Chapter 1:Semiconductor Marerials and Crystal Properties

Example 1.1 Page No.23

In [2]:
#Example 1.1
#Find the miller indices for a plane.

#Given
#Length of intercept
l1=2.0
l2=3.0
l3=2.0

#Calcuation
#reciprocal of intercept
r1=1/l1
r2=1/l2
r3=1/l3
m1=6*r1
m2=6*r2
m3=6*r3

#Result
print"Miller indices of the given plane are",m1,m2,m3

Miller indices of the given plane are 3.0 2.0 3.0

Example 1.2 Page No.24

In [6]:
#Example 1.2
#Find the miller indices for a plane.

#Given
#Length of intercept
l1=1.0
l2=2.0
l3=0

#Calcuation
#reciprocal of intercept
r1=1/l1
r2=1/l2
r3=0
m1=2*r1
m2=2*r2
m3=2*r3

#Result
print"Miller indices of the given plane are",m1,m2,m3

Miller indices of the given plane are 2.0 1.0 0

Example 1.3 Page No.24

In [17]:
#Example 1.3
#Obtain lattice constant and radius of the atom.

#Given
V=3*(10**22)                 #kg/m**3, density of SCC lattice
p=(1/3.0)*10**-22

#Calculation
n=1                       #no. of lattice point     
a=(n*p)**(1/3.0)                     #lattice constant
r=(a*10**8/2)

#Result
print"Lattice constant is",round(a*10**8,2),"A"
print"radius of simple lattice is",round(r,2),"A"

Lattice constant is 3.22 A
radius of simple lattice is 1.61 A

Example 1.4 Page no.25

In [18]:
#Exampe  1.4
#Determine the density of crystal

#given data
import math
r=1.278                      #in Angstrum
AtomicWeight=63.5            #constant
AvogadroNo=6.023*10**23      #constant

#Calculation
#For FCC structure a=4*r/math.sqrt(2)
a=4*r*10**-10/math.sqrt(2)   #in meter
V=a**3                       #in meter**3
#mass of one atom = m
m=AtomicWeight/AvogadroNo    #in gm
m=m/1000                     #in Kg
n=4          # no. of atoms per unit cell for FCC structure
rho=m*n/V                    #in Kg/m**3

#Result
print "Density of crystal is",round(rho,2),"Kg/m**3"

Density of crystal is 8928.8 Kg/m**3

Example 1.5 Page no.26

In [19]:
#Example 1.5
#What is Density of silicon crystal .

#given data
n=4                     # no. of atoms per unit cell of silicon
AtomicWeight=28         #constant
AvogadroNo=6.021*10**23 #constant

#calculation
m=AtomicWeight/AvogadroNo  #in gm
m=m/1000                   #in Kg
a=5.3                      #lattice constant in Angstrum
a=a*10**-10                #in meter
V=a**3                     #in meter**3
rho=m*n/V                  #in Kg/m**3

#result
print"Density of silicon crystal is",round(rho,0),"Kg/m**3"

Density of silicon crystal is 1249.0 Kg/m**3

Example 1.6 Page no.26

In [2]:
#Example 1.5
#What is Surface density in FCC .

#given data
a=4.75                     #lattice constant in Angstrum
a=a*10**-10                #in meter

#Calculation
dp=2.31/a**2               #in atom/m**2
dp=dp/10**6                #in atom/mm**2

#Result
print "Surface density in FCC on (111)Plane is %.e",dp,"atoms/mm**2"

Surface density in FCC on (111)Plane is %.e 1.02382271468e+13 atoms/mm**2

Example 1.7 Page no. 28

In [28]:
#Example 1.7
#find the Interpolar distance

#given data
import math
l=1.539         #in Angstrum
theta=22.5           #in degree
n=1                  #order unitless

#Calculation
d=n*l/(2*math.sin(theta*math.pi/180))    #in Angstrum

#result
print "Interpolar distance in Angstrum ",round(d,2),"A"

Interpolar distance in Angstrum  2.01 A

Example 1.8 Page no. 28

In [4]:
#Example 1.8
#Find the wavelength of X-rays 

#given data
import math

theta=16.8/2.0             #in degree
n=2.0                      #order unitless
d=0.4                    #in nm

#Calculation
l=(2*d*10**-9*sin(theta*math.pi/180.0))/n     #in Angstrum

#result
print "wavelength of X-rays in Angstrum ",round(l*10**10,3),"A"

wavelength of X-rays in Angstrum  0.584 A