# Semiconducting Materials¶

## Example number 7.1, Page number 208¶

In :
#To calculate the approximate donor binding energy

#importing modules
import math

#Variable declaration
me = 9.11*10**-31;          #mass of electron(kg)
epsilon_r = 13.2;
epsilon0 = 8.85*10**-12;
h = 6.63*10**-34;
e = 1.6*10**-19;          #charge of electron(C)

#Calculation
m_nc = 0.067*me;
E = m_nc*e**4/(8*(epsilon0*epsilon_r*h)**2);       #energy(J)
E = E/e;                #energy(eV)
E = math.ceil(E*10**5)/10**5;   #rounding off to 5 decimals
E_meV = E*10**3;        #energy(meV)

#Result
print "donor binding energy is",E,"eV or",E_meV,"meV"

donor binding energy is 0.00521 eV or 5.21 meV


## Example number 7.2, Page number 208¶

In :
#To calculate the equilibrium hole concentration

#importing modules
import math
import numpy as np

#Variable declaration
Nd = 10**16;         #donor concentration(atoms/cm**3)
ni = 1.5*10**10;        #concentration(per cm**3)
T = 300;                #temperature(K)
kT = 0.0259;

#Calculation
n0 = Nd;           #for Nd>>ni, assume n0=Nd
p0 = ni**2/n0;        #equilibrium hole concentration(per cm**3)
p0 = p0*10**-4;
EF_Ei = kT*np.log(n0/ni);
EF_Ei = math.ceil(EF_Ei*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "equilibrium hole concentration is",p0,"*10**4 per cm**3"
print "value of EF-Ei is",EF_Ei,"eV"

equilibrium hole concentration is 2.25 *10**4 per cm**3
value of EF-Ei is 0.3474 eV


## Example number 7.3, Page number 209¶

In :
#To calculate the resistivity of sample

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;          #charge of electron(C)
Nd = 10**14;              #donor density(atoms/cm**3)
mew_n = 3900;

#Calculation
n = Nd;
sigma = n*e*mew_n;        #conductivity(ohm-1 cm-1)
rho = 1/sigma;            #resistivity(ohm cm)
rho = math.ceil(rho*100)/100;   #rounding off to 2 decimals

#Result
print "resistivity of sample is",rho,"ohm cm"

resistivity of sample is 16.03 ohm cm


## Example number 7.4, Page number 209¶

In :
#To calculate the resistivity, Hall coefficient and Hall voltage

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;          #charge of electron(C)
n0 = 5*10**16;              #donor density(atoms/cm**3)
mew_0 = 800;
Ix = 2;             #current(mA)
Bz = 5*10**-5;
d = 200;            #thickness(micrometre)

#Calculation
Ix = Ix*10**-3;          #current(A)
d = d*10**-4;            #thickness(m)
sigma = e*n0*mew_0;        #conductivity(ohm-1 cm-1)
rho = 1/sigma;            #resistivity(ohm cm)
rho = math.ceil(rho*10**4)/10**4;   #rounding off to 4 decimals
RH = -1/(e*n0);          #Hall coefficient(cm**3/C)
VH = Ix*Bz*RH/d;         #Hall voltage(V)
VH = VH*10**5;

#Result
print "resistivity of sample is",rho,"ohm cm"
print "Hall coefficient is",RH,"cm**3/C"
print "Hall voltage is",VH,"*10**-5 V"

resistivity of sample is 0.1563 ohm cm
Hall coefficient is -125.0 cm**3/C
Hall voltage is -62.5 *10**-5 V


## Example number 7.5, Page number 210¶

In :
#To calculate the intrinsic carrier concentration, intrinsic conductivity and resistivity

#importing modules
import math
from __future__ import division

#Variable declaration
T = 300;          #temperature(K)
mew_n = 0.4;      #electron mobility(m**2/Vs)
mew_p = 0.2;      #hole mobility(m**2/Vs)
Eg = 0.7;         #band gap(eV)
me = 9.11*10**-31;       #mass of electron(kg)
k = 1.38*10**-23;        #boltzmann constant
T = 300;                 #temperature(K)
h = 6.625*10**-34;
kT = 0.0259;
e = 1.6*10**-19;          #charge of electron(C)

#Calculation
mn_star = 0.55*me;           #electron effective mass(kg)
mp_star = 0.37*me;           #hole effective mass(kg)
a = (2*math.pi*k*T/(h**2))**(3/2);
b = (mn_star*mp_star)**(3/4);
c = math.exp(-Eg/(2*kT));
ni = 2*a*b*c;     #intrinsic concentration(per m**3)
sigma = ni*e*(mew_n+mew_p);               #intrinsic conductivity(per ohm m)
sigma = math.ceil(sigma*10**4)/10**4;   #rounding off to 4 decimals
rho = 1/sigma;                            #intrinsic resistivity(ohm m)
rho = math.ceil(rho*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "intrinsic concentration is",ni,"per m**3"
print "intrinsic conductivity is",sigma,"per ohm m"
print "intrinsic resistivity is",rho,"ohm m"
print "answers given in the book are wrong"

intrinsic concentration is 1.02825111151e+19 per m**3
intrinsic conductivity is 0.9872 per ohm m
intrinsic resistivity is 1.013 ohm m
answers given in the book are wrong


## Example number 7.6, Page number 211¶

In :
#To calculate the Fermi energy

#importing modules
import math
import numpy as np
from __future__ import division

#Variable declaration
Nd = 10**16;           #donor concentration(per cm**3)
ni = 1.45*10**10;         #concentration(per cm**3)
kT = 0.0259;

#Calculation
#ni = Nc*math.exp(-(Ec-Ei)/kT)
#Nd = Nc*(math.exp(-(Ec-Efd)/kT)
#dividing Nd/ni we get
EFd_Ei = kT*np.log(Nd/ni);
EFd_Ei = math.ceil(EFd_Ei*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "Fermi energy is",EFd_Ei,"eV"

Fermi energy is 0.3482 eV


## Example number 7.7, Page number 211¶

In :
#To calculate the resistance

#The given information in the question is not sufficient to solve the entire problem. And the problem is completely wrong in the book


## Example number 7.8, Page number 212¶

In :
#To calculate the forbidden energy gap

#importing modules
import math
import numpy as np
from __future__ import division

#Variable declaration
T = 300;          #temperature(K)
mew_n = 0.36;      #electron mobility(m**2/Vs)
mew_p = 0.17;      #hole mobility(m**2/Vs)
rho = 2.12;         #resistivity(ohm m)
me = 9.11*10**-31;       #mass of electron(kg)
kT = 0.0259;
h = 6.625*10**-34;
k = 1.38*10**-23;        #boltzmann constant
e = 1.6*10**-19;          #charge of electron(C)

#Calculation
mn_star = 0.55*me;           #electron effective mass(kg)
mp_star = 0.37*me;           #hole effective mass(kg)
sigma = 1/rho;               #conductivity(per ohm m)
sigma = math.ceil(sigma*10**3)/10**3;   #rounding off to 3 decimals
ni = sigma/(e*(mew_n+mew_p));          #concentration of electrons(per m**3)
a = (2*math.pi*kT/(h**2))**(3/2);
Nc = 2*a*(mn_star**(3/2));
Nv = 2*a*(mp_star**(3/2));
b = (Nc*Nv)**(1/2);
Eg = 2*kT*np.log(b/ni);

#Result
print "forbidden energy gap is",Eg,"eV"
print "answer given in the book is wrong"

forbidden energy gap is 4.09465494989 eV
answer given in the book is wrong


## Example number 7.9, Page number 213¶

In :
#To calculate the conductivity

#importing modules
import math

#Variable declaration
ni = 2.4*10**19;       #concentration(per m**3)
mew_n = 0.39;      #electron mobility(m**2/Vs)
mew_p = 0.19;      #hole mobility(m**2/Vs)
e = 1.6*10**-19;          #charge of electron(C)

#Calculation
sigma = ni*e*(mew_n+mew_p);         #conductivity(per ohm m)
sigma = math.ceil(sigma*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "conductivity of sample is",sigma,"ohm-1 m-1"

conductivity of sample is 2.228 ohm-1 m-1


## Example number 7.10, Page number 214¶

In :
#To calculate the new position of Fermi level

#importing modules
import math
from __future__ import division

#Variable declaration
Ec = 0.3;          #initial position(eV)
T1 = 300;           #initial temperature(K)
T2 = 330;           #increased temperature

#Calculation
#Ec/T1 = Ec_EF330/T2
Ec_EF330 = Ec*T2/T1;        #new position of Fermi level(eV)

#Result
print "new position of Fermi level is",Ec_EF330,"eV"

new position of Fermi level is 0.33 eV


## Example number 7.11, Page number 214¶

In :
#To calculate the concentration in conduction band

#importing modules
import math
from __future__ import division

#Variable declaration
k = 1.38*10**-23;         #boltzmann constant
T = 300;           #temperature(K)
me = 9.1*10**-31;        #mass of electron(kg)
h = 6.63*10**-34;        #planck's constant
Ec_Ev = 1.1;             #energy gap(eV)
e = 1.6*10**-19;         #charge of electron(C)

#Calculation
me_star = 0.31*me;
A = (2*math.pi*k*T*me_star/(h**2))**(3/2);
B = math.exp(-(Ec_Ev*e)/(2*k*T));
ni = A*B;                  #concentration in conduction band(per m**3)

#Result
print "intrinsic electron concentration is",ni,"per m**3"
print "answer given in the book is wrong"

intrinsic electron concentration is 1.26605935487e+15 per m**3
answer given in the book is wrong


## Example number 7.12, Page number 214¶

In :
#To calculate the drift mobility of electrons

#importing modules
import math

#Variable declaration
RH = 0.55*10**-10;          #Hall coefficient(m**3/As)
sigma = 5.9*10**7;          #conductivity(ohm-1 m-1)

#Calculation
mew = RH*sigma;              #drift mobility(m**2/Vs)
mew = mew*10**3;
mew = math.ceil(mew*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "drift mobility of electrons is",mew,"*10**-3 m**2/Vs"

drift mobility of electrons is 3.25 *10**-3 m**2/Vs


## Example number 7.13, Page number 215¶

In :
#To calculate the concentration and average number of electrons

#importing modules
import math
from __future__ import division

#Variable declaration
A = 6.022*10**23;           #avagadro constant
d = 8.96*10**-9;            #density(kg/m**3)
n = 9.932*10**14;           #no. of free electrons per atom
sigma = 5.9*10**7;          #conductivity(ohm-1 m-1)
e = 1.6*10**-19;            #electron charge(C)
mew = 3.2*10**-3;           #drift mobility(m**2/Vs)
w = 63.5;                   #atomic weight of Cu(kg)

#Calculation
ni = sigma/(mew*e);         #conductivity(per m**3)
N = A*d*n/w;                #concentration of free electrons in pure Cu
AN = ni/N;                  #average number of electrons contributed per Cu atom

#Result
print "concentration of free electrons in pure Cu is",N,"per m**3"
print "average number of electrons contributed per Cu atom is",int(AN)

concentration of free electrons in pure Cu is 8.43940339906e+28 per m**3
average number of electrons contributed per Cu atom is 1


## Example number 7.14, Page number 215¶

In :
#To calculate the charge carrier density and electron mobility

#importing modules
import math
from __future__ import division

#Variable declaration
RH = 3.66*10**-11;          #hall coefficient(m**3/As)
e = 1.6*10**-19;            #electron charge(C)
sigma = 112*10**7;          #conductivity(ohm-1 m-1)

#Calculation
n = 1/(e*RH);               #charge carrier density(per m**3)
mew_n = sigma/(n*e);        #electron mobility(m**2/As)
mew_n = math.ceil(mew_n*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "charge carrier density is",n,"per m**3"
print "electron mobility is",mew_n,"m**2/As"
print "answers given in the book are wrong"

charge carrier density is 1.70765027322e+29 per m**3
electron mobility is 0.041 m**2/As
answers given in the book are wrong


## Example number 7.15, Page number 216¶

In :
#To calculate the magnitude of Hall voltage

#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
B = 1.5;                    #magnetic field(T)
I = 50;                     #current(Amp)
n = 8.4*10**28;             #free electron concentration(per m**3)
d = 0.2;                    #thickness of slab(cm)

#Calculation
d = d*10**-2;               #thickness of slab(m)
VH = B*I/(n*e*d);           #hall voltage(V)

#Result
print "magnitude of Hall voltage is",VH,"V"
print "answer given in the book is wrong"

magnitude of Hall voltage is 2.79017857143e-06 V
answer given in the book is wrong


## Example number 7.16, Page number 216¶

In :
#To calculate the resistance of intrinsic Ge rod

#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
n = 2.5*10**19;             #free electron concentration(per m**3)
mew_n = 0.39;               #electron mobility(m**2/Vs)
mew_p = 0.19;               #hole mobility(m**2/Vs)
L = 1;                      #length(cm)
w = 1;                      #width(mm)
t = 1;                      #thickness(mm)

#Calculation
L = L*10**-2;               #length(m)
w = w*10**-3;               #width(m)
t = t*10**-3;               #thickness(m)
A = w*t;                    #area(m**2)
sigma = n*e*(mew_n+mew_p);         #conductivity(ohm-1 m-1)
R = L/(sigma*A);                   #resistance(ohm)

#Result
print "resistance of intrinsic Ge rod is",int(R),"ohm"

resistance of intrinsic Ge rod is 4310 ohm


## Example number 7.17, Page number 216¶

In :
#To determine the position of Fermi level

#importing modules
import math
import numpy as np
from __future__ import division

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
Eg = 1.12;                  #band gap(eV)
me = 1;
mn_star = 0.12*me;               #electron mobility(m**2/Vs)
mp_star = 0.28*me;               #hole mobility(m**2/Vs)
k = 1.38*10**-23;                #boltzmann constant
T = 300;                         #temperature

#Calculation
a = mp_star/mn_star;
EF = (Eg/2)+((3*k*T/(4*e))*np.log(a));
EF = math.ceil(EF*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "position of Fermi level is",EF,"eV"

position of Fermi level is 0.577 eV


## Example number 7.18, Page number 217¶

In :
#To calculate the electrical conductivity

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
ni = 1.5*10**16;            #intrinsic carrier density(per m**3)
mew_n = 0.13;               #electron mobility(m**2/Vs)
mew_p = 0.05;               #hole mobility(m**2/Vs)

#Calculation
sigma = ni*e*(mew_n+mew_p);        #electrical conductivity
sigma = sigma*10**4;

#Result
print "electrical conductivity is",sigma,"*10**-4 ohm-1 m-1"

electrical conductivity is 4.32 *10**-4 ohm-1 m-1


## Example number 7.19, Page number 217¶

In :
#To calculate the intrinsic resistivity

#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
ni = 2.15*10**-13;            #intrinsic carrier density(per cm**3)
mew_n = 3900;               #electron mobility(cm**2/Vs)
mew_p = 1900;               #hole mobility(cm**2/Vs)

#Calculation
sigmai = ni*e*(mew_n+mew_p);        #electrical conductivity(ohm-1 cm-1)
rhoi = 1/sigmai;                    #intrinsic resistivity(ohm cm)

#Result
print "intrinsic resistivity is",rhoi,"ohm cm"
print "answer given in the book is wrong"

intrinsic resistivity is 5.01202886929e+27 ohm cm
answer given in the book is wrong


## Example number 7.20, Page number 217¶

In :
#To calculate the electrical conductivity

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
ni = 2.1*10**19;            #intrinsic carrier density(per m**3)
mew_n = 0.4;               #electron mobility(m**2/Vs)
mew_p = 0.2;               #hole mobility(m**2/Vs)

#Calculation
sigma = ni*e*(mew_n+mew_p);        #electrical conductivity

#Result
print "intrinsic resistivity is",sigma,"ohm-1 m-1"

intrinsic resistivity is 2.016 ohm-1 m-1


## Example number 7.21, Page number 218¶

In :
#To calculate the Hall coefficient and electron mobility

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
V = 1.35;                   #voltage supply(V)
I = 5;               #current(mA)
b = 5;               #breadth(mm)
d = 1;               #thickness(mm)
L = 1;               #length(cm)
H = 0.45;            #magnetic field(Wb/m**2)
Vy =20;              #Hall voltage(mV)

#Calculation
Vy = Vy*10**-3;       #Hall voltage(V)
L = L*10**-2;         #length(m)
d = d*10**-3;         #thickness(m)
b = b*10**-3;         #breadth(m)
I = I*10**-3;         #current(A)
R = V/I;              #resistance(ohm)
A = b*d;              #area(m**2)
rho = R*A/L;          #resistivity(ohm m)
Ey = Vy/d;            #Hall field(V/m)
Jx = I/A;
a = Ey/(H*Jx);         #current density(m**3/C).Here a is 1/ne
RH = a;               #Hall coefficient(m**3/C)
RH = math.ceil(RH*10**4)/10**4;   #rounding off to 4 decimals
mew_n = RH/rho;       #electron mobility(m**2/Vs)
mew_n = math.ceil(mew_n*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "Hall coefficient is",RH,"m**3/C"
print "electron mobility is",mew_n,"m**2/Vs"

Hall coefficient is 0.0445 m**3/C
electron mobility is 0.33 m**2/Vs


## Example number 7.22, Page number 219¶

In :
#To calculate the Hall potential difference

#importing modules
import math

#Variable declaration
e = 1.6*10**-19;            #electron charge(C)
Ix = 200;               #current(A)
Bz = 1.5;               #magnetic field(Wb/m**2)
p = 8.4*10**28;         #electron concentration(per m**3)
d = 1;               #thickness(mm)

#Calculation
d = d*10**-3;         #thickness(m)
VH = Ix*Bz/(e*p*d);         #Hall potential(V)
VH = VH*10**6;              #Hall potential(micro V)

#Result
print "Hall potential is",int(VH),"micro V"

Hall potential is 22 micro V

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