# Ch-9 : Optical Detectors¶

## Ex:9.1 Pg: 374¶

In [1]:
from __future__ import division
e_c=550## number of electron collected
p=800## number of photon incident
n=e_c/p## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=1.3*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
print "The responsivity =%0.2f Amp/Watt"%( R)

The responsivity =0.72 Amp/Watt


## Ex:9.2 Pg: 374¶

In [2]:
from __future__ import division
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6# wavelength in m
R=0.274## responsivity in A/W
n=(R*h*c)/(e*y)## quantum efficiency
n1=n*100## % of quantum efficiency
print "The quantum efficiency =%0.2f %%"%( n1)

The quantum efficiency =40.00 %


## Ex:9.3 Pg: 374¶

In [3]:
from __future__ import division
e_c=1## number of electron collected
p=3## number of photon incident
n=e_c/p## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.8*10**-6# wavelength in m
Eg=(h*c)/y## band gap energy in J
R=(n*e*y)/(h*c)## responsivity in A/W
Po=10**-7## in W
Ip=R*Po## output photo current
print "The quantum efficiency =%0.2f %%"%( n*100)#
print "\n band gap energy =%0.2f*10**-20 J"%( Eg*10**20)#
print "\n The output photo current =%0.2f nA"%( Ip*10**9)

The quantum efficiency =33.33 %

band gap energy =24.85*10**-20 J

The output photo current =21.49 nA


## Ex:9.4 Pg: 375¶

In [4]:
from __future__ import division
n=0.50## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Ip=10**-6## mean photo current
Po=Ip/R## received optical power in W
f=c/y#
re=(n*Po)/(h*f)#
rp=re/n## number of received photons
print "The responsivity =%0.2f A/W"%( R)#
print "\n The received optical power =%0.2f uW"%( Po*10**6)#
print "\n The number of received photons =%0.2f*10**13 photons/sec"%( rp/10**13)

The responsivity =0.34 A/W

The received optical power =2.92 uW

The number of received photons =1.25*10**13 photons/sec


## Ex:9.5 Pg: 375¶

In [5]:
from __future__ import division
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
Eg=1.43## in eV
Eg1=Eg*1.602*10**-19## in J
y=(h*c)/Eg1## cut off wavelength in m
print "The cut off wavelength =%0.2f um"%( y*10**6)

The cut off wavelength =0.87 um


## Ex:9.6 Pg: 376¶

In [6]:
from math import pi
from __future__ import division
vd=2.5*10**4## carrier velocity in m/s
w=30*10**-6## width in m
Bm=vd/(2*pi*w)#
Tm=1/Bm## max response time in sec
Tm1=Tm*10**9## max response time in ns
print "The max response time =%0.2f ns"%( Tm1)

The max response time =7.54 ns


## Ex:9.7 Pg: 376¶

In [7]:
from math import ceil,pi
from __future__ import division
n=0.65## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Po=0.35*10**-6## in W
Ip=R*Po## output photo current
I=9*10**-6## output current in A
M=I/Ip## multiplication factor
M1=ceil(M)#
print "The multiplication factor =%d"%( M1)

The multiplication factor =58


## Ex:9.8 Pg: 377¶

In [1]:
from __future__ import division
n=0.50## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
Eg=1.5*10**-19## in J
y=(h*c)/Eg## cut off wavelength in m
f=c/y#
R=(n*e)/(h*f)## responsivity in A/W
Ip=2.7*10**-6## photo current in A
Po=Ip/R## incident optical power in W
Po1=Po*10**6## incident optical power in uW
print "The cut off wavelength =%0.2f um"%( y*10**6)#
print "\n The responsivity =%0.2f A/W "%( R)#
print "\n The incident optical power =%0.2f uW"%( Po1)

The cut off wavelength =1.33 um

The responsivity =0.53 A/W

The incident optical power =5.06 uW


## Ex:9.9 Pg: 377¶

In [2]:
from __future__ import division
n=0.15## quantum efficiency
e=1.6*10**-19## charge
h=6.63*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6## cut off wavelength in m
f=c/y## frequency in Hz
R=(n*e)/(h*f)## responsivity in A/W
print "The responsivity =%0.2f A/W "%( R)

The responsivity =0.10 A/W


## Ex:9.10 Pg: 377¶

In [3]:
from __future__ import division
Iph=75*10**-6## output photocurrent in A
y=0.85## operating wavelength in um
Pi=750*10**-6## incident optical power in uW
R=Iph/Pi## responsivity in A/W
n=1.24*R/y## external quantum efficiency
n1=n*100## percentage of external quantum efficiency
print "The responsivity =%0.2f A/W "%( R)#
print "\n The external quantum efficiency =%0.2f%% "%( n1)

The responsivity =0.10 A/W

The external quantum efficiency =14.59%


## Ex:9.11 Pg: 378¶

In [4]:
from __future__ import division
Vs=10**5## saturation in m/s
W=7*10**-6## depletion layer width in m
tr=W/Vs## transit time in sec
print "The transit time =%0.2f ps"%( tr*10**12)

The transit time =70.00 ps


## Ex:9.12 Pg: 378¶

In [6]:
from __future__ import division
Vs=3*10**4## saturation in m/s
W=25*10**-6## depletion layer width in m
tr=W/Vs## transit time in sec
f=0.35/tr## max 3 dB bandwidth Hz
f1=f/10**6## max 3 dB bandwidth Hz
print "The max 3 dB bandwidth =%d MHz"%( f1)#
print "\n The answer is wrong in the textbook"

The max 3 dB bandwidth =420 MHz

The answer is wrong in the textbook


## Ex:9.13 Pg: 378¶

In [7]:
from __future__ import division
Vs=3*10**4## saturation in m/s
W=25*10**-6## depletion layer width in m
E=10.5*10**-11## in F/m
RL=15*10**6## load resister in ohm
A=0.25*10**-6## area in m**2
tr=W/Vs## transit time in sec
Cj=E*A/W## junction capacitance in F
t=RL*Cj## time constant in sec
print "The transit time =%0.2f ns"%( tr*10**9)#
print "\n The junction capacitance =%0.2f pF"%( Cj*10**12)#
print "\n The time constant =%0.2f us"%( t*10**6)

The transit time =0.83 ns

The junction capacitance =1.05 pF

The time constant =15.75 us


## Ex:9.14 Pg: 379¶

In [8]:
from __future__ import division
Eg1=1.12## band gap for Si in eV
Eg2=0.667## band gap for Ge in eV
y_si=1.24/Eg1## cut off wavelength for Si in um
y_he=1.24/Eg2## cut off wavelength for Ge in um
print "The cut off wavelength for Si  =%0.2f um"%( y_si)#
print "\n The cut off wavelength for Ge =%0.2f um"%( y_he)

The cut off wavelength for Si  =1.11 um

The cut off wavelength for Ge =1.86 um


## Ex:9.15 Pg: 379¶

In [9]:
from __future__ import division
n=0.50## quantum efficiency
e=1.6*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.9*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Ip=10**-6## mean photo current
Po=Ip/R## received optical power in W
f=c/y#
re=(n*Po)/(h*f)#
rp=re/n## number of received photons
print "The responsivity =%0.2f A/W"%( R)#
print "\n The received optical power =%0.2f uW"%( Po*10**6)#
print "\n The number of received photons =%0.2f*10**13 photons/sec"%( rp/10**13)

The responsivity =0.36 A/W

The received optical power =2.76 uW

The number of received photons =1.25*10**13 photons/sec


## Ex:9.16 Pg: 379¶

In [10]:
from __future__ import division
R=0.40## Responsivity in A/W
m=100*10**-6## incident flux in W/m-m
A=2## area in m-m
Po=m*A## incident power in W
Ip=R*Po## photon current in A
print "The photon current =%d uA"%( Ip*10**6)

The photon current =80 uA


## Ex:9.17 Pg: 380¶

In [11]:
from __future__ import division
n=0.65## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
Eg=1.5*10**-19## in J
y=(h*c)/Eg## cut off wavelength in m
f=c/y#
R=(n*e)/(h*f)## responsivity in A/W
Ip=2.5*10**-6## photo current in A
Po=Ip/R## incident optical power in W
Po1=Po*10**6## incident optical power in uW
print "The cut off wavelength =%0.2f um"%( y*10**6)#
print "\n The responsivity =%0.2f A/W "%( R)#
print "\n The incident optical power =%0.2f uW"%( Po1)

The cut off wavelength =1.33 um

The responsivity =0.69 A/W

The incident optical power =3.60 uW


## Ex:9.18 Pg: 380¶

In [12]:
from __future__ import division
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
Eg=1.43## in eV
Eg1=Eg*1.602*10**-19## in J
y=(h*c)/Eg1## cut off wavelength in m
print "The cut off wavelength =%0.2f um"%( y*10**6)

The cut off wavelength =0.87 um


## Ex:9.19 Pg: 381¶

In [13]:
from __future__ import division
n=0.45## quantum efficiency
h=6.62*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=1.2*10**-6## cut off wavelength in m
Ic=20*10**-6## collector current in A
Po=120*10**-6## incident optical power in W
e=1.602*10**-19## charge
Go=(h*c*Ic)/(y*Po*e)## optical gain
h_e=Go/n## common emitter gain
print "The optical gain =%0.2f"%( Go)#
print "\n The common emitter gain =%0.2f"%( h_e)

The optical gain =0.17

The common emitter gain =0.38


## Ex:9.20 Pg: 381¶

In [14]:
from __future__ import division
n=0.5## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=1.3*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Po=0.4*10**-6## in W
Ip=R*Po## output photo current
I=8*10**-6## output current in A
M=I/Ip## multiplication factor
print "The multiplication factor =%d"%( M)

The multiplication factor =38


## Ex:9.21 Pg: 382¶

In [15]:
from __future__ import division
n=0.85## quantum efficiency
e=1.6*10**-19## charge
h=6.625*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.9*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Po=0.6*10**-6## in W
Ip=R*Po## output photo current
I=10*10**-6## output current in A
M=I/Ip## multiplication factor
print "The multiplication factor =%d"%( M)

The multiplication factor =27


## Ex:9.22 Pg: 382¶

In [16]:
from __future__ import division
e_c=1.2*10**11## number of electron collected
p=2*10**11## number of photon incident
n=e_c/p## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
E=1.5*10**-19## energy in J
y=(h*c)/E# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Ip=2.6*10**-6## photocurrent in A
Po=Ip/R## incident optical power in W
print "The quantum efficiency =%d %%"%( n*100)#
print "\n The wavelength =%0.2f um"%( y*10**6)#
print "\n The responsivity =%0.2f Amp/Watt"%( R)#
print "\n The incident optical power =%0.2f uW"%( Po*10**6)

The quantum efficiency =60 %

The wavelength =1.33 um

The responsivity =0.64 Amp/Watt

The incident optical power =4.06 uW


## Ex:9.23 Pg: 383¶

In [17]:
from __future__ import division
n=0.40## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=1.35*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Po=0.2*10**-6## in W
Ip=R*Po## output photo current
I=4.9*10**-6## output current in A
M=I/Ip## multiplication factor
print "The multiplication factor =%d"%( M)

The multiplication factor =56


## Ex:9.24 Pg: 383¶

In [18]:
from __future__ import division
n=0.55## quantum efficiency
e=1.6*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6# wavelength in m
R=(n*e*y)/(h*c)## responsivity in A/W
Ip=2*10**-6## mean photo current
Po=Ip/R## received optical power in W
re=(n*Po*y)/(h*c)## number of received photons
print "The responsivity =%0.2f A/W"%( R)#
print "\n The received optical power =%0.2f uW"%( Po*10**6)#
print "\n The number of received photons =%0.2f*10**13 photons/sec"%( re/10**13)

The responsivity =0.38 A/W

The received optical power =5.31 uW

The number of received photons =1.25*10**13 photons/sec


## Ex:9.25 Pg: 384¶

In [19]:
from __future__ import division
h=6.625*10**-34## plank constant
c=3*10**8## speed of light in m/s
n=1## quantum efficiency
e=1.602*10**-19## charge
E=1.3*10**-19## energy in J
y=(h*c)/E## wavelength in m
M=18## multiplication factor
rp=10**13## no. of photon per sec
Po=rp*E## output power in w
Ip=(n*Po*e)/E## output photocurrent in A
I=M*Ip## photocurrent in A
print "The wavelength =%0.2f um"%( y*10**6)#
print "\n The output power =%0.2f uW"%( Po*10**6)#
print "\n The photocurrent =%0.2f uA"%( I*10**6)

The wavelength =1.53 um

The output power =1.30 uW

The photocurrent =28.84 uA


## Ex:9.26 Pg: 384¶

In [20]:
from __future__ import division
e_c=2*10**10## number of electron collected
p=5*10**10## number of photon incident
n=e_c/p## quantum efficiency
e=1.602*10**-19## charge
h=6.626*10**-34## plank constant
c=3*10**8## speed of light in m/s
y=0.85*10**-6## wavelength in m
y1=0.85## wavelength in um
Eg=(h*c)/y##  bandgap energy in J
Eg1=1.24/y1## bandgap energy in terms of eV
Po=10*10**-6## incident power in W
Ip=(n*e*Po)/Eg## mean output photocurrent in A
print "The quantum efficiency =%d %%"%( n*100)#
print "\n The bandgap energy =%0.2f*10**-19 J"%( Eg*10**19)#
print "\n The bandgap energy =%0.2f eV"%( Eg1)#
print "\n The mean output photocurrent =%0.2f uA"%( Ip*10**6)

The quantum efficiency =40 %

The bandgap energy =2.34*10**-19 J

The bandgap energy =1.46 eV

The mean output photocurrent =2.74 uA