Chapter 6 - LED light source

Exa 6.1 : page no. 113

In [16]:
from __future__ import division
#given data :
Tr=40 #in ns
Tnr=90 #in ns
T=Tr*Tnr/(Tr+Tnr) #in ns
print "Bulk recombination life-time = %0.1f nano second " %T
ETAint=(T/Tr)*100 #in %
print "Internal Quantum Efficiency = %0.f %% "  % ETAint

Bulk recombination life-time = 27.7 nano second 
Internal Quantum Efficiency = 69 %

Exa 6.2 : page no. 113

In [17]:
#given data :
lamda=1310 #in nm
lamda=lamda*10**-9 #in meter
ETAint=70 #in %
I=50 #in mA
I=I*10**-3 #in A
h=6.63*10**-34 #constant
c=3*10**8 #speed of light in m/s
q=1.6*10**-19 #in coulamb
Pint=(ETAint/100)*I*h*c/(q*lamda) #in Watts
print "Internally generated optical power = %0.1f mW " %(Pint*10**3) 

Internally generated optical power = 33.2 mW

Exa 6.3 : page no. 114

In [18]:
#given data : 
Pint=28.4 #in mw
Pint=Pint*10**-3 #in Watts
I=60 #in mA
I=I*10**-3 #in A
h=6.63*10**-34 #constant
c=3*10**8 #speed of light in m/s
q=1.6*10**-19 #in coulamb
#Tr=Tnr
#Formula : Pint=(Tnr/(Tr+Tnr))*(I*h*c/(q*lambda))
#as Tr=Tnr : (Tnr/(Tr+Tnr))=1/2
lamda=(1/2)*(I*h*c/(q*Pint)) #in m
print "Peak emission wavelength from the device = %0.3f micro meter "  %(lamda*10**6)

Peak emission wavelength from the device = 1.313 micro meter

Exa 6.4 : page no. 114

In [19]:
#given data :
L=20 #in um
L=L*10**-6 #in meter
Tr=80 #in ns
Tnr=80 #in ns
tau=Tr*Tnr/(Tr+Tnr) #in ns
#Formula : L=(D*tau)**(1/2)
D=(L**2)/(tau*10**-9) #in m**2-s**-1
print "Diffusion Coefficient of LED = %0.2f m^2-s^-1 " %D

Diffusion Coefficient of LED = 0.01 m^2-s^-1

Exa 6.5 : page no. 115

In [20]:
from math import sqrt, pi
#given data :
EBW=50 #MHz in 3dB
#Formula : EBW(3dB)=OpticalBW(3dB)/sqrt(2)
OpticalBW=sqrt(2)*EBW #in 3dB
print "3dB Optical Bandwidth = %0.1f MHz  " %OpticalBW 

3dB Optical Bandwidth = 70.7 MHz

Exa 6.6 : page no. 115

In [21]:
from math import sqrt, pi
#given data :
tau=5 #in ns
# 1/((1+omega*tau)**2)**(1/2) = 1/2
#Formula :omega=2*pi*F 
F=sqrt(3)/(2*pi*tau*10**-9) #in Hz
print "Optical Modulation Bandwidth = %0.f MHz " %(F*10**-6)  

Optical Modulation Bandwidth = 55 MHz

Exa 6.7 : page no. 115

In [22]:
from math import sqrt, pi
#given data :
tau=10 #in ns
# 1/((1+omega*tau)**2)**(1/2) = 1/2" 
#Formula :omega=2*pi*F 
F=sqrt(3)/(2*pi*tau*10**-9) #in Hz
F=F*10**-6 #in MHz
EMB=F/sqrt(2) #in MHz
print "Electrical Modulation Bandwidth = %0.2f MHz " %EMB  

Electrical Modulation Bandwidth = 19.49 MHz

Exa 6.8 : page no. 116

In [23]:
#given data :
Po=200 #in uwatts
tau=10 #in ns
F=10 #in MHz
print "We have : P(w)/P(o)=Po/((1+2*pi*F*tau)**2)**(1/2)" 
Pw=(Po*10**-6)/(1+(2*pi*F*10**6*tau*10**-9)**2)**(1/2) #in Watts
print "Optical output power = %0.1f micro watts " %(Pw*10**6)  

We have : P(w)/P(o)=Po/((1+2*pi*F*tau)**2)**(1/2)
Optical output power = 169.3 micro watts

Exa 6.9 : page no. 116

In [24]:
#given data :
Po=200 #in uwatts
tau=10 #in ns
F=50 #in MHz
print "We have : P(w)/P(o)=Po/((1+2*pi*F*tau)**2)**(1/2)" 
Pw=(Po*10**-6)/(1+(2*pi*F*10**6*tau*10**-9)**2)**(1/2) #in Watts
print "Optical output power = %0.1f micro watts " %(Pw*10**6)  

We have : P(w)/P(o)=Po/((1+2*pi*F*tau)**2)**(1/2)
Optical output power = 60.7 micro watts

Exa 6.10 : page no. 116

In [25]:
#given data :
nm=3.5 #refractive index of InP unitless
n=1 #refractive index of air  unitless
F=0.6 #Transmission factor at crystal-air interface
#Part (a)
# Pe=Pint*F*n**2/(4*nm**2)
#Let F*n**2/(4*nm**2)=x
x=F*n**2/(4*nm**2) 
print "Pint =",x
print "Hence the power emitted into air is only 1.2% of the internal optical power." 
#Part (b)
print "ETAext=(Pe/P)*100" 
print "ETAext=(0.012*Pint/P)*100"
#given : Pint=0.5P
print "ETAext=(0.012*0.5*P/P)*100"
print "ETAext :",(0.012*0.5)*100,"%" 

Pint = 0.0122448979592
Hence the power emitted into air is only 1.2% of the internal optical power.
ETAext=(Pe/P)*100
ETAext=(0.012*Pint/P)*100
ETAext=(0.012*0.5*P/P)*100
ETAext : 0.6 %
In [26]:
from sympy import symbols
#given data :
nm=3.5 #refractive index of InP unitless
n=1 #refractive index of air  unitless
F=0.6 #Transmission factor at crystal-air interface
#Part (a)
Pint, P = symbols('Pint, P')
Pe=Pint*F*n**2/(4*nm**2)
print "Power emitted into air is only",round(Pe/Pint*100,1),"% of the internal optical power." 
#Part (b)
Pint = 0.5*P
Pe=Pint*F*n**2/(4*nm**2)
ETAext=(Pe/P)*100
print "ETAext =",round(ETAext,2),"%" 

Power emitted into air is only 1.2 % of the internal optical power.
ETAext = 0.61 %

Exa 6.11 : page no. 117

In [27]:
from sympy import symbols

#given data :
#given : Pint=0.3*P
nm=3.6 #refractive index of InP unitless
n=1 #refractive index of air  unitless
F=0.68 #Transmission factor at crystal-air interface
Pint, P = symbols('Pint, P')
Pe=Pint*F*n**2/(4*nm**2)
Pint=0.3*P
ETAext=Pint*100*F*n**2/(4*P*nm**2)
print "External Power Efficiency = %0.2f %% " %ETAext 

External Power Efficiency = 0.39 %

Exa 6.12 : page no. 117

In [28]:
#given data :
ETAext=1.5 #in %
I=25 #in mA
V=4 #in Volt
F=0.8 #Transmission factor at crystal-air interface
nm=3.6 #refractive index of GaAs unitless
n=1 #refractive index of air  unitless
# formula : ETAext = Pint*F*n^2/(4*nm^2*P)*100
P = V*I*1e-3  # W
Pint = ETAext/(F*n**2/(4*nm**2*P)*100)
print "Optical power generated in the device = %0.1f mW " %(Pint*1000) 

Optical power generated in the device = 97.2 mW