# Chapter - 8 : Optical detectors¶

## Example 8.1, page 454¶

In [1]:
#Variable declaration
n=1.2*10**11                           #no of electrons
m=3*10**11                             #no of photons
e=1.602*10**-19                        #1 electron volt
h=0.85*10**-6                          #wavelength
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light

#Calculation
Q=n/m                                  #quantum efficiency
R=(Q*e*h)/(h1*c)                       #responsivity

#Result
print'Quantum efficiency = %.1f '%Q
print'Responsivity = %.3f A W^-1'%R

Quantum efficiency = 0.4
Responsivity = 0.274 A W^-1


## Example 8.2, page 454¶

In [1]:
import math

#Variable declaration
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light
E=1.5*10**-19                          #energy of photons
n=0.65                              #quantum efficiency
e=1.602*10**-19                        #1 electron volt
io=2.5*10**-6                          #photocurrent

#Calculation
h=h1*c/E                          #wavelength
R=(n*e)/(E)                       #responsivity
po=io/R                           #incident optical power

#Result
print'(a) Wavelength = %.2f um'%(h*10**6)
print'(b) Incident optical power = %.2f uW'%(po*10**6)

(a) Wavelength = 1.32 um
(b) Incident optical power = 3.60 uW


## Example 8.3, page 456¶

In [3]:
import math

#Variable declaration
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light
e=1.602*10**-19                        #1 electron volt
E=1.43                                 #bandgap energy in eV

#Calculation
h=h1*c/(E*e)                             #wavelength

#Result
print'Wavelength = %.3f um'%(h*10**6)

Wavelength = 0.867 um


## Example 8.4, page 463¶

In [4]:
import math

#Variable declaration
w=20*10**-6                                   #width
vd=10**5                                      #drift velocity
r=500*10**-6                                  #diameter in meter
es=10.5*10**-13                               #permitivity

#Calculation
td=w/vd                                      #drift time
A=math.pi*r**2                               #area
cj=es*A/w                                   #junction capacitance

#Result
print'Drift time = %.1f x 10^-10 S'%(td*10**10)
print'Junction capacitance = %.2f x 10^-13 F'%(cj*10**13)

Drift time = 2.0 x 10^-10 S
Junction capacitance = 0.41 x 10^-13 F


## Example 8.5, page 464¶

In [5]:
import math

#Variable declaration
vd=3*10**4                                      #drift velocity
w=25*10**-6                                   #width

#Calculation
Bm=vd/(2*math.pi*w)                            #maximum bandwidth
tr=1/Bm                                        #maximum response time

#Result
print'Maximum response time = %.1f ns'%(tr*10**9)

Maximum response time = 5.2 ns


## Example 8.6, page 470¶

In [6]:
import math

#Variable declaration
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light
e=1.602*10**-19                        #1 electron volt
l=8*10**-9                              #dark current
n=0.55                                  #quantum efficiency
h=1.3*10**-6                            #wavelength
A=100*50*10**-12

#Calculation
nep=(h1*c*math.sqrt(2*e*l))/(n*e*h)     #Noise equivalent power
D=math.sqrt(A)/nep                      #Specific detectivity

#Result
print'Noise equivalent power = %.2f x 10^-14 W'%(nep*10**14)
print'Specific detectivity = %.1f x 10^8 m Hz^(1/2) W^-1'%(D*10**-8)

Noise equivalent power = 8.78 x 10^-14 W
Specific detectivity = 8.1 x 10^8 m Hz^(1/2) W^-1


## Example 8.7, page 482¶

In [7]:
import math

#Variable declaration
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light
e=1.602*10**-19                        #1 electron volt
n=0.8                                  #quantum efficiency
h=0.9*10**-6                          #wavelength
po=0.5*10**-6                          #incident optical power
I=11*10**-6                            #output current

#Calculation
R=(n*e*h)/(h1*c)                       #resposivity
Ip=po*R                                #photocurrent
M=I/Ip                                 #multiplication factor

#Result
print'Multiplication factor = %.2f '%M

Multiplication factor = 37.89


## Example 8.8, page 487¶

In [8]:
import math

#Variable declaration
h1=6.626*10**-34                       #plancks constant
c=2.998*10**8                          #speed of light
e=1.602*10**-19                        #1 electron volt
h=1.26*10**-6                          #wavelength
Ic=15*10**-3                           #collector current
po=125*10**-6                          #incident optical power
n=0.4                                   #quantum efficiency

#Calculation
go=(h1*c*Ic)/(h*e*po)                     #Optical gain
hfe=go/n                                   #Common emitter current gain

#Result
print'Optical gain, Go = %.1f'%go
print'Common emitter current gain, hfe = %.1f '%hfe

Optical gain, Go = 118.1
Common emitter current gain, hfe = 295.2


## Example 8.9, page 491¶

In [9]:
import math

#Variable declaration
t=5*10**-12                                    #electron transit time
G=70                                          #Optical gain

#Calculation
B=1/(2*math.pi*t*G)                           #Maximum 3dB bandwidth

#Result
print'Maximum bandwidth = %.1f MHz'%(B*10**-6)

Maximum bandwidth = 454.7 MHz