Chapter 13: Impurity Doping

Example 13.1 Page 458

In [1]:
#initialisation of variable
from math import *
T=1000;#temperature
C=10**19;#concentration
t=3600;#time
D=2*10**-14;#diffusivity
C2=10**15;#concentration

#calculation
Ld=(D*t)**.5;#diffusion length
Q=1.13*C*Ld;
G1=-C/((pi)**.5*Ld);#gradient
x=2*Ld*2.75;#distance
G2=-C/((pi)**.5*Ld)*exp(-x**2/(4*Ld**2));#gradient

#result
print"Q(t) is",round(Q,1),"atoms/cm^2"
print"gradient 1 at x=0 is",round(G1,2),"cm^-4"
print"gradient 2 at x=0 is",round(G2,2),"cm^-4"

Q(t) is 9.58836795289e+13 atoms/cm^2
gradient 1 at x=0 is -6.64903800669e+23 cm^-4
gradient 2 at x=0 is -3.45467180896e+20 cm^-4

Example 13.2 Page 460

In [2]:
#initialisation of variable
from math import *
d=10**14;#dopant
d=1;#depth
Db=10**15;#doping
T=1473;#temperature
Do=24;
Ea=4.08;
k=8.614*10**-5;

#calculation
#D=Do*exp(-Ea/(k*T));#diffusion
t=1190.0;#seconds
#on solving equation for t

#result
print"time required is",round(t/60,0),"minute"

time required is 20.0 minute

Example 13.3 Page 473

In [3]:
#initialisation of variable
from math import *
v=100;#KeV
l=20;#mm
d=5*10**14;#dose
t=60;#time
Pr=.31*10**-4;#range
Ps=.07*10**-4;#straggle
q=1.6*10**-19;#charge

#calculation
N=d/((2*pi)**.5*Ps);#peak concentration
Q=d*pi*(l/2)**2;#ions
I=q*Q/t;#current

#result
print"peak concetration is at x=Rp and is",round(N,2),"ions/cm^3"
print"ion current is",round(I*1000,2),"mA"

peak concetration is at x=Rp and is 2.84958771715e+19 ions/cm^3
ion current is 0.42 mA

Example 13.4 Page 483

In [4]:
#initialisation of variable
from math import *
V=200;#KeV
p=99.996;#%
Rp=.53;
Sp=.093;
T=10**-4;

#calculation
A=log(2*(pi)**.5*T);
#-(u**2+log(u))=A;
u=2.8;
d=2**.5*Sp*u+Rp;

#result
print"parameter u is",round(u,2)
print"thickness required is",round(d,3),"micro-m"

parameter u is 2.8
thickness required is 0.898 micro-m