Chapter 10 , Semiconductors¶

Example 10.1 , Page Number 183¶

In [2]:
import math

#Variables

R = 1000.0                          #Resistance (in ohm)
sig = 5.8 * 10**7                   #Conductivity in (Siemen per meter)
d = 10**-3                          #diameter (in meter)
E = 10 * 10**-3                     #Eletric field (in Volt per meter)

#Calculation

l = R *sig * math.pi * d**2 /4      #length (in meter)
J = sig * E                         #Current density (in Ampere per metersquare)

#Result

print "Length of wire is ",round(l/1000,2)," km.\nCurrent desity is ",J," A/(m*m)."

Length of wire is  45.55  km.
Current desity is  580000.0  A/(m*m).


Example 10.2 , Page Number 184¶

In [3]:
import math

#Variables

d = 2* 10**-3             #diameter (in meter)
sig = 5.8 * 10**7         #conductivity (in siemen per meter)
mu = 0.0032               #mobilty (in metersquare per volt-second)
E = 20 * 10**-3           #Electric field (in Volt per meter)
q = 1.6 * 10**-19         #Charge on electron (in Coulomb)

#Calculation

n = sig / (q * mu)        #charge density (in cubic-meter)
J = sig * E               #Charge density (in Ampere per square-meter)
A = math.pi * d**2 / 4    #Cross section of wire (in square-meter)
I = J * A                 #Current (in Ampere)
v = mu * E                #Drift velocity (in meter per second)

#Result

print "Charge density of free electrons is ",round(n,3)," m**-3.\nThe current density is ",J," A/m**3.\nCurrent flowing in the wire is ",round(I,3)," A.\nElectron drift velocity is ",v," m/s."

Charge density of free electrons is  1.1328125e+29  m**-3.
The current density is  1160000.0  A/m**3.
Current flowing in the wire is  3.644  A.
Electron drift velocity is  6.4e-05  m/s.


Example 10.3 , Page Number 185¶

In [4]:
import math

#Variables

n = 5.8 * 10**28                  #number of free electrons (in per cubic-meter)
p = 1.54 * 10**-8                 #resistivity (in ohm-meter)
q = 1.6 * 10**-19                 #charge (in Coulomb)
m = 9.1 * 10**-31                 #mass of electron (in kg)

#Calculation

sig = 1/p                         #conductivity (in siemen per meter)
mu = sig /(q * n)                 #mobility (in meter-square/volt-second)
t = mu * m / q                    #time (in second)

#Result

print "Mobility of electrons is ",round(mu,6)," m**2/V-s.\nRelaxation time is ",round(t*10**12,6)," ps."

#Calculation error in book.

Mobility of electrons is  0.006997  m**2/V-s.
Relaxation time is  0.039797  ps.


Example 10.4 , Page Number 186¶

In [31]:
import math

#Variables

un = 0.38                            #mobility of electrons in germanium (in meter-square/volt-second)
up = 0.18                            #mobility of holes in germanium (in meter-square/volt-second)
ni = n = p = 2.5 * 10**19            #mobile ions for germanium (in per cubic-meter)
un1 = 0.13                           #mobility of electrons in germanium (in meter-square/volt-second)
up1 = 0.05                           #mobility of holes in germanium (in meter-square/volt-second)
ni1 = n1 = p1 = 1.5 * 10**16         #mobile ions for germanium (in per cubic-meter)
q = 1.6 * 10**-19                    #charge of electron (in Coulomb)

#Calculation

#for germanium:

sig = q * ni * (un + up)             #Conductivity of germanium (in siemen per metre)
sig1 = q * ni1 * (un1 + up1)         #Conductivity of silicon (in siemen per metre)

#Result

print "Intrinsic conductivity of germanium is ",sig," S/m and of silicon is ",sig1," S/m."

Intrinsic conductivity of germanium is  2.24  S/m and of silicon is  0.000432  S/m.


Example 10.5 , Page Number 187¶

In [30]:
import math

#Variables

ni = 1.41 * 10**16                    #intrinsic concentration (in per cubic-metre)
un = 0.145                            #mobility of electrons in germanium (in metre-square/volt-second)
up = 0.05                             #mobility of holes in germanium (in metre-square/volt-second)
q = 1.6 * 10**-19                     #charge of electron (in Coulomb)

#Calculation

sig = q * ni * (un + up)              #Conductivity of germanium (in siemen per metre)

#Result

print "Intrinsic conductivity of silicon is ",sig," S/m."
print "Contribution by electron is ",q*ni*un," S/m."
print "Contribution by electron is ",q*ni*up," S/m."

Intrinsic conductivity of silicon is  0.00043992  S/m.
Contribution by electron is  0.00032712  S/m.
Contribution by electron is  0.0001128  S/m.


Example 10.6 , Page Number 187¶

In [29]:
import math

#Variables

l = 0.2 * 10**-3                    #length (in meter)
A = 0.04 * 10**-6                   #Area of cross section (in square-meter)
V = 1                               #Voltage (in volts)
I = 8 * 10**-3                      #current (in Ampere)
un = 0.13                           #mobility of electron (in m**2 per volt-second)
q = 1.6 * 10**-19                   #charge on electron (in Coulomb)

#Calculation

R = V/I                              #Resistance (in ohm)
p = R * A/l                          #Resistivity (in ohm-meter)
sig = 1/p                            #Conductivity (in siemen per meter)
n = sig / (q * un)                   #concentration (in per cubic-meter)
J = I/A                              #current density (in Ampere per square-meter)
v = J/(n*q)

#Result

print "Concentration of free electrons is ",round(n,3)," m**-3.\nDrift velocity is ",v," m/s."

Concentration of free electrons is  1.92307692308e+21  m**-3.
Drift velocity is  650.0  m/s.


Example 10.7 , Page Number 188¶

In [28]:
import math

#Variables

p = 0.47                         #Resistivity (in ohm-meter)
q = 1.6 * 10**-19                #charge on electron (in Coulomb)
un = 0.39                        #mobility of electron in germanium (in m**2 per volt-second)
up = 0.19                        #mobility of hole in germanium (in m**2 per volt-second)

#Calculation

sig = 1/p                        #Conductivity (in siemen per meter)
ni = sig / (q *(un +up))         #intrinsic concentration (in per cubic-meter)

#Result

print "Intrinsic concentration is ",ni," m**-3."

Intrinsic concentration is  2.29273661042e+19  m**-3.


Example 10.8 , Page Number 190¶

In [27]:
import math

#Variables

ND = 10**21                 #Donor concentration (in per cubic-meter)
NA = 5 * 10**20             #Acceptor concentration (in per cubic-meter)
un = 0.18                   #mobility of electron in silicon (in m**2 per volt-second)
q = 1.6 * 10**-19           #charge on electron (in Coulomb)

#Calculation

n = ND -NA                  #net donor density (in per cubic-meter)
sig = n * q * un            #Conductivity (in Siemen per meter)

#Result

print "Conductivity of silicon is ",sig," (ohm-meter)**-1."

Conductivity of silicon is  14.4  (ohm-meter)**-1.


Example 10.9 , Page Number 190¶

In [26]:
import math

#Variables

p = 100.0              #resistivity (in ohm-meter)
q = 1.6 * 10**-19      #Charge on a electron (in Coulomb)
un = 0.36              #donor concentration (in per cubic-meter)

#Calculation

sig = 1/p              #conductivity (in siemen per meter)
n = sig /(q * un)      #intrinsic concentration (in per cubic-meter)
ND = n                 #Donor concentration (in per cubic-meter)

#Result

print "Donor concentration is ",ND," m**-3."

Donor concentration is  1.73611111111e+17  m**-3.


Example 10.10 , Page Number 191¶

In [25]:
import math

#Variables

ND = 2 * 10**14                     #Donor atom concentration (in atoms per cubic-centimeter)
NA = 3 * 10**14                     #Acceptor atom concentration (in atoms per cubic-centimeter)
ni = 2.3 * 10**19                   #intrinsic concentration (in atoms per cubic-centimeter)

#Calculation

n = ni**2 / NA                      #concentration of electrons (in electrons per cubic-centimeter)
p = ni**2 / ND                      #concentration of holes (in holes per cubic-centimeter)

#Result

print "Electron concentration is ",n," electrons/cm**3.\nHole concentration is ",p," holes/cm**3."

Electron concentration is  1.76333333333e+24  electrons/cm**3.
Hole concentration is  2.645e+24  holes/cm**3.


Example 10.11 , Page Number 191¶

In [24]:
import math

#Variables

ND = 5 * 10**8                      #Donor atom concentration (in atoms per cubic-centimeter)
NA = 6 * 10**16                     #Acceptor atom concentration (in atoms per cubic-centimeter)
ni = 1.5 * 10**10                   #intrinsic concentration (in atoms per cubic-centimeter)

#Calculation

n = ni**2/NA                        #number of electrons (in per cubic-centimeter)
p = ni**2/ND                        #number of holes (in per cubic-centimeter)

#Result

print "Density of electrons is ",n," cm**-3.\nDensity of holes is ",p," cm**-3."

Density of electrons is  3750.0  cm**-3.
Density of holes is  4.5e+11  cm**-3.


Example 10.12 , Page Number 192¶

In [23]:
import math

#Variables

d = 0.001                      #diameter (in meter)
ND = 10**20                    #Number of phosphorus ions (in per cubic-meter)
R = 1000                       #Resistance (in ohm)
un = 0.1                       #mobility (in meter-square per volt-second)
q = 1.6 * 10**-19              #charge on electron (in Coulomb)

#Calculation

n = ND                         #Number of free electron (in per cubic-meter)
sig = q*n*un                   #conductivity (in Siemen per meter)
A = math.pi * d**2 / 4         #Area of cross section (in meter-square)
l = R * sig * A                #length (in meter)

#Result

print "Length of the silicon would be ",round(l*1000,3)," mm."

Length of the silicon would be  1.257  mm.


Example 10.13 , Page Number 192¶

In [22]:
import math

#Variables

q = 1.6 * 10**-19            #Charge on electron (in Coulomb)
sig = 100.0                  #Conductivity of Ge (in per ohm-centimeter)
sig1 = 0.1                   #Conductivity of Si (in per ohm-centimeter)
ni = 1.5 * 10**10            #intrinsic conductivity for Si (in per cubic-centimeter)
un = 3800.0                  #mobility of electrons for Ge (in square-centimetermeter per volt-second)
up = 1800.0                  #mobility of holes for Ge (in square-centimeter per volt-second)
un1 = 1300.0                 #mobility of electrons for Si (in square-centimetermeter per volt-second)
up1 = 500.0                  #mobility of holes for Si (in square-centimeter per volt-second)
ni1 = 2.5 * 10**13           #intrinsic concentration for Ge (in per cubic-centimeter)

#Calculation

p = sig / (q * up)           #Concentration of p-type germanium (in cubic-centimeter)
n = ni1**2 / p               #Concentration of electrons in germanium (in cubic-centimeter)
n1 = sig1 / (q * un1)        #Concentration of N-type silicon (in cubic-centimeter)
p1 = ni**2 / n1              #Concentration of holes in silicon (in cubic-centimere)

#Result

print "For p-type germanium, hole concentration is ",p,"/cm**3.\nFor p-type germanium, electron concentration is ",n,"/cm**3."
print "For n-type silicon, hole concentration is ",p1,"/cm**3.\nFor n-type silicon, electron concentration is ",n1,"/cm**3."

For p-type germanium, hole concentration is  3.47222222222e+17 /cm**3.
For p-type germanium, electron concentration is  1800000000.0 /cm**3.
For n-type silicon, hole concentration is  468000.0 /cm**3.
For n-type silicon, electron concentration is  4.80769230769e+14 /cm**3.


Example 10.14 , Page Number 193¶

In [21]:
import math

#Variables

un = 3800                             #mobility of electrons (in centimeter-square per volt-second)
up = 1800                             #mobility of holes (in centimeter-square per volt-second)
ni = 2.5 * 10**13                     #intrinsic concentration (in per cubic-centimeter)
Nge = 4.41 * 10**22                   #concentration of germanium (in per cubic-centimeter)
q = 1.6 * 10**-19                     #charge on electron (in Coulomb)

#Calculation

ND = Nge/10**8                       #Number of donor atoms (in per cubic-centimeter)
p = p = ni**2/ND                     #Number of holes (in per cubic-centimeter)
sig = q * ND * un                    #Conductivity of n-type germanium (in per ohm-centimeter)
p = 1/sig                            #resistivity (in ohm-centimeter)

#Result

print "resistivity of the germanium sample is ",round(p,3)," ohm-cm."

resistivity of the germanium sample is  3.73  ohm-cm.


Example 10.15 , Page Number 194¶

In [14]:
import math

#Variables

un = 1350                             #mobility of electrons (in centimeter-square per volt-second)
up = 480                              #mobility of holes (in centimeter-square per volt-second)
ni = 1.52 * 10**10                    #intrinsic concentration (in per cubic-centimeter)
Nsi = 4.96 * 10**22                   #concentration of silicon (in per cubic-centimeter)
q = 1.6 * 10**-19                     #charge on electron (in Coulomb)

#Calculation

sigi = q * ni * (un + up)             #conductivity of intrinsic silicon (in per ohm-centimeter)
p = 1/sig                             #resitivity (in ohm-centimeter)
ND = Nsi/(50 * 10**6)                 #Number of donor atoms (per cubic-centimeter)
n = ND                                #NUmber of free electrons (in per cubic-centimeter)
p = ni**2/n                           #number of holes (in per cubic-centimeter)
sig = q * n * un                      #conductivity of doped silicon (in per ohm-centimeter)
p = 1/sig                             #resistivity (in ohm-centimeter)

#Result

print "Resistivity of doped silicon is ",round(p,2)," ohm-cm."

Resistivity of doped silicon is  4.67  ohm-cm.


Example 10.16 , Page Number 196¶

In [3]:
#Variables

up = 0.048                      #hole mobility (in meter-square per volt-second)
un = 0.135                      #electron mobility (in meter-square per volt-second)
q = 1.602 * 10**-19             #charge on electron (in Coulomb)
Nsi1 = 5 * 10**28               #concentration of intrinsic silicon (in atoms per cubic-meter)
ni = 1.5 * 10**16               #number of electron-hole pairs (per cubic-meter)
alpha = 0.05                    #temperature coefficient (in per degree Celsius)
dT = 14                         #change in temperature (in degree celsius)

#Calculation

sig1 = q * ni * (un + up)       #conductivity of intrinsic silicon (in per ohm-meter)
NA = Nsi1/10**7                 #Number of indium atoms (in per cubic-meter)
p = NA                          #Number of holes (in per cubic meter)
n = ni**2/p                     #Number of free electrons (in per cubic-meter)
sig2 = q * p * up               #Conductivity of doped silicon (in per ohm-meter)
sig34 = sig1*(1 + alpha * dT)   #Conductivity at 34 degree Celsius (in per ohm-meter)

#Result

print "Conductivity of intrinsic silicon is ",round(sig1,5)," per ohm-meter.\nConductivity of doped Silicon is ",round(sig2,2)," per ohm-meter.\nConductivity of silicon at 34 degree Celsius is ",round(sig34,5)," per ohm-meter."

Conductivity of intrinsic silicon is  0.00044  per ohm-meter.
Conductivity of doped Silicon is  38.45  per ohm-meter.
Conductivity of silicon at 34 degree Celsius is  0.00075  per ohm-meter.


Example 10.17 , Page Number 199¶

In [2]:
import math

#Variables

un = 3600.0 * 10**-4             #mobility of electrons (in meter-square per volt-second)
up = 1700.0 * 10**-4             #mobility of holes (in meter-square per volt-second)
k = 1.38 * 10**23                #Boltzmann constant
T = 300.0                        #Temperature (in kelvin)

#Calculation

VT = T/11600                     #Voltage (in volts)
Dp = up * VT                     #Coefficient of holes (in meter-square per second)
Dn = un * VT                     #Coefficient of electrons (in meter-square per second)

#Result

print "Coefficient of holes is ",round(Dp,6)," m**2/s.\nCoefficient of electrons is ",round(Dn,4)," m**2/s."
#un and up in book should be in (cm**2/V-sec)

Coefficient of holes is  0.004397  m**2/s.
Coefficient of electrons is  0.0093  m**2/s.


Example 10.18 , Page Number 202¶

In [19]:
import math

#Variables

RH = 160                #Hall coeffficient (in cubic-centimeter per Coulomb)
p = 0.16                #Resistivity (in ohm-centimeter)

#Calculation

sig = 1/p               #Conductivity (in per ohm-centimeter)
un = sig * RH           #Electron mobility (in cmentimeter-square per volt-second)

#Result

print "Electron mobility is ",un," cm**2/V-s."

Electron mobility is  1000.0  cm**2/V-s.


Example 10.19 , Page Number 203¶

In [18]:
import math

#Variables

I = 50                    #Current (in Ampere)
B = 1.2                   #Magnetic field (in Weber per meter-square)
t = 0.5 * 10**-3          #thickness (in meter)
VH = 100                  #Hall coltage (in volts)
q = 1.6 * 10**-19         #Charge on electron (in Coulomb)

#Calculation

n = B * I / (VH * q * t)  #number of conduction electrons (in per cubic-meter)

#Result

print "Number of conduction electrons is ",n," m**-3."

Number of conduction electrons is  7.5e+21  m**-3.


Example 10.20 , Page Number 203¶

In [17]:
import math

#Variables

p =  20 * 10**-2             #Resistivity (in ohm-meter)
u = 100 * 10**-4             #mobility (in meter-square per volt-second)

#Calculation

sig = 1/p                    #Conductivity (in per ohm-meter)
n = sig / (q * u)            #number of electron carriers (in per cubic-meter)

#Result

print "Number of electron carriers is ",round(n,1)," m**-3."

Number of electron carriers is  3.125e+21  m**-3.


Example 10.21 , Page Number 203¶

In [1]:
import math

#Variables

RH = 3.66 *10**-4                  #Hall coefficient (in cubic-meter per Coulomb)
p = 8.93 * 10 **-3                 #Resistivity (in ohm-meter)
q = 1.6 * 10**-19                  #Charge on electron (in Coulomb)

#Calculation

sig = 1/p                          #Conductivity (in per ohm-meter)
u = sig * RH                       #mobility (in meter-square per volt-second)
n = 1 / (RH * q)                   #Density of charge carriers (in per cubic-meter)

#Result

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

Mobility of charge carriers is  0.041  m**2/V-s.
Density of charge carriers is  1.70765027322e+22  m**-3.


Example 10.22 , Page Number 204¶

In [15]:
import math

#Variables

p = 9 * 10**-3           #Resistivity (in ohm-meter)
up = 0.03                #Mobility (in meter-square per volt-second)

#Calculation

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

#Result

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

Value of Hall-coefficient is  0.00027  m**3/C.