1. Lecture 2: Photodetection and
Photodetectors
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 1

2. Photodetection (Continued)
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 2

3. Electrical Signal-to-Noise Ratio (SNR)
➥ At the receiver, there is noise on the signal arriving at the input and and after detection
added to that is noise that is injected at various stages of the receiver
➥ The current output of the receiver in(t) has current contributions from
➥ Electrical shot noise
➥ Thermal noise
➥ APD detectors have additional multiplication noise
➥ Amplifier noise photodetector
Popt(t) = PSig(t) + Pn(t) I(t) = Ip(t) + in(t)
Receiver
Detector Output Current (I)
2σ1
<I1>
<I0>
2σ0
t
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 3

4. Modeling Detector SNR
 When observing the detector current output, it is difficult to tell which noise was
present at the optical input and which noise was generated internal to the detector.
So we tend to use several different models and combine them
Optical signal = DC Current = DC Current = DC Current = DC
component + component + component + component +
variance (Poisson variance (Poisson variance (Filtered variance (Filtered
Process) Process) Poisson Process) Poisson Process +
Hd(ω) = FT {hd (t)} additive noise)
!
Ideal
photodetector Filtering
Internal
Detector
Noise
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 4

5. Noise Current
 To quantify the statistical nature of noise, we can’t determine random events ahead
of time, but we can use their “spectral” characteristics to quantify statistical
behavior
 Define an Average (mean) value to quantify the amount of power (energy) in the non-
time varying part of the signal
 Define a Variance to quantify the amount of power (energy) in the noisy part of the
signal
 Define the “noise” current as
i(t) = I DC + inoise (t)
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 5

6. Shot Noise Mean and Variance
 For constant power illumination, the rate parameter is constant, and the signal is the mean
 The noise corresponds to the photocurrent variance
 For a filter, homogeneous Poisson process
t
!q
Mean (Amps) is (t) = i(t) = Precvd $ hd (# )d# • Both mean and variance are
h" 0 linear with Prevd
t • As Prcvd is increased, both
2 !q 2 signal and noise increase
Variance (Amps2) i (t) = var{i(t)} =
n Precvd $ hd (# )d#
h" 0
Power Spectrum
2
I DC Total Shot Noise =
Area = 2qI DC B
2
in (0) = 2qI DC
f
B
Detector Bandwidth
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 6

7. Photodetector Shot Noise
 The shot noise generated in the photodetection process is physically due to the “quantum
granularity” of the received (and photo converted) optical signal
 Shot noise sets the ultimate limit of an optical receiver
 Shot noise is a Poisson noise, but it is usually approximated as a Gaussian noise
 Hallmark of shot noise is dependence on q, the electron charge
Constant Input Optical Power Detector Shot Noise
Optically induced current + random electron fluctuations
σ2Shot = 2q(Ip + Id)Δf
Popt I
Pin Detector <Ip>
(BW = Δf)
I(t) = <Ip> + ishot(t)
2σshot
t t
Poisson,
no-modulation
Thermally induced current + random electron fluctuations
Dark Current (Id) Detector Shot Noise
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 7

8. Shot Noise with Data Modulation
 Consider how the picture changes when we have information modulated on the optical carrier
 Let m(t) be the information transmitted
 Then Prcvd (t) and λ(t) are functions of m(t)
 Assuming the photodetector filter impulse function can change in amplitude from time period to time
period, let Gj be a time varying parameter
N
i(t) = # G j hd (t ! " j )
j =1
Power Spectrum
t
!
is (t) = i(t) = G ' Prcvd (# )hd (t % # )d#
$ 2
I DC Total Shot Noise =
h" %& Modulation Area = 2qI DC B
t
2 ! 2 2
2qI DC
i (t) = var{i(t)} =
n G & Prcvd (# )hd (t $ # )d#
h" $%
f
Modulation Bandwidth
B
Detector Bandwidth
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 8

9. Ideal Direct Detection (1)
Ideal Amplifier = unity gain,
zero noise, equivalent load RL
Ei(t) i’(t) Hd(ω) = FT {hd(t)} AV=1
i(t) Vout(t)
Ideal
Detector
RL
# !q Ei (t) 2 &
i(t) = LPF % (
Ei (t) = 2Ps Z 0 cos(! s t + " ) % h" Z 0 (
$ ' Vout (t) = i(t)RL
# Ei (t) 2 & # !q 2Ps Z 0 &
= LPF % Cos 2 () s t + * ) ( !q
% ( $ h" Z 0 ' = idc RL = Ps RL
Pavg =% 2 ( = Ps h"
% Z0 ( # !q 1 &
= LPF % 2Ps [1 + cos 2() s t + * )](
%
$ (
' $ h" 2 '
!q
= idc = Ps
h"
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 9

10. Ideal Direct Detection (2)
 Electrical SNR is found using the ratio between the signal power (DC) generated in the load
resistor and the noise power (shot noise) generated in the load resistor
2
# !q &
Psignal (
Psignal isignal RL % h"
2
$ ' 1 !Psignal
SNRdd = = 2 = =
Pnoise inoise RL 2qh" Psignal B 2 h" B
 This equation shows the fundamental, quantum shot noise limit, where the SNR is limited
only by the shot noise itself -> Shot Noise Limited Direct (Incoherent) Detection
 SNR improves linearly with input signal strength
 We will discuss other noise contributions that exist that make it difficult to reach this limit
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 10

11. Ideal Coherent Detection (1)
 Consider the following ideal Heterodyne Coherent Receiver
 Heterodyne implies that a non-zero intermediate frequency (ωIF) is generated prior to data recovery
Elo(t) Ideal Amplifier = unity gain, zero
Local noise, equivalent load RL
Oscillator ε Plo+ (1-ε) Psignal
ε
Es(t)
i’(t) Hd(ω) = FT {hd(t)} AV=1
Ideal i(t) Vout(t)
Input Power
Detector
Combiner
RL
' !q 1 2*
i(t) = LPF ) # 2Plo Z 0 cos($ lot + % ) + 1 & # 2Prcvd Z 0 cos($ s t + % ) ,
Ei (t) = ! Elo (t) + 1 " ! Es (t) ( h" Z 0 +
1 1
= ! 2Plo Z 0 cos(# lot + $ ) using cos - cos . = cos(- & . ) + cos(- + . )
2 2
+ 1 " ! 2Prcvd Z 0 cos(# s t + $ ) ' !q *
i(t) = LPF )
( h"
{ ( }
Plo# + Prcvd (1 & # ) + 2 Plo Prcvd # (1 & # ) cos '($ s & $ lo ) t + % * ,
+
+
% Ei (t) 2 (
' * Since typically Prcvd = Plo
Pavg =' 2 * = Ps !q
Z0 I DC ; Plo#
' * h"
'
& *
) Assuming the intermmediate frequency ($ IF = $ s & $ lo ) falls within the LPF bandwidth
!q
i(t) = 2 Plo Prcvd # (1 & # ) cos [$ IF t + % ]
h"
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 11

12. Ideal Coherent Detection (2)
 Using the same approach as in direct detection to obtain the SNR
2
! i peak $
SNRhet =
Psignal
= 2
2
isignal RL
=
(irms )2 = # 2 &
" %
Pnoise inoise RL 2qI DC BRL 2qI DC BRL
2
! 'q $
2 Plo Prcvd ) (1 * ) )
# h( &
# 2 &
#
" &
% '(1 * ) )Prcvd 'Prcvd
= = ;
! 'q $ h( B h( B limit Plo +,, ) +0
2q # Plo) & BRL
" h( %
 Note that shot noise limited heterodyne coherent detection, in the limit where the local
oscillator is much stronger than the received signal,
 Is a factor of 2 (3dB) better than the shot noise limited incoherent detection
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 12

13. Ideal Coherent Detection (3)
 The other coherent approach is Homodyne Coherent Detection
 The intermediate frequency (ωIF) is driven to zero (ωIF=0) at phase is driven to φ=0 bringing the data
immediately to baseband
Automatic
Local Ideal Amplifier = unity gain, zero
Frequency/Phase
Oscillator noise, equivalent load RL
Elo(t) Control
ε Plo+ (1-ε) Psignal
ε
Es(t)
i’(t) Hd(ω) = FT {hd(t)} AV=1
Ideal i(t) Vout(t)
Input Power
Detector
Combiner
RL
' !q 1 2*
Ei (t) = ! Elo (t) + 1 " ! Es (t) i(t) = LPF ) # 2Plo Z 0 cos($ lot + % ) + 1 & # 2Prcvd Z 0 cos($ s t + % ) ,
( h" Z 0 +
= ! 2Plo Z 0 cos(# lot + $ )
+ 1 " ! 2Prcvd Z 0 cos(# s t + $ ) Since we are using an AFC/APC control to drive $ IF = 0
' !q *
% Ei (t) 2 ( i(t) = LPF )
( h"
{ }
Plo# + Prcvd (1 & # ) + 2 Plo Prcvd # (1 & # ) ,
+
' *
Pavg =' 2 * = Ps Since typically Prcvd = Plo
Z0
' * !q
' * I DC ; Plo#
& ) h"
!q
i(t) = 2 Plo Prcvd # (1 & # )
ECE228B, Prof. D. J. Blumenthal h" Lecture 2, Slide 13

14. Ideal Coherent Detection (4)
 Using the same approach as in direct detection to obtain the SNR
SNRhet =
Psignal
=
2
isignal RL
=
(irms )2
2
Pnoise inoise RL 2qI DC B
2
% !q (
' 2 Plo Prcvd # (1 $ # ) *
& h" ) ! 2(1 $ # )Prcvd !P
= = ; 2 rcvd
% !q ( h" B h" B limit Plo +,, # +0
2q ' Plo# * B
& h" )
 Note that shot noise limited homodyne coherent detection, in the limit where the local
oscillator is much stronger than the received signal,
 Is a factor of 2 (3dB) better than the shot noise limited heterodyne receiver and factor of 4 (6dB)
better than the shot noise limited incoherent detection
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 14

15. Photodetectors
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 15

16. Photoconductors (1)
➱ Photon absorption in semiconductor materials.
➱ Three main absorption mechanisms: Intrinsic (band-to-band), Free-Carrier Absorption and
Band-and-Impurity Absorption
➱ Intrinsic (band-to-band) is the dominant effect in most SC photoconductors
Intrinsic (band-to-band) Free-Carrier Absorption Band-and-Impurity Absorption
e-
e- Ephoton = hν
Ec h+ Ec e- Ec
Ephoton = hν
Ephoton = hν + Donor Level
- Acceptor Level
Ephoton = hν
h+ Ev Ev Ev
h+
•Incident photon Ephoton= hν= Ec - Ev
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 16

17. Photoconductors (2)
➱ For intrinsic absorption, photons can be absorbed if
hc 1.24
! ( µ m) > =
Ec " EV Eg (eV )
1240
! (nm) >
Eg (eV )
Material Bandgap (eV) Maximum λ (nm) Typical Operating
Range (nm)
Si 1.12 1110 500-900
Ge 0.67 1850 900-1300
GaAs 1.43 870 750-850
InxGa1-xAsyP1-y 0.38-2.25 550-3260 1000-1600
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 17

18. Photoconductors (3)
Ephoton = hν Semiconductor ➱ Define:
➱ Pi = incident optical power
➱ R(λ) power reflectivity from input
Pi medium to semiconductor
Pi(1-R) Pi(1-R)e-αx ➱ α(λ) = 1/e absorption length
➱ 1/ α(λ) = penetration depth
x
1/α
➱ Power absorbed by the semiconductor is
Pabs (x) = Pi (1 ! R)(1 ! e!" ( # )x )
= $(#, x)Pi
➱ defining the efficiency
number of photocarriers produced
!(", x) =
number of incident photons
= (1 # R)(1 # e#$ ( " )x )
0 % !(", x) % 1
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 18

19. Photoconductive Photodetectors (1)
 Photogenerated current will have time and wavelength dependence
!q
i photo (t) = GPrcvd (t) + idark
h" Pi
# carrier = mean free carrier lifetime
# transit = transit time between eletrical contacts
$# '
G = & carrier ) = photoconductive gain
% # transit (
idark = dark current
Metal
Metal
Semiconductor
 The transit time for electrons and holes can be different and in many SCs the
eletron mobility is greater than that of the hole
! e = µe E > µh E = ! h
+ iphoto
 The SC must remain charge neutral, for every electron generated, multiple holes
will get pulled in until the photogenerated electron reaches the other contact. The
carrier and transit times are limited by the slower carrier and the photoconductive Vbias
gain is given by the ratio of the transit times
L
! carrier = a
"h
L
! transit = a
"e
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 19

20. Photoconductive Photodetectors (2)
 The carrier velocity is a linear function of electric field strength up to a saturation
velocity (which is the same for both electrons and holes)
 Field strength of about 105 V/cm result in velocities in range of 6x106 to 107 cm/s
 Some materials have an electron drift velocity that peaks at 2x107 cm/s at 104 V/cm
 When photoconductive gain is desirable, detector is operated at low voltages
 Carrier lifetime also impacts the frequency response of the photoconductive
photodetector
Prcvd (! )
i photo (! ) = "G
2
#!&
1+ % (
$ !c '
1
!c = = cutoff frequency
) carrier
ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 20