ieg 4030 optical communications part iii. photodiode and receiver

Prof. Lian K Chen Part 3 - Photodioe and Receiver 1

IEG 4030 Optical Communications

Part III. Photodiode and Receiver

Professor Lian K. ChenDepartment of Information EngineeringThe Chinese University of Hong Kong

[email protected]


Outline• Photo-diode

– pn, p-i-n, APD• Quantum Efficiency and Responsivity• Noises in Photodiode

– Shot Noise, Thermal Noise, Gain Noise• Receiver Performance

– Signal-to-Noise Ratio– Bit-Error-Rate

• Receiver sensitivity and Noise-equivalent power (NEP)• Optical Receiver

– high impedance, low impedance, and transimpedance receiver front-end

Ref: [Keiser Ch6 and Ch7.1, 7.2, 7.4, 7.5 ][Agrawal Ch4]


Performance requirement• high sensitivity (at 1.3 and 1.55 μm for telecommunication) • high conversion efficiency (P I) • fast response (multi-GHz)• high fidelity (linearity, dynamic range)• low noise (low dark current, leakage current)• temperature stability • cost


• p-n diode • P-I-N diode• avalanche photo-diode (APD)• schottky-barrier diode (Metal-Semiconductor-Metal) • photo conductor• photo transistor• photonmultiplier

used for optical communication

Types of common Photo-detectors


• P-N junction operates in reversed-bias voltage• When an incident photon has energy > bandgap

energy, an electron-hole pair (photocarrier) can be generated.

• The carriers are separated by the electric field in the depletion region and collect by the reverse-bias junction.

photo-current Iphoto is generated.

P-N DiodeV+

Ec

Ev

hνEg

Depletion regionn p

E

barrier potential

--------

--------

----++++

++++

++++

++++

++++

+ -


Region (1) : depletion region, electrons & holes swept by E (electric field)-- drift current (fast)

Region (2) : hole and electrons diffuse randomly towards depletion region -- diffusion current (slow)

Region (3) : far away from depletion region (useless)

Diode response is fastest if electron/hole pairs generate mainly in depletion region.

(3) (2) (1) (2) (3)

P N

P-N Diode


Transit time• Usually receivers are operated in strong reverse-biased region, thus

– create strong electric field E in the depletion region increase drift velocity v.

– increase the width, w, of depletion region increase the photon absorption.

• Longer width smaller junction capacitance:C= εA/w

ε : the permittivity of the semiconductor A: layer area

• Transit time tr=w/v where v is the drift velocity, a function of E.

trade-off : E increases v↑ and w ↑, then tr ↑↓ ?


Response Time

• Response time of photodiode is determined bycarrier transit time (fast)carrier diffusion time (slow)RC time constantAvalanche build up time (only for APD)

• Bandwidth (due to transit time):

• Carrier drift velocity is a function of1) materials (GaAs, InGaAsP,......)2) Electric field E

• Velocity value saturates at high E (due to collision with host lattice).

0.440.44 1 or if RC constant dominant2

sat

r

VBt w πRC

⎛ ⎞≈ = =⎜ ⎟⎝ ⎠


Cutoff wavelengthcutoff wavelength : λc

When the incident photon wavelength is longer than a certain wavelength λc, the photon energy is < Eg. Photon cannot be absorbed.

λc : Si:1.06 μm, GaAs 0.87 μm, and Ge:1.6 μm.

1.24 or (in )(in )c c

g g

hc mE E eV

λ λ μ= =Ec

Ev

hν

Eg

Note: Two-photon or three-photon absorption are possible, but with very small probability.(e.g. check out the three-photon lasing at http://optics.org/article/news/8/2/14 )


The photo-currentThe current generated at photodiode is given by

where

(1 )(1 )s

photo dark

wphoto inc e

I I IqI P R e

hα

ν−

= +

= − −

Iphoto:photo-current Idark:dark currentPinc:incident optical power Re : Reflectionαs: absorption coefficient. w : absorption depthq : electron charge (=1.6 x 10-19 C)h :Planck’s constant (=6.625 x 10-34 J⋅s)ν : optical frequency


The absorption coefficient

• α ∼104 /cm• 1.55 μm - In 0.53 Ga 0.47 As(III − V), Ge(IV)• 1.3 μm) - In 0.7 Ga 0.3 As 0.64 P 0.36 (III-V) • 0.85 μm - Si or GaAs

• Sharp cut-off wavelength for direct bandgap material

Q: Can Si be used for 1550nm optical signal detection?


Quantum Efficiency and Responsivity

Photo-current:

Note: Ro is wavelength-dependent. Below λc, Ro increases as λ increases.

and Responsivity:

( )( )ν

α

hqeRPI w

erecps−−−= 11

Define Quantum efficiency :

Thus,

Example: A InGaAs detector has an energy bandgap=0.73eV and η=60% for 1.3 μm optical signal. The responsivity is

Ro=0.6(1.609×10-19) λ /(6.6256×10-34 ⋅ 3×108)= 0.63 (A/W). The cutoff wavelength=1.24/Eg=1.70 μm.

Unit: A/W

( )( )we

seR αη −−−= 11

νηh

qRo =

orecp RPI =

( )νη

hPqI

rec

p=


• A P-I-N diode is a P-N junction with an intrinsic (undoped or lightly-doped) layer sandwiched between the P-N layers

increase the width of the depletion region

P-I-N Photodiode

P NI

hν+ -• Advantages of P-I-N:

1. Increasing the width of the depletion region, w:- most carriers can be transported by drift

process- increases the photon capturing area.

2. w ↑ the junction capacitance ↓RC constant ↓ (bandwidth ↑ )

However, transit time increases as w increases.

Common practice: ss

wαα21

<<


Characteristics of P-I-N Photodiodes

5-66-1050-100VVbBias voltage

1-50.5-30.3-0.6GHzBBandwidth0.05-0.50.1-0.50.5-1nsTrRise time

1-2050-5001-10nAIdDark current

60-7050-5575-90%ηQuantum efficiency

0.6-0.90.5-0.70.4-0.6A/WRoResponsivity

1.0-1.70.8-1.80.4-1.1μmλWavelength

InGaAsGeSiUnitSymbolParameter


APD and pin photodiode

pp+

n

hνSiO2

guard ring(n)

Depletion region

Metal contact

Avalanche photodiode

n

n+

p+

Depletion region

SiO2

Metal contact

pn photodiode


Avalanche Photodiode (APD)• APD is similar to P-I-N diode; except that its reverse-biased

voltage is high enough (≥ 100Volt) to create photo-current gain.• The gain process is due to impact ionization of carriers with

lattice atoms.

Multiplication n+

p

π

p+

Electric field

Multiplication region

Depletion region

Minimum field required for impact ionization

n+ region

Photon carrier

p+ region

hν

• Separate absorption and multiplication (SAM) structure → localize the multiplication process in a narrow region and separate from absorption region → more efficient


Impact Ionization of APDImpact ionization• a single primary electron (hole), generated

through absorption of a photon, creates many secondary electrons and holes

impact ionization coefficients: αe (electrons), αh (holes)

• ionization probability per unit length (cm-1)αe

-1 : average distance between ionization for electrons.αh

-1 : average distance between ionization for holes.

• When E (electric field) increases and temperature decreases, αe and αhincrease.

• Ionization ratio : kA=αh/αe (typical values are 0.01 to 100)

• Multiplication factor: M(kA) (if kA =1, M ∞ avalanche breakdown)

(1) if kA<< 1, most of the ionization is achieved by electrons.(2) if kA>> 1, most of the ionization is achieved by holes.

n+ region

Photon carrier

p+ region

hν

n+ region

Photon carrier

p+ region

hν


Pros and cons of APD • Pros:

– provides gain on photo-current generation

• Cons:– fabrication difficulties (complex structure, high cost) – multiplication process (random) gives additional noise – high bias voltages (100-400 volts) – temperature dependence of device (can be compensated by

feedback control)


Characteristics of Avalanche Photodiode

20-3020-40200-250VVbBias voltage

1-30.4-70.2-1.0GHzBBandwidth

0.1-0.50.5-0.80.1-2nsTrRise time

1-550-5000.1-1nAIdDark current

0.5-0.70.7-1.00.02-0.05-kAkA-factor

10-4050-200100-500-MAPD gain

5-203-3080-130A/WRoResponsivity

1.0-1.70.8-1.80.4-1.1μmλWavelength

InGaAsGeSiUnitSymbolParameter


Noise in Photodetectors


Noise in Photodetectors – shot noise

• Photon arrivals are discrete and random in nature → Poisson distributed( )!

exp)(n

nnnpn −

=where n

• For a certain quantum efficiency η at the photodetector, the mean number of photoelectron generated ( ) ism nm η=

• Mean photocurrent generated is ;mqip ⎟⎠⎞

⎜⎝⎛=

τVariance: 2

22

miq στ

σ ⎟⎠⎞

⎜⎝⎛=

Shot noise Biq pi 22 =σ

In the presence of dark current iD of the PN junction ⇒ ( )Biiq Dpi += 22σ

Shot Noise

is the mean value of n.

Since both n and m are Poisson distributed, mm =2σ

Thus, Biqiqmqqmqppi 2

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

ττττσ since

τ21

=B

(B: bandwidth)

Probability of receiving n photons in time interval τ is

q: electron charge


Noise in Photodetectors – thermal noiseThermal Noise• also called Johnson noise or Nyquist noise• at a certain temperature, electrons move randomly in any conductor• random thermal motion of electrons in a resistor ⇒ fluctuating current

even with no applied voltage bias, thermal noise still exists

• Thermal noiseeq

BT R

TBk42 =σ

where kB is the Boltzmann constant (1.38×10-23 J/K), T is the operating temperature in Kelvin scale, Req is the equivalent receiver resistance.

• In the presence of FET preamplifier,eq

tBT R

BTFk42 =σ

where Ft is the amplifier noise figure (Ft represents the factor by which thermal noise is enhanced by various resistors used in the preamplifier)


Noise in Photodetectors – APD Gain noise

APD Gain M1 2 5 10 20 50 100 200 500

Exc

ess

Noi

se F

acto

r FA

1

2

5

10

20

50

100

kA=10.5

0.20.1

0.050.02

0

0.0050.01

• the impact ionization process is random → generation of multiplied photoelectrons is also random → additionally contributed to shot noise

• multiplication factor, M, is also a random variable

• Shot noise in APD:

( ) BFMiiq ADpi

22 2 +=σ

where FA is the excess noise factor of APD with

)/12)(1( MkMkF AAA −−+=

assume kA << 1

• If kA=0, FA is at most 2 and nearly independent of APD gain M at high M e.g. For Si APD with kA=~0.1, M=100 FA=11.8

mean detected photocurrent increases 100 times.noise increases by a factor of 11.8.


Signal-to-Noise Ratio (SNR)

( )( )

( ) eqtBLADreco

reco

eqtBLADp

p

RTBFkBqiBMFiPRq

PRM

RTBFkBqiBMFiiq

iMSNR

/422/4222

2

2

22

+++=

+++=

where ip is the mean generated photocurrent, iD is the dark current,iL is the surface dark/leakage current,M is the mean APD gain,

FA is the excess noise factor of the APD,Ro is the responsivity,

Prec is the mean received optical power,B is the receiver bandwidth,

Ft is the noise figure of the FET preamplifier,Req is the equivalent receiver circuit resistance,

T is the operating temperature (in Kelvin scale), kB is the Boltzmann constant (1.38×10-23 J/K),

q is the electric charge (1.609×10-19 C)

• SNR is an important parameter to evaluate the performance of a photodetector

Thermal noiseShot/Gain noise

Signal photocurrent

*For P-I-N photodiode, =1, FA=1*If no FET preamplifier is used, Ft=1

M


Signal-to-Noise Ratio (SNR)Example: For InGaAs P-I-N diode with the following parameters:

incident power 300nW @1300 nm, ID=4 nA, η=0.65, RL=1000 Ω and negligible leakage current. If the receiver has bandwidth 20MHz, the signal and noises are

Ip=RoP=(ηq/hν)P=0.205 μAσs

2=2 q Ip M2 B FA =1.32×10-18 A2

σD2 =2 q ID M2 B FA =2.57×10-20 A2

σth2= 4 kBTB/RL =3.31×10-16 A2 at T=27oC

Example: For a P-I-N photodiode with a load resistance of 1 kΩ without FET preamplifier. The quantum efficiency at 1550 nm is 0.8 and the receiver bandwidth is 500-MHz. The operating temperature is 27oC.

( )eqBreco

reco

RTBkBPqRPR

SNR/42

2

+= ⇒ SNR = 118.47 =20.74 dB

hcqRo

λη= =1.0Responsivity

If the detected power is -30dBm, i.e. Prec= 1 μW, and with B=500MHz, Req=1 kΩ, T=300K, and Ro=1.0

Use


Optimal APD Gain

• Increase in APD gain does not guarantee better SNR performance

• Recall:( )

( ) eqtBADreco

reco

RTBFkBMFiPRq

PRMSNR

/422

2

++=

⇒ ( ) ( )Drecoeq

tBoptAoptA iPRqR

TFkMkMk

+=−+

41

3

Note that recP ↑ ⇒ Mopt ↓

• There exists an optimum APD gain (Mopt) to achieve the maximum SNR

and differentiate SNR w. r. t. M

( ) 0=dMSNRd

Substitute )/12)(1( MkMkF AAA −−+=


Optimal APD GainFor example, if Ro=1, iD=2 nA, kA=0.8, B=500-MHz, T=300K, Ft=2, Req=1kΩ.

APD Gain, M20 40 60 80 100

SN

R (d

B)

2

4

6

8

10

12

14

16

18

= -40dBmPrec

At low , the optimum APD gain, Mopt >1 ⇒ APD can improve the SNR ⇒ use APD photodetector

recP

At high , the optimum APD gain, Mopt =1 ⇒ APD even worsen the SNR ⇒ use P-I-N photodetector

recP

APD Gain, M20 40 60 80 100

45

50

55

60

65

70

Prec =0dBm

SN

R (d

B)


Bit-Error-Rate (BER)

(1) (0 |1) (0) (1| 0)Pe P P P P= +i iProbability of detection error:

V

0


Decision and BER Gaussian approximation :

Assume the output is a Gaussian random variable with mean V for "1" bit and 0 for "0" bit.

If P(1)=P(0)=0.5 and assume σ1=σ0=σ, the BER is given by

where

Note that Pe only depends on V/σ, which is related to the SNR as (S/N)dB=20 log (V/σ) .

1= 1- erf 2 2 2

VPeσ

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

2

0

2erf( )x yx e dy

π−= ∫


Decision and BER (contd.)• To have BER=10-9 v/σ=12.

• More generally, if "0" bit amplitude is not 0,

where Q is defined as

• von, voff, and vth are the mean amplitude of "1" bit, "0" bit, and the threshold, respectively.

• Q≈ 6 for BER=10-9 or ≈7 for BER=10-12

• (Need to find the optimum threshold value)

1= 1-erf 2 2

QPe⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

th off on th

off on

v v v vQσ σ− −

= =


Receiver sensitivity and NEPReceiver sensitivity :

the required minimum average (One and Zero Bit) incident optical power or energy to achieve a desired BER (typical value=10-9) at a specific bit-rate.

Typical value (@1550nm) 2.5 Gbit/s : ~ -24dBm for for PIN and -32dBm for APD receivers.10 Gbit/s : ~ -21dBm for PIN and -27dBm for APD


Noise Equivalent Power NEPNoise Equivalent Power (NEP):

the optical signal power required to generate a photocurrent that is equal to the total noise at the detector for given wavelength and within a bandwidth of 1 Hz.

Ex. A Si pin photodiode has an NEP of 1x10-13 WHz-1/2. What is the optical power needed for an SNR=1 if the the bandwidth is operating at 1 GHz?

1/ 20 [2 ( ) ] ----- assume shot noise dominantp d eR P q I I B= +

1/ 2 -1/21/ 2

01Hz

1NEP= [2 ( )] (unit: W Hz )e

p de B

P q I IB R

=

= +

1/ 2 -13 -1/2 9 1/2=NEP =(10 W Hz )(10 Hz) 3.16 nWeP B⋅ =


Typical optical communication link

Components FunctionsDetectors (Photodiode PD) Convert hν to e-

Preamplifier 1st amplification brings μV to mV(incoming signal ~ -30 dBm, 1A/W)

Postamplifier 2nd amplification brings mV to a usable range of a few VAutomatic Gain Control(AGC)

Fixes the gain / dynamic range

Timing and Data Recovery Retrieval of data and timing (for digital)

Laser DriverLaser Driver

Fiber

Timing /Data Recovery

PreAmp.

Post Amp.

AGC

PDLD

Data InData Out

Q: Why two Amp and what is the function of timing/data recovery?


Receiver Front-end (Preamplifier)*

• Three types of front-end:– low impedance front-end (LZ) – high impedance front-end (HZ)– transimpedance front-end (TZ)

• Front end of a receiver consists of a photodiode followed by a preamplifier.

• Design of the front-end requires trade-off between speed and sensitivity.

(1). Low impedance front-end (LZ)-low impedance bias resistor, e.g. 50 Ω, into a low impedance amplifier-simple but with limited sensitivity (large thermal noise)

CTRLIp



(2). High impedance front-end (HZ) – noise is reduced by using high bias resistor and amplifier with high

input impedance improve the receiver sensitivity. – smaller bandwidth (large RC constant)– need equalizer to compensate the high frequency cut-off due to large

RC constant. (integration-and-differentiation).– smaller dynamic range (easier to saturate the receiver).– the need of equalizer implies more adjustment to optimize (required

special adjustment for each unit)

For examples: Si bipolar preamp or GaAs MESFET are used for high frequency (>~ GHz) and Si MOSFET or JFET preamp are used for low frequency (<50MHz).

CTRLIp



(3). Transimpedance front-end (TZ) (utilizing a negative feedback resistor Rf)– provide improved dynamic range over HZ.– bandwidth is improved by G times over the high impedance front-end

for the same RL and CT.– however, gain at the low frequency is also reduced by G → less likely

to have saturation.– no or little equalization is needed.

2 f T

GBR Cπ

≤

f

tBT R

TBFk42 =σCTRL

Rf

-GIp


Analog receiverFor digital communication performance index : BERFor analog communication performance index : SNR

Amplitude Modulation :

where P0 is the received DC optical power and m is the optical modulation index. s(t) is the analog modulation signal.

For AM modulation, the DC portion does not carry information.

0[1 ( )]P P m s t= +

Po

Ps

IDC

IthI (mA)

P (mW)

IS


Analog ReceiversExample: s(t)=cos(ωt), m=Ps/Po.

The modulation index in electricaldomain is given by

me=Is/(IDC-Ith)

If the P-I curve is a straight line (linear),then m=me

For analog AM modulation, the SNR is

Po

Ps

IDC

IthI (mA)

P (mW)

IS

( )( ) eqtBLADp

p

RTBFkBqiBMFiiq

iMmSNR

/422

21

2

2

+++=

[ ])(1)( tmsPtP o +=


Optical Receiver Products• Bookham:

http://www.bookham.com/common/receiver_lines.cfm2.5G APD Rx:http://www.bookham.com/datasheets/receivers/ATM2400C.cfm (file)

• JDSU: http://www.jdsu.com/products/optical-communications/products/detectors-receivers.html

Photodiode, PIN/TIA, 1310/1550 nm, 2.5 Gb/s, ROSAhttp://www.jdsu.com/product-literature/pl-slr-00-l23-cx_ds_cc_ae.pdf

ieg 4030 optical communications part iii. photodiode and receiver

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