Optoelectronics Lecture notes

1. Chapter 6:
Photodetectors

2. Principle of the pn-junction photodiode
• Photodetectors convert a light signal to an
electrical signal such as voltage and current
• In photodetectors such as photoconductors
and photodiodes
– This conversion is achieved by the creation of free
Electron-Hole-Pairs (EHPs) by the absorption of
photons

3. pn-junction photodiode
• In some devices such as pyroelectric detectors
– Energy conversion involves the generation heat
which increases the temperature of the device
which changes its polarization and hence its relative
permittivity
• pn-junction base photodiode type devices
– Small, high speed and good sensitivity
– Use in various optoelectronics applications, optical
communications

4. pn-junction photodiode
• Fig.1 shows a typical pn-junction photodiode that has a
p+n type of junction
– Acceptor concentration Na in the p-side is much greater than
donor concentration Nd in the n-side.
– The illuminated side has a window (annular electrode) to
allow photons to enter
– There is an antireflection coating (Si3N4) to reduce light
reflection
• Fig.1 shows the net space charge distribution in the
depletion region
– Exposed negatively charged acceptors in the p+-side and
exposed positively charged donors in the n-side

5. (a) A schematic diagram of a reverse biased pn junction
photodiode. (b) Net space charge across the diode in the
depletion region. Nd and Na are the donor and acceptor
concentrations in the p and n sides. (c). The field in the
depletion region.
p
+
SiO2
Electrode
rnet
–eNa
eNd
x
x
E(x)
R
Emax
e–h+
Iph
hu > Eg
W
E
n
Depletion region
(a)
(b)
(c)
Antireflection
coating
Vr
Electrode
Vout
Fig.1: pn-junction
photodiode

6. The photodiode is reverse biased.
• The applied reverse bias Vr drops across the highly
resistive depletion layer width W
• Voltage across W is Vo+Vr,
where Vo is built in voltage
• The field is the integration of the net space charge
density rnet across W
– The field only exists in the depletion region and varies across
the depletion region
• The regions outside the depletion layer are the neutral
regions in which there are majority carriers

7. Photogeneration
• When a photon with an energy greater than Eg
is incident, the photon is absorbed to
photogenerate a free EHP
– The photogeneration takes place in the depletion
layer
• The field, E, in the depletion layer then
separates the EHP and drift them in opposite
directions until they reach the neutral region

8. Photocurrent
• Drifting carriers generate a current called
photocurrent Iph in the external circuit
– Provide electrical signal
– When hole reaches neutral p+ region, it recombines with a
electron from negative electrode
– The electron reaches the neutral n-side, an electron leaves
the n-side into the positive electrode
• Iph depends on
– The number of EHPs photogenerated
– The drift velocities of the carriers

9. Photocurrent in external circuit
• Iph in the external circuit is due to the flow of
electrons only
– even though there are both electrons and holes
drifting within the device
• Suppose there are N number of EHP
photogenerated, total charge flowing in the
circuit Q is
– due to the total number of photogenerated
electrons (eN)
– Not due to both electrons and holes (2eN)

10. Quantum Efficiency (QE)
• Not all the incident photons are absorbed to create free
EHPs that can be collected and give rise to a photocurrent
• The efficiency of the conversion process of received
photons to free EHPs is measured by the quantum efficiency
h (QE) of the detector defined as
.
u
h
h
hP
eI
o
ph
/
/
photonsincidentofNumber
collectedandgeneratedEHPfreeofNumber



11. Quantum Efficiency (QE)
• The measured Iph in the external circuit is due to the
flow of electrons per second to the terminals of the
photodiode. Number of electrons per second is
Iph/e.
• If Po is the incident optical power then the number
of photons arriving per second is Po/hu
o
ph
eP
Ihu
h 

12. Quantum Efficiency (QE), cont
• Not all of the absorbed photons may photogenerate
free EHPs that can be collected.
– Some may disappear by recombination or become
immediately trapped
– If the semiconductor length is comparable with the
penetration depth (1/), then not all the photon will be
absorbed.
• The device QE is therefore always less than unity
– Depends on the absorption coefficient  of the
semiconductor at the wavelength of interest
– Depends on the structure of the device

13. Quantum Efficiency (QE), cont
• QE can be increased
– By reducing the reflections at the
semiconductor surface
– By Increasing absorption within the depletion
layer
– By preventing the recombination or trapping of
carriers

14. Quantum Responsivity
• The responsivity R of a photodiode characterizes its
performance in terms of photocurrent (Iph) generated per
incident optical power (Po ) at a given wavelength
• Responsivity therefore clearly depends on the wavelength.
• R is also called the spectral responsivity /radiant sensitivity
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R
R

15. Responsivity (R) vs. wavelength ( ) for an ideal
photodiode with QE = 100% ( h = 1) and for a typical
commercial Si photodiode.
0 200 400 600 800 1000 1200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength (nm)
SiPhotodiode
g
Responsivity (A/W)
Ideal Photodiode
QE = 100% (h = 1)
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig.2: R vs 
characteristics

16. R vs  characteristics
• R vs  characteristics as indicated in Fig.2.
– represents the spectral response of the photodiode
– and is generally provided by manufacturer
– Ideally with a quantum efficiency of 100% (h =1), R should
increase with  up to g
• In practice, QE limits the responsivity to lie below the
ideal photodiode line with upper and lower
wavelength limits as shown in Fig.2.
– The QE of a well designed Si photodiode in the wavelength
range 700-900nm can be close to 90-95%.

17. The simple pn junction has two drawback.
1. Its junction or depletion layer capacitance is not
sufficiently to allow photodetection at high
modulation frequencies
2. Its depletion is at most a few microns
– At long wavelength, the penetration depth is greater than
the depletion layer width where there is no field to
separate the EHPs & drift them
– QE is correspondingly low at these long wavelengths
• These problems are substantially reduced in the pin
photodiode.

18. pin photodiode
• pin refers to a device that has the structure p+-intrinsic-n+ as
illustrated in Fig.3.
• In the idealized pin diode, the i-Si region is truly intrinsic
– It is much wider than p+ & n+ regions (5-50mm)
• When the structure is first formed,
– Holes diffuse from the p+-side and electrons from n+-side into the i-Si layer
where they recombine and disappear.
– This leaves a thin layer of negatively charged acceptor ions in the p+-side
and positively donor ions in the n+-side.
– The two charges are separated by the i-Si layer of thickness W
• There is a uniform built-in field Eo in i-Si layer from the exposed
positive ions to exposed negative ions

19. p
+
i-Si n
+
SiO2
Electrode
rnet
–eNa
eNd
x
(a)
(b)
(a) The schematic structure of an
idealized photodiode (b) The netpin
space charge density across the
photodiode.
Electrode
Fig.3: pin photodiode

20. x
E(x)
R
Eo
E
e–
h+
Iph
hu > E g
W
(c)
(d)
Vr
(c) The built-in field
across the diode. (d) The pin
photodiode in photodetection is
reverse biased.
Vout
Fig.3: pin photodiode

21. Depletion Layer Capacitance
• The separation of two very thin layers of negative and positive
charges by a fixed distance, width W of the i-Si, is the same as
that in a parallel plate capacitor
• The junction depletion or depletion layer capacitance of the
pin diode is given by
where A is the cross sectional area and eoer is the permittivity of
the semiconductor (Si)
• Since W is fixed by the structure, the junction capacitance
does not depend on applied voltage
• Cdep is typically of the order of a pF in fast pin photodiodes so
that a 50W resistor, the RCdep time constant is about 50 ps.
W
A
C ro
dep
ee


22. Reverse bias
• When a reverse bias voltage Vr is applied across the pin
device, it drops almost entirely across the width of i-Si
layer.
– The depletion widths in the p+ and n+ sides are negligible
compared width W
– The reverse bias increases the built-in voltage to Vo+Vr.
– The field E in the i-Si layer is still uniform and increase to
 or
rr
VV
W
V
W
V
 oEE

23. Response time
• The pin structure is designed so that photon absorption
occurs over the i-Si layer
– The photogenerated EHPs are then separated by the field E and drifted
towards the n+ and p+ sides respectively.
• While the photogenerated carriers are drifting through the i-Si
layer they give rise to an external photocurrent
– which is detected as a voltage across a small resistor R
• The response time of the pin diode is determined by the
transit time of the carriers across the width W.
– Increasing W allows more photons to be absorbed which increases the
QE but it slow down the speed of response
– because carrier transit time become longer

24. Transit time of carrier
• For a charge carrier that is photogenerated at the
edge on the i-Si, the transit time or drift time tdrift
across the i-Si layer is
• To reduce the drift time, that is increase the speed of
response,
– we have to increase vd and therefore increase the applied
field E.
citydrift veloitsiswhere, d
d
drift v
v
W
t 

25. Drift velocity vs electric field in Si
• Fig.4 shows the variation of the drift velocity of electrons and
holes with the field in Si
• The mdE behavior is only observed at low field
– Where md is the drift mobility
• At high field, vd does not follow the expected mdE behavior
– both velocities tend to saturate at vsat which is of the order of 105ms–1
at field greater than 106Vm–1
• For an i-Si layer of width 10mm, with carriers drifting as
saturation velocities, the drift time is about 0.1ns which is
longer than RCdep time constant
– The speed of pin diodes are invariably limited by the transit time

26. Drift velocity vs. electric field for holes and electrons in Si.
102
103
104
105
107106105104
Electric field (V m -1)
Electron
Hole
Drift velocity (m s -1)
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig.4: Drift Velocity vs Electric Field
7104

27. Example:
Operation and speed of a pin photodiode
• A Si pin photodiode has an i-Si layer of width 20mm.
The p+ layer on the illumination side is very thin
0.1mm. The pin is reverse biased by a voltage of 100V
and then illuminated with a very short optical pulse
of wavelength 900nm. What is the duration of the
photocurrent if absorption occurs over the whole i-Si
layer?

28. Solution
• The absorption coefficient at 900nm is ~3104m–1 so that the absorption
depth is ~33mm. We assume that absorption and hence photogeneration
occurs over the entire width W of the i-Si layer. The field in the Si layer is
E  Vr/W = (100V)/(2010–6m) = 5106Vm–1
• At this field the electron drift velocity ve is very near its saturation at
105ms–1, whereas the hole drift velocity vh is about 7104ms–1. Holes are
slightly slower than the electrons. The transit time th of holes across the i-Si
layer is
th  W/vh = (2010–6m)/(7104ms–1) = 2.8610–10s
• This is the response time of the pin as determined by the transit time of
the slowest carriers, holes, across the i-Si layer. To improve the response
time the width of the i-Si layer has to be narrowed but this decreases the
quantity of absorbed photons and hence reduces the responsivity. There is
therefore a trade off between speed and responsitivity.

29. Example:
Responsivity of a pin photodiode
• A Si pin photodiode has an active light
receiving area of diameter 0.4mm. When
radiation of wavelength 700nm (red light) and
intensity 0.1mWcm–2 is incident, it generates a
photocurrent of 56.6nA. What is responsivity
and QE of the photodiode at 700nm?

30. Solution
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31. Avalanche Photodiode (APD)
• APDs are widely used in optical communications due
to their high speed and internal gain.
• The n+ side is thin and it is the side that is illuminated
through a window.
• There are three p-type layers of different doping
levels next to n+ layer to suitably modify the field
distribution across the diode
– The first is a thin p-type layer
– The second is a thick lightly p-type doped -layer
– The third is a heavily doped p+ layer

32. (a) A schematic illustration of the structure of an
avalanche photodiode (APD) biased
for avalanche gain. (b) The net space charge density
across the photodiode. (c) The
field across the diode and the identification of
absorption and multiplication regions.
 p+
SiO2Electrode
rnet
x
x
E(x)
R
E
hu > Eg
p
Iph
e– h+
Absorption
region
Avalanche
region
( a)
( b)
( c)
Electrode
n+
Fig.5: Avalanche
Photodiode

33. Reverse bias
• The diode is reverse biased to increase the fields in
the depletion regions
• Under zero bias, the depletion layer in the p-region
does not normally extend across this layer to the -
layer.
• But when a sufficient reverse bias is applied, the
depletion region in the p-layer widens to reach-
through to the -layer
– The field extends from the exposed positively charged
donors in the thin depletion layer in n+ side, all the way to
the exposed negatively charged acceptors in the thin
depletion layer in p+-side.

34. Electric field
• The electric field is given by the integration of the
net space charge density rnet across the diode is
shown in Fig.5.
• The field lines start at positive ions and end at
negative ions, which exist through the p,  & p+
layers.
– It is maximum at n+p junction, then decreases slowly
through the p layer.
– Through the -layer, it decreases slightly as the net space
charge here is small
– The field vanishes at the end of the narrow depletion
layer in the p+ side.

35. Avalanche of impact ionization processes
• The absorption of photons and photogeneration mainly occur
in the long -layer.
– The nearly uniform field here separates the EHPs and drifts them at
velocities near saturation towards the n+ and p+ sides respectively.
• When the drifting electrons reach p-layer, they experience
even greater fields
– therefore acquire sufficient kinetic energy (>Eg) to impact-ionize some
of the Si covalent bonds and release EHPs.
– These generated EHPs also be accelerated by the high fields to
sufficiently large kinetic energies to further cause impact ionization
and release more EHPs
– It leads to an avalanche of impact ionization processes.
– Thus, a single electron entering the p-layer can generate a large
number of EHPs, which contribute to observed photocurrent.

36. h+
E
šn+
p
e–
Avalanche region
e–
h+
Ec
Ev
(a) (b)
E
(a) A pictorial view of impact ionization processes releasing EHPs and
the resulting avalanche multiplication. (b) Impact of an energetic
conduction electron with crystal vibrations transfers the electron's
kinetic energy to a valence electron and thereby excites it to the
conduction band.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig.6: Avalanche of impact ionization
processes

37. Internal gain mechanism
• A single photon absorption leads to a large number of EHPs
generated called internal gain mechanism
• The photocurrent with the presence of avalanche
multiplication
– can has an effective quantum efficiency in excess of unity
• The reason for keeping the photogeneration within -region
and reasonably separated from the avalanche p-region is that
– Avalanche multiplication is a statistical process and hence leads to
carrier generation fluctuation, which leads to excess noise in the
avalanche multiplied photocurrent.
– This is minimized if impact ionization is restricted to the carrier with the
highest impact ionization efficiency which is the electron.

38. Avalanche multiplication factor
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39. M function
• The multiplication of carriers in the avalanche region
depends on the probability of impact ionization,
– which depends strongly on the field in this region and
hence on the reverse bias Vr
• The multiplication M is a strong function of the
reverse bias and also the temperature
• For Si APDs, M values can be as high as 100, but for
many commercial Ge APDs, M are typically around
10.

40. Empirical avalanche multiplication factor
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41. Speed of the reach-through APD
• The speed of the reach-through APD depends on
three factors
1. The time it takes for the photogenerated electron to
cross the absorption region (-layer) to the
multiplication region (p-layer)
2. The time it takes for the avalanche process to build up in
the p-region and generate EHPs
3. The time it takes for the last hole released in the
avalanche process to transit through the -region

42. Speed of photodetector
• The response time of an APD to an optical pulse is
longer than a corresponding pin structure
– But, in practice, the multiplication gain makes up for the
reduction in the speed.
• The overall speed of a photodetector circuit
– includes limitation from the electronic pre-amplifier
connected to the photodetector.
• The APD requires less subsequent electronic
amplication
– Which translates to an overall speed that can be faster than
a corresponding detector circuit using a pin photodiode

43. Example: InGaAs APD responsivity
• An InGaAs APD has a quantum efficiency (QE)
of 60% at 1.55mm in the absence of
multiplication (M=1). It is biased to operate
with a multiplication of 12.
Calculate the photocurrent if the incident
optical power is 20nW.
What is the responsivity when the
multiplication is 12?

44. Solution
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