Chapter11:SEMICONDUCTOR OPTOELECTRONICS

Ex11.1:pg-462

In [2]:
hw=1.7
Eg = 1.43
alpha= 4.21*10**4*((hw-Eg)/(hw))
print"The absorption coefficient(alpha) for GaAs is ,alpha=","{:.1e}".format(alpha),"cm**-1"

The absorption coefficient(alpha) for GaAs is ,alpha= 6.7e+03 cm**-1

Ex11.2:pg-462

In [3]:
hw=1.43
alpha = 2.5*10**4
amt = 0.9
L= -(1/alpha)*log(1-amt)
print"The length of the material  is ,L=","{:.2e}".format(L),"cm"

The length of the material  is ,L= 9.21e-05 cm

Ex11.3:pg-463

In [4]:
Pop = 10.0
hw=1.65
alpha = 7*10**3
T = 10**-9
GL = (alpha*Pop)/(hw*1.6*10**-19)
print"The rate of e-h pair production is ,GL =","{:.2e}".format(GL),"cm**-3s**-1"
dn = (GL*T)
print"The excess carrier density is ,dn =","{:.2e}".format(dn),"cm**-3"

The rate of e-h pair production is ,GL = 2.65e+23 cm**-3s**-1
The excess carrier density is ,dn = 2.65e+14 cm**-3

Ex11.4:pg-468

In [2]:
A= 10**4*10**-8
Na=2*10**16
Nd=10**16
Dn = 20
Dp = 12
Tn = 10**-8
Tp = 10**-8
GL = 10**22
kbT = 0.026
Es = 11.9*8.85*10**-14
e = 1.6*10**-19
VR = 2.0
ni = 1.5*10**10
Ln = sqrt(Dn*Tn)
print"The electron diffusion length is ,Ln =","{:.1e}".format(Ln),"cm"
Lp = sqrt(Dp*Tp)
print"The hole diffusion length is ,Lp =","{:.2e}".format(Lp),"cm"
Vbi = kbT*log((Na*Nd)/(ni)**2)
print"The built in voltage is ,Vbi =","{:.2e}".format(Vbi),"V"
W = sqrt((2*Es*(Na+Nd)*(Vbi+VR))/(e*Na*Nd))
print"The depletion width is ,W =","{:.2e}".format(W),"cm"
IL= (e*A*GL*(W+Ln+Lp))
print"The photocurrent is ,IL=","{:.2e}".format(IL),"A"

The electron diffusion length is ,Ln = 4.5e-04 cm
The hole diffusion length is ,Lp = 3.46e-04 cm
The built in voltage is ,Vbi = 7.15e-01 V
The depletion width is ,W = 7.32e-05 cm
The photocurrent is ,IL= 1.39e-04 A

Ex11.5:pg-469

In [4]:
A= 1.0
Na=5*10**17
Nd=10**16
Dn = 20.0
Dp = 10.0
Tn = 3*10**-7
Tp = 10**-7
kbT = 0.026
IL = 25*10**-3
e = 1.6*10**-19
ni = 1.5*10**10
Ln = sqrt(Dn*Tn)
print"The electron diffusion length is ,Ln =","{:.2e}".format(Ln),"cm"
Lp = sqrt(Dp*Tp)
print"The hole diffusion length is ,Lp =","{:.2e}".format(Lp),"cm"
Io = A*e*(ni)**2*((Dn/(Ln*Na))+(Dp/(Lp*Nd)))
print"The saturation current is ,Io =","{:.2e}".format(Io),"A"
Voc= (kbT)*log(1+(IL/Io))
print"The open circuit voltage is ,Voc=","{:.1e}".format(Voc),"V"

The electron diffusion length is ,Ln = 2.45e-03 cm
The hole diffusion length is ,Lp = 1.00e-03 cm
The saturation current is ,Io = 3.66e-11 A
The open circuit voltage is ,Voc= 5.3e-01 V

Ex11.6:pg-469

In [6]:
A= 1.0
Na=5*10**17
Nd=10**16
Dn = 20.0
Dp = 10.0
Tn = 3*10**-7
Tp = 10**-7
kbT = 0.026
IL = 25*10**-3
e = 1.6*10**-19
ni = 1.5*10**10
Io = 3.66*10**-11
Voc= (kbT)*log(1+(IL/Io))
print"The open circuit voltage is ,Voc=","{:.2e}".format(Voc),"V"
P = 0.8*IL*Voc 
print"The power per solar cell is ,P=","{:.2e}".format(P),"W"
# Note: Answer given in the book is incorrect it is 10.6 mW not 1.06 mW
N_series = 10/(0.9*Voc)
print"The number of solar cell needed to produce output power 10V is ,N_series =",round(N_series,2)
N_parallel = 10/(0.9*IL*10)
print"The number of solar cell needed to produce output power 10W is ,N_parallel =",round(N_parallel,2)
# Note : due to different precisions taken by me and the author ... my answer differ 

The open circuit voltage is ,Voc= 5.29e-01 V
The power per solar cell is ,P= 1.06e-02 W
The number of solar cell needed to produce output power 10V is ,N_series = 21.01
The number of solar cell needed to produce output power 10W is ,N_parallel = 44.44

Ex11.7:pg-471

In [9]:
Pop = 1.0
hw=1.43
a = 700.0
W = 10**-3
e = 1.6*10**-19
Phi_o =(Pop)/(hw*1.6*10**-19)
print"The photon flux incident on the detector Phi_o =","{:.2e}".format(Phi_o),"cm**-2s**-1"
JL=e*Phi_o*(1-exp(-(a*W)))
print"The photocurrent density is ,JL=","{:.2e}".format(JL),"A/cm**2"

 The photon flux incident on the detector Phi_o = 4.37e+18 cm**-2s**-1
The photocurrent density is ,JL= 3.52e-01 A/cm**2

Ex11.8:pg-479

In [18]:
import math
h=1.05*10**-34
mo = 9.1*10**-31
me = 0.067*9.1*10**-31
kbT = 0.026
mh = 0.45*9.1*10**-31
To = 0.6*10**-9
p = 1.0*10**21
T = (p/(2.0*To))*((2.0*(math.pi)*h**2)/(kbT*1.6*10**-19*(me+mh)))**(3.0/2.0)
print"T =","{:.2e}".format(T),"s**-1"
Tr = 1.0/T
print"The e-h recombination time is Tr =""{:.2e}".format(Tr),"s"

T = 1.75e+05 s**-1
The e-h recombination time is Tr =5.70e-06 s

Ex11.9:pg-480

In [19]:
h=1.05*10**-34
mo = 9.1*10**-31
me = 0.067*9.1*10**-31
kbT = 0.026
mh = 0.45*9.1*10**-31
To = .6*10**-9
tnr = 10**-7
p = 10**21
mr = 1.0/((1.0/me)+(1.0/mh))
print"The reduced mass for the e-h system is mr* =","{:.2e}".format(mr),"kg"
print"           For low p-doping such as 10**16, the recombination time is given as below"
T1 = (p/(2.0*To))*((2.0*(math.pi)*h**2)/(kbT*1.6*10**-19*(me+mh)))**(3.0/2.0)
print"T =","{:.2e}".format(T),"s**-1"
Tr1 = 1.0/T1
print"The e-h recombination time is Tr1 =","{:.2e}".format(Tr1),"s"
nQr1 = 1.0/(1+(Tr1/tnr))
print"The internal quantum efficiency  is nQr1 =""{:.2e}".format(nQr1)
print"         For high p-doping such as 5*10**17, the recombination time is given as below"
T2 = (1.0/To)*((mr/mh)**(3.0/2.0))
print"T2 =","{:.2e}".format(T2),"s**-1"
Tr2 = 1.0/T2
print"The e-h recombination time is Tr2 =","{:.2e}".format(Tr2),"s"
nQr2 = 1.0/(1+(Tr2/tnr))
print"The internal quantum efficiency  is nQr2 =""{:.2e}".format(nQr2)
# Note : due to different precisions taken by me and the author ... my answer differ 

The reduced mass for the e-h system is mr* = 5.31e-32 kg
           For low p-doping such as 10**16, the recombination time is given as below
T = 1.75e+05 s**-1
The e-h recombination time is Tr1 = 5.70e-06 s
The internal quantum efficiency  is nQr1 =1.72e-02
         For high p-doping such as 5*10**17, the recombination time is given as below
T2 = 7.78e+07 s**-1
The e-h recombination time is Tr2 = 1.29e-08 s
The internal quantum efficiency  is nQr2 =8.86e-01

Ex11.10:pg-480

In [23]:
Na=5*10**16
Nd=5*10**17
Dn = 30.0
Dp = 15.0
Tn = 10**-8
Tp = 10**-7
e = 1.6*10**-19
ni = 1.84*10**6
kbT = 0.026
V = 1.0
nQr=0.5
np = ni**2/Na
pn = ni**2/Nd
Ln = sqrt(Dn*Tn)
print"The electron diffusion length is ,Ln =","{:.3e}".format(Ln),"cm"
Lp = sqrt(Dp*Tp)
print"The hole diffusion length is ,Lp =","{:.2e}".format(Lp),"cm"
Yinj = ((e*Dn*np)/Ln)/(((e*Dn*np)/Ln)+((e*Dp*pn)/Lp))
print"The injection efficiency is ,Yinj =""{:.1e}".format(Yinj)

The electron diffusion length is ,Ln = 5.477e-04 cm
The hole diffusion length is ,Lp = 1.22e-03 cm
The injection efficiency is ,Yinj =9.8e-01

Ex11.11:pg-481

In [24]:
A= 10**-2
Na=5*10**16
Nd=5*10**17
Dn = 30.0
Dp = 15.0
Tn = 10**-8
Tp = 10**-7
e = 1.6*10**-19
ni = 1.84*10**6
kbT = 0.026
V = 1.0
nQr=0.5
Eph = 1.41
np = ni**2/Na
pn = ni**2/Nd
Ln = sqrt(Dn*Tn)
print"The electron diffusion length is ,Ln =","{:.2e}".format(Ln),"cm"
Lp = sqrt(Dp*Tp)
print"The hole diffusion length is ,Lp =","{:.2e}".format(Lp),"cm"
In = ((A*e*Dn*np)/Ln)*(exp(V/kbT)-1)
print"The injected current is ,In =","{:.2e}".format(In),"A"
Iph = (In*nQr)/e
print"The photon generated per second is ,Iph =","{:.2e}".format(Iph),"s**-1"
P = Iph*e*Eph
print"The optical power is ,P =","{:.2e}".format(P),"W"

The electron diffusion length is ,Ln = 5.48e-04 cm
The hole diffusion length is ,Lp = 1.22e-03 cm
The injected current is ,In = 3.00e-04 A
The photon generated per second is ,Iph = 9.37e+14 s**-1
The optical power is ,P = 2.11e-04 W

Ex11.12:pg-489

In [26]:
R =.33
alpha_R = 20
L= (-1.0/alpha_R)*log(R)
print"The length of the cavity is ,L=","{:.2e}".format(L),"cm"

 The length of the cavity is ,L= 5.54e-02 cm

Ex11.14:pg-494

In [27]:
n = 1.1*10**18
nth=1.32*10**18
e = 1.6*10**-19
d = 2*10**-4
Tr = 2.4*10**-9
Jth = (e*nth*d)/Tr
print"The current density is Jth =","{:.2e}".format(Jth),"A/cm**2"

The current density is Jth = 1.76e+04 A/cm**2