Optical Fibres and Telecommunications
Lecture 10 – Detection and Noise
Optical Fibres and Telecommunications - Introduction
Introduction
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Where are we?
Review of PiN Sturctures.
Avalanche Photodiodes.
Time behaviour of photodiodes.
Noise
Optical Fibres and Telecommunications - Introduction
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Last time
• Real laser diodes
• External modulation
• Detectors
– Photodiodes
– PiN Structures
• Dark current
• Biasing photodiodes
Optical Fibres and Telecommunications - Introduction
P-i-N Devices
Front Illuminated
p-type
i-layer
n-type
Back Illuminated
p-type
i-layer
n-type
n+-type
• In practice most detectors rely on P-iN structure.
• A thick layer of undoped (intrinsic)
material sandwiched between p and n
type layers.
• Thick absorption layer means efficient
device (most of the incident photons
absorbed.)
• No free charge carriers in i-layer →
large electric field.
• Thermally generated carriers swept
away. Reduced dark current.
• Lower reverse bias needed.
• Wide i-layer decreases bandwidth.
Optical Fibres and Telecommunications - Introduction
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Photodiode Bandwidth Considerations
• Bandwidth:
‘The maximum frequency or bit rate that a photodiode can
detect without making essential errors.’
• Sometimes use bit-rate (Bits/sec) for digital systems.
• Limited by two time constants τtr, the transit time and τRC, the
capacitance time constant of the diode.
• Think about a pn photodiode. After creation by a photon, charge
carriers have to travel across the depletion region bfore being picked
up. This takes τtr.
• τtr=w/vsat
• w = width of depletion zone and vsat is the saturation velocity (~105ms-1)
• In P-i-N devices w is large → τtr is long.
• For a typical device τtr ~ 100ps.
Optical Fibres and Telecommunications - Introduction
Equivalent Circuit For a Photodiode
RS
IP
Cin
Rj
RL
Rj and Rs are the junction and series resistance of the photodiode.
These are internal to the device.
Optical Fibres and Telecommunications - Introduction
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τRC for a photodiode.
• Photodiode acts as two charged plates with a space (depletion region)
between.
• This is a classical capacitor.
• Inherent capacitance – Cin= εA/w.
• ε= permitivity, A = active area, w = width of depletion region
• Rj is the resistance of the depletion region – very high. (1-10’s MΩ)
• Rs is the series resistance of the p-type, n-type and contacts. Can be kept
low.
• Internal resistance is the parallel combination of Rj and Rs ≈ Rs
τRC=(Rs+RL)Cin ≈ RLCin (Typical values RL=50Ω , Cin=1pF → tRC=50ps)
• BW=1/[2π(τRC+τtr)]
Optical Fibres and Telecommunications - Introduction
Example of Photodiode Bandwidth
• Consider a P-i-N Structure with a wide i-layer:
– τtr~w, τRC~1/w → τtr>>τRC
– BW=1/(2πτtr) = 1/[2π(w/vsat)]
• For Si photodiode, w=40µm, vsat=105m/s
– BW = 0.398 Gbit/s
• For GaAs photodiode, w=4µm, vsat=105m/s
– BW=3.98 Gbit/s
Optical Fibres and Telecommunications - Introduction
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Avalanche Photodiodes
i
p
n+
E-Field
p+
Distance
• Incoming photon creates carriers in ilayer.
• On reaching pn+ junction, large electric
field accelerates charge carriers.
• Impact ionisation takes place with
neutral atoms.
• Further carriers produced.
• Avalanche process.
• Gives much greater sensitivity at the
cost of higher power requirements.
• High reverse bias may be required.
• Changing voltage can vary the gain of
the diode.
• Higher gains produce a lower
bandwidth: Gain x BW = K.
• K is the gain bandwidth constant.
Optical Fibres and Telecommunications - Introduction
Other Detector Types
Metal-semiconductor-metal (MSM)
Phototransistors
Very fast
Very Slow
Low responsivity, small active area
Optical Fibres and Telecommunications - Introduction
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Detectors - Comparison
Understanding Fiber Optics p. 257
Optical Fibres and Telecommunications - Introduction
Noise
• In an ideal world, detectors would only respond to incident
photons.
• This is not the case (e.g. Dark Current.)
• Other sources of noise exist.
• The worse the noise, the lower the detector sensitivity.
• Limit of a photodiode’s sensitivity is the signal to noise ratio
(SNR).
• Increasing noise also increases the Bit Error Rate (BER.)
• In a commercial system we want a BER better than 10-9.
• What are the sources of noise ?
Optical Fibres and Telecommunications - Introduction
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Equivalent Circuit
RS
IP
IS
Shot Noise
It
I1/f
ID
Cin
Rj
RL
1/f Noise
Thermal Noise
Dark Current
Optical Fibres and Telecommunications - Introduction
Shot Noise
• Current measured is the average current.
• In practice photons arrive at random intervals.
– Hence number of electrons produced is random.
– Also number of electrons producing photocurrent is random – some
undergo absorptions and recombinations.
• The current is given by the number of electrons arriving in a given time
interval.
• Probability of receiving n electrons is governed by Poisson statistics.
• Problem at low currents.
• is=[2e(Ip*)BWpd]0.5
– e = charge of electron, Ip* = average photocurrent, BWPD=Photodiode
Bandwidth, is=Root mean square shot noise current.
• Note that shot noise is independent of frequency (white noise.)
Optical Fibres and Telecommunications - Introduction
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Thermal Noise
• Electrons move in response to temperature (Brownian
motion).
• Deviation from the average value due to thermal
considerations is called thermal or Johnson noise.
• Occurs across the bandwidth of the detector, so again this
is white noise.
• iT=[(4kBT/RL)BWPD]0.5
– kB id Boltzmann’s Constant, T=Absolute Temperature.
RMS Value
Optical Fibres and Telecommunications - Introduction
1/f Noise and Dark Current Noise
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Origin of 1/f noise is not understood.
Disappears when working at high (>100Hz) bit rates.
i1/f~[BWPD]-0.5
Can consider dark current as another shot noise source.
RMS value of dark current noise:
– id=[2eID*BWPD]0.5
• ID* is the average value of the dark current.
• Total noise is given by summing the noise
contributions in quadradture.
– inoise=[is2+it2+id2+i1/f2]0.5
Optical Fibres and Telecommunications - Introduction
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Examples
Input power = 0.1µW
λ=1550nm
R=1µA/µW
BW=2.5GHz
RL=50Ω
Dark Current = 3nA
T=300K
Dark noise:
Shot noise:
=[2e(Ip*)BWpd]0.5
=[2eID*BWPD]0.5
=8.9nA
=1.5nA
Thermal noise:
Thermal noise (RL=50kΩ):
=[(4kBT/RL)BWPD]0.5
=[(4kBT/RL)BWPD]0.5
=910nA
=28.8nA
Noise often limited by thermal noise!
Increasing load resistance
reduces thermal noise!
Optical Fibres and Telecommunications - Introduction
Real Photodiodes
Optical Fibres and Telecommunications - Introduction
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Summary
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PiN Photodiodes
Avalanche Photodiodes
Other detectors
Time response of photodiodes
Sources of noise
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Shot noise
Thermal Noise
Dark Noise
1/f noise
• Summing noise
• Real photodiodes
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