Optoelectronic
Detectors
Optoelectronic
Detectors
Detectors perform the opposite function of light emitters. They
convert optical signals back into electrical impulses that are used by the
receiving end of the fiber optic data, video, or audio link. The most
common detector is the semiconductor photodiode, which produces current
in response to incident light.
Optoelectronic Detectors
• Principles of optoelectronic detection
• Defining parameters of optoelectronic
detectors: quantum efficiency,responsivity,
cut-off wavelength
• Types of photodiodes
• Noise considerations
Optoelectronic Detectors
In any fiber-optic system, it is required to convert the optical signals at the
receiver end back into electrical signals for further processing and display of the
transmitted information. This task is normally performed by an optoelectronic
detector. Therefore, the overall system performance is governed by the
performance of the detector.
Optoelectronic Detectors
Detectors should have
•high sensitivity at operating wavelengths,
•high fidelity,
•fast response,
•high reliability,
•low noise, and
•low cost.
Further, its size should be comparable with that of the
core of fiber employed in the optical link.
THE BASIC PRINCIPLE OF OPTOELECTRONIC DETECTION
When a photon of energy greater than the
band gap of the semiconductor material
(i.e., h Eg) is incident on or near the
depletion region of the device, it excites an
electron from the valence band into the
conduction band.
A reverse-biased p-n junction.
The vacancy of an electron creates a hole in
the valence band.
Electrons and holes so generated experience
a strong electric field and drift rapidly
towards the n and p sides, respectively.
The resulting flow of current is proportional
to the number of incident photons. Such a
reverse-biased p-n junction, therefore, acts
as a photodetector and is normally referred
to as a p-n photodiode.
Energy band diagram showing
carrier generation and their drift.
Optical Absorption Coefficient and Photocurrent
The absorption of photons of a specific wavelength in a photodiode to produce electron–
hole pairs and thus a photocurrent depends on the absorption coefficient  of the
semiconductor for that particular wavelength.
Pin : the total optical power incident on the photodiode
R: the Fresnel reflection coefficient at the air–semiconductor interface
Thus, the optical power entering the semiconductor will be Pin(1 – R).
the power absorbed by the Photodetector is given by
Pabs = Pin(1 – R) [1 – exp(–d)]
Where d is the width of the absorption region.
: absorption coefficient of the semiconductor at incident wavelength.
Let us assume that the incident light is monochromatic and the energy of each photon
is h. Then the rate of photon absorbtion will be given by
It is clear from these curves that  depends strongly on the
wavelength of incident light. Thus, a specific semiconductor
material can be used only in a specific range.
Further, if we assume that
(i) the semiconductor is an intrinsic absorber (i.e., the absorption of photons
excites the electrons from the valence band directly to the conduction
band),
(ii) each photon produces an electron–hole pair, and
(iii)all the charge carriers are collected at the electrodes, then the
photocurrent (rate of flow of charge carriers) Ip so produced will be
given by
where e is the electronic charge.
Quantum Efficiency
Quantum efficiency  is defined as the ratio of the rate (re) of electrons
collected at the detector terminals to the rate rp of photons incident on the
device. That is,
 = re / r p
 may be increased if the Fresnel reflection coefficient R is decreased and
the product d is much greater than unity.
 is also a function of the photon wavelength.
Responsivity 
The responsivity  of a photodetector is defined as the output photocurrent per unit
incident optical power. Thus, if Ip is the output photocurrent in amperes and Pin is the
incident optical power in watts,
The output photocurrent Ip may be written in terms of the rate, re, of electrons collected
as follows:
Further
Ip = ere
Ip = erp
Where  and c are the wavelength and speed of the incident light in vacuum,
respectively. the responsivity is directly proportional to the quantum
efficiency at a particular wavelength and in the ideal case, when = 1,  is
directly proportional to .
For a practical diode, as the wavelength of the incident photon becomes
longer, its energy becomes smaller than that required for exciting the electron
from the valence band to the conduction band. The responsivity thus falls off
near the cut-off wavelength c.
Long-wavelength Cut-off
In an intrinsic semiconductor, the absorption of a photon is possible only
when h Eg , band gap Energy of the semiconductor used to fabricate the
photodiode.
Thus, there is a long wavelength cut-off c, above which photons are simply
not absorbed by the semiconductor, given by
Or,
This expression allows us to calculate c for different semiconductors in order
to select them for specific detection purposes.
Exercise 1: A p-n photodiode has a quantum efficiency of 70% for photons of
energy 1.52  10–19 J. Calculate (a) the wavelength at which the diode is
operating and (b) the optical power required to achieve a photocurrent of 3
A when the wavelength of incident photons is that calculated in part (a).
Exercise 2: A p-i-n photodiode, on an average, generates one electron–hole
pair per two incident photons at a wavelength of 0.85 m. Assuming all the
photo-generated electrons are collected, calculate
(a) the quantum efficiency of the diode;
(b) the maximum possible band gap energy (in eV) of the semiconductor,
assuming the incident wavelength to be a long-wavelength cut-off; and
(c) the mean output photocurrent when the incident optical power is 10 W.
Exercise 3 : Photons of wavelength 0.90 m are incident on a p-n photodiode
at a rate of 5  1010 s–1 and, on an average, the electrons are collected at the
terminals of the diode at the rate of 2  1010 s–1. Calculate
(a) the quantum efficiency and
(b) the responsivity of the diode at this wavelength.
TYPES OF PHOTODIODES
p-n Photodiode
The simplest structure is that of a p-n photodiode.
Incident photons of energy, h, are absorbed not
only inside the depletion region but also outside it.
The photons absorbed within the depletion region
generate electron–hole pairs. Because of the built-in
strong electric field electrons and holes generated
inside this region get accelerated in opposite
directions and thereby drift to the n-side and the pside, respectively. The resulting flow of photocurrent
constitutes the response of the photodiode to the
incident optical power. The response time is
governed by the transit time drift, which is given by
(a) Structure of a p-n photodiode
and the associated depletion
region under reverse bias. (b)
Variation of optical power within
the diode. (c) Variation of electric
field inside the diode.
TYPES OF PHOTODIODES
where w is the width of the depletion region and vdrift is the average drift velocity.
drift is of the order of 100 ps, which is small enough for the photodiode to
operate up to a bit rate of about 1 Gbit/s. In order to minimize drift, both w and
vdrift can be tailored. The depletion layer width w is given (Sze 1981) by
Where  is the dielectric constant,
e is the electronic charge,
Vbi is the built-in voltage and depends on the semiconductor,
V0 is the applied bias voltage,
and Na and Nd are the acceptor and donor concentrations used to fabricate the p-n
junction.
The drift velocity vdrift depends on the bias voltage but attains a saturation value
depending on the material of the diode.
Incident photons are absorbed
outside the depletion region.
The electrons generated in the pside have to diffuse to the
depletion-region boundary before
they can drift (under the built in
electric field) to the n-side. In a
similar
fashion,
the
holes
generated in the n-side have to
diffuse to the depletion region
boundary for their drift towards
the p-side. The diffusion process is
inherently slow and hence the
presence of a diffusive component
may distort the temporal response
of a photodiode
p-i-n-Photodiode
The diffusion component of a p-n photodiode
may be reduced by decreasing the widths of
the p-side and n-side and increasing the width
of the depletion region so that most of
incident photons are absorbed inside it.
To achieve this, a layer of semiconductor, so
lightly doped that it may be considered
intrinsic, is inserted at the p-n junction.
As the middle layer is intrinsic in nature, it
offers high resistance, and hence most of the
voltage drop occurs across it. Thus, a strong
electric field exists across the middle i-region.
Such a configuration results in the drift
component of the photocurrent dominating
the diffusion component, as most of the
incident photons are absorbed inside the iregion.
A double heterostructure improves
performance of the p-i-n photodiodes.
the
Herein,
the
middle
i-region
of
a
material with lower band gap is sandwiched
between p- and n-type materials of higher
band gap, so that incident light is absorbed
only within the i-region. The band gap of InP is
1.35 eV and hence it is transparent for light of
wavelength greater than 0.92 m, whereas the
band gap of lattice-matched InGaAs is about
0.75 eV, which corresponds to a c of 1.65 m.
Thus the intrinsic layer of InGaAs absorbs
strongly in the wavelength range 1.3–1.6 m.
The diffusive component of the photocurrent
is completely eliminated in such a
heterostructure simply because the incident
photons are absorbed only within the
depletion region. Such photodiodes are very
useful for fiber-optic systems operating in the
range 1.3–1.6 m.
Avalanche Photodiode
Avalanche photodiodes (APDs) internally multiply the primary photocurrent
through multiplication of carrier pairs. This increases receiver sensitivity because
the photocurrent is multiplied before encountering the thermal noise associated
with the receiver circuit.
Through an appropriate structure of a photodiode, it is possible to create a highfield region within the device upon biasing. When the primary electron–
hole pairs generated by incident photons pass through this region, they get
accelerated and acquire so much kinetic energy that they ionize the bound
electrons in the valence band upon collision and in the process create secondary
electron–hole pairs. This phenomenon is known as impact ionization.
If the field is high enough, the secondary carrier pairs may also gain sufficient
energy to create new pairs. This is known as the avalanche effect. Thus the
carriers get multiplied, all of which contribute to the photocurrent.
A commonly used configuration for achieving carrier
multiplication with little excess noise is shown and is called
a reach through avalanche photodiode (RAPD).
It is composed of a lightly doped p-type intrinsic layer
(called a -layer) deposited on a p+ (heavily doped p-type)
substrate. A normal p-type diffusion is made in the
intrinsic layer, which is followed by the construction of an
n+ (heavily doped n-type) layer. Such a configuration is
called a p+--p-n+ reach through structure. When the
applied reverse-bias voltage is low, most of the potential
drop is across the p-n+ junction. As the bias voltage is
increased, the depletion layer widens and the latter just
reaches through to the -region when the electric field at
the p-n+ junction becomes sufficient for impact ionization.
Normally, an RAPD is operated in a fully depleted mode.
The photons enter the device through the p+-layer and are
absorbed in the intrinsic -region. The absorbed photons
create primary electron–hole pairs, which are separated
by the electric field in this region. These carriers drift to
the p-n+ junction, where a strong electric field exists. It is
in this region that the carriers are multiplied first by
impact ionization and then by the avalanche breakdown.
The average number of carrier pairs generated by an electron per
unit length of its transversal is called the electron ionization rate e.
Similarly, the hole ionization rate h may also be defined.
The ratio K = e / h is a measure of the performance of APDs.
An APD made of a material in which one type of carrier dominates
impact ionization exhibits low noise and high gain. It has been
found that there is a significant difference between e and h only
in silicon and hence it is normally used for making RAPDs for
detection around 0.85 m. For longer wavelengths, advanced
structures of APDs are used.
Example: An APD has a quantum efficiency of 40% at 1.3m. When illuminated
with optical power of 0.3 W at this wavelength, it produces an output photocurrent
of 6 A, after avalanche gain. Calculate the multiplication factor of the diode.
PHOTOCONDUCTING DETECTORS
The basic detection process involved in a photoconducting detector is raising an
electron from the valence band to the conduction band upon absorption of a photon
by a semiconductor, provided the photon energy is greater than the band gap energy
(i.e., h  Eg). As long as an electron remains in the conduction band, it will contribute
toward increasing the conductivity of the semiconductor. This phenomenon is known
as photoconductivity.
A photoconducting detector for long-wavelength operation
In operation, the incident photons are absorbed by the conducting
layer, thereby generating additional electron–hole pairs. These
carriers are swept by the applied field towards respective electrodes,
which results in an increased current in the external circuit. In the
case of III-V alloys such as InGaAs, electron mobility is much higher
than hole mobility. Thus whilst the faster electrons are collected at
the anode, the corresponding holes are still proceeding towards the
cathode. The process creates an absence of electrons and hence a
net positive charge in the region. However, the excess charge is
compensated for, almost immediately, by the injection of more
electrons from the cathode into this region.
In essence, this process leads to the generation of more electrons upon the absorption of
a single photon. The overall effect is that it results in a photoconductive gain G, which
may be defined as the ratio of transit time ts for slow carriers to the transit time tf for fast
carriers. Thus,
G= ts / tf
The photocurrent Ig produced by the photoconductor can be written as
Pine
Ig 
G  I pG
h
where η is the quantum efficiency of the device, Pin is the incident optical power, and Ip is
the photocurrent in the absence of any gain. Gain in the range 50–100 and a 3-dB
bandwidth of about 500 MHz are currently achievable with the InGaAs photoconductors
discussed above.
Example: The maximum 3-dB bandwidth permitted by an InGaAs photoconducting
detector is 450 MHz when the electron transit time in the device is 6 ps. Calculate (a) the
gain G and (b) the output photocurrent when an optical power of 5 W at a wavelength
of 1.30 mm is incident on it, assuming quantum efficiency of 75%.
Solution: The current response in the photoconductor decays exponentially with time
once the incident optical pulse is removed. The time constant of this decay is equal to
the slow carrier transit time ts. Therefore, the maximum 3-dB bandwidth (f)m of the
device will be given by
Spectral response characteristics of various IR detectors of different
materials/technologies. Detectivity (vertical axis) is a measure of signalto-noise ratio (SNR) of an imager normalized for its pixel area and noise
bandwidth
Optoelectronic Modulators
In a fiber-optic communication system, data are encoded in the form of the
variation of some property of the optical output of a light-emitting diode
(LED) or an injection laser diode (ILD).
This property may be the amplitude or the phase of the optical signal or the
width of the pulses being transmitted.
There are two ways of modulating an optical signal from a LED or ILD.
1.
Direct modulation: a circuit is designed to modulate the current injected
into the device.
2.
Indirect modulation: an optical signal from the source is passed through
a material (or device) whose optical properties can be altered by
external means.
Optoelectronic Modulators
Direct modulation: Direct modulation is simple but has several
disadvantages: the upper modulation frequencies are limited to
about 40 GHz; the emission frequency may change as the drive
current is changed; and only amplitude modulation is possible
with ease (for phase or frequency modulation, additional care is
required to design the drivers).
Optoelectronic Modulators
Indirect Modulation: In this scheme, the device speed is
controlled by the modulator property and may be quite fast; the
emission frequency remains unaffected and both amplitude and
phase modulation are possible with ease.
The only disadvantage is that the modulator is normally large
on the scale of microelectronic devices and hence cannot
become a part of the same integrated circuit (IC).
The
design
of
these
modulators
is
based either on the electro-optic effect or the acousto-optic
effect.
Devices based on the electro-optic effect are most common in
high-speed communications. The technology used in these
devices is also becoming compatible with that of
semiconductor devices.
REVIEW OF BASIC PRINCIPLES
•polarization,
•birefringence
•double refraction,
(a) A plane-polarized transverse wave, shown only by the electric vector E. The
direction of propagation is shown by the point of an arrow coming out of
the page and perpendicular to it.
(b) An unpolarized transverse wave depicted as comprising many randomly
oriented plane-polarized transverse wave trains.
(c) An equivalent description of an unpolarized transverse wave. Here the
unpolarized wave has been depicted as consisting of two plane-polarized
waves which have a random phase difference. The orientation of the x
andy axes about the direction of propagation is also completely arbitary.
An instantaneous snapshot of a plane-polarized transverse wave showing
the electric- and magnetic-field vectors E and H, with the wave moving to
the right.
An electromagnetic wave is said to be plane-polarized if the vibrations of its
electric field vector, say, E, are parallel to each other for all points in the wave .
At all these points the vibrating E-vector and the direction of propagation
form a plane called the plane of vibration or the plane of polarization.
Representation of Plane polarized light
  

Plane polarized light with
Vibration perpendicular to the
Plane of paper
Plane polarized light with
vibrations parallel to the plane
of paper
Mathematical representation of Plane polarized light
Suppose light is propagating in z-direction .
Mathematically a plane polarized light can be
represented as:
E x  z , t   i E0 x coskz  t 
or
E y  z , t   j E0 y coskz  t 
X
Z
Y
Production of polarized light
1.
2.
3.
4.
By Reflection: Brewster’s Law
By Refraction: Malus Law
By selective absorption: Dichroic material
By double refraction:
-Nicol Prism
- Wave plates
Law of Malus
I  I 0 cos 2 
Where
I - is intensity of transmitted
light.
I0 - is intensity of incident
light.
θ - is angle between plane of
incident light and direction of
polarizer.
•
Unpolarized light can have E field vibration in all directions.
•
Therefore I = I0 <cos2> = I0/2
Birefringence
The refractive index of a material is independent of the direction of
propagation in the medium and of the state of polarization of the light. The
materials that show this behavior are called optically isotropic. Ordinary
glass, for example, is isotropic in its behavior.
There are certain crystalline materials, such as calcite, quartz, KDP
(potassium dihydrogen phosphate) etc., that are optically anisotropic, that
is, the velocity of propagation in such materials, in general, depends on the
direction of propagation and also the state of polarization of light known as
birefringent or doubly refracting.
DOUBLE REFRACTION
Phenomenon of double refraction exhibited by a birefringent crystal. The electricfield vectors of the o-ray and the e-ray are shown to vibrate perpendicular and
parallel to the plane of the
(Extraordinary)
figure, respectively.
E-ray

1020


re 
i
Here re > ro
Hence o > e
780



 O-ray

(ordinary)
ro
Principal section
Optic axis
The o-ray propagates inside the crystal with the same speed vo in all the directions and
hence the refractive index no (defined by c/vo, where c is the speed of light in vacuum) of
this crystal for this wave is constant.
On the other hand, the e-wave propagates inside the crystal with a speed that varies with
direction from vo to ve (ve > vo for calcite), which means that the refractive index of the
crystal, for the wave, varies with direction from no to ne ( ne < no for calcite).
However, there exists one direction along which both the o- and e-ray travel with the same
velocity. This direction is referred to as the optic axis of the crystal.
The quantities no and ne are referred to as the principal refractive indices for the crystal.
Such crystals, e.g., calcite, which are described by two principal refractive indices and one
optic axis, are called uniaxial crystals.
However, some birefringent crystals (e.g., mica, topaz, lead oxide, etc.) are more complex
as compared to calcite and, therefore, require three principal refractive indices and two
optic axes for a complete description of their optical behaviour.
Such crystals are referred to as biaxial crystals. It should be noted that in a biaxial crystal,
the wave velocities of the o- and e-wave (and not the ray velocities) are equal along the
two optic axes.
Huygen’s principle
all the points on a wavefront can be
considered
as
point
sources
of
secondary wavelets.
Let us consider an imaginary point
source of light, S, embedded in a
uniaxial
crystal.
This
source
will
generate two wavefronts—a spherical
one corresponding to the o-ray and an
ellipsoid of revolution about the optic
axis corresponding to the e-ray.
Huygen’s principle
The two wave surfaces represent light having two
different polarization states.
the plane of polarization of the o-rays is
perpendicular to the plane of the figure and that of
the e-rays coincides with the plane of the figure.
In a crystal, if vo >ve (or no < ne) in all the directions
(except the optic axis), then the spherical
wavefront would be completely outside the
ellipsoidal wavefront. The two surfaces will touch
at two diametrically opposite points on the optic
axis, along which the two wavefronts travel with
equal velocities. Such a crystal is called a positive
uniaxial crystal examples are Quartz and rutile
(titanium oxide).
If vo < ve (or no > ne), the spherical wavefront lies
completely inside the ellipsoidal wavefront, and
the crystal is referred to as a negative uniaxial
crystal. Eg. Calcite, KDP, etc.
In negative uniaxial crystals the sphere lies inside the ellipsoid, while in
positive uniaxial the ellipsoid lies inside the sphere.
In quartz the velocity of O ray
is greater than velocity of E
ray.
vo > ve so o <
e and ro > re
In calcite the velocity of O ray
is less than velocity of E ray.
vo < ve so o > e and ro <
re
Huygen’s explanation of double refraction in uniaxial crystal
•one ray obeys the laws of refraction, known as ordinary ray (oray).
•Other ray does not obey the snell’s law for which sin i /sin r
does not remain constant, known as extra-ordinary ray (e-ray).
•Along optic axis velocities of the two rays are same.
•In a direction perpendicular to the optic axis both rays travel
along the same path but with different velocities.
•difference between the refractive indices for O ray and E ray is
known as birefringence =(o-e)
•Substance which exhibits different properties in different
direction called anisotropic substance.
Representation
of
Huygen’s wavefronts for
the o- and e-wave in a
negative uniaxial crystal
when the optic axis is
(a) perpendicular,
(b) and (c) parallel
(d) at an oblique angle to
the crystal surface.
Double
refraction
negative
uniaxial
by
a
crystal
when the optic axis is at an
arbitrary angle to the crystal
surface. The o-ray and e-ray
are polarized perpendicular
to and in the plane of figure,
respectively
Retarders or wave plates
This is a class of optical devices which introduce a phase difference
between extra-ordinary and ordinary rays.
These are in the form of plates of doubly refracting crystal cut in such a
way that optic axis is parallel to the refracting surfaces.
Optic axis
 Et
 ot
(E ~ O)d
t
= path difference between
Extraordinary and ordinary
Rays.
Retardation Plates
Consider a plane-polarized light of angular frequency  incident normally on a
thin slab, thickness d, of a uni-axial crystal that has been cut so that its optic axis
is parallel to the surface of the slab.
The phase change suffered by the o-wave when it emerges from the crystal
slab will be
0 = knod
where k = /c = 2 / is the free-space wave number, and that suffered by the ewave will be e = kned.
Thus, the slab introduces a phase difference
 = e - o = k(ne – no) d = 2 /(ne – no)d
between the two emergent waves, polarized at right angles to each other.
Thus by appropriate choice of the thickness d, it is possible to introduce a
predetermined phase difference between the two components for a given
wavelength of light.
Quarter wave plate (QWP)
This is a plate of double refracting crystal having thickness 'd'
such that path difference between E-ray
and O-ray is  /4
( E  o )d   / 4 or (4n  1) / 4
(2n  1) / 4
where n=0,1,2,3,...
Phase difference   (2n  1) / 2
Use: QWP Convert plane polarized (PP) to circular polarized
(CP) or elliptically polarized (EP) light and vice verse.
Note: Birefringence is (E ~ O)
Half wave plate (HWP)
• This is a plate of double refracting crystal having thickness t
such that path difference between E-ray and O-ray is /2.
(E ~ O)t = /2 or (2n+1)λ/2
n=0,1,…
Phase difference:  =π
Use: HWP Convert Right
circular polarized (RCP) or
right elliptically polarized
(REP) light to LCP or LEP
and vice verse.
Note: Birefringence is (E ~ O)
Similarly λ (Full wave Plate) , λ/6 plate or λ/8 plate etc
ELECTRO-OPTIC MODULATORS
Electro-optic Effect: The application of an electric field across a
crystal may change its refractive indices. Thus, the field may
induce birefringence in an otherwise isotropic crystal or change
the birefringent property of a doubly refracting crystal.
If the refractive index varies linearly with the applied electric
field, it is known as the Pockels effect, and if the variation in
refractive index is proportional to the square of the applied field,
it is referred to as the Kerr effect.
ELECTRO-OPTIC MODULATORS
we will study the Pockels effect in detail and see how such an
effect may be used to modulate a light beam in accordance with
the applied field. Such modulators are very useful in fiber-optic
communications.
Longitudinal Electro-optic Modulator
The precise effects of an applied electric field across a crystal showing the
Pockels or linear electro-optic effect depend on the crystal structure and
symmetry.
Let us consider the example of KDP, which is one of the most widely used
electro-optic crystals. KDP is a uniaxial birefringent crystal. It possesses a
fourfold axis of symmetry (that is, the rotation of the crystal structure about
this axis by an angle 2 /4 leaves it invariant), which is chosen as the optic
axis of the crystal, normally designated the z-axis. It also possesses two
mutually orthogonal twofold axes of symmetry, esignated the x-axis and yaxis.
Longitudinal Electro-optic Modulator
Upon the application of electric field Ez along the z-axis, the crystal no longer
remains uniaxial but becomes biaxial. The principal x-axis and y-axis of the crystal
are rotated through 45° into new principal axes x’ and y’.
Longitudinal Electro-optic Modulator