# Chapter 5 : Semiconductors¶

## Example 5.1 Page No : 193¶

In :
import math

# Given
e = 1.6*10**-19     # in coulombs
h = 6.6*10**-34     # in J s
m = 9.1*10**-31     # in Kg
me = 1.08*m
mh = 0.56*m
T = 300.0           # in Kelvin
Eg = 1.10           # in eV
ue = 1350.0         # in cm2/V/s
uh = 450.0          # in cm2/V/s
k = 1.38*10**-23    # m2 kg s-2 K-1

# Calculations and Results
Nc = 2*((2*math.pi*me*k*T)/h**2)**(3.0/2.0)  # in m**-3
Nc *= 10**-6        # in cm**-3
Nv = 2*((2*math.pi*mh*k*T)/h**2)**(3.0/2.0)  # in m**-3
Nv *= 10**-6  # in cm**-3
ni = math.sqrt(Nc*Nv)*math.exp(-Eg*e/(2*k*T))
print("Intrinsic concentration of Si in cm**-3 is {0:.4g}".format(ni))
sigma = e*ni*(ue+uh)
p = 1.0/sigma
print("Intrinsic resistivity of Si in ohm cm is {0:.4g}".format(p))

Intrinsic concentration of Si in cm**-3 is 1.02e+10
Intrinsic resistivity of Si in ohm cm is 3.404e+05


## Example 5.2 Page No : 194¶

In :
import math
# Given
T = 300.0         # in kelvin
k = 1.38*10**-23  # in m2 kg s-2 K-1
me = 9.1*10**-31  # in Kg
m = 0.26*me

# Calculations and Results
Ve = math.sqrt(3*k*T/m)
print("Mean speed of electrons in conduction band in m/s is {0:.4g}".format(Ve))

Mean speed of electrons in conduction band in m/s is 2.291e+05


## Example 5.3 Page No : 195¶

In :
# Given
e = 1.6*10**-19     # in coulombs
ue = 1350.0         # in cm2/V/s
uh = 450.0          # in cm2/V/s
ni = 1.45*10**10    # in cm**-3
L = 1.0             # in cm
A = 1.0             # in cm2
N_Si = 5*10**22     # in cm**-3

# Calculations and Results
sigma = e*ni*(ue+uh)
R = L/(sigma*A)
print("Resistance of a pure Silicon crystal in ohms is {0:.4g}".format(R))
Nd = N_Si/10**9
n = Nd              # at room temperature
p = ni**2/Nd
sigma = e*n*ue
R = L/(sigma*A)
print("Resistance in ohms of Silicon crystal when doped with Arsenic with 1 in 10**9 is {0:.4f}".format(R))

Resistance of a pure Silicon crystal in ohms is 2.395e+05
Resistance in ohms of Silicon crystal when doped with Arsenic with 1 in 10**9 is 92.5926


## Example 5.4 Page No : 197¶

In :
# Given
Na = 10**17         # acceptor atoms /cm3
Nd = 10**16         # donor atoms /cm3
p = Na-Nd           # in cm**-3
ni = 1.45*10**10    # in cm**-3

# Calculations and Results
n = ni**2/p
print("Electron concentration in cm**-3 is {0:.4f}".format(n))

Electron concentration in cm**-3 is 2336.1111


## Example 5.5 Page No : 202¶

In :
import math

# Given
Na = 2*10**17       # acceptor atoms /cm3
Nd = 10**16         # acceptor atoms /cm3
ni = 1.45*10**10    # in cm**-3
K = 0.0259          # in eV

# Calculations and Results
# math.since Nd>>ni
n = Nd
# let EFn-EFi=E
E = K*math.log(Nd/ni)
print("Position of the fermi energy w.r.t fermi energy in intrinsic Si in eV is {0:.4f}".format(E))
# for intrinsic Si
# ni=Nc*exp(-(Ec-E_Fi)/(k*T))
# for doped Si
# Nd=Nc*exp(-(Ec-E_Fn)/(k*T))
# let x=Nd/ni
# let K=k*T
p = Na-Nd
# let E=EFp-EFi
# let n=p/ni
E = -K*math.log(p/ni)
print("Position of the fermi energy w.r.t fermi energy in n-type case in eV is {0:.4f}".format(E))

Position of the fermi energy w.r.t fermi energy in intrinsic Si in eV is 0.3482
Position of the fermi energy w.r.t fermi energy in n-type case in eV is -0.4245


## Example 5.7 Page No : 208¶

In :
import math

# Given
Nd = 10**15         # in cm**-3
Nc = 2.8*10**19     # in cm**-3
Ti = 556.0            # in Kelvin
k = 8.62*10**-5     # in eV/K
delta_E = 0.045     # in eV
T = 300.0             # in kelvin

# Calculations and Results
# part(a)
print("From fig 5.16 the estimated temperature above which the si sample behaves as if intrinsic is 556 Kelvin")
# part(b)
Ts = delta_E/(k*math.log(Nc/(2*Nd)))
Nc_Ts = Nc*(Ts/T)**(3.0/2.0)
print("Lowest temperature in kelvin is {0:.4f}".format(Ts))
# the improved temperature
Ts = delta_E/(k*math.log(Nc_Ts/(2*Nd)))
print("Extrinsic range of Si is {0:.4f} K to 556 K".format(Ts))

From fig 5.16 the estimated temperature above which the si sample behaves as if intrinsic is 556 Kelvin
Lowest temperature in kelvin is 54.6823
Extrinsic range of Si is 74.6473 K to 556 K


## Example 5.9 Page No : 214¶

In :
# Given
e = 1.6*10**-19   # in coulombs
Nd = 10**17       # in cm**-3
Na = 9*10**16     # in cm**-3

# Calculations and Results
# part(a)
ue1 = 800.0         # at 300 kelvin ue in cm2/V/s
sigma1 = e*Nd*ue1
ue2 = 420.0         # at 400 kelvin ue in cm2/V/s
sigma2 = e*Nd*ue2
print("when Si sample is doped with 10**17 arsenic atoms/cm3, the conductivity of "
"the sample at 300K and 400K in ohm**-1*cm**-1 is {0:.4f}, {1:.4f} respectively".format(sigma1, sigma2))
# part(b)
ue1 = 600.0         # at 300 kelvin ue in cm2/V/s
sigma1 = e*(Nd-Na)*ue1
ue2 = 400.0         # at 400 kelvin ue in cm2/V/s
sigma2 = e*(Nd-Na)*ue2
print("when n-type Si is further doped with 9*10**16 boron atoms /cm3, the conductivity of"
" the sample at 300K and 400K in ohm**-1*cm**-1 is {0:.4f}, {1:.4f} respectively".format(sigma1, sigma2))

when Si sample is doped with 10**17 arsenic atoms/cm3, the conductivity of the sample at 300K and 400K in ohm**-1*cm**-1 is 12.8000, 6.7200 respectively
when n-type Si is further doped with 9*10**16 boron atoms /cm3, the conductivity of the sample at 300K and 400K in ohm**-1*cm**-1 is 0.9600, 0.6400 respectively


## Example 5.11 Page No : 218¶

In :
# Given
# part(a)
h = 6.63*10**-34            # in Js
c = 3*10**8                 # in m/s
e = 1.6*10**-19             # in coulombs
ue = 0.034                  # in m2/V/s
uh = 0.0018                 # in m2/V/s
t = 1*10**-3                # in seconds
L = 1*10**-3                # in m
D = 0.1*10**-3              # in m
W = 1*10**-3                # in m
I = 1.0                     # mW/cm**2
I = I*10**-3*10**4          # conversion of units to W/m**2
n = 1.0                     # quantum efficiency
lambda_val = 450*10**-9     # in m
V = 50.0                    # in volts

# Calculations and Results
# part(a)
A = L*W                     # in m3
EHP_ph = (A*n*I*lambda_val)/(h*c)
print("No.of EHP/s generated per second is {0:.4g}".format(EHP_ph))
# part(b)
delta_sigma = e*n*I*lambda_val*t*(ue+uh)/(h*c*D)
print("Photo conductivity of the sample in ohm**-1 m**-1 is {0:.4g}".format(delta_sigma))
# part(c)
A = 0.1*10**-6              # m2
E = V/W
delta_J = E*delta_sigma
delta_I = A*delta_J
print("Photo-current produced in mA is {0:.4g}".format(delta_I*10**3))

No.of EHP/s generated per second is 2.262e+13
Photo conductivity of the sample in ohm**-1 m**-1 is 1.296
Photo-current produced in mA is 6.48


## Example 5.13 Page No : 223¶

In :
# Given
e = 1.6*10**-19     # in coulombs
T = 300.0           # in kelvin
ue = 1300.0         # in cm2/V/s

# Calculations and Results
# V=k*T/e
V = 0.0259          # thermal voltage in Volts
# D=ue*k*T/e
D = ue*V
print("Diffusion coefficient of electrons at room temperature in cm2/s is {0:.4f}".format(D))

Diffusion coefficient of electrons at room temperature in cm2/s is 33.6700


## Example 5.17 Page No : 229¶

In :
# Given
Eg = 1.42       # in eV
# letE=hc/lambda=hf
E = 1.96        # in eV
P_L = 50.0      # in mW
kT = 0.0259     # in eV

# Calculations and Results
delta_E = E-(Eg+(3.0/2.0)*kT)
P_H = (P_L/E)*delta_E
print("Amount of power dissipated as heat in mW is {0:.4f}".format(P_H))

Amount of power dissipated as heat in mW is 12.7844


## Example 5.18 Page No : 234¶

In :
import math

# Given
phi_m = 4.28            # in eV
e = 1.6*10**-19         # in coulombs
X = 4.01                # in eV
kT = 0.026              # in eV
Vf = 0.1                # in V
T = 300.0                 # in kelvin
Be = 30.0                 # A/K2/cm2
A = 0.01                # cm2

# Calculations and Results
# part(a)
phi_B = phi_m-X
print("Theoretical barrier height in eV is {0:.4f}".format(phi_B))
# part(b)
phi_B = 0.5             # in eV
Io = A*Be*T**2*math.exp(-phi_B/kT)
print("Saturation current in micro amperes is {0:.4f}".format(Io*10**6))
# let/E=e*Vf            #in eV
E = 0.1                 # in eV
If = Io*(math.exp((E/kT))-1)
print("Forward current in milli amperes is {0:.4f}".format(If*10**3))

Theoretical barrier height in eV is 0.2700
Saturation current in micro amperes is 120.1011
Forward current in milli amperes is 5.5021