# Chapter 17: Electrical Properties of Materials¶

## Example 17.1 Page 640¶

In :
#initiation of variable
sigma=10**-6  # ( Electrical Conductivity in Ohm-m)^-1
e=1.6*10**-19  # Charge on electron in Coulomb
m_e=0.85 #Mobility of electron in m^2/V-s
m_h=0.04 # Mobility of holes in m^2/V-s

#calculation
n_i=sigma/(e*(m_e+m_h))#n_i is Intrinsic carrier concentration

#result
print" Intrinsic Carrier Concentration is %.1e m^-3" %n_i;

 Intrinsic Carrier Concentration is 7.0e+12 m^-3


## Example 17.2 Page 647¶

In :
#initiation of variable
e=1.6*10**-19  #Charge on electron in Coulomb
ni=4*10**19 #  number of electron per unit volume for Si at 423 K   (m^-3)
#Values of m_e and m_h are deduced from graphs at page No.689
m_e=0.06  #Mobility of electron in m^2/V-s
m_h=0.022  #  Mobility of holes in m^2/V-s

#calculation
sigma=ni*e*(m_e+m_h) # electrical conductivity

#result
print" Electrical Conductivity is %.2f (Ohm-m)^-1\n" %sigma

 Electrical Conductivity is 0.52 (Ohm-m)^-1



## Example 17.3 Page 648¶

In :
#initiation of variable
n=10.0**23 #  Carrier Concentration in m^-3
e=1.6*10**-19  #Charge on electron in Coulomb
#From graph 18.18 m_e is calculated corresponding to n=10^23
m_e=0.07  # Mobility of electron in m^2/V-s
m_e2=0.04  #  Mobility of electron m^2/V-s

#part A
#result
print" Material is n-type  "

# Part B
#calculation
sigma=n*e*m_e # electrical conductivity calculation for extrinsic n-type

#result
print "Conductivity is just %d (Ohm-m)^-1" %sigma

#partC
#From graph 18.19a m_e2 is calculated corresponding to 373 K
sigma2=n*e*m_e2

#result
print"Conductivity at T=373 K becomes %d (Ohm-m)^-1\n" %sigma2;

 Material is n-type
Conductivity is just 1120 (Ohm-m)^-1
Conductivity at T=373 K becomes 640 (Ohm-m)^-1



## Example 17.4 Page 651¶

In :
#intiiation of variable
sigma=3.8*10**7  # Electrical Conductivity in (Ohm-m)^-1
m_e=0.0012  # Mobility of electron in m^2/V-s
I_x=25.0  # Current in Ampere(A)
d=15.0*10**-3 #Thickness in m
B_z=0.6  # Magnetic field in Tesla

#calculation
Rh=-m_e/sigma  #Hall coefficient
Vh=Rh*I_x*B_z/d

#result
print" Hall coefficient is %.2e V-m/A-Tesla" %Rh
print"Hall Voltage is %.2e V" %Vh

 Hall coefficient is -3.16e-11 V-m/A-Tesla
Hall Voltage is -3.16e-08 V


## Example 17.5 Page 665¶

In :
#initiation of variable
from math import ceil
A = 6.45e-4 # Area of plat in m^2
l = 2.0e-3 # separation between plates in m
epsilon_r = 6.0 #dielectric constant of material
epsilon_0 = 8.85e-12 # universal constant
V = 10.0 # Applied voltage in Volt

# Part A
#calculation
C = epsilon_0*epsilon_r*A/l #Capacitance of a parallel plat capacitor

#result
print" Capacitance of capacitor is %.2e F" %C

#partB
Q = C*V # Stored charge calculation

#result
print" Stored charge in capacitor is %.2e C" %Q

#partC
D = epsilon_0*epsilon_r*V/l # Dielectric displacement

#result
print" Dielectric displacement in capacitor is %.2e C/m^2" %(ceil(D*1e9)/1e9)

#partD
P = D - epsilon_0*V/l # Polarisation

#result
print" Polarization is %.2e C/m^2" %(ceil(P*1e9)/1e9)

 Capacitance of capacitor is 1.71e-11 F
Stored charge in capacitor is 1.71e-10 C
Dielectric displacement in capacitor is 2.66e-07 C/m^2
Polarization is 2.22e-07 C/m^2


## Example 17.6 (Design Problem 17.1) Page 649¶

In :
#initiation of variable
p1 = 1.0e22 # Number of electrons per unit volume
e = 1.6e-19 # Charge on electron in coulomb
mu_h1 = 0.04 # concentration of holes mobility in m^/Vs
sigma_d = 50.0 # Desired conductivity in (ohm-m)^-1
p2 = 1.0e21# Number of electrons per unit volume
mu_h2 = 0.045#concentration of holes mobility in m^/Vs
p3 = 8.0e21# Number of electrons per unit volume
mu_h3 = mu_h1# concentration of holes mobility in m^/Vs
N_a = 6.023e23 # Avogadro’s constant
rho_si = 2.33e6 # density of silicon in g/m^3
A_si = 28.09 # molecular weight in g/mol

#calculation
sigma1 = p1*e*mu_h1
sigma2 = p2*e*mu_h2
sigma3 = p3*e*mu_h3
N_Si = N_a*rho_si/A_si
Ca  = p3*100/(p3+N_Si)

#result
print " Silicon material of p-type of conductivity %d (ohm-m)^-1" %sigma_d, " must have %.2e doping material" %Ca

 Silicon material of p-type of conductivity 50 (ohm-m)^-1  must have 1.60e-05 doping material