Chapter 3 , Semiconductor Physics

Example 3.1 , Page Number 54

In [3]:
#Variables

m = 9.107 * 10**-31               #Mass of electron (in kilogram)
E = 2.1                           #Energy associated (in electon-volt)
e = 1.6 * 10**-19                 #Charge on electron (in Coulomb)

#Calculation

E = E * e                         #Energy associated (in Joules)
v = (2 * E / m)**0.5              #Velocity of electron (in meter per second)

#Result

print "Velocity of electron at fermi level is ",round(v,2)," m/s."

#Slight variation due to higher precision.

Velocity of electron at fermi level is  859007.52  m/s.

Example 3.2 , Page Number 63

In [4]:
#Variables

J = 2.4 * 10**6                 #Current Density (in Ampere per meter-square)               
n = 5.0 * 10**28                #Electron density     
e = 1.6 * 10**-19               #Charge on electron (in Coulomb)

#Calculation

v = J / (e * n)                 #Drift velocity (in meter per second) 

#Result

print "Drift velocity is ",v," m/s."

Drift velocity is  0.0003  m/s.

Example 3.3 , Page Number 64

In [5]:
#Variables

n = 10**24                     #Electron density           
e = 1.6 * 10**-19              #Charge on electron (in Coulomb)
v = 1.5 * 10**-2               #Drift velocity (in meter per second)
A = 1.0 * 10**-4               #Area of cross-section (in meter-square)

#Calculation

I = e * n * v * A              #Current (in Ampere) 

#Result

print "Magnitude of current is ",I," A."

Magnitude of current is  0.24  A.

Example 3.4 , Page Number 64

In [4]:
#Variables

p = 0.039                       #Resistivity of doped material (in ohm-centimeter)
e = 1.602 * 10**-19             #Charge on electron (in Coulomb)
ue = 3600.0                     #Carrier mobility (in centimeter-square per volt-second)
ni = 2.5 * 10**13               #Intrinsic concentration (in per cubic-centimeter)

#Calculation


sign = 1/p                      #Conductivity (in per ohm-centimeter)
ND = sign /(e * ue)             #Concentration of donor atoms (in per cubic-centimeter)
n = ND                          #Concentration of electron (per cubic-centimeter)
p = ni**2 / n                   #Concentration of hole (per cubic-centimeter)

#Result

print "Concentration of electrons is ",n," /cm**3.\nConcentration of holes is ",p,"  \cm**3."

#Slight variation due to higher precision.

Concentration of electrons is  4.44600943977e+16  /cm**3.
Concentration of holes is  14057550000.0   \cm**3.

Example 3.5 , Page Number 64

In [9]:
#Variables

N = 5.0 * 10**22                #Number of silicon atoms (per cubic-centimeter)
N1 = 10**-6                     #Donor impurity 
ni = 1.45 * 10**10              #Intrinsic concentration (in per cubic-centimeter)  
l = 0.5                         #Length (in centimeter)
A = (50.0 * 10**-4)**2          #Area of cross-section (in centimeter-square)
ue = 1300.0                     #Mobility of electron (in ) 

#Calculation

ND = 5 * 10**16                 #Donor concentration (in per cubic-centimeter)
n = ND                          #Mobile electron concentration (in per cubic-centimeter)
p = ni**2 / ND                  #Hole concentration (in centimeter-square per volt-second)
sig = n * e * ue                #Conductivity of doped silicon sample (in per ohm-cetimeter)
p1 = 1/sig                      #Resistivity (in ohm-centimeter)
R = p1 * l / A                  #Resistance (in ohm)

#Result

print "Resulting donor concentration is ",ND," /cm**3.\nResulting mobile electron concentration is ",n," /cm**3.\nResulting hole concentration is ",p," /cm**3."
print "Conductivity of doped silicon sample is ",sig," (ohm-cm)**-1.\nResistivity is ",p1," ohm-cm and Resistance is ",R," ohm."

Resulting donor concentration is  50000000000000000  /cm**3.
Resulting mobile electron concentration is  50000000000000000  /cm**3.
Resulting hole concentration is  4205.0  /cm**3.
Conductivity of doped silicon sample is  10.413  (ohm-cm)**-1.
Resistivity is  0.096033803899  ohm-cm and Resistance is  1920.67607798  ohm.

Example 3.6 , Page Number 65

In [10]:
#Variables

ni = 1.4 * 10**18                   #intrinsic concentration (in per cubic-centimeter)
ND = 1.4 * 10**24                   #Donor concentration (in per cubic-centimeter)
n = ND                              #Concentration of electrons (in per cubic-centimeter)

#Calculation

p = ni**2 / ND                      #Concentration of holes (in per cubic-centime) 
ratio = n / p                       #Ratio of electron to hole concentration 

#Result

print "Ratio of electron to hole concentration is ",ratio,"."

Ratio of electron to hole concentration is  1e+12 .

Example 3.7 , Page Number 65

In [12]:
#Variables

Ef = 5.5                             #Fermi energy (in electron-volt)
ue = 7.04 * 10**-3                   #Mobility of electrons (in meter-square per volt-second)
n = 5.8 * 10**28                     #Concentration of electrons (in per cubic-centimeter)
e = 1.6 * 10**-19                    #Charge on electron (in Coulomb)
m = 9.1 * 10**-31                    #Mass of electron (in kilogram)  

#Calculation

tau = ue * m / e                     #Relaxation time (in seconds)
p = 1 / (n * e * ue)                 #Resistivity (in ohm-meter) 
vf = (2 * Ef * e / m)**0.5           #Velocity of electron with fermi energy (in meter per second)

#Result

print "Relaxation time is ",tau," s.\nResistivity of conductor is ",p,"ohm-meter.\nVelocity of electrons with fermi energy is ",vf," m/s."

#Slight variation due to higher precision.

Relaxation time is  4.004e-14  s.
Resistivity of conductor is  1.53066222571e-08 ohm-meter.
Velocity of electrons with fermi energy is  1390706.99073  m/s.

Example 3.8 , Page Number 68

In [14]:
#Variables

ni = 2.5 * 10**13                 #Intrinsic concentration (in per cubic-centimeter)
e = 1.6 * 10**-19                 #Charge on electron (in Coulomb)
uh = 1800.0                       #Mobility of holes (in per cubic-centimeter)
ue = 3800.0                       #Mobility of electrons (in per cubic-centimeter)

#Calculation

sigi = ni * e * (ue + uh)         #Conductivity (in per ohm-centimeter)
pi = 1/sigi                       #Resistivity (in ohm-centimeter)

#Result

print "Conductivity is ",sigi," (ohm-cm)**-1.\nResistivity is ",round(pi,2)," ohm-cm."

Conductivity is  0.0224  (ohm-cm)**-1.
Resistivity is  44.64  ohm-cm.

Example 3.9 , Page Number 68

In [1]:
#Variables

pi = 0.47                        #intrinsic resistivity (in ohm-meter)
ue = 0.39                        #Electron mobility (in meter-square per volt-second)
uh = 0.19                        #Hole mobility (in meter-square per volt-second)
e = 1.6 * 10**-19                #Charge on electron (in Coulomb)
E = 10**4                        #Electric field (in volt per meter)

#Calculation

sigi = 1 / pi                    #Conductivity (in per ohm-meter)
ni = sigi/(e * (ue + uh))        #Intrinsic concentration (in per cubic-meter)
vn = ue * E                      #Drift velocity of electrons (in meter per second)
vh = uh * E                      #Drift velocity of holes (in meter per second) 

#Result

print "Density of electrons is ",ni," /m**3.\nDrift velocity of electrons is ",vn," m/s.\nDrift velocity of holes is ",vh," m/s."

Density of electrons is  2.29273661042e+19  /m**3.
Drift velocity of electrons is  3900.0  m/s.
Drift velocity of holes is  1900.0  m/s.

Example 3.10 , Page Number 69

In [2]:
#Variables

ni = 1.5 * 10**10                #Intrinsic concentration (in per cubic-centimeter)
uh = 450.0                       #mobility of holes (in centimeter-square per volt-second)
ue = 1300.0                      #mobility of electrons (in centimeter-square per volt-second)
NA = 10**18                      #Doping level (in per cubic-centimeter)

#Calculation

sigi = ni * e * (ue + uh)        #Conductivity of silicon (in per ohm-centimeter)
sigp = e * NA * uh               #COnductivity of P-type silicon (in per ohm-centimeter)

#Result

print "Conductivity of intrinsic silicon is ",sigi," /ohm-cm.\nConductivity of P type silicon is ",sigp," ohm-cm."

Conductivity of intrinsic silicon is  4.2e-06  /ohm-cm.
Conductivity of P type silicon is  72.0  ohm-cm.

Example 3.11 , Page Number 69

In [5]:
#Variables

ni = 2.5 * 10**13                          #Intrinsic concentration (in per cubic-centimeter)
e = 1.6 * 10**-19                          #Charge on electron (in Coulomb)
uh = 1800.0                                #mobility of holes (in centimeter-square per volt-second)
ue = 3800.0                                #mobility of electrons (in centimeter-square per volt-second)
ND = 4.41 * 10**22 * 10**-7                #Number of Germanium atoms (in per cubic-centimeter)

#Calculation

sigi = ni * e * (uh + ue)                  #Intrinsic concentration (in per ohm-centimeter)
n = ND                                     #Concentration of electrons (in per cubic-centimeter)
p = ni**2 / ND                             #Concentration of holes (in per cubic-centimeter)
sign = e * ND * ue                         #Conductivity of N-type germanium semiconductor (in per ohm-meter)

#Result

print "Conductivity of intrinsic semiconductor is ",sigi," /ohm-cm.\nConductivity of N-type semiconductor is ",round(sign,2)," /ohm-cm."

Conductivity of intrinsic semiconductor is  0.0224  /ohm-cm.
Conductivity of N-type semiconductor is  2.68  /ohm-cm.

Example 3.12 , Page Number 69

In [11]:
#Variables

V = 10.0                              #Voltage (in volts)
l = 0.025                             #Length (in meter)
uh = 0.18                             #mobility of holes (in meter-square per volt-second)
ue = 0.38                             #mobility of electrons (in meter-square per volt-second)
ni = 2.5 * 10**19                     #Intrinsic concentration (in per cubic-imeter)
a = 4.0 * 1.5 *10**-6                 #Area of cross-section (in meter-square)

#Calculation

E = V / l                             #Electric field (in volt per meter)
ve = ue * E                           #Drift velocity of electrons (in meter per second)
vh = uh * E                           #Drift velocity of holes (in meter per second)
sigi = ni * e * (ue + uh)             #Conductivity of intrinsic semiconductor (in per ohm-meter)
I = sigi * E * a                      #Total current (in Ampere) 

#Result

print "Electron drift velocity is ",ve," m/s.\nHoles drift velocity is ",vh," m/s.\nIntrinsic conductivity of Ge is ",sigi," /ohm-m.\nTotal current is ",I * 10**3," mA." 

Electron drift velocity is  152.0  m/s.
Holes drift velocity is  72.0  m/s.
Intrinsic conductivity of Ge is  2.24  /ohm-m.
Total current is  5.376  mA.

Example 3.13 , Page Number 70

In [13]:
#Variables

ni = 2.5 * 10**13                          #Intrinsic concentration (in per cubic-centimeter)
e = 1.6 * 10**-19                          #Charge on electron (in Coulomb)
uh = 1700.0                                #mobility of holes (in centimeter-square per volt-second)
ue = 3600.0                                #mobility of electrons (in centimeter-square per volt-second)
k = 1.38 * 10**-23                         #Boltzmann constant (in Joule per kelvin)
T = 300.0                                  #Temperature (in kelvin)

#Calculation

De = ue * k * T / e                        #Diffusion constant of electrons (in centimeter-square per second)
Dh = uh * k * T / e                        #Diffusion constant of holes (in centimeter-square per second)

#Result

print "Diffusion constant of electron is ",round(De)," cm**2/s.\nDiffusion constant of holes is ",Dh," cm**2/s."

#Slight variation in Dh due to higher precision.

Diffusion constant of electron is  93.0  cm**2/s.
Diffusion constant of holes is  43.9875  cm**2/s.

Example 3.14 , Page Number 72

In [15]:
#Variables

p = 9.0 * 10**3                   #Resistivity (in ohm-meter)
RH = 3.6 * 10**-4                 #Hall coefficient (in cubic-meter per Coulomb) 
e = 1.6 * 10**-19                 #Charge on electron (in Coulomb)

#Calculation

sig = 1/p                         #Conductivity (in per ohm-meter)
P = 1/ RH                         #Charge density (in Coulomb per cubic meter)
n = P / e                         #Density of charge carriers (in per cubic-meter)
u = sig * RH                      #Mobility (in meter-square per volt-second)

#Result

print "Mobility of charge carriers is ",u," m**2/V-s.\nDensity of charge carriers is ",n," /m**3."

Mobility of charge carriers is  4e-08  m**2/V-s.
Density of charge carriers is  1.73611111111e+22  /m**3.

Example 3.15 , Page Number 73

In [18]:
#Variables

E = 100.0                           #Electric field (in volt per meter)
RH = 0.0145                         #Hall coefficient (in cubic-meter per Coulomb)
un = 0.36                           #Mobility of electrons (in meter-square per volt-second)

#Calculation

n = 1/(e * RH)                      #Concentration (in per cubic-meter)
J = n * e * un * E                  #Current density (in Ampere per cubic-meter)  

#Result

print "The current density in the specimen is ",round(J,2)," A/m**2"

#Slight variation due to higher precision.

The current density in the specimen is  2482.76  A/m**2

Example 3.16 , Page Number 73

In [20]:
#Variables

p = 9.0 * 10**-3                  #Resistivity (in ohm-meter)
e = 1.6 * 10**-19                 #Charge on electron (in Coulomb)
u = 0.03                          #Mobility of carrier ion (in meter-square per volt-second)


#Calculation

sig = 1/p                         #Conductivity (in per ohm-meter)
RH = u / sig                      #Hall coefficient (in cubic-meter per Coulomb)             

#Result

print "Hall coefficient is ",RH," m**3/C."

Hall coefficient is  0.00027  m**3/C.

Example 3.17 , Page Number 73

In [6]:
#Variables

p = 9.0 * 10**3                   #Resistivity (in ohm-meter)
e = 1.6 * 10**-19                 #Charge on electron (in Coulomb)
n = 2.05 * 10**22                 #Charge carrier density (in per cubic-meter)  

#Calculation

RH = 1/(n * e)                    #Hall coefficient (in cubic-meter per Coulomb) 

#Result

print "Hall coefficient is ",round(RH,7)," m**3/C."

#Slight variation due to higher precision.

 Hall coefficient is  0.0003049  m**3/C.

Example 3.18 , Page Number 73

In [26]:
#Variables

Ex = 5.0 * 10**2                     #Applied Electric field (in volt per meter)
ue = 3800.0 * 10**-4                 #Mobility of electron (in meter-square per volt-second) 
Bz = 0.1                             #Magnetic flux density (in Weber per meter-square) 
d = 4.0 * 10**-3                     #width (in meter) 

#Calculation

v = ue * Ex                          #Drift velocity (in meter per second)
VH = Bz * v * d                      #Hall voltage (in volts)  

#Result

print "Hall voltage is ",VH * 10**3," mV."

Hall voltage is  76.0  mV.

Example 3.19 , Page Number 74

In [30]:
#Variables

p = 200.0 * 10                      #Bar resistivity (in ohm-meter) 
VH = 50.0 * 10**-3                  #Hall voltage (in volts)
BZ = 0.1                            #Magnetic flux density (in Weber per meter-square) 
w = 3.0 * 10**-3                    #width (in meter)
d = w                               #length (in meter)
I = 10.0 * 10**-6                   #Current (in Ampere)

#Calculation

RH = VH * w / (BZ * I)              #Hall coefficient (in cubic-meter per Coulomb)
uh = RH / p                         #Mobility of holes (in meter-square per volt-second)  

#Result

print "Mobility of holes is ",uh," m**2/V-s."

Mobility of holes is  0.075  m**2/V-s.

Example 3.20 , Page Number 74

In [33]:
#Variables

ND = 1.0 * 10**21                       #Concentration of donor atoms (in per cubic-meter)
BZ = 0.2                                #Magnetic field density (in Tesla)
J = 600.0                               #Current density (in Ampere per meter-square)
n = ND                                  #Concentration of electrons (in per cubic-meter)
d = 4.0 * 10**-3                        #Length (in meter) 
e = 1.6 * 10**-19                       #Charge on electron (in Coulomb)

#Calculation

VH = BZ * J * d / (n * e)               #Hall voltage (in volts) 

#Result

print "Hall voltage is ",VH * 10**3," mV."

Hall voltage is  3.0  mV.

Example 3.21 , Page Number 82

In [37]:
#Variables

T = 300.0                                #Temperature (in kelvin)
Ec_Ef = 0.3                              #Energy level (in electron-volt)  
T1 = 273 + 55                            #New temperature (in kelvin)

#Calculation

logencbyND = Ec_Ef/T                     #Value of loge(nc / ND)
Ec_Ef1 = T1 * logencbyND                 #New position of Fermi level (in electron-volt)    

#Result

print "New position of Fermi level is ",Ec_Ef1," eV"

#Unit in the book should be eV instead of V.

New position of Fermi level is  0.328  eV

Example 3.22 , Page Number 83

In [41]:
import math

#Variables

ND = NA = 8.0 * 10**14                     #Concentration (in per cubic-meter)
ni = 2.0 * 10**13                          #Intrinsic concentration (in per cubic-meter)
k = 8.61 * 10**-5                          #Boltzmann constant (in electron-volt per kelvin)
T = 300.0                                  #Temperature (in kelvin)

#Calculation

Vo = k * T * math.log(ND * NA/ni**2)

#Result

print "Potential barrier is ",round(Vo,2)," eV."

#Unit in the book should be eV instead of V.

Potential barrier is  0.19  eV.

Example 3.23 , Page Number 83

In [44]:
#Variables

ID1 = 2.0 * 10**-3                     #Diode current1 (in Ampere)
VD1 = 0.5                              #Diode voltage1 (in volts)
ID2 = 20.0 * 10**-3                    #Diode current2 (in Ampere)
VD2 = 0.8                              #Diode voltage2 (in volts)
ID3 = -1.0 * 10**-6                    #Diode current3 (in Ampere)
VD3 = -10.0                            #Diode voltage3 (in volts)

#Calculation

R1 = VD1 / ID1                         #Resistance1 (in ohm)
R2 = VD2 / ID2                         #Resistance2 (in ohm)
R3 = VD3 / ID3                         #Resistance3 (in ohm)

#Result

print "R1 is ",R1," ohm.\nR2 is ",R2," ohm.\nR3 is ",R3 * 10**-6," Mega-ohm."

R1 is  250.0  ohm.
R2 is  40.0  ohm.
R3 is  10.0  Mega-ohm.

Example 3.24 , Page Number 83

In [9]:
import math

#Variables

k = 8.61 * 10**-5                          #Boltzmann constant (in electron-volt per kelvin)
T = 300.0                                  #Temperature (in kelvin)
EG = 0.72                                  #Energy band gap (in electron-volt) 

#Calculation

EF = 1.0/2 * EG                            #Fermi level (in electron-volt)
ncbyn = 1/(1 + math.exp((EG-EF)/(k*T)))    #Ratio

#Result

print "Fraction of the total number of electrons in the conduction band at 300 K is ",round(ncbyn*pow(10,7),2),"e-7 ."

Fraction of the total number of electrons in the conduction band at 300 K is  8.85 e-7 .

Example 3.25 , Page Number 83

In [1]:
import math

#Variables

Ao = 4.83 * 10**21                         #Constant
T = 300.0                                  #Temperature (in kelvin)
EG = 1.1                                   #Energy level (in electron-volt)
kT = 0.026                                 #Product of k and T (in electron-volt)
ND = 5.0 * 10**15                          #Donor concentration (in per cubic-meter)  
NA = 2.0 * 10**16                          #Acceptor concentration (in per cubic-meter) 

#Calculation

ni = Ao * T**1.5 * math.exp(-EG/(2*kT))    #Intrinsic concentration (in per cubic-meter)
h = ni**2 / NA                             #Hole concentration (in per cubic-meter)
n = ni**2 / ND                             #Electron concentration (in per cubic-meter)

#Result

print "Since electron concentration",round(n*10**-16,2),"e+16 is more than hole concentration ",round(h*10**-16,2),"e+16 .Therefore , Si is of n-type."

#Slight variations due to higher precision.

Since electron concentration 5.32 e+16 is more than hole concentration  1.33 e+16 .Therefore , Si is of n-type.