import math
#variable declaration
Ephoton = 1.5; # energy of photon in eV
Eg = 1.4; # energy gap in eV
m = 9.1*10**-31; # mass of electron in kg
e = 1.6*10**-19; #charge of electron in coulombs
me_GaAs = 0.07; #times of electro mass in kilograms
mh_GaAs = 0.068; #times of electro mass in kilograms
# Calculations
Eke = Ephoton - Eg; #energy on eV
pe = math.sqrt(2*m*me_GaAs*Eke*e) # momentum of electrons in kg m/s
ph = math.sqrt(2*m*mh_GaAs*Eke*e) # momentum of electrons in kg m/s
# Result
print'Kinetic Energy = %3.1f'%Eke,'eV';
print'Momentum of electrons = %3.1e'%pe,'kg m/s';
print'Momentum of holes = %3.1e'%ph,'kg m/s';
import math
#variable declaration
T1 = 300; # temperature in kelvin
nv = 1.04*10**19; #in cm**-3
T2 = 400; #temperature in K
fl = 0.25; #fermi level position in eV
#Calculations
Nv = (1.04*10**19)*(T2/float(T1))**(3/float(2)); #Nv at 400 k in cm**-3
kT = (0.0259)*(T2/float(T1)); #kT in eV
po = Nv*math.exp(-(fl)/float(kT)); #hole oncentration in cm**-3
# Result
print'Thermal equilibrium hole concentration = %3.2e '%po,'cm**-3';
print'Note: Calculation mistake in textbook Nv is not multiplied by exponentiation';
import math
#variable declaration
Nc = 3.8*10**17; #constant in cm**-3
Nv = 6.5*10**18; #constant in cm**-3
Eg = 1.42; # band gap energy in eV
KT1 = 0.03885; # kt value at 450K
T1 = 300; #temperature in K
T2 = 450; #temperature in K
# calculation
n1i = math.sqrt(Nc*Nv*math.exp(-Eg/float(0.0259))); #intrinsic carrier concentration in cm**-3
n2i = math.sqrt(Nc*Nv*((T2/float(T1))**3) *math.exp(-Eg/float(KT1))); # intrinsic carrier conc at 450K in cm**-3
# Result
print'Intrinsic Carrier Concentration at 300K = %3.2e'%n1i,'cm**-3';
print'Intrinsic Carrier Concentration at 300K = %3.2e'%n2i,'cm**-3';
print' Note : Calculation mistake in textbook in finding carrier conc. at 450K';
import math
#variable declaration
mh = 0.56; #masses interms of m0
me = 1.08; #masses interms of m0
t = 27; #temperature in °C
k = 8.62*10**-5;
# Calculations
T = t+273; #temperature in K
fl = (3/float(4))*k*T*math.log(mh/float(me)); #position of fermi level in eV
#result
print'The position of Fermi level with respect to middle of the bandgap is %3.1f'%(fl*10**3),'meV';
import math
#variable declaration
mo = 9.11*10**-31; #mass of electron inkilograms
e = 1.6*10**-19; # charge of electron in coulombs
er = 13.2; #relative permitivity in F/m
eo = 8.85*10**-12; # permitivity in F/m
h = 6.63*10**-34; # plancks constant J.s
# Calculations
me = 0.067*mo;
E = (me*(e**4))/float((8*(eo*er)**2)*(h**2)*e); #energy in eV
# Result
print'Donor binding energy = %3.4f'%E,'eV';
import math
#variable declaration
no = 10**17; # doping carrier conc
ni = 1.5*10**10; #intrinsic concentration
kT = 0.0259
#Calculations
po = (ni**2)/float(no); #Equlibrium hole concentration in cm**-3
fl = kT*math.log10(no/float(ni)); #Position of fermi energy level in eV
#Result
print'Equlibrium hole concentration = %3.2e'%po,'cm**-3';
print'Position of fermi energy level = %3.3f'%fl,'eV';
import math
#variable declaration
k = 8.62*10**-5; #in eV/K
Eg = 1.10; #energy in eV
t1 = 200; #temperature in °C
t2 = 27; #temperature in °C
psi = 2.3*10**3;
# Calculations
# sigma = sigmao*exp(-Eg/(2kT))
# k = sigma_473/sigma_300;
t3 = t1+273; #temperature in K
t4 = t2+273; #temperature in K
k1 = math.exp((-Eg)/float(2*k*t3)); #electrical conductivity in cm**-1.m**-1
k2 = math.exp((-Eg)/float(2*k*t4)); #lectrical conductivity in cm**-1.m**-1
k = k1/float(k2);
pm = k/float(psi);
#Result
print'electrical conductivity of pure silicon =%3.2e'%k,'ohm**-1.m**-1';
print'Note:calculation mistake in electrical conductivity,and units of conductivity';
import math
#variable declaration
ni = 2.5*10**19; # carrier density in per m**3
q = 1.6*10**-19; # charge of electron in coulombs
un = 0.35; #mobility of electrons in m**2/V-s
up = 0.15; #mobility of electrons in m**2/V-s
# Calculations
sigma = ni*q*(un + up); #conductivity in per Ω-m
p = 1/float(sigma); #resistivity in Ω-m
# Result
print'Resistivity = %3.1f'%p,'Ω-m';
import math
#variable declaration
p = 3.16*10**3; # resistivity Ω-m
e = 1.6*10**-19; # charge of electron in coulombs
ue = 0.14; #mobility of electrons in m**2/V-s
uh = 0.05; #mobility of holes in m**2/V-s
# Calculations
n = 1/float((p*e)*(ue + uh)); #carrier density in m**-3
# Result
print'Intrinsic Carrier Concentration = %3.2e'%n,'m**-3';
import math
#variable declaration
p = 5.32*10**3; #density of germanium
Nav = 6.023*10**26; # Avagadros number
AW = 72.59; # atomic wt
ni = 1.5*10**19; # carrier density
ue = 0.36;
uh = 0.18;
e = 1.6*10**-19;
# calculations
N = (p*Nav)/float(AW); # no of germanium atoms per unit volume
Nd = N*10**-6 ; # no of pentavalent impurity atoms/m**3
f = Nd/float(ni);
nh = (ni**2)/float(Nd); # hole concentration
sigma = e*((Nd*ue)+(nh*uh));
#Result
print'The factor by which the majority conc. is more than the intrinsic carrier conc = %d'%f;
print'Hole concentration = %3.1e'%nh,'m**-3';
print'Conductivity = %d'%sigma,'ohm**-1 m**-1';
import math
#variable declaration
p = 5*10**-3; # resistivity in Ω-m
ue = 0.3; # electron mobility m**2/volt-s
uh = 0.1; # hole mobility m**2/volt-s
e = 1.6*10**-19 # charge of electron in coulombs
# calculations
sigma = 1/float(p); # conductivity in per Ω -m
n = sigma/float(e*(ue + uh)); # carrier density per m**3
#Result
print'Carrier Density = %3.1e'%n,'m**-3';
import math
#variable declaration
Jd = 500; # current density A/m**2
p = 0.05; # resistivity in Ω-m
l = 100*10**-6; # travel length m
ue = 0.4; # electron mobility m**2/Vs
e = 1.6*10**-19; # charge of electron in coulombs
# Calculations
ne = 1/float(p*e*ue); #in per m**3
vd = Jd/float(ne*e); #drift velocity in m/s
t = l/float(vd); #time teken in s
#result
print'Drift velocity = %d'%vd,'m/s';
print' time = %3.0e'%t,'s';
import math
#variable declaration
#psi1 is increased by 30%, psi1/ps2 is 130/100
a = 1.3; #ratio of psi1/psi2
K = 8.82*10**-5; #constant in eV/K
Eg = 0.719; #band gap in eV/K
T = 300; #temperature in K
#calculation
d=1/float((1/float(T))-((2*K/float(Eg))*math.log(1.3)));
dT=d-T; #temperature rise in K
#result
print'temperature rise is of = %3.2f'%dT,'K';
import math
#variable declaration
v = 5; # voltage in volts
r = 10; # resistance in k-ohm
J = 60; # current density in A/cm**2
E = 100; # electric field in V.m**-1
Nd = 5*10**15; # in cm**-3
up = 410; # approx hole mobility cm**2/V-s
Na = 1.25*10**16; # approx in cm**-3
e = 1.6*10**-19; # charge of electron in coulombs
#Calculations
I = v/float(r); # total current A
A = I/float(J); # cross sectional area cm**2
L = v/float(E) # length of resistor cm
sigma = L/float(r*A); #conductivity in (Ω-cm)**-1
sigma_comp = e*up*(Na - Nd); #conductivity in (Ω-cm)**-1
# Result
print'Conductivity of the compensated p-type semiconductor is %3.3f'%sigma_comp;
import math
#variable declaration
e = 1.6*10**-19; # charge of electron in coulombs
Dn = 250; # electron diffusion co-efficient cm**2/s
n1 = 10**18; # electron conc. in cm**-3
n2 = 7*10**17; # electron conc. in cm**-3
dx = 0.10; # distance in cm
# Calculations
Jdiff = e*Dn*((n1-n2)/float(dx)); #diffusion current density A/cm**2
#Result
print'Diffusion Current Density = %d '%Jdiff,'A/cm**2';
import math
# Variable declaration
e = 1.6*10**-19; # charge of electron in coulombs
Eg = 0.75; #bandgap energy eV
c = 3*10**8; # velocity of light in m
h = 6.62*10**-34; # plancks constant in J.s
# Calculations
lamda = (h*c)/float(Eg*e); # wavelength in Å
#Result
print'Wavelength at which Ge starts to absorb light = %d '%(lamda*10**10),'Å';
# import math
#variable declaration
Eg = 1.35*1.6*10**-19; #energy in eV
h = 6.63*10**-34; #plancks constant in J.s
c = 3*10**8; #velocity in m
#calculation
lamda = (h*c)/float(Eg); #wavelength in m
#result
print'cutoff wavelength =%3.2f '%(lamda*10**6),'um';
import math
#variable declaration
h = 6.62*10**-34 # plancks constant J.s
c = 3*10**8; # velocity of light in m
lamda = 1771*10**-9; # wavelengthg in m
e = 1.6*10**-19 # charge of electron in coulombs
# Calculations
Eg = (h*c)/float(lamda*e); #bandgap energy eV
#Result
print'bandgap energy = %3.3f'%Eg,'eV';
import math
#variable declaration
Nd = 10**21; # donar density per in m**3
H = 0.6; # magnetic field in T
J = 500; # current density A/m**2
d = 3*10**-3; # width in m
e = 1.6*10**-19 # charge of electron coulombs
#Calculations
Ey = (J*H)/float(Nd*e); # field in V/m
vh = Ey*d; # hall voltage V
#Result
print'Hall Voltage = %3.1f '%(vh*10**3),'mV';
import math
#variable declaration
e = 1.6*10**-19; # charge of electron in coulomb
Rh = -0.0125; # hall co-efficient
ue = 0.36; # electron mobility
E = 80; # electric field
# Calculations
n = -1/float(Rh*e);
J = n*e*ue*E # current density in Ampere/m**2
# Result
print'Current density = %d '%J,'Ampere/m**2';
import math
#variable declaration
p = 0.00893; # resistivity in ohm-m
Hz = 0.5; # field in weber/m**2
Rh = 3.66*10**-4; # hall co-efficient hall coefficient in m**3
# Calculations
u = Rh/float(p); #mobility of charge cerrier in m**2*(V**-1)*s**-1
theta_h = (math.atan(u*Hz))*(180/float(math.pi)); # hall angle in degrees
# Result
print'Hall angle = %3.4f '%theta_h,'°';