);

W=1.0e4*sqrt(2*KS*e0/q.*(Vbi)./ND);

%Plot
close
loglog(ND, W,'-')
axis([1.0e10 1.0e20 0.5e-2 2.0e1])
grid
xlabel('NA or ND (cm^-3)')
ylabel('W (micrometers)')
title('Plot of W vs NA or ND');

Plotted waveform:

Plot of W vs NA or ND 101 W (micrometers) 101010121014101610181020 NA or ND (cm 3)

. From the two figures, we can conclude that the built in potential is increased by increasing the doping Gantention. The width of depletion region is decreased with the increase of doping concentration.