•Lecture 9
–Photodetectors
ECE 4606 Undergraduate Optics Lab
Photodetectors
Outline
•
•
•
•
Photodiode physics
Responsivity
Biasing
Noise
– Shot noise
– Dark current
– Thermal
– Figures of merit
Robert R. McLeod, University of Colorado
Pedrotti3, Chapter 17
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•Lecture 9
–Photodiode physics
ECE 4606 Undergraduate Optics Lab
Diodes
A reminder of the basic physics
Anode
+ v
−
Cathode
Conventions
Long lead
p-doped
Short lead
i
-
-
+
+
+
+
+
+
+
+
+
+
+
+
Doping creates free holes
on the anode side and free
electrons on the cathode
side.
n-doped
E
Q
x
Diffusion of charge across
junction establishes the
insulating depletion layer
x
The separation of charge
establishes a field which
counteracts diffusion.
x
The electric field causes
the anode to be at a lower
potential than the cathode.
E
V
Forward bias
opposes the built-in field, shrinking
the insulating depletion region,
increasing current flow.
Robert R. McLeod, University of Colorado
Reverse bias
adds to the built-in field, expanding
the insulating depletion region,
resulting in very low current flow.
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•Lecture 9
–Photodiode physics
ECE 4606 Undergraduate Optics Lab
Diffusion
pn:
+
Depletion
Diffusion
pn & pin Photodiodes
E
e- & h+ drift
under E field
e- & h+ may
diffuse into
depletion region
n
e- & h+ recombine and
do not contribute to
current
p
Diffusion
Diffusion
pin:
+
Depletion
p
i
n
E
pn: Response time faster than photoconductor (due to E) but limited by diffusion which
may be as large as carrier recombination lifetime.
pin: Increased depletion layer width gives:
• larger capture area
• decreased capacitance (faster response)
• dominated by diffusion, not drift
Robert R. McLeod, University of Colorado
113
•Lecture 9
–Responsivity
ECE 4606 Undergraduate Optics Lab
Responsivity
Basic input/output relation
We primarily use photodiodes as current sources and thus define the
response as the electrical current generated over the input optical power.
Photocurrent flows from the cathode to the anode, swept out of the
depletion region by the space-charge field.
iP
R≡
P
P [W]
A
 W 
iP [A]
Both quantities can be found by counting of quanta
]e[
]Φ[
P = hν [
ip = η
[
electrons
photon
Coulombs
electron
Joules
photon
photons
second
]
]Φ[photons
second
]
Yielding
R =η
e
eλ
λ[µm]
=η
≈η
hν
hc
1.24
The quantum efficiency, η, goes
to zero when the photon energy
is less than the bandgap of the
semiconductor.
Robert R. McLeod, University of Colorado
114
•Lecture 9
–Biasing
ECE 4606 Undergraduate Optics Lab
Bias of photodiodes
3 modes
 ev K BT

i = irs  e
− 1 − i P


P
i P ≡ ηe
hν
Open circuit
•aka “Photovoltaic”
•Solar cells
•Low dark current
•Slow response
P
Short circuit
P
Reversed biased
• Drift field incr speed
• Lower capacitance “ “
• Larger sensitive area
> R gives > sensitivity,
< range, < BW
P
Robert R. McLeod, University of Colorado
115
•Lecture 9
–Photodetection noise
ECE 4606 Undergraduate Optics Lab
Shot noise
Photons are discrete
p(n), Probability of receiving n photons
For uncorrelated photon arrival times, the probability of detecting n photons in a time
period T for which the average photon arrival rate is n is Poisson’s distribution:
0.4
n ne −n
p(n ) =
n!
1
0.3
0.2
Curves are different n
Bars show ± 1 σ
5
10
0.1
0
0
5
10
15
n, Number of photons actually received
20
∞
σn ≡
2
(
)
n
−
n
p (n ) =
∑
n
n =0
SNROptical ≡
n
σn
=
n
= n
n
2
SNRElectrical ≡ SNROptical
=n
SNROptical = 1 or n = 1
Robert R. McLeod, University of Colorado
Standard deviation (aka “RMS”) of
photon count, n
Optical power SNR is average photon
count over standard deviation
Because PElectrical = R i2 ∼ n2
Shot noise limit when signal = noise is
average of 1 received photon per period,
(assuming η = 1).
116
•Lecture 9
–Photodetection noise
ECE 4606 Undergraduate Optics Lab
Dark current noise
Thermal excitation of photocarriers
Typical dark current for Si photodiode
id vs bias at 25 oC
id vs temperature at VR = 10 V
Sharp PD412PI
• Assume that average dark current is calibrated and subtracted so no signal error.
• Dark current then adds shot noise (only) due to greater number of carriers in circuit.
• Since shot noise variance is mean of photocarriers, variances of two sources add.
Signal = photoelectron count squared
SNRElectrical =
Variance of photoelectron count
(ηn )2
ηn + md
=
ηn
md
1+
ηn
Variance of dark current
Result is new excess noise factor due to dark current given by ratio of darkcurrent electrons to photoelectrons.
Robert R. McLeod, University of Colorado
117
•Lecture 9
–Photodetection noise
ECE 4606 Undergraduate Optics Lab
Circuit noise
aka Johnson,Nyquist + Amp
Thermal motion of electronics in load resistor R give rise to zero mean noise.
σ i2 = 4k BTe B / R
Contribution of amplifier included via effective Te
The amplifier contribution can also be written as “noise figure” FT
σ i2 = 4k B F T0 B / R
where
Te
FT ≡ 1 +
290 o K
290 oK is standard chosen for definiteness
Including thermal noise, the total SNR would be:
SNR ≡
(signal in photoelectrons)2
=
∑ noise variance in electrons
(η n )2
η n + md + 4k BTe B / (e 2 R )
Thermal noise occurs in all circuits. The RMS (standard deviation) voltage is
v RMS = 4k BTe R B
Proportional to sqrt of bandwidth
Numerically, a 50Ω resistor at room temperature generates 1 nV RMS noise
in a 1 Hz bandwidth or 1 µV in a MHz bandwidth.
kB
Boltzman’s constant = 1.380622 10-23
Robert R. McLeod, University of Colorado
[J/ o K]
118
•Lecture 9
–Photodetection noise
ECE 4606 Undergraduate Optics Lab
Detector figures-of-merit
Noise equivalent power & specific detectivity
Noise equivalent power is incident optical signal required to generate
a photocurrent equal to the RMS noise current:
σ
i
NEP ≡ RMS − Noise = i =
R
R
∑σ
2
[W]
R
Variances add
Since both shot noise and Johnson noise variances are proportional to
bandwidth, some sources define NEP/Sqrt[B] :
NEP B
σi
i
≡ RMS − Noise =
=
R B
R B
∑σ
R
2
/B
 W 
 Hz 


Since NEP is proportional to the square root of BW (B) and area (A), it
is common to define a figure-of-merit, the specific detectivity:
D∗ ≡
AB
NEP
Robert R. McLeod, University of Colorado
119