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Chapter 6 Photodetectors
 6.1 Principles of Photodiodes
 6.1.1 The PIN Photo-Detector
 6.1.2 Avalanche Photodiodes
 6.2 Photo-Detector Noise
 6.2.1 Noise Sources
 6.2.2 Signal-to-Noise Ratio
 6.3 Detector Response Time
 6.4 Avalanche Multiplication Noise
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光纖通訊實驗室 黃振發教授 編撰
6.1.1 The PIN Photo-Detector
 The PIN photodiode is structured with p and n
regions separated by a lightly n-doped intrinsic (i)
region (Fig. 6-1).
 Incident photon with energy > band-gap energy of
the photodiode will generate free electron-hole pairs,
known as photo-carriers (Fig. 6-2).
 The high electric field present in the depletion region
causes the carriers to separate and be collected
across the reverse-biased junction.
 This gives rise to a photo-current flow in an external
circuit, with one electron flowing for every carrier
pair generated.
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6.1.1 The PIN Photo-Detector
Figure 6-1. Schematic representation of a PIN
photodiode circuit with an applied reverse bias.
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6.1.1 The PIN Photo-Detector
Figure 6-2. Simple energy-band diagram for a
PIN photodiode. Photons with energy > band-gap
energy can generate free electron-hole pairs.
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6.1.1 The PIN Photo-Detector
 As the charge carriers flow through the material,
some electron-hole pairs will recombine and
disappear.
 On the average, the charge carriers move a diffusion
length Ln or Lp for electrons and holes, respectively.
 The time it takes for an electron or hole to recombine
is known as the carrier lifetime and is represented by
tn and tp, respectively.
 The lifetimes and the diffusion lengths are related by
Ln = (Dntn)1/2
and
Lp = (Dptp)1/2
where Dn and Dp are the electron and hole diffusion
coefficients, expressed in units of cm2/sec.
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6.1.1 The PIN Photo-Detector
 Optical radiation is absorbed in the semiconductor
material according to the exponential law
P(x) = Po[1 - exp(-as(l)x)]
 Here, as(l) is the absorption coefficient at
wavelength l,
Po is the incident optical power level,
and P(x) is the optical power absorbed in a
distance x.
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(6-1)
6.1.1 The PIN Photo-Detector
 The optical absorption coefficient versus wavelength
is shown in Fig. 6-3 for several photodiode materials.
 The cutoff lc is determined by the band-gap energy
Eg of the material:
lc(mm) = hc/Eg = 12.4 / Eg(eV)
(6-2)
 The cutoff wavelength is about 1.06-µm for Si and
1.6-µm for Ge.
 For longer wavelengths, the photon energy is not
sufficient to excite an electron from the valence to
the conduction band.
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6.1.1 The PIN Photo-Detector
Figure 6-3. Optical absorption coefficient as a
function of wavelength for Si, Ge, and GaAs.
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6.1.1 The PIN Photo-Detector
 Example 6-1:
A photodiode constructed of GaAs has a band-gap
energy of 1.43eV at 300oK.
 From Eq. (6-2), the long-wavelength cutoff is
lc = hc/Eg
(6.625x10-34J.s)(3x108m/s)
= ---------------------------------- = 869 nm.
(1.43eV)(1.6x10-19J/eV)
 This GaAs photodiode will not operate for photons of
l > 869 nm.
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6.1.1 The PIN Photo-Detector
 At the lower-wavelength end, the photo-response
cuts off with very large values of as at the shorter
wavelengths.
 The photons are absorbed very close to the photodetector surface, the recombination time of the
generated electron-hole pairs is very short.
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6.1.1 The PIN Photo-Detector
 If the depletion region has a width w, then the total
power absorbed in the distance w is
P(w) = Po[1 - exp(-asw)]
(6-3)
 Take into account the reflectivity Rf at the entrance
face of the photodiode, the primary photocurrent Ip
resulting from the power absorption of Eq. (6-3) is
given by
Ip = (q/hn)Po[1-exp(-asw)](1-Rf)
(6-4)
 where Po is the optical power incident on the photodetector, q is the electron charge, and hv is the
photon energy.
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6.1.1 The PIN Photo-Detector
 The quantum efficiency h is the number of the photocarrier pairs generated per incident photon of energy
hv and is given by
number of electron-hole generated
h = -----------------------------------------number of incident photons
(6-5)
= (Ip/q) / (Po/hv).
 Here, Ip is the average photocurrent generated by a
steady-state average optical power Po incident on the
photo-detector.
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6.1.1 The PIN Photo-Detector
 Example 6-2:
In a 100-ns pulse, 6.0x106 photons at 1300-nm fall
on an InGaAs photo-detector. On the average,
5.4x106 electron-hole pairs are generated.
 The quantum efficiency is found from Eq. (6-5) as
number of e-h pairs generated
h = ----------------------------------------number of incident photons
= (5.4x106) / (6x106) = 0.9.
Thus, the quantum efficiency at 1300-nm is 90 %.
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6.1.1 The PIN Photo-Detector
 To achieve a high quantum efficiency, the depletion
layer must be thicker.
 However, the thicker the depletion layer, the longer
it takes for the photo-generated carriers to drift
across the reverse-biased junction.
 Compromise has to be made between response speed
and quantum efficiency.
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6.1.1 The PIN Photo-Detector
 The performance of a photodiode is often
characterized by the responsivity R.
 This is related to the quantum efficiency h by
R = Ip/Po = hq/hn
(6-6)
Typical PIN responsivities are shown in Fig. 6-4.
 Representative values are 0.65-A/W for Si at 900nm and 0.45-A/W for Ge at 1.3-µm.
 For InGaAs, typical values are 0.9-A/W at 1.3-µm
and 1.0-A/W at 1.55-µm.
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6.1.1 The PIN Photo-Detector
 Example 6.3:
Photons of energy 1.53x10-19J are incident on a
photodiode which has a responsivity of 0.65A/W.
 If the optical power level is 10mW, then from Eq.
(6-6) the photo-current is
Ip = RPo = (0.65A/W)(10mW) = 6.5mA
 The responsivity is a linear function of the optical
power. The photocurrent Ip is directly proportional
to the optical power Po incident upon the photodetector, so that the responsivity R is constant at a
given wavelength.
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6.1.1 The PIN Photo-Detector
 For a given material, as the wavelength of the
incident photon becomes longer, the photon energy
becomes less than that required to excite an electron
from the valence band to the conduction band.
 The responsivity thus falls off rapidly beyond the
cutoff wavelength, as can be seen in Fig. 6-4.
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6.1.1 The PIN Photo-Detector
Figure 6-4. Comparison of the responsivity and
quantum efficiency as a function of wavelength for
different PIN photodiodes.
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6.1.1 The PIN Photo-Detector
 Example 6-4 :
As shown in Fig. 6-4, for the wavelength range
1300-nm < l < 1600-nm, the quantum efficiency for
InGaAs is around 90 %. Thus, in this wavelength
range the responsivity is
R = hq/hn = hql/hc
= (0.90)(1.6x10-19C)l/(6.625x10-34J.s)(3x108m/s)
= 7.25x105 l
For example, at 1300-nm we have
R = [7.25x105(A/W)/m](1.30x10-6m)
= 0.92 A/W
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6.1.1 The PIN Photo-Detector
 At wavelengths higher than 1600-nm, the photon
energy is not sufficient to excite an electron from the
valence band to the conduction band.
 For example, In0.53Ga0.47As has an energy gap Eg =
0.73 eV, so that from Eq. (6-2) the cutoff wavelength
is
lc = 1.24/Eg = 1.24/0.73 = 1.7 mm
 At wavelengths < 1100-nm, the photons are absorbed
very close to the photo-detector surface, where the
recombination rate of the generated electron-hole
pairs is very short. The responsivity thus decreases
rapidly for smaller wavelengths.
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6.1.2 Avalanche Photodiodes
 APDs internally multiply the primary signal
photocurrent in a mechanism known as impact
ionization.
 The created carriers are accelerated by the high
electric field, gaining enough energy to cause further
impact ionization. This phenomenon is the avalanche
effect.
 A commonly used structure for achieving carrier
multiplication with very little excess noise is the
reach-through construction shown in Fig. 6-5.
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6.1.2 Avalanche Photodiodes
Figure 6-5. Reach-through avalanche
photodiode structure and the electric fields
in the depletion and multiplication regions.
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6.1.2 Avalanche Photodiodes
 In normal usage, the RAPD is operated in the fully
depleted mode. Light enters the device through the
p+ region and is absorbed in the p material, which
acts as the collection region for the photo-generated
carriers.
 The photo-generated electrons drift through the p
region in the pn+ junction, where a high electric
field exists.
 It is in this high-field region that carrier
multiplication takes place.
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6.1.2 Avalanche Photodiodes
 The average number of electron-hole pairs created
by a carrier per unit distance traveled is called the
ionization rate.
 Most materials exhibit different electron ionization
rates a and hole ionization rates b.
 Values of a and b for five different semiconductor
materials are shown in Fig. 6-6.
 The ratio k = b/a of the electron and hole ionization
rates is a measure of the photo-detector
performance.
 APDs constructed of materials in which one type of
carrier largely dominates impact ionization exhibit
low noise and large gain-bandwidth products.
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6.1.2 Avalanche Photodiodes
Figure 6-6. Carrier ionization rates obtained
experimentally for Si, Ge, Ga, As, GaAsSb, and
InGaAs.
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6.1.2 Avalanche Photodiodes
 The multiplication M for all carriers generated in
the photodiode is defined by
M = IM / Ip
(6-7)
where IM is the average value of the total multiplied
output current and Ip is the primary unmultiplied
photocurrent defined in Eq. (6-4).
 The performance of an APD is characterized by
the responsivity given by
RAPD = (hq/hn)M = RoM
(6-8)
where Ro is the unity gain responsivity.
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6.2 PHOTODETECTOR NOISE
 The power SNR at the output of an optical receiver is
(6-9)
 To achieve a high SNR,
1. PD must have a high h to generate a large signal power.
2. PD and amplifier noises should be kept as low as
possible.
 The sensitivity of a photodiode is describable in terms of
the minimum detectable optical power. This is the optical
power necessary to produce a photo-current of the same
magnitude as the total rms noise current, or equivalently,
a SNR of 1.
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6.2.1 Noise Sources
 In the receiver model of Fig. 6-8, the photodiode has
a small series resistance Rs, a total capacitance Cd
consisting of junction and packaging capacitances,
and a bias (or load) resistor RL.
 The amplifier following the photodiode has an input
capacitance Ca and a resistance Ra.
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6.2.1 Noise Sources
Figure 6-8. (a) Simple model of a photo-detector
receiver, and (b) its equivalent circuit.
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6.2.1 Noise Sources
 If a modulated signal of optical power P(t) falls on the
detector, the primary photo-current iph(t) generated is
iph(t) = (hq/hn)P(t)
(6-10)
 The primary current consists of a dc value Ip -- the
average photo-current due to the signal power, and a
signal component ip(t).
 For PINs, the mean-square signal current <is2> for a
sinusoidally varying input signal of modulation index m
is
<is2> = s2s,PIN = <ip2(t)>
(6-11a)
= sp2 = m2Ip2/2
(6-12)
where s2 is the variance.
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6.2.1 Noise Sources
 For APDs, the mean-square signal current <is2> is
<is2> = s2s,APD = <ip2(t)>M2
(6-11b)
where M is the average avalanche gain.
 The quantum or shot noise follow a Poisson process.
The quantum noise current has a mean-square
value
<iQ2> = sQ2 = 2qIpBM2F(M)
(6-13)
 where F(M) = Mx, 0 < x < 1.0, is a noise figure
associated with the random nature of the avalanche
process. For PIN photodiodes, M and F(M) are
unity.
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6.2.1 Noise Sources
 The mean-square value of the bulk dark current iDB arisen
from thermally generated electrons and/or holes is given by
<iDB2> = sDB2 = 2qIDBM2F(M)
(6-14)
where ID is the primary (unmultiplied) detector bulk dark
current.
 The surface dark current is simply referred to as leakage
current. The mean-square value of this current is given by
<iDS2> = sDS2 = 2qILB
(6-15)
where IL is the surface leakage current. The surface dark
current is not affected by the avalanche gain.
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6.2.1 Noise Sources
 The dark currents and the signal current are
uncorrelated, the mean-square PD noise current
<iN2> can be written as
<iN2> = sN2 = <iQ2> + <iDB2> + <iDS2>
= sQ2 + sDB2 + sDS2
= 2q(Ip + ID)M2F(M)B + 2qILB
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(6-16)
6.2.1 Noise Sources
 The PD load resistor contributes a mean-square
thermal (Johnson) noise current
<iT2> = sT2 = 4kBTB/RL,
(6-17)
where kB is Boltzmann's constant and T is the
absolute temperature.
 This Johnson noise can be reduced by using a load
resistor which is large but still consistent with the
receiver bandwidth requirements.
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6.2.2 Signal-to-Noise Ratio
 Substituting Eqs. (6-11), (6-16), and (6-17) into Eq. (6-9)
for the SNR at the input of the amplifier, we have
(6-18)
 For PINs, the dominating noise currents are those of
the detector load resistor (the thermal current iT) and
the active elements of the amplifier circuitry (iamp).
 For APDs, the thermal noise is of lesser importance
and the photo-detector noises usually dominate.
 From Eq. (6-18), it is seen that the signal power is
multiplied by M2 and the quantum noise plus bulk
dark current is multiplied by M2F(M).
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6.2.2 Signal-to-Noise Ratio
 The optimum gain at the maximum SNR can be
found by differentiating Eq. (6-18) with respect to
M, setting the result equal to zero, and solving for
M.
 For a sinusoidally modulated signal, with m = 1 and
F(M) approximated by Mx, will yield
(6-19)
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6.3 Detector Response Time

The response time of a photodiode together with its
output circuit depends on the factors:
1. The transit time of the photo-carriers in the
depletion region.
2. The diffusion time of the photo-carriers generated
outside the depletion region.
3. The RC time constant of the photodiode and its
associated circuit.
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6.3 Detector Response Time
 The transit time td the photo-carriers take to travel
across the depletion region depends on the carrier
drift velocity vd and the depletion layer width w, and
is given by
td = w / vd
(6-27)
 The electric field in the depletion region is large
enough so that the carriers have reached their
scattering-limited velocity.
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6.3 Detector Response Time
 The A typical response time of a partially depleted
photodiode is shown in Fig. 6-12.
 The fast carriers allow the device output to rise to 50
% of its maximum value in approximately 1 ns, but
the slow carriers cause a relatively long delay before
the output reaches its maximum value.
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6.3 Detector Response Time
Figure 6-12. Typical response time of a photodiode
that is not fully depleted.
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6.3 Detector Response Time
 To achieve a high quantum efficiency, the depletion
layer width must be much larger than 1/a, so that
most of the light will be absorbed.
 The response to a rectangular input pulse of a lowcapacitance photodiode having w >> 1/a is shown in
Fig. 6-13b.
 If the photodiode capacitance is larger, the response
time becomes limited by the RC time constant of the
load resistor RL and the photodiode capacitance.
 The photodetector response then begins to appear as
that shown in Fig. 6-13c.
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6.3 Detector Response Time
 Devices with very thin depletion regions tend to show
distinct slow- and fast-response components, as
shown in Fig. 6-13d.
 The fast component in the rise time is due to carriers
generated in the depletion region, whereas the slow
component arises from the diffusion of carriers that
are created with a distance L from the edge of the
depletion region.
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6.3 Detector Response Time
Figure 6-13. Photodiode pulse responses under
various detector parameters.
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6.3 Detector Response Time
 If RT is the combination of the load and amplifier
input resistances and CT is the sum of the photodiode
and amplifier capacitances,
as shown in Fig. 6-8,
 the detector behaves like a simple RC low-pass filter
with a passband given by
B = 1/(2pRTCT)
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(6-29)
6.3 Detector Response Time
 Example 6-7 :
If the photodiode capacitance is 3 pF, the amplifier
capacitance is 4 pF, the load resistor is 1 kW, and the
amplifier input resistance is 1 MW,
 then CT = 7 pF and RT = 1 kW, so that the circuit
bandwidth is
B = 1/(2pRTCT) = 23 MHz
(6-30)
 If we reduce the photo-detector load resistance to 50W,
then the circuit bandwidth becomes B = 455 MHz.
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6.4 AVALANCHE
MULTIPLICATION NOISE
 If m denotes the statistically varying APD gain, then
〈m2〉>〈m〉2 = M2
(6-31)
where the symbols〈.〉denote an ensemble average and
〈m〉= M is the average carrier gain defined in Eq. (6-7).
 Since the noise created by the avalanche process depends
on the mean-square gain〈m2〉, the noise in an APD can
be relatively high.
 It has been found that,〈m2〉can be approximated by
〈m2〉= M2+x
(6-32)
where the exponent x varies between 0 and 1.0 depending
on the photodiode material and structure.
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6.4 AVALANCHE
MULTIPLICATION NOISE
 The ratio of the actual noise generated in an APD to
the noise that would exist if all carrier pairs were
multiplied by M is called the excess noise factor F
and is defined by
F =〈m2〉/〈m〉2 =〈m2〉/ M2
(6-33)
 This excess noise factor is a measure of the increase
in detector noise resulting from the randomness of
the multiplication process.
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6.4 AVALANCHE
MULTIPLICATION NOISE
 McIntyre has shown that, for injected electrons and
holes, the excess noise factors are
(6-34)
(6-35)
where the subscripts e and h refer to electrons and
holes, respectively.
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光纖通訊實驗室 黃振發教授 編撰
6.4 AVALANCHE
MULTIPLICATION NOISE
 The weighted ionization rate ratios k1 and k2 take
into account the nonuniformity of the gain and the
carrier ionization rates in the avalanche region.
 To a first approximation k1 and k2 can be
considered as constant and equal. Eqs. (6-34) and
(6-35) can be simplified as
(6-38)
for electron injection,
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
6.4 AVALANCHE
MULTIPLICATION NOISE
and
(6-39)
for hole injection,
 where the effective ionization rate ratios are
and
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(6-40)
6.4 AVALANCHE
MULTIPLICATION NOISE
 Figure 6-14 shows Fe as a function of the average
electron gain Me for various values of the effective
ionization rate ratio keff.
 If the ionization rates are equal, the excess noise is
at its maximum so that Fe is at its upper limit of Me.
 As the ionization rates ratio b/a decreases from
unity, the electron ionization rate a starts to be the
dominant contributor to impact ionization, and the
excess noise factor becomes smaller.
 If only electrons cause ionization, b = 0 and Fe
reaches its lower limit of 2.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
6.4 AVALANCHE
MULTIPLICATION NOISE
Figure 6-14. Variation of the electron excess noise
factor Fe as a function of the electron gain for various
values of the effective ionization rate ratio keff.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
6.4 AVALANCHE
MULTIPLICATION NOISE
 From the empirical relationship for the mean-square
gain given by Eq. (6-32), the excess noise factor can
be approximated by
F = Mx
(6-41)
 The parameter x takes on values of 0.3 for Si, 0.7 for
InGaAs, and 1.0 for Ge avalanche photodiodes.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰