Chapter 6:Photodetectors

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

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

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

(a) A schematic diagram of a reverse biased pn junctionphotodiode. (b) Net space charge across the diode in the

depletion region. Nd and Na are the donor and acceptorconcentrations in the p and n sides. (c). The field in thedepletion region.

p+

SiO2Electrode

r net

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x

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hu > Eg

W

En

Depletion region

(a)

(b)

(c)

Antireflectioncoating

Vr

Electrode

Vout

Fig.1: pn-junction photodiode

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

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

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

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)

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

.

hP

eI

o

ph

/

/

photonsincident ofNumber

collected and generated EHP free ofNumber

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

Ih

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

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

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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Responsivity (R) vs. wavelength () for an idealphotodiode with QE = 100% ( = 1) and for a typicalcommercial Si photodiode.

0 200 400 600 800 1000 12000

0.10.20.30.40.50.60.70.80.9

1

Wavelength (nm)

Si Photodiode

g

Responsivity (A/W)

Ideal Photodiode

QE = 100% ( = 1)

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Fig.2: R vs l characteristics

R vs l characteristics

• R vs l 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 l up to lg

• 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%.

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.

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

p+

i-Si n+

SiO2Electrode

rn et

–eNa

eNd

x

(a)

(b)

(a) The schematic structure of an idealized photodiode (b) The netpinspace charge density across the photodiode.

Electrode

Fig.3: pin photodiode

x

E (x)

R

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(c)

(d)

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(c) The built-in fieldacross the diode. (d) The pin

photodiode in photodetection is

reverse biased.

Vout

Fig.3: pin photodiode

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

AC ro

dep

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

orrr VV

W

V

W

V oEE

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

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 velo its is where, dd

drift vv

Wt

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

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

7104

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?

Solution• The absorption coefficient at 900nm is ~3104m–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)/(2010–6m) = 5106Vm–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 7104ms–1. Holes are slightly slower than the electrons. The transit time th of holes across the i-Si layer is

th W/vh = (2010–6m)/(7104ms–1) = 2.8610–10s

• 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.

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?

Solution

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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 p-layer– The third is a heavily doped p+ layer

(a) A schematic illustration of the structure of an avalanche photodiode (APD) biasedfor avalanche gain. (b) The net space charge density across the photodiode. (c) Thefield across the diode and the identification of absorption and multiplication regions.

p p+

SiO2Electrode

r n et

x

x

E (x)

R

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hu > Eg

p

Iph

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Avalancheregion

(a)

(b)

(c)

Electrode

n+

Fig.5: Avalanche Photodiode

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 p-layer.

• But when a sufficient reverse bias is applied, the depletion region in the p-layer widens to reach-through to the p-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.

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 & p+

layers.– It is maximum at n+p junction, then decreases slowly

through the p layer.– Through the p-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.

Avalanche of impact ionization processes

• The absorption of photons and photogeneration mainly occur in the long p-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.

h+

E

šn+ p

e–

Avalanche region

e–

h+

Ec

Ev

(a) (b)

E

(a) A pictorial view of impact ionization processes releasing EHPs andthe resulting avalanche multiplication. (b) Impact of an energeticconduction electron with crystal vibrations transfers the electron'skinetic energy to a valence electron and thereby excites it to theconduction band.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Fig.6: Avalanche of impact ionization processes

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 p-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.

Avalanche multiplication factor

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• 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.

Empirical avalanche multiplication factor

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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 (p-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 p-region

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

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?

Solution

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