Chapter 6: Nonequilibrium Excess Carriers in Semiconductors

Example 6.5, Page 212

In [1]:
#Variable declaration
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
un=1200.
Nd=10**16 #cm**-3
esp0=8.85*10**-14 
espr=11.7

#Calculations&Results
sigma=e*un*Nd
print "conductivity is %.2f per ohm cm "%sigma

esp=espr*esp0
print "permittivity of silicon is %.2e F/cm"%esp

taud=esp/sigma
print "dielectric relaxtion time constant is %.2e sec "%taud

conductivity is 1.92 per ohm cm 
permittivity of silicon is 1.04e-12 F/cm
dielectric relaxtion time constant is 5.39e-13 sec

Example 6.6, Page 217

In [2]:
import math

#Variable declaration
T=300#K
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
n0=10**15 #cm^-3
p0=10**5 #cm^-3
ni=10**10 #cm^-3
deltan=10**13 #cm**-3
deltap=10**13 #cm**-3


#Calculations&Results
#Ef-Efi=a
a=(k*T)*math.log(n0/ni)
print "fermi level for thermal equlibrium is %.4f eV "%a

#Efn-Efi=b
b=(k*T)*math.log((n0+deltan)/ni)
print "quasi fermi level for electrons is %.4f eV "%b

#Efi-Efp=c
c=(k*T)*math.log((p0+deltap)/ni)
print "quasi fermi level for holes is %.3f eV "%c

#answers vary due to roundinf-off errors

fermi level for thermal equlibrium is 0.2976 eV 
quasi fermi level for electrons is 0.2979 eV 
quasi fermi level for holes is 0.179 eV

Example 6.8, Page 225

In [3]:
import math

#Variable declaration
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
x=0
taup0=10**-6#ses
taup01=10**-7 #sec
deltapb=10**14 #cm**-3
Dn=10 #cm^2/sec
Dp=10 #cm^2/sec
B=-9*10**13

#Calculations&Results
deltap=deltapb*(taup01/taup0)
print "deltap is %.e cm^-3 "%deltap

g=deltap/taup0
print "g generation is %.e cm^-3s^-1 "%g  #incorrect solution in textbook

#deltapx=10**14*(1-0.9*math.exp(-x/Lp))
Lp=math.sqrt(Dp*taup0)
print "Lp is %f meter "%Lp
deltapx=10**14*(1-0.9*math.exp(-x/Lp))
print "distance from the surface = %.e"%deltapx

deltap is 1e+13 cm^-3 
g generation is 1e+19 cm^-3s^-1 
Lp is 0.003162 meter 
distance from the surface = 1e+13

Example 6.10, Page 228

In [5]:
#Variable declaration
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
Dp=10#cm^2/sec
Lp=31.6*10**-4 #m
g1taup0=10**14 #cm^-3
deltap0=10**13 #cm6-3

#Calculations
#deltap0=g1taup0*[g/((Dp/Lp)+s)]
s=(Dp/Lp)*((g1taup0/deltap0)-1)

#Result
print "surface recombination velocity is %.2e cm per sec "%s

surface recombination velocity is 2.85e+04 cm per sec