Chapter Two : Elements Of Solid State Physics

Example 2.1, Page Number 51

In [1]:
d1=8.93*(10**3) #Density of Copper in Kg/meter cube
N=63.54 #atomic mass number of copper
t=2.6*(10**-14)#Mean free time between collision in seconds
m=9.1*(10**-31) #Mass of electron 
em=0.135 #Electron Mobility
hm=0.048 #Hole Mobility
n=p=1.6*(10**16) #Concentration per meter cube
ac=6*(10**26)  #a given Constant
e=1.6*(10**-19)  #Charge of electron

n1=(ac*d1)/N #Free electron concentration/No. of atoms per unit volume

#from equation 2.22
rhoc=(n1*e*em)/3 #Conductivity of copper in per ohm m
rhoc=round(rhoc,2)

#from equation 2.24
rhos=n*e*(em+hm) #Conductivity of Copperintrinsic silicon in per ohm m
rhos=round(rhos,5)

print "Free Electron Concentration is %.2e /meter cube"%(n1)

print "Conductivity of copper and intrinsic silicon is "+str(rhoc)+" and "+str(rhos)+" respectively in per ohm meter"

Free Electron Concentration is 8.43e+28 /meter cube
Conductivity of copper and intrinsic silicon is 607138810.2 and 0.00047 respectively in per ohm meter

Example 2.2, Page Number 55

In [2]:
r=11.8 #Relative Permaebility
m=9.1*(10**-31) #Mass of electron
me=0.26*m #Effective mass 

#From equation 2.28

E=13.6*(me/m)*((1/r)**2) #where E is the excitation energy
E=round(E,5)

print "The Excitation Energy is given by "+str(E)+" eV"

The Excitation Energy is given by 0.0254 eV

Example 2.3, Page Number 60

In [3]:
from math import pow

PI=3.14
m=9.1*(10**-31) #Mass of electron
me=0.55*m #Effective mass
T=300 #Temperature in Kelvin
k=1.38*(10**-23) #Boltzmann Constant
h=6.6*(10**-34) #Plancks Constant

#From equation 2.33

N=2*(pow((2*PI*me*k*T)/(h*h),1.5)) #Where N is the Effective density of states in the conduction band


print "The Effective Density of States in the Conduction Band is %.2e Per Meter Cube"%(N)

The Effective Density of States in the Conduction Band is 1.03e+25 Per Meter Cube

Example 2.4, Page Number 64

In [4]:
n=5*(10**24) #Donor Concentration in per meter cube

#For GaAs
t1=1/((7.2*(10**-16))*n) #where t1 is the Hole lifetime

#For Si
t2=1/((1.8*(10**-21))*n) 
t2=round(t2,5)
print "The Hole Lifetime For GaAs is %.2e seconds"%(t1)
print "The Hole Lifetime For Si is "+str(t2)+" seconds"

The Hole Lifetime For GaAs is 2.78e-10 seconds
The Hole Lifetime For Si is 0.00011 seconds

Example 2.5, Page Number 70

In [5]:
from math import log1p

nd=10**22 #Donor Impurity Level in per meter cube
na=10**24 #Acceptor Impurity Level in per meter cube
n=2.4*(10**19) #Intrinsic Electron Concentration in per meter cube
T=290 #Temperature in Kelvin
k=1.38*(10**-23) #Botlzmann Constant
e=1.6*(10**-19) #Charge of a electron

#From Equation 2.45 
v=(k*T/e)*log1p((nd*na)/(n**2)) #Where v is the contact potentital difference in volts
v=round(v,2)
print "The Contact Potential Difference is "+str(v)+" Volts"

The Contact Potential Difference is 0.42 Volts

Example 2.6, Page Number 73

In [6]:
nd=10**21 #Donor Concentration per meter cube
na=10**22 #Acceptor Concentration per meter cube
de=3.4*(10**-3) #Drift current-electron
dh=1.2*(10**-3) #Drift current-holes
le=7.1*(10**-4) #per meter
lh=3.5*(10**-4) #per meter
n=1.6*(10**16)  #per meter cube
e=1.6*(10**-19)  #charge of the electron

#Assuming all ions are ionized

pn=(2.56*(10**32))/nd
np=pn/10

#From Equation 2.51a
jo=e*((dh/lh)*pn+(de/le)*np) #where Jo is the saturation current density

A=10**6 #Junction area
io=jo/A #where io is the reverse bias saturation current


print "P-N concentration is "+str(pn)+" /meter cube"
print "N-P concentration is "+str(np)+" /meter cube"
print "The Saturation Current Density is %.2e A/meter square"%(jo)
print "The Reverse Bias Saturation Current is %.2e A"%(io)

P-N concentration is 2.56e+11 /meter cube
N-P concentration is 25600000000.0 /meter cube
The Saturation Current Density is 1.60e-07 A/meter square
The Reverse Bias Saturation Current is 1.60e-13 A

Example 2.7, Page Number 78

In [7]:
from math import sqrt

V=-4 #Reverse Bias voltage
nd=4*(10**21) #in per meter cube
Vo=0.8 
A=4*(10**-7) #Junction Area
er=11.8 #Relative permittivity
e=1.6*(10**-19) #Charge of a Electron
eo=8.85*(10**-12) #absolute permittivity 

#Since in A p+-n junction
#By equation 2.63

C=(A/2)*sqrt((2*eo*er*e*nd)/(Vo-V))

print "The Junction Capacitance is %.2e Farad"%(C)

The Junction Capacitance is 3.34e-11 Farad

Example 2.8, Page Number 84

In [8]:
Lz=10*(10**-9) #Thickness in meter
m=9.1*(10**-31) #Mass of Electron
me=0.068*m #Effective mass of electron
mh=0.56*m #Effective mass of holes
h=6.6*(10**-34) #Plancks Constant
e=1.6*(10**-19) #Charge of electron

Eg=((h*h)/(8*(Lz*Lz)))*((1/me)+(1/mh)) #Where Eg is the effective increase in the width of the energy gap
Eg1=Eg/e #Converting in eV
Eg1=round(Eg1,3)
print "The Effective Increase in the width of the Energy Gap is "+str(Eg1)+" eV"

The Effective Increase in the width of the Energy Gap is 0.062 eV