# Chapter - 2 : Physics Of Semiconductor¶

## Example - 2.1 : Page No - 54¶

In :
#Given data
miu= 0.3 # in m**2/vs
V= 50 # in mV
V=V*10**-3 # in V
d=0.4 # in mm
d=d*10**-3 # in m
# Part (a)
# miu= vd/E and vd= miu*E, so
vd= miu*V/d # in m/s
print "(a) : Drift velocity = %0.1f m/s" %vd

# Part (b)
T= d/vd # in sec
print "(b) : Time required for an electron to move = %0.2f µs" %(T*10**6)

(a) : Drift velocity = 37.5 m/s
(b) : Time required for an electron to move = 10.67 µs


## Example - 2.2 : Page No - 55¶

In :
#Given data
miu_n= 0.36 # in m**2/vs
miu_p= 0.17 # in m**2/vs
ni= 2.9*10**19 # in /m**3
q=1.6*10**-19 # in C
sigma_i= q*ni*(miu_n+miu_p) # in (Ωm)**-1
print "Intrinsic conductivity of Ge = %0.2f (Ωm)**-1" %sigma_i

Intrinsic conductivity of Ge = 2.46 (Ωm)**-1


## Example - 2.3 : Page No - 55¶

In :
from __future__ import division
#Given data
rho= 0.60 # in Ωm
q=1.6*10**-19 # in C
miu_n= 0.38 # in m**2/vs
miu_p= 0.18 # in m**2/vs
sigma= 1/rho # in (Ωm)**-1
ni= sigma/(q*(miu_n+miu_p)) # in /m**3
print " The intrinsic carrier concentration = %0.3e per meter cube" %ni

 The intrinsic carrier concentration = 1.860e+19 per meter cube


## Example - 2.4 : Page No - 56¶

In :
#Given data
N_D= 10**21 # in /m**3
N_A= 2*10**20 # in /m**3
miu_n= 0.15 # in m**2/vs
N_DeshD= N_D-N_A # in /m**3
n=N_DeshD # in /m**3
q=1.6*10**-19 # in C
sigma= q*n*miu_n # in (Ωm)**-1
print " Conductivity of silicon = %0.1f (Ωm)**-1" %sigma

 Conductivity of silicon = 19.2 (Ωm)**-1


## Example - 2.5 : Page No - 56¶

In :
#Given data
n=6.023*10**23*7.4/63.54
miu= 32.6 # in cm**2/Vs
q=1.6*10**-19 # in C
sigma= n*q*miu # in (Ωcm)**-1
print "Conductivity of copper = %0.2e (Ωcm)**-1" %sigma

Conductivity of copper = 3.66e+05 (Ωcm)**-1


## Example - 2.6 : Page No - 56¶

In :
#Given data
# For silicon
q=1.6*10**-19 # in C
ni= 2.5*10**12 # in /cm**3
miu_n= 1700 # in cm**2/Vs
miu_p= 600 # in cm**2/Vs
sigma= 0.2 # in (Ωm)**-1
# Formula sigma= q*n*miu_n
n= sigma/(q*miu_n) # in /cm**3
p= ni**2/n # in /cm**3
print "For silicon : "
print " Concentration of electron = %0.2e /cm**3" %n
print " Concentration of holes = %0.1e /cm**3" %p
# For germanium
ni= 3.4*10**15 # in /cm**3
miu_n= 3600 # in cm**2/Vs
miu_p= 1600 # in cm**2/Vs
sigma= 150 # in (Ωm)**-1
p= sigma/(q*miu_p) # in /cm**3
n= ni**2/p # in /cm**3
print "For germanium :"
print " Concentration of electron = %0.2e /cm**3" %n
print " Concentration of holes = %0.2e /cm**3" %p

For silicon :
Concentration of electron = 7.35e+14 /cm**3
Concentration of holes = 8.5e+09 /cm**3
For germanium :
Concentration of electron = 1.97e+13 /cm**3
Concentration of holes = 5.86e+17 /cm**3


## Example - 2.7 : Page No - 57¶

In :
#Given data
miu_n= 3900 # in cm**2/Vs
miu_p= 1900 # in cm**2/Vs
ni= 2.5*10**10 # in /cm**3
Nge= 4.41*10**22 # in /cm**3
q=1.6*10**-19 # in C
N_D= Nge/10**8 # in /cm**3
n=N_D # approx
p= ni**2/N_D # in /cm**2
sigma= q*n*miu_n # in (Ωcm)**-1
rho= 1/sigma # in Ωcm
print " Resistivity of the doped germanium = %0.2f Ωcm" %rho

 Resistivity of the doped germanium = 3.63 Ωcm


## Example - 2.8 : Page No - 58¶

In :
#Given data
Nsi = 4.9*10**22 # in /cm**3
ni= 2.5*10**12 # in /cm**3
q=1.6*10**-19 # in C
miu_n= 1600 # in cm**2/Vs
miu_p= 400 # in cm**2/Vs
N_D= Nsi/(100*10**6)
sigma= q*ni*(miu_n+miu_p) # in (Ωcm)**-1
rho= 1/sigma # in Ωcm
print " Resistivity of silicon = %0.f Ωcm" %rho
n=N_D # approx
p= ni**2/n # in /cm**3
sigma= q*n*miu_n # in (Ωcm)-1
rho= 1/sigma # in Ωcm
print " Resistivity of doped silicon = %0.2f Ωcm" %rho

 Resistivity of silicon = 1250 Ωcm
Resistivity of doped silicon = 7.97 Ωcm


## Example - 2.9 : Page No - 59¶

In :
#Given data
N_D= 5*10**28/(20*10**6) # in /m**3
# For the Fermi level
# E_F= E_C if N_C= N_D,
# N_D= 4.82*10**21 * T**(3/2)  /m**3
T= (N_D/( 4.82*10**21 ))**(2/3) # in K
print " Temperature = %0.3f K" %T

 Temperature = 0.646 K


## Example - 2.10 : Page No - 59¶

In :
from math import log
#Given data
ni= 1.8*10**15 # in /m**3
rho= 2*10**5 # in Ωm
q=1.6*10**-19 # in C
dopingConcentration= 10**25 # in /m**3
n=dopingConcentration
MCC= ni**2/dopingConcentration  # Minority carrier concentration per cube meter
miu_n= 1/(2*rho*q*ni) # in m**3/Vs
print "(a) : The value of µn = %0.1e m**3/Vs" %miu_n

# Part (b)
sigma= q*n*miu_n #in (Ωm)**-1
rho= 1/sigma # in Ωm
print "(b) : Resistivity     = %0.2e Ωm" %rho

# Part(c)
kT= 26*10**-3 #in V
no= n # in /m**3
Shift_inFermiLevel= kT*log(no/ni) # in eV
print "(c) : Shift in Fermi level due to doping = %0.3f eV" %Shift_inFermiLevel
print "      Hence, E_F lies ",round(Shift_inFermiLevel,3)," eV above Fermi level Ei"

# Part (d)
MCC= ni**2/dopingConcentration  # Minority carrier concentration per cube meter
print "(d) : Minority carrier concentration = %0.2e per cube meter" %MCC

(a) : The value of µn = 8.7e-03 m**3/Vs
(b) : Resistivity     = 7.20e-05 Ωm
(c) : Shift in Fermi level due to doping = 0.583 eV
Hence, E_F lies  0.583  eV above Fermi level Ei
(d) : Minority carrier concentration = 3.24e+05 per cube meter


## Example - 2.11 : Page No - 60¶

In :
#Given data
miu_n= 1700 #in cm**2/Vs
miu_p= 560 #in cm**2/Vs
ni= 2.5*10**10 # in /cm**3
q=1.6*10**-19 # in C
sigma= q*ni*(miu_n+miu_p) #in (Ωcm)**-1
rho= 1/sigma # in Ωcm
print "Conductivity of intrinsic sample = %0.2e (Ωcm)**-1" %sigma
print "Resistivity of intrinsic sample = %0.3e Ωcm" %rho

Conductivity of intrinsic sample = 9.04e-06 (Ωcm)**-1
Resistivity of intrinsic sample = 1.106e+05 Ωcm


## Example - 2.12 : Page No - 61¶

In :
#Given data
ni= 1.45*10**10 # in /cm**3
q=1.6*10**-19 # in C
miu_n= 1300 # in cm**2/Vs
density= 5*10**26 # density of silicon atom in /cm**3
N_D= density/10**12
n=N_D
# n*p= ni**2
p= ni**2/n #in /cm**3
sigma= q*n*miu_n # in (Ωcm)**-1
rho= 1/sigma # in Ωcm
print " Resistivity of silicon = %0.2f Ωcm" %rho

 Resistivity of silicon = 9.62 Ωcm


## Example - 2.13 : Page No - 62¶

In :
from sympy import symbols, solve, N
p= symbols('p')
#Given data
q=1.6*10**-19 # in C
rho=75 #in Ωcm
N_D= 10**13 # in /cm**3
N_A= 5*10**12 #in /cm**3
E=3 # in V/cm
ni= 2.7*10**12 # in /cm**3
sigma= 1/rho # in (Ωcm)**-1
# miu_p/miu_n= 1/3 or miu_n=3*miu_p
# sigma= q*ni*(miu_n+miu_p) = q*ni*(3*miu_p+miu_p) = q*ni*(4*miu_p)
miu_p= sigma/(q*ni*4)
miu_n= 3*miu_p
# n+N_A= p+N_D  or  n= p+N_D-N_A
# n*p= ni**2  or  (p+N_D-N_A)*p= ni**2
# p**2 + (N_D-N_A)*p-ni**2 =0
expr= p**2 + (N_D-N_A)*p-ni**2
root = solve(expr, p)
p= root #discarding -ve value
n=p+N_D-N_A
I= q*(n*miu_n+p*miu_p)*E# in A/m**2
print "The total conduction current = %0.4f A/m**2" %I
# Note: There is some difference between book answer and coding. The reson behind this is that
#          The value of P is evaluated 1.8*10**12 while accurate value is 1.179674*10**12

The total conduction current = 0.0730 A/m**2


## Example - 2.14 : Page No - 63¶

In :
#Given data
N_D= 10**20 # in /cm**3
ni= 2.5*10**12 # in /cm**3
kT=26 # in meV
kT=kT*10**-3 # in eV
n= N_D # as N_D>>ni
p= ni**2/n #in /cm**3
print "(a) : The minority carrier concentration = %0.1e per cm**3" %p

# Part (b)
LocationOfFermiLevel= kT*log(N_D/ni) # in eV
print "(b) : The Fermi Level will be ",round(LocationOfFermiLevel,3)," eV above Fermi level"

#Note: The value of Minority carrier concentration of part(a) is calculated wrong because
#      the value of (2.5*10**12)**2/(10**20) will be 62500 not 2.5*10**4

(a) : The minority carrier concentration = 6.2e+04 per cm**3
(b) : The Fermi Level will be  0.455  eV above Fermi level


## Example - 2.15 : Page No - 63¶

In :
#Given data
miu_n= 1300 # in cm**2/Vs
q=1.6*10**-19 # in C
ni= 4.3*10**-6 # in /cm**3
V= 1 # in volt
L=8 # in cm
A=0.8*0.8 # in cm**2
I=4*10**-3 # in A
# R= rho*L/A = V/I
R= V/I # in Ω
sigma= L/(R*A) # in (Ωcm)**-1
# sigma= q*n*miu_n
n= sigma/(q*miu_n)
N_D= n
print "(a) : The value of N_D = %0.3e" %N_D
# Part (b)
d=L
E= V/d
vd=miu_n*E # in cm/s
print "(b) : Drift velocity = %0.1f cm/s" %vd

(a) : The value of N_D = 2.404e+14
(b) : Drift velocity = 162.5 cm/s


## Example - 2.16 : Page No - 64¶

In :
#Given data
E= 1 #in v/m
miu= 32*10**-4 # in m**2/Vs
m= 9.1*10**-28 # in gram
m=m*10**-3 # in kg
q=1.6*10**-19 # in C
toh_r= 2*miu*m/q # in sec
Vd= miu*E # in m/sec
print "The relaxation time = %0.2e sec" %toh_r
print "Drift velocity      = %0.2f cm/sec" %(Vd*10**2)

The relaxation time = 3.64e-14 sec
Drift velocity      = 0.32 cm/sec


## Example - 2.17 : Page No - 64¶

In :
#Given data
miu_n= 0.145 # in m**2/Vs
miu_p= 0.05 # in m**2/Vs
q=1.6*10**-19 # in C
n=10**15 # per m**3
p=10**2 # per m**3
rho= 1/(q*(n*miu_n+p*miu_p)) # in Ωm
print "The resistivity = %0.2e Ωm" %rho

The resistivity = 4.31e+04 Ωm


## Example - 2.18 : Page No - 65¶

In :
#Given data
miu_n= 0.13 # in m**2/Vs
miu_p= 0.05 # in m**2/Vs
q=1.6*10**-19 # in C
ni=1.5*10**16 # per m**3
sigma_intrinsic= q*ni*(miu_n+miu_p) # in (Ωm)**-1
print "(a) : The conductivity of silicon in Intrinsic condition = %0.2e (Ωm)**-1" %sigma_intrinsic

# Part (b)
n= 5*10**28/10**9
sigma= q*n*miu_n # in (Ωm)**-1
print "(b) : The conductivity with donar impurity               = %0.2f (Ωm)**-1" %sigma

# Part (c)
p= 5*10**28/10**8
sigma= q*p*miu_p # in (Ωm)**-1
print "(c) : The conductivity with acceptor impurity            = %0.f (Ωm)**-1" %sigma

# Part (d)
p_desh= p-n # in /m**3
sigma= q*p_desh*miu_p # in (Ωm)**-1
print "(d) : The conductivity with donar and acceptor impurity  = %0.1f (Ωm)**-1" %sigma

# Note : Answer in the book of part (a) may be miss printed or wrong

(a) : The conductivity of silicon in Intrinsic condition = 4.32e-04 (Ωm)**-1
(b) : The conductivity with donar impurity               = 1.04 (Ωm)**-1
(c) : The conductivity with acceptor impurity            = 4 (Ωm)**-1
(d) : The conductivity with donar and acceptor impurity  = 3.6 (Ωm)**-1


## Example - 2.19 : Page No - 66¶

In :
#Given data
rho= 1.2 # in Ωm
miu_n= 0.14 # in m**2/Vs
q=1.6*10**-19 # in C
ni= 1.8*10**16 # per m**3
# sigma = 1/rho = q*n*miu_n
n= 1/(rho*q*miu_n) # per m**3
p= ni**2/n # per m**3
print " The value of n = %0.2e per m**3" %n
print " The value of p = %0.1e per m**3" %p

 The value of n = 3.72e+19 per m**3
The value of p = 8.7e+12 per m**3


## Example - 2.20 : Page No - 66¶

In :
#Given data
N_D= 5*10**22/10**8
q=1.6*10**-19 # in C
ni= 1.45*10**10 # per m**3
miu_n= 1300 # in m**2/Vs
# n*p= ni**2 or N_D*p = ni**2
p= ni**2/N_D # in /cm**3
sigma= q*miu_n*N_D # in (Ωcm)**-1
rho= 1/sigma #in Ωcm
print " Resistivity = %0.2f Ωcm" %rho

 Resistivity = 9.62 Ωcm


## Example - 2.21 : Page No - 67¶

In :
#Given data
q=1.6*10**-19 # in C
n=8.4*10**28
rho= 6.51 # in Ω/1000ft
rho= rho/(3.05*10**4) # in Ω/cm
sigma= 1/rho # in mho/cm
sigma=sigma*10**2 # in mho/m
# sigma= n*q*miu
miu= sigma/(n*q) # in m**2/v-s
print " Conductivity = %0.2e mho/m" %sigma
print " Mobility     = %0.2e m**2/v-s" %miu

 Conductivity = 4.69e+05 mho/m
Mobility     = 3.49e-05 m**2/v-s


## Example - 2.22 : Page No - 67¶

In :
#Given data
miu_n= 1350 # in cm**2/v-sec
miu_p= 480 # in cm**2/v-sec
ni=1.52*10**10 # in /cm**3
q=1.6*10**-19 # in C
sigma= q*ni*(miu_n+miu_p) # in (Ωcm)**-1
rho= 1/sigma # in Ωcm
print " Conductivity = %0.3e (Ωcm)**-1" %sigma
print " Resistivity  = %0.2e Ωcm" %rho

 Conductivity = 4.451e-06 (Ωcm)**-1
Resistivity  = 2.25e+05 Ωcm


## Example - 2.23 : Page No - 67¶

In :
#Given data
ni=2.5*10**19 # in /m**3
miu_n= 0.38 # in m**2/v-sec
miu_p= 0.18 # in m**2/v-sec
q=1.6*10**-19 # in C
sigma= q*ni*(miu_n+miu_p) # in (Ωm)**-1
print " Conductivity = %0.2f (Ωm)**-1" %sigma

 Conductivity = 2.24 (Ωm)**-1


## Example - 2.24 : Page No - 68¶

In :
#Given data
rho= 0.5 # in
miu_n= 0.39 # in m**2/v-sec
miu_p= 0.19 # in m**2/v-sec
q=1.6*10**-19 # in C
sigma= 1/rho # in (Ωm)**-1
# Formula sigma= q*ni*(miu_n+miu_p)
ni= sigma/(q*(miu_n+miu_p)) # in /m**3
print " The intrinsic carrier concentration of germanium = %0.3e /m**3" %ni

 The intrinsic carrier concentration of germanium = 2.155e+19 /m**3


## Example - 2.25 : Page No - 68¶

In :
#Given data
q=1.6*10**-19 # in C
miu_n= 0.18 # in m**2/v-s
N_D= 10**21 # per m**3
N_A= 5*10**20 # per m**3
N_deshD= N_D-N_A # per m**3
n=N_deshD # per m**3
sigma= q*n*miu_n # in (Ωm)**-1
print " Conductivity of the silicon sample = %0.1f (Ωm)**-1" %sigma

 Conductivity of the silicon sample = 14.4 (Ωm)**-1


## Example - 2.26 : Page No - 69¶

In :
#Given data
q=1.6*10**-19 # in C
miu_n= 0.36 # in m**2/v-s
miu_p= 0.17 # in m**2/v-s
ni= 2.5*10**19 # per m**3
sigma= q*ni*(miu_n+miu_p) # in s/m
rho= 1/sigma # in Ωm
print " Conductivity of Ge = %0.2f s/m" %sigma
print " Resistivity        = %0.2f Ωm" %rho

 Conductivity of Ge = 2.12 s/m
Resistivity        = 0.47 Ωm


## Example - 2.27 : Page No - 69¶

In :
#Given data
e=1.6*10**-19 # in C
miu_n= 0.13 # in m**2/v-s
miu_p= 0.05 # in m**2/v-s
N_D= 5*10**28/(2*10**8) # per m**3
n=N_D # per m**3
ni= 1.5*10**16 # per m**3
p= ni**2/N_D # per m**3
sigma= e*(n*miu_n+p*miu_p) # in s/m
print " Conductivity of the intrinsic semiconductor = %0.1f s/m is " %sigma

 Conductivity of the intrinsic semiconductor = 5.2 s/m is


## Example - 2.28 : Page No - 69¶

In :
from math import exp
#Given data
Eg= 0.72 # in eV
Ef= Eg/2 #in eV
K= 8.61*10**-5 # in eV/K
T=300 #in K
nc= 1
n= 1+exp(((Eg-Ef)/(K*T)) )
ncBYn= nc/n
print " The fraction of the total number or electrons = %0.2e" %ncBYn

 The fraction of the total number or electrons = 8.85e-07


## Example - 2.29 : Page No - 70¶

In :
#Given data
N_D= 1.4*10**24 # per m**3
ni= 1.4*10**18 # per m**3
n=N_D #per m**3
p=ni**2/n # per m**3
R= n/p # ratio of electron to holes concentration
print " Ratio of electron to holes concentraiton = %0.1e" %R

 Ratio of electron to holes concentraiton = 1.0e+12


## Example - 2.30 : Page No - 70¶

In :
from numpy import pi
#Given data
e=1.6*10**-19 # in C
miu_e= 0.0032 # in m**2/v-s
sigma= 5.8*10**7 # in s/m
E= 20*10**-3 # in V/m
d=0.002 # in m
Area= pi*d**2/4 # in m**2

# Part (a)
n= sigma/(e*miu_e) # per m**3
print "(a) : The charge density          = %0.3e per meter cube" %n

# Part (b)
J= sigma*E # in A/m**2
print "(b) : Current density             = %0.2e A/m**2" %J

# Part (c)
I= J*Area # in A
print "(c) : Current flowing in the wire = %0.3f ampere" %I

# Part (d)
v=miu_e*E # in m/sec
print "(d) : Electron drift velocity     = %0.1e m/sec" %v

(a) : The charge density          = 1.133e+29 per meter cube
(b) : Current density             = 1.16e+06 A/m**2
(c) : Current flowing in the wire = 3.644 ampere
(d) : Electron drift velocity     = 6.4e-05 m/sec


## Example - 2.31 : Page No - 71¶

In :
#Given data
rho= 0.5 # in Ω-m
miu_c= 0.4 # in m**2/v-sec
J=100 #in A/m**2
distance=10 # µm
distance=distance*10**-6 #in sec
# V= miu_c*E = miu_c*J/sigma = miu_c*J*rho
V=  miu_c*J*rho  # in m/sec
print " Drift velocity = %0.f m/sec" %V
T= distance/V # in second
print " The time taken by the electron to travel 10 micro meter in the crystal = %0.1e second" %T

 Drift velocity = 20 m/sec
The time taken by the electron to travel 10 micro meter in the crystal = 5.0e-07 second


## Example - 2.32 : Page No - 71¶

In :
#Given data
e=1.6*10**-19 # in C
miu_e= 3800 # in cm v-s
miu_p= 1800 # in cm v-s
ni= 2.5*10**13 # per cm**3
N_D= 4.4*10**22*10**-7 # per cm**3
n=N_D # per cm**3
p= ni**2/N_D # holes/cm**3
sigma_i= ni*e*(miu_e+miu_p) # in (Ωcm)**-1
sigma_n= e*N_D*miu_e # in (Ωcm)**-1
print " Intrinsic conductivity                      = %0.4f (Ωcm)**-1" %sigma_i
print " Concentration of electrons                  = %0.1e per cm**3" %n
print " Concentration of holes                      = %0.2e per cm**3" %p
print " The conductivity in n-type Ge semiconductor = %0.2f (Ωcm)**-1" %sigma_n

 Intrinsic conductivity                      = 0.0224 (Ωcm)**-1
Concentration of electrons                  = 4.4e+15 per cm**3
Concentration of holes                      = 1.42e+11 per cm**3
The conductivity in n-type Ge semiconductor = 2.68 (Ωcm)**-1


## Example - 2.33 : Page No - 72¶

In :
#Given data
e=1.6*10**-19 # in C
a= 0.004*0.0015 # in m**2
ni= 2.5*10**19 # per m**3
miu_e= 0.38 # in m**2/ v-s
miu_p= 0.18 # in m**2/v-s
V=10 # in V
i= 25 # in mm
i=i*10**-3 # in m
E= V/i # in V/m
# Part (a)
ve= miu_e*E # in m/sec
print "(a) : Electric drift velocity              = %0.f m/sec" %ve
vp= miu_p*E # in m/sec
print "      Hole drift velocity                  = %0.f m/sec" %vp

# Part (b)
sigma_i= ni*e*(miu_e+miu_p) # in (Ωcm)**-1
print "(b) : Intrinsic carrier conductivity of Ge = %0.2f (Ωcm)**-1" %sigma_i

# Part (c)
I= sigma_i*E*a # in A
I=I*10**3 # in mA
print "(c) : Total current                        = %0.3f mA" %I

(a) : Electric drift velocity              = 152 m/sec
Hole drift velocity                  = 72 m/sec
(b) : Intrinsic carrier conductivity of Ge = 2.24 (Ωcm)**-1
(c) : Total current                        = 5.376 mA


## Example - 2.34 : Page No - 73¶

In :
from math import exp
#Given data
miu_e= 0.14 # in m**2/ v-s
miu_p= 0.05 # in m**2/v-s
e=1.6*10**-19 # in C
N=3*10**25 # per m**3
Eg= 1.1 # in eV
Eg= Eg*1.602*10**-19 # in J
k= 1.38*10**-23 # in J/K
T=300 # in K
ni= N*exp((-Eg/(2*k*T))) # in /m**3
sigma= ni*e*(miu_e+miu_p) # in s/m
print " The intrinsic carrier concentration = %0.3e /m**3" %ni
print " Conductivity of Si = %0.2e s/m" %sigma

 The intrinsic carrier concentration = 1.715e+16 /m**3
Conductivity of Si = 5.21e-04 s/m


## Example - 2.35 : Page No - 73¶

In :
#Given data
N_A= 4.4*10**22/10**8 # in /m**3
N_D= 10**3*N_A # in /m**3
ni= 2.5*10**13 # /cm**3
Vt= 26 # in mV
Vt= Vt*10**-3 # in V
Vj= Vt*log(N_A*N_D/ni**2) # in V
print " The junction potential = %0.4f volts" %Vj

# Note : There is miss print in the book answer

 The junction potential = 0.3287 volts


## Example - 2.36 : Page No - 74¶

In :
#Given data
I_o= 0.3 # in µA
I_o= I_o*10**-6 # in A
V_F= 0.15 # in V
I= I_o*exp(40*V_F) # in A
print " Current flowing in the diode = %0.2f µA" %(I*10**6)

 Current flowing in the diode = 121.03 µA


## Example - 2.37 : Page No - 74¶

In :
#Given data
Io= 1 # in nA
Io= Io*10**-9 # in A
T= 27+273 #in K
V_T= T/11600 # in V
V_F= 0.3 # in V
n=1
I_F= Io*(exp(V_F/(n*V_T))-1) # in A
print " The forward current of diode = %0.3e ampere" %I_F

 The forward current of diode = 1.091e-04 ampere


## Example - 2.38 : Page No - 75¶

In :
#Given data
I_F= 2 # in mA
I_F= I_F*10**-3 # in A
V_T= 25 # in mV
V_T=V_T*10**-3 # in V
n=1
r_F= n*V_T/I_F # in Ω
print " The dynamic resistance of a Ge p-n junction diode = %0.1f Ω" %r_F

 The dynamic resistance of a Ge p-n junction diode = 12.5 Ω


## Example - 2.39 : Page No - 75¶

In :
#Given data
T=300 # in K
n=1
V_T= 26 # in mV
V_T=V_T*10**-3 # in V
V_F= 200 # in mV
V_F=V_F*10**-3 # in V
Io= 1 # in µA
Io= Io*10**-6 # in A
r_F= n*V_T/(Io*exp(V_F/(n*V_T))) # in Ω
print " The ac resistance of a semiconductor diode = %0.2f Ω" %r_F

 The ac resistance of a semiconductor diode = 11.86 Ω


## Example - 2.40 : Page No - 75¶

In :
n=2
V_T= 26 # in mV
V_T=V_T*10**-3 # in V
I= 1 # in mA
I= I*10**-3 # in A
r= n*V_T/I # in Ω
print " The magnitude of r = %0.f Ω" %r

 The magnitude of r = 52 Ω