Conducting materials

Example number 8.1, Page number 231

In [1]:
#Variable declaration
m=9.1*10**-31;      #mass of the electron in kg
n=2.533*10**28;    #concentration of electrons per m^3
e=1.6*10**-19;
tow_r=3.1*10**-14;    #relaxation time in sec

#Calculation
rho=m/(n*(e**2*tow_r));

#Result
print("electrical resistivity in ohm metre is",rho);

('electrical resistivity in ohm metre is', 4.526937967219795e-08)

Example number 8.2, Page number 231

In [3]:
#importing modules
import math

#Variable declaration
s=3.75*10**3;       #slope
k=1.38*10**-23;

#Calculation
Eg=2*k*s;
Eg=Eg/(1.6*10**-19);    #converting J to eV
Eg=math.ceil(Eg*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("band gap of semiconductor in eV is",Eg);

('band gap of semiconductor in eV is', 0.647)

Example number 8.3, Page number 231

In [4]:
#importing modules
import math

#Variable declaration
T=989;       #temperature in C
k=1.38*10**-23;
#let E-EF be E
E=0.5;        #occupied level of electron in eV

#Calculation
T=T+273;     #temperature in K
E=E*1.6*10**-19;       #converting eV to J
#let fermi=dirac distribution function f(E) be f
f=1/(1+math.exp(E/(k*T)));
f=math.ceil(f*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("probability of occupation of electrons is",f);

('probability of occupation of electrons is', 0.011)

Example number 8.4, Page number 232

In [1]:
#Variable declaration
mew_e=0.0035;    #mobility of electrons in m^2/Vs
E=0.5;       #electric field strength in V/m

#Calculation
vd=mew_e*E;
vd=vd*10**3;

#Result
print("drift velocity of free electrons in m/sec is",vd,"*10**-3");

#answer given in the book is wrong

('drift velocity of free electrons in m/sec is', 1.75, '*10**-3')

Example number 8.5, Page number 232

In [16]:
#importing modules
import math

#Variable declaration
A=6.022*10**23;    #avagadro number
e=1.6*10**-19;
rho=1.73*10**-8;    #resistivity of Cu in ohm metre
w=63.5;     #atomic weight 
d=8.92*10**3;     #density in kg/m^3

#Calculation
d=d*10**3;
sigma=1/rho;
sigmaa=sigma/10**7;
sigmaa=math.ceil(sigmaa*10**3)/10**3;   #rounding off to 3 decimals
n=(d*A)/w;
mew=sigma/(n*e);     #mobility of electrons
mew=mew*10**3;
mew=math.ceil(mew*10**4)/10**4;   #rounding off to 4 decimals

#Result
print("electrical conductivity in ohm-1 m-1",sigmaa,"*10**7");
print("concentration of carriers per m^3",n);
print("mobility of electrons in m^2/Vsec is",mew,"*10**-3");

('electrical conductivity in ohm-1 m-1', 5.781, '*10**7')
('concentration of carriers per m^3', 8.459250393700786e+28)
('mobility of electrons in m^2/Vsec is', 4.2708, '*10**-3')

Example number 8.6, Page number 232

In [18]:
#importing modules
import math

#Variable declaration
n=18.1*10**28;       #concentration of electrons per m^3
h=6.62*10**-34;   #planck constant in Js
me=9.1*10**-31;    #mass of electron in kg

#Calculation
X=h**2/(8*me);
E_F0=X*(((3*n)/math.pi)**(2/3));
E_F0=E_F0/(1.6*10**-19);    #converting J to eV

#Result
print("Fermi energy in eV is",E_F0);

#answer given in the book is wrong

('Fermi energy in eV is', 3.762396978021977e-19)

Example number 8.7, Page number 233

In [19]:
import math

#Variable declaration
E_F0=5.5;    #fermi energy in eV
h=6.63*10**-34;   #planck constant in Js
me=9.1*10**-31;    #mass of electron in kg

#Calculation
E_F0=E_F0*1.6*10**-19;    #converting eV to J
n=((2*me*E_F0)**(3/2))*((8*math.pi)/(3*h**3));

#Result
print("concentration of free electrons per unit volume of silver per m^3 is",n);

#answer given in the book is wrong

('concentration of free electrons per unit volume of silver per m^3 is', 4.603965704817037e+52)

Example number 8.8, Page number 233

In [21]:
#importing modules
import math

#Variable declaration
Eg=1.07;    #energy gap of silicon in eV
k=1.38*10**-23;
T=298;     #temperature in K

#Calculation
Eg=Eg*1.6*10**-19;     #converting eV to J
#let the probability of electron f(E) be X
#X=1/(1+exp((E-Ef)/(k*T)))
#but E=Ec and Ec-Ef=Eg/2
X=1/(1+math.exp(Eg/(2*k*T)))

#Result
print("probability of an electron thermally excited is",X);

('probability of an electron thermally excited is', 9.122602463573379e-10)

Example number 8.9, Page number 234

In [24]:
#importing modules
import math

#Variable declaration
k=1.38*10**-23;
m=9.1*10**-31;     #mass of the electron in kg
vf=0.86*10**6;    #fermi velocity in m/sec

#Calculation
Efj=(m*vf**2)/2;
Ef=Efj/(1.6*10**-19);    #converting J to eV
Ef=math.ceil(Ef*10**3)/10**3;   #rounding off to 3 decimals
Tf=Efj/k;
Tf=Tf/10**4;
Tf=math.ceil(Tf*10**4)/10**4;   #rounding off to 4 decimals

#Result
print("fermi energy of metal in J is",Efj);
print("fermi energy of metal in eV is",Ef);
print("fermi temperature in K is",Tf,"*10**4");

('fermi energy of metal in J is', 3.3651800000000002e-19)
('fermi energy of metal in eV is', 2.104)
('fermi temperature in K is', 2.4386, '*10**4')

Example number 8.10, Page number 234

In [25]:
#Variable declaration
sigma=5.82*10**7;      #electrical conductivity in ohm^-1m^-1
K=387;      #thermal conductivity of Cu in W/mK
T=27;     #temperature in C

#Calculation
T=T+273;       #temperature in K
L=K/(sigma*T);

#Result
print("lorentz number in W ohm/K^2 is",L);

('lorentz number in W ohm/K^2 is', 2.2164948453608246e-08)

Example number 8.11, Page number 235

In [29]:
import math

#Variable declaration
m=9.1*10**-31;     #mass of the electron in kg
e=1.6*10**-19;
k=1.38*10**-23;
n=8.49*10**28;     #concentration of electrons in Cu per m^3
tow_r=2.44*10**-14;   #relaxation time in sec
T=20;     #temperature in C

#Calculation
T=T+273;     #temperature in K
sigma=(n*(e**2)*tow_r)/m;
sigmaa=sigma/10**7;
sigmaa=math.ceil(sigmaa*10**4)/10**4;   #rounding off to 4 decimals
K=(n*(math.pi**2)*(k**2)*T*tow_r)/(3*m);
K=math.ceil(K*100)/100;   #rounding off to 2 decimals
L=K/(sigma*T);

#Result
print("electrical conductivity in ohm^-1 m^-1 is",sigmaa,"*10**7");
print("thermal conductivity in W/mK is",K);
print("Lorentz number in W ohm/K^2 is",L);

#answer for lorentz number given in the book is wrong

('electrical conductivity in ohm^-1 m^-1 is', 5.8277, '*10**7')
('thermal conductivity in W/mK is', 417.89)
('Lorentz number in W ohm/K^2 is', 2.4473623172034308e-08)
In [ ]: