Chapter 2 : Growth and Crystal properties of Semiconductor

Example number 2.1 , Page number 42

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

#Variable declaration
print("Each corner sphere of the bcc unit cell is shared with eigth neighbouring  cells.Thus each cell contains one eigth of a sphere at all the eigth corners.Each unit cell also contains one central sphere")
S=2 #Sphere per unit cell

#Calculations
f=S*math.pi*math.sqrt(3)/16 #maximum fraction of a unit cell

#Result
print("bcc unit cell volume filled with hard sphere= %i %%" %round(f*100))

Each corner sphere of the bcc unit cell is shared with eigth neighbouring  cells.Thus each cell contains one eigth of a sphere at all the eigth corners.Each unit cell also contains one central sphere
bcc unit cell volume filled with hard sphere= 68 %

Example number 2.2 , Page number 43

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

#Variable declaration
# r = p*a + q*b + s*c
p=1
q=2
s=3
LCM=6

#Calculations
rx=1/p*LCM #reciprocals
ry=1/q*LCM
rz=1/s*LCM

#Result

print("The plane depicted in the figure is denoted by (%i,%i,%i)" %(rx,ry,rz))

The plane depicted in the figure is denoted by (6,3,2)

Example number 2.3 , Page number 43

In [6]:
#importing module
import math
from __future__ import division

#Variable declaration
#Atomic weigths
Si=28.1 
Ga=69.7
As=74.9
Na=6.02*10**23 # Avagadro Number in mol**-1

#(a)Si
a=5.43*10**-8 #in cm
n=8 #no. of atoms/cell

#(b)GaAs
a1=5.65*10**-8 #in cm                

#Calculations
N=8/a**3 #Atomic Concentration in atoms/cc
N1=4/a1**3 #Atomic Concentration in atoms/cc
Density=(N*Si)/(Na)
Density1=(N1*(Ga+As))/(Na)

#Result
print("Density of Si= %1.2f g/cm**3\n" %Density)#answer vary due to round-off error
print("Density of GaAs= %1.2f g/cm**3" %Density1)

Density of Si= 2.33 g/cm**3

Density of GaAs= 5.33 g/cm**3

Example number 2.4 , Page number 44

In [10]:
#importing module
import math
from __future__ import division

#Variable declaration
a=5*10**-10 #lattice constatnt in m

#Calculations
n111=1/(a**2*math.sqrt(3))

#Result
print("n(111)= %.1f*10**18 atoms/m**2" %(n111/10**18))

n(111)= 2.3*10**18 atoms/m**2

Example number 2.5 , Page number 56

In [13]:
#importing module
import math
from __future__ import division

#Variable declaration
Cs=5*10**16 #impurity concentration in solid in atoms/cm**3
ks=0.35 #segregation coefficient 
d=2.33 #density of Si in g/cm**3
Na=6.02*10**23 # Avagadro Number in mol**-1
Si=31 #weight of Si
loadSi=4000 #initial load in gm

#Calculations
Cl=Cs/ks #impurity concentration in liquid
V=loadSi/d #volume of the melt in cm**3
Nummber_of_atoms=Cl*V #in atoms
Wt=(Cl*V*Si)/(Na)

#Result
print("(a)Cl= %1.2f*10**17 cm**-3\n" %(Cl/10**17))
print("(b)Wt of P= %.2f*10**-3 g" %(Wt/10**-3)) #The answers vary due to round off error

(a)Cl= 1.43*10**17 cm**-3

(b)Wt of P= 12.63*10**-3 g

Example number 2.7 , Page number 59

In [14]:
#importing module
import math
from __future__ import division

#Variable declaration
# r = p*a + q*b + s*c
x=3 #intercept on x axis
y=4 #intercept on y axis
z=5 #intercept on z zxis
LCM=60 

#Calculations
rx=1/x*LCM #reciprocal
ry=1/y*LCM
rz=1/z*LCM

#Result
print("Miller indices of plane are (%i,%i,%i)" %(rx,ry,rz))

Miller indices of plane are (20,15,12)

Example number 2.9 , Page number 60

In [17]:
#importing module
import math
from __future__ import division

#Variable declaration
a=8 #number of atoms shared by 8 cells
b=6 #number of atoms shared by 2 cells
c=4 #number of atoms shared by a single cell
L=5.43*10**-8 #Lattice constant in cm

#Calculations
N=(a/8)+(b/2)+c #no. of atoms in each cell
Volume=L**3
Density=8/Volume

#Result
print("(a)no. of atoms in each cell= %i\n" %N)
print("(b)Density of atoms in silicon= %i*10**22 atoms cm**-3" %round(Density/10**22))
#The answer provided in the textbook is wrong

(a)no. of atoms in each cell= 8

(b)Density of atoms in silicon= 5*10**22 atoms cm**-3

Example number 2.10, Page number 60

In [18]:
#importing module
import math
from __future__ import division

#Variable declaration
Na=6.02*10**23 # Avagadro Number in mol**-1
AtWt=28.09 #in g/mole
Density=5*10**22 #in atoms/cm**-3

#Calculations
DensityPerUnitVolume=(Density*AtWt)/(Na)

#Result
print("Density per unit volume= %1.2f g cm**-3" %DensityPerUnitVolume)

Density per unit volume= 2.33 g cm**-3