# Chapter 2: Semiconductor Physics¶

## Example 2.21.1,Page number 2-47¶

In :
import math

#given data

ro=1.72*10**-8                           #resistivity of Cu
s=1/ro                                   #conductivity of Cu
n=10.41*10**28                           #no of electron per unit volume
e=1.6*10**-19                            #charge on electron

u=s/(n*e)

print"mobility of electron in Cu =","{0:.3e}".format(u),"m^2/volt-sec"

mobility of electron in Cu = 3.491e-03 m^2/volt-sec


## Example 2.21.2,Page number 2-47¶

In :
import math

#given data

m=63.5                                  #atomic weight
u=43.3                                  #mobility of electron
e=1.6*10**-19                           #charge on electron
d=8.96                                  #density

ro=1/(n*e*u)

print"Resistivity of Cu =","{0:.3e}".format(ro),"ohm-cm"

Resistivity of Cu = 1.699e-06 ohm-cm


## Example 2.21.3,Page number 2-47¶

In :
import math

#given data

e=1.6*10**-19                            #charge on electron
ne=2.5*10**19                            #density of carriers
nh=ne                                   #for intrinsic semiconductor
ue=0.39                                 #mobility of electron
uh=0.19                                 #mobility of hole

s=ne*e*ue+nh*e*uh                       #conductivity of Ge

ro=1.0/s                                  #resistivity of Ge

print"Resistivity of Ge =",round(ro,4),"ohm-m"

Resistivity of Ge = 0.431 ohm-m


## Example 2.21.5,Page number 2-48¶

In :
import math

#given data

Eg=1.2                                  #energy gap
T1=600                                  #temperature
T2=300                                  #temperature

#since ue>>uh for intrinsic semiconductor

#s=ni*e*ue

K=8.62*10**-5                            #Boltzman constant

s=1l

s1=s*exp((-Eg)/(2*K*T1))

s2=s*exp((-Eg)/(2*K*T2))

m=(s1/s2)

print'Ratio between conductivity =',"{0:.3e}".format(m)

Ratio between conductivity = 1.092e+05


## Example 2.21.6,Page number 2-49¶

In :
import math

#given data

c=5*10**28                               #concentration of Si atoms
e=1.6*10**-19                            #charge on electron
u=0.048                                 #mobility of hole
s=4.4*10**-4                             #conductivity of Si

#since millionth Si atom is replaced by an indium atom

n=c*10**-6

sp=u*e*n                                #conductivity of resultant

print"conductivity =",(sp),"mho/m"

conductivity = 384.0 mho/m


## Example 2.21.7,Page number 2-49¶

In :
import math

#given data

m=28.1                                   #atomic weight of Si
e=1.6*10**-19                            #charge on electron
d=2.4*10**3                              #density of Si
p=0.25                                   #resistivity

#no. of Si atom/m**3

#impurity level is 0.01 ppm i.e. 1 atom in every 10**8 atoms of Si

#since each impurity produce 1 hole

nh=n

print"1) hole concentration =",round(n,4),"holes/m^3"

up=1/(e*p*nh)

print"2) mobility =",round(up,4),"m^2/volt.sec"

1) hole concentration = 5.14163701068e+20 holes/m^3
2) mobility = 0.0486 m^2/volt.sec


## Example 2.22.1,Page number 2-50¶

In :
import math

#given data

t=27                                    #temp in degree
T=t+273                                 #temp in kelvin
K=8.62*10**-5                           #Boltzman constant in eV
Eg=1.12                                 #Energy band gap

#For intrensic semiconductor (Ec-Ev)=Eg/2

#let (Ec-Ev)=m

m=Eg/2

a=(m/(K*T))

#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))

p=1/(1+exp(a))

print"probability of an electron being thermally excited to conduction band=","{0:.3e}".format(p)

probability of an electron being thermally excited to conduction band= 3.938e-10


## Example 2.22.2,Page number 2-50¶

In :
import math

#given data

T=300                                    #temp in kelvin
K=8.62*10**-5                            #Boltzman constant in eV
m=0.012                                  #energy level(Ef-E)

a=(m/(K*T))

#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))

p=1.0/(1+exp(a))

p1=1-p

print"probability of an energy level not being occupied by an electron=",round(p1,4)

probability of an energy level not being occupied by an electron= 0.614


## Example 2.22.3,Page number 2-51¶

In :
import math

#given data

t=20                                    #temp in degree
T=t+273                                 #temp in kelvin
K=8.62*10**-5                           #Boltzman constant in eV
Eg=1.12                                 #Energy band gap

#For intrensic semiconductor (Ec-Ev)=Eg/2

#let (Ec-Ev)=m

m=Eg/2

a=(m/(K*T))

#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))

p=1.0/(1+exp(a))

print"probability of an electron being thermally excited to conduction band=","{0:.3e}".format(p)

probability of an electron being thermally excited to conduction band= 2.348e-10


## Example 2.22.4,Page number 2-51¶

In :
import math

#given data

T=300                                   #temp in kelvin
K=8.62*10**-5                           #Boltzman constant in eV
Eg=2.1                                  #Energy band gap

#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))

m=K*T

#for f(E)=0.99

p1=0.99

b=abs(1.0-(1.0/p1))

a=math.log(b)                             #a=(E-2.1)/m

E=2.1+m*a

print"1) Energy for which probability  is 0.99=",round(E,4),"eV"

#for f(E)=0.01

p2=0.01

b2=abs(1-1.0/p2)

a1=math.log(b2)                            #a=(E-2.1)/m

E1=2.1+m*a1

print"2)Energy for which probability  is 0.01=",round(E1,4),"eV"

1) Energy for which probability  is 0.99= 1.9812 eV
2)Energy for which probability  is 0.01= 2.2188 eV


## Example 2.23.1,Page number 2-52¶

In :
import math

#given data

ni=2.4*10**19                            #density of intrensic semiconductor
n=4.4*10**28                             #no atom in Ge crystal
Nd=n/10**6                               #density
Na=Nd
e=1.6*10**-19                           #charge on electron
T=300                                   #temerature at N.T.P.
K=1.38*10**-23                          #Boltzman constant

Vo=(K*T/e)*log(Na*Nd/(ni**2))

print"Potential barrier for Ge =",round(Vo,4),"Volts"

Potential barrier for Ge = 0.3888 Volts


## Example 2.23.2,Page number 2-52¶

In :
import math

#given data

B=0.6                                   #magnetic field
d=5*10**-3                              #distancebetween surface
J=500                                   #current density
Nd=10**21                               #density
e=1.6*10**-19                           #charge on electron

Vh=(B*J*d)/(Nd*e)                       #due to Hall effect

print"Hall voltage =","{0:.3e}".format(Vh),"Volts"

Hall voltage = 9.375e-03 Volts


## Example 2.23.3,Page number 2-53¶

In :
import math

#given data

Rh=6*10**-7                             #Hall coefficient
B=1.5                                   #magnetic field
I=200                                   #current in strip
W=1*10**-3                              #thickness of strip

Vh=Rh*(B*I)/W                           #due to Hall effect

print"Hall voltage =",(Vh),"Volt"

Hall voltage = 0.18 Volt


## Example 2.23.4,Page number 2-53¶

In :
import math

#given data

Rh=2.25*10**-5                           #Hall coefficient
u=0.025                                 #mobility of hole

r=Rh/u

print"Resistivity of P type silicon =","{0:.3e}".format(r),"ohm-m"

Resistivity of P type silicon = 9.000e-04 ohm-m


## Example 2.23.5,Page number 2-53¶

In :
import math

#given data

B=0.55                                  #magnetic field
d=4.5*10**-3                            #distancebetween surface
J=500                                   #current density
n=10**20                                #density
e=1.6*10**-19                           #charge on electron
Rh=1/(n*e)                              #Hall coefficient

Vh=Rh*B*J*d                             #Hall voltage

print"1) Hall voltage =",round(Vh,4),"Volts"

print"2) Hall coefficient =",(Rh),"m^3/C"

u=0.17                                  #mobility of electrom

m=math.atan(u*B)

a=m*180/math.pi                         #conversion randian into degree

print"3) Hall angle =",round(a,4),"degree"

1) Hall voltage = 0.0773 Volts
2) Hall coefficient = 0.0625 m^3/C
3) Hall angle = 5.3416 degree


## Example 2.23.6,Page number 2-54¶

In :
import math

#given data

Rh=3.66*10**-4                           #Hall coefficient
r=8.93*10**-3                            #resistivity
e=1.6*10**-19                            #charge on electron

#Hall coefficient Rh=1/(n*e)

n=1/(Rh*e)                              #density

print"1) density(n) =",round(n,4),"/m^3"

u=Rh/r                                  #mobility of electron

print"2) mobility (u) =",round(u,4),"m^2/v-s"

1) density(n) = 1.70765027322e+22 /m^3
2) mobility (u) = 0.041 m^2/v-s


## Example 2.23.7,Page number 2-55¶

In :
import math

#given data

B=0.2                                   #magnetic field
e=1.6*10**-19                           #charge on electron
ue=0.39                                 #mobility of electron
l=0.01                                  #length
A=0.001*0.001                           #cross section area of bar
V=1*10**-3                              #Applied voltage
d=0.001                                 #sample of width

r=1/(ue*e)                              #resistivity
R=r*l/A                                 #resistance of Ge bar

#using ohm's law

I=V/R
Rh=r*ue                                 #hall coefficient

#using formulae for hall effect

J=I/A                                   #current density
Vh=Rh*B*J*d

print"Hall voltage =",(Vh)

Hall voltage = 7.8e-06


## Example 2.24.1,Page number 2-55¶

In :
import math

#given data

x1=0.4                                  #difference between fermi level and conduction band(Ec-Ef)
T=300                                   #temp in kelvin
K=8.62*10**-5                           #Boltzman constant in eV

#ne=N*e**(-(Ec-Ef)/(K*T))
#ne is no of electron in conduction band
#since concentration of donor electron is doubled

a=2                                     #ratio of no of electron

#let x2 be the difference between new fermi level and conduction band(Ec-Ef')

x2=-math.log(a)*(K*T)+x1                     #arranging equation ne=N*e**(-(Ec-Ef)/(K*T))

print"Fermi level will be shifted towards conduction band by",round(x2,4),"eV"

Fermi level will be shifted towards conduction band by 0.3821 eV

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