17: Statistics and band theory of solids

Example number 17.1, Page number 23

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
rhoCu=8.96*10**3;   #density of Cu(kg/m**3)
awCu=63.55;   #atomic weight of Cu
nfCu=1*10**3;   #number of free electrons per Cu atom
rhoZn=7.14*10**3;   #density of Zn(kg/m**3)
awZn=65.38;   #atomic weight of Zn
nfZn=2*10**3;   #number of free electrons per Zn atom
rhoAl=2.7*10**3;   #density of Al(kg/m**3)
awAl=27;   #atomic weight of Al
nfAl=3*10**3;   #number of free electrons per Al atom
N=6.022*10**23;   #avagadro constant
h=6.626*10**-34;   #planck's constant
me=9.1*10**-31;   #mass of electron(kg)
e=1.6*10**-19;   #electron charge(c)

#Calculation
nCu=rhoCu*N*nfCu/awCu;   #concentration of electrons in Cu(per m**3)
EF0Cu=(h**2/(8*me))*(3*nCu/math.pi)**(2/3);   #fermi energy of Cu at 0K(J)
EF0Cu=EF0Cu/e;    #fermi energy of Cu at 0K(eV)
nZn=rhoZn*N*nfZn/awZn;   #concentration of electrons in Zn(per m**3)
EF0Zn=(h**2/(8*me))*(3*nZn/math.pi)**(2/3);   #fermi energy of Zn at 0K(J)
EF0Zn=EF0Zn/e;    #fermi energy of Zn at 0K(eV)
nAl=rhoAl*N*nfAl/awAl;   #concentration of electrons in Al(per m**3)
EF0Al=(h**2/(8*me))*(3*nAl/math.pi)**(2/3);   #fermi energy of Al at 0K(J)
EF0Al=EF0Al/e;    #fermi energy of Al at 0K(eV)

#Result
print "fermi energy of Cu at 0K is",round(EF0Cu,4),"eV"
print "fermi energy of Zn at 0K is",round(EF0Zn,2),"eV"
print "fermi energy of Al at 0K is",round(EF0Al,2),"eV"

fermi energy of Cu at 0K is 7.0608 eV
fermi energy of Zn at 0K is 9.45 eV
fermi energy of Al at 0K is 11.68 eV

Example number 17.2, Page number 25

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
nCu=8.4905*10**28;     #concentration of electrons in Cu(per m**3)
h=6.626*10**-34;   #planck's constant
me=9.1*10**-31;   #mass of electron(kg)
gama=6.82*10**27;

#Calculation
EF0=(h**2/(8*me))*(3*nCu/math.pi)**(2/3);   #fermi energy of Cu at 0K(J)
EF=EF0/e;    #fermi energy of Cu at 0K(eV)
DE=(gama/2)*math.sqrt(EF);    #density of states for Cu at fermi level(per m**3)

#Result
print "density of states for Cu at fermi level is",int(DE/10**27),"*10**27 per m**3"

density of states for Cu at fermi level is 9 *10**27 per m**3

Example number 17.3, Page number 26

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
rhoNi=69*10**-9;   #resistivity of Ni(ohm m)
rhoCr=129*10**-9;  #resistivity of Cr(ohm m)
rho=1120*10**-9;   #resistivity(ohm m) 
X=0.8;   

#Calculation
C=rho/(X*(1-X));   #Nordheim's coefficient(ohm m)

#Result
print "Nordheim's coefficient is",C,"ohm m"

Nordheim's coefficient is 7e-06 ohm m

Example number 17.4, Page number 26

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=2.7*10**3;   #density of Al(kg/m**3)
M=27;   #atomic weight of Al 
tow_r=10**-14;   #relaxation time(s)
e=1.6*10**-19;   #charge of electron(c)  
NA=6.022*10**23;   #avagadro constant
m=9.1*10**-31;   #mass of electron(kg)
f=3*10**3;   #number of free electrons per atom

#Calculation
n=rho*NA*f/M;    #number of electrons available per m**3
sigma=n*e**2*tow_r/m;    #conductivity of Al(ohm m) 

#Result
print "conductivity of Al is",round(sigma/10**7,4),"*10**7 ohm m"

conductivity of Al is 5.0823 *10**7 ohm m