Chapter2 : Energy Bands and Charge Carriers in semiconductor

Example 2.1 Page No.58

In [9]:
dE1=0.1             #eV
dE2=-0.1           #eV
k=8.61*10**-5     #Boltzman constant
T=300             #K

import math
FE1=1/(1+math.exp(dE1/(k*T)))
FE2=1/(1+math.exp(dE2/(k*T)))

print"Probability when the energy of the state is above 0.1 eV",round(FE1,2)
print"Probability when the energy of the state is below 0.1 eV",round(FE2,2)

Probability when the energy of the state is above 0.1 eV 0.02
Probability when the energy of the state is below 0.1 eV 0.98

Example 2.2 Page No. 58

In [2]:
Ef=6.25         #EV  fermi energy level
dE=-0.30        #eV
k=8.61*10**-5    #Boltzman constant
fE=0.99

T=(dE)/(k*math.log(1/fE-1))

print"The Temprature is",round(T,1),"K" 

The Temprature is 758.3 K

Example 2.3 Page No. 64

In [1]:
Eg=0.72            #eV
Ef=0.5*Eg
dE=Eg-Ef           #eV
k=8.61*10**-5     #Boltzman constant
T=300             #K

import math
N=1/(1+math.exp(dE/(k*T)))


print"the fraction of total no. of electron is ",round(N,9)

the fraction of total no. of electron is  8.85e-07

Example 2.4 Page No. 64

In [22]:
E=300*1.602*10**-19            #eV Energy
m=9.108*10**-31                #kg, mass of electron
h=6.626*10**-34                #Planck constant

v=math.sqrt(2*E/m)
lam=h*v/E

print"The wavwlength is",round(lam*10**10,3),"A"

The wavwlength is 1.416 A

Example 2.5 Page No. 70

In [25]:
ni=1.4*10**18			#in atoms/m**3
Nd=1.4*10**24			#in atoms/m**3
n=Nd				#in atoms/m**3

p=ni**2/n			#in atoms/m**3
ratio=n/p			#unitless

print"Ratio of electron to hole concentration : ",round(ratio,2)

Ratio of electron to hole concentration :  1e+12

Example 2.7 Page no 74

In [35]:
n=10**24          #Electron density
e=1.6*10**-19     #Electron charge
v=0.015           #m/s drift velocity
A=10**-4            #m**2 area

I=n*e*v/A

print"The magnitude of current is",round(I/10**8,2),"A"

The magnitude of current is 0.24 A

Example 2.8 Page No. 74

In [32]:
Ef=5.5			#in eV
MUe=7.04*10**-3		#in m**2/V-s
n=5.8*10**28		#in m**-3
e=1.6*10**-19		#constant
m=9.1*10**-31		#in Kg

import math
tau=MUe*m/e		#in sec
rho=1/(n*e*MUe)		#in ohm-m
vF=math.sqrt(2*Ef*1.6*10**-19/m)

print"Relaxation time in sec : ",tau,"s"
print"Resistivity of conductor in ohm-m : ",round(rho,11),"ohm m"
print"velocity of electron with fermi energy is ",round(vF,0),"m/s"

Relaxation time in sec :  4.004e-14 s
Resistivity of conductor in ohm-m :  1.531e-08 ohm m
velocity of electron with fermi energy is  1390707.0 m/s

Example 2.9 Page No. 75

In [51]:
rho=1.73*10**-8       #resistivity
Tav=2.42*10**-14      #Average Time
e=1.6*10**-19		#constant
m=9.1*10**-31		#in Kg

n=m/(e**2*Tav*rho)
mu=(e*Tav)/m

print"NO. of free electrons are",round(n,-26)
print"mobility of  electrons is",round(mu,3),"m**2/Vs"

NO. of free electrons are 8.49e+28
mobility of  electrons is 0.004 m**2/Vs

Example 2.10 page No. 75

In [57]:
Ef=100			#in V/m Applied electric field
n=6*10**28		#in m**-3
e=1.6*10**-19		#constant electronic charge
m=9.1*10**-31		#in Kg  mass of electron
rho=1.5*10**-8      #Density

import math
tau=m/(n*e**2*rho)		#in sec
vF=e*Ef*tau/m

print"Relaxation time in sec : ",round(tau,16),"s"
print"velocity of electron with fermi energy is ",round(vF,1),"m/s"

Relaxation time in sec :  3.95e-14 s
velocity of electron with fermi energy is  0.7 m/s

Example 2.11 Page No.75

In [69]:
d=0.002             #m, diameter of pipe
s=5.8*10**7         #Conductivity S/m
mu=0.0032            #m**2/Vs, Electron mobility
e=1.6*10**-19		#constant electronic charge
m=9.1*10**-31		#in Kg  mass of electron
E=0.02               #V/m Electric field

import math
n=s/(e*mu)
J=s*E
I=J*(math.pi*d**2/4.0)
v=mu*E

print"Charge density is",round(n,-26),"m**-3"
print"current density is",round(J,6),"A/m**2"
print"curret flowing is",round(I,3),"A"
print"electron drift velocityis",round(v,6),"m/s"

Charge density is 1.133e+29 m**-3
current density is 1160000.0 A/m**2
curret flowing is 3.644 A
electron drift velocityis 6.4e-05 m/s

Example 2.12 page no 76

In [156]:
rho=0.5        #ohm-m Resistivity
J=100          #A/m**2 Current density
mue=0.4        #m**2/Vs Electron mobility
d=10*10**-6    #m distance

Ve=mue*J*rho
t=d/Ve

print"The drift velocity is ",Ve,"m/s"
print"Time taken by the electron is",round(t,8),"s"

The drift velocity is  20.0 m/s
Time taken by the electron is 5e-07 s

Example 2.13 Page No.76

In [76]:
e=1.6*10**-19		#constant electronic charge
m=9.1*10**-31		#in Kg  mass of electron
rho=0.039             #ohm-cm resistivity
mu=3600               #cm**2/Vs  Carrier mobility
ni=2.5*10**13

Nd=(1/(rho*e*mu))
n=Nd
p=(ni**2/n)

print"Concentration of electron is",round(n,-14),"/cm**3"
print"Concentration of holes is",round(p,0),"/cm**3"

Concentration of electron is 4.45e+16 /cm**3
Concentration of holes is 14040000000.0 /cm**3

Example 2.14 page No 76

In [4]:
rho=5.32              #kg/m**3, density
Aw=72.6               #kg/K kmol atomic weight
ni=2.5*10**13
di=10**8              #Donor impurity
e=1.6*10**-19         #Electronic charge
mue=0.38              #m**/Vs
muh=0.18               #m**/Vs

N=6.023*10**23*rho/Aw       #No 0f germanium atoms per cm**3
Nd=N/di
n=Nd
p=(ni**2/n)
s=n*e*mue*10**4

print"Concentration of electrons is",round(n,-12),"atoms/cm**3"
print"Concentration of holes is",round(p,-10),"atoms/cm**3"

if n > p:
    
    print"Conductivity of N-type germanium",round(s*100,1),"/ohm-m" 
else:
    print "Calculate p-type germanium conductivity"

Concentration of electrons is 4.41e+14 atoms/cm**3
Concentration of holes is 1.42e+12 atoms/cm**3
Conductivity of N-type germanium 26.8 /ohm-m

Example 2.15 Page no.79

In [5]:
e=1.6*10**-19         #Electronic charge
mue=0.39              #m**/Vs
muh=0.19               #m**/Vs
rhoi=0.47              #ohm-m, intrinsic resistivity
E=10**4                #Electric field

sigmai=1/rhoi
ni=sigmai/(e*(mue+muh))
Vn=mue*E
Vh=muh*E

print"Density of electrons is",round(ni,-17),"/m**3"
print"Drift velocity for electrons",round(Vn,0),"m/s"
print"Drift velocity for holes",round(Vh,0),"m/s"

Density of electrons is 2.29e+19 /m**3
Drift velocity for electrons 3900.0 m/s
Drift velocity for holes 1900.0 m/s

Example 2.16 page No.80

In [10]:
i=10**7            #IMpurity in Ge atom
ni=2.5*10**13      #/cm**3
N=4.4*10**22       #No. of atoms of Ge
mue=3800            #cm**2/Vs
muh=1800            #cm**2/Vs
e=1.6*10**-19       #Electronic charge
E=400               #Electric field

sigmai=ni*e*(mue+muh)
Nd=N/i
n=Nd
p=ni**2/(Nd)
sigman=e*Nd*mue

print"Intrinsic conductivity of Ge is ",sigmai,"ohm-cm**-1"
print"Conductivity of N type Ge semiconductor is",round(sigman,2),"ohm-cm**-1"

Intrinsic conductivity of Ge is  0.0224 ohm-cm**-1
Conductivity of N type Ge semiconductor is 2.68 ohm-cm**-1

Example 2.17 Page No. 80

In [8]:
V=10              #Volt
l=0.025           #m, length
w=0.004           #m width
t=0.0015         #m thickness

ni=2.5*10**19      #/cm**3
mue=0.38               #m**2/Vs
muh=0.18               #m**2/Vs
e=1.6*10**-19           #Electronic charge
E=400              #Electric field

E=V/l
Ve=mue*E
Vh=muh*E
sigmai=ni*e*(mue+muh)
I=sigmai*E*w*t

print"(i)Electron drift velocity is ",Ve,"m/s"
print"   hole drift velocity is ",Vh,"m/s"
print"(ii)Intrinsic Conductivity of Ge is",sigmai,"ohm-m**-1"
print"(iii)The total current is ",I*1000,"mA"

(i)Electron drift velocity is  152.0 m/s
   hole drift velocity is  72.0 m/s
(ii)Intrinsic Conductivity of Ge is 2.24 ohm-m**-1
(iii)The total current is  5.376 mA

Example 2.18 page no.80

In [11]:
Ie=3/4.0           #Current due to electron
Ih=1-Ie            #Current due to holes
Vh=1               #Hole velocity
Ve=3                #Electron velocity 3 times the hole velocity

R=(Ie*Vh/(Ih*Ve))

print"The ratio of electrons to holes drift velocity is ",R

The ratio of electrons to holes drift velocity is  1.0

Example 2.19 Page No.81

In [17]:
e=1.6*10**-19			#in coulamb
T=300				#in Kelvin
MUh=0.025			#in m**2/V-s
MUe=0.17			#in m**2/V-s
k=1.38*10**-23			#in J/K
De=MUe*k*T/e			#in cm**2/s
Dh=MUh*k*T/e			#in cm**2/s

print"Diffusion constant of electron is ",round(De*10000,2),"(in cm**2/s)"
print"Diffusion constant of hole is ",round(Dh*10000,2),"(in cm**2/s)"

Diffusion constant of electron is  43.99 (in cm**2/s)
Diffusion constant of hole is  6.47 (in cm**2/s)

Example 2.20 Page no. 81

In [40]:
N=3*10**25          #No of atoms
e=1.6*10**-19
Eg=1.1*e         #eV
k=1.38*10**-23   #j/k  boltzman's constant
T=300            #K
mue=0.14
muh=0.05

ni=N*math.exp(-Eg/(2*k*T))
sigma=ni*e*(mue+muh)

print"The intrinsic carries concentration is ",round(ni,-14),"/m**3"
print"The conductivity of Si is ",round(sigma,5),"S/m"

The intrinsic carries concentration is  1.76e+16 /m**3
The conductivity of Si is  0.00054 S/m

Example 2.21 Page No.84

In [44]:
a=1.5        #a=me/mo
T=300     #K

Nc=4.82*10**21*(a)**(1.5)*T**(1.5)

print"The effective density is",round(Nc,-23),"/m**3"

The effective density is 4.6e+25 /m**3

Example 2.22 page no. 84

In [55]:
a=0.07          #a=me/mo
b=0.4            #b=mh/mo
T=300           #K
Eg=0.7          #eV
k=8.62*10**-5   # Boltzman constant

import math
ni=math.sqrt(2.33*10**43*(a*b)**(1.5)*T**3*math.exp(-Eg/(k*T)))

print"The intrinsic concentration of charge carrier is",round(ni,-16),"/m**3"

The intrinsic concentration of charge carrier is 2.27e+18 /m**3

Example 2.23 Page no. 85

In [61]:
C=5*10**28            #atom/m**3, concentration of Si atoms
DL=2*10**8            #Doping level 
m=1
me=m
Nd=C/DL
nc=Nd
T=((nc/(4.82*10**21))*(m/me)**(1.5))**(2/3.0)

print"The absolute temprature is",round(T,2),"K"

The absolute temprature is 0.14 K

Example 2.24 Page No. 85

In [110]:
T1=300.0          #K temprature
T2=400.0
k=1.38*10**-23  #J/k
m=1.25*9.107*10**-31
h=6.625*10**-34
dE=0.3           #eV
k_=8.62*10**-5

import math
nc1=2*(2*math.pi*m*k*T1/(h**2))**(1.5)
n1=nc1*math.exp(-(0.3/(k_*T1)))

nc2=2*(2*math.pi*m*k*T2/(h**2))**(1.5)
n2=nc2*math.exp(-(0.3/(k_*T2)))

print"The effective density at temprature 300 K is",round(n1,-19),"/m**3"
print"The effective density at temprature 400 K is",round(n2,-19),"/m**3"

The effective density at temprature 300 K is 3.2e+20 /m**3
The effective density at temprature 400 K is 8.98e+21 /m**3

Example 2.25 Page no.86

In [116]:
T=300.0
k=8.62*10**-5  #J/k
m=9.107*10**-31
me=0.6*m
mh=0.4*m


dE=-3*k*T*math.log((me/mh)**(1))/4.0   #dE=Ef-Emidgap

print"The position of fermi level is",round(dE,4),"eV"

The position of fermi level is -0.0079 eV

Example 2.26 Page no 86

In [131]:
T=300.0
Eg=0.72      #eV Energy gap
k=8.62*10**-5  #J/k
me=1
mh=5.0

import math
dE=(Eg/2.0)-3*k*T*math.log(me/mh)/4.0 #dE=Ef-Emidgap

print"The position of fermi level is",round(dE,4),"eV"

The position of fermi level is 0.3912 eV

Example 2.27 Page no 87

In [134]:
T1=300.0
T2=350
Eg=0.24        #eV Energy gap

import math
dE=(T2/T1)*Eg

print"The position of fermi level is",round(dE,4),"eV"

The position of fermi level is 0.28 eV

Example 2.28 Page no.88

In [133]:
T1=300.0
T2=400
Eg=0.27        #eV Energy gap

import math
dE=(T2/T1)*Eg

print"The position of fermi level is",round(dE,4),"eV"

The position of fermi level is 0.36 eV

Example 2.29 page no.88

In [137]:
dE1=0.3        #eV Energy gap
kT=0.026       #eV

import math
x=math.exp(-dE1/kT)    #x=Nd/nc
y=5           #y=Nd2/Nd1
dE2=-math.log(y)*kT+dE1

print"The position of fermi level is",round(dE2,3),"eV"

The position of fermi level is 0.258 eV

Example 2.30 Page no.89

In [143]:
dE1=0.39        #eV Energy gap
kT=0.026        #eV

import math
x=math.exp(-dE1/kT)    #x=NA1/nV
y=3           #y=NA2/NA1
dE2=((dE1/kT)-math.log(y))*kT


print"The position of fermi level is",round(dE2,2),"eV"

The position of fermi level is 0.36 eV

Example 2.31 Page no.91

In [9]:
rho=1       #ohm-m Resistivity
Rh=100.0       #cm**3/coulomb
e=1.6*10**-19

con=1/rho   #Conductivity
R=1/Rh      #Charge density
ED=R*10**6/e
mu=con/(R*10**6)

print"The electron density is",ED,"/m**3"
print"The mobility is %.e"%mu,"/m**3"

The electron density is 6.25e+22 /m**3
The mobility is 1e-04 /m**3

Example 2.32 Page no. 92

In [146]:
w=0.1      #m width
t=0.01     #m thickness
F=0.6       #T, field
Rh=3.8*10**-4  #Hall Coefficient
I=10        #mA

Vh=(Rh*F*I/w)

print"Hall Voltage is",Vh*1000,"micro V"

Hall Voltage is 22.8 micro V

Example 2.33 Page No. 92

In [19]:
e=1.6*10**-19			#in coulamb
ND=10**17			#in cm**-3
Bz=0.1				#in Wb/m**2
w=4				#in mm
d=4				#in mm
Ex=5				#in V/cm
MUe=3800			#in cm**2/V-s

v=MUe*Ex			#in cm/s
v=v*10**-2			#in m/s
VH=Bz*v*d			#in mV

print"Magnitude of hall voltage is",VH,"mV"

Magnitude of hall voltage is 76.0 mV

Example 2.34 Page No.92

In [22]:
e=1.6*10**-19			#in coulamb
ND=10**21			#in m**-3
Bz=0.2				#in T
d=4				#in mm
d=d*10**-3			#in meter
J=600				#in A/m**2
n=ND				#in m**-3

VH=Bz*J*d/(n*e)			#in V

print"Magnitude of hall voltage is ",VH*10**3,"mV"

Magnitude of hall voltage is  3.0 mV

Example 2.35 Page No.

In [169]:
e=1.6*10**-19			#in coulamb
rho=0.00912			#in ohm-m
B=0.48				#in Wb/m**2
RH=3.55*10**-4			#in m**3-coulamb**-1
SIGMA=1/rho			#in (ohm=m)**-1

import math
THETAh=math.atan(SIGMA*B*RH)	#in Degree

print"Hall angle is",round(THETAh*180/3.14,4),"degree"

Hall angle is 1.0709 degree
In [ ]: