OPTOELECTRONIC Sources & Detectors 7c-8

8/13/2019 OPTOELECTRONIC Sources & Detectors 7c-8

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INJECTION LASER DIODES

Consider a system of atoms present in 2

energy levels, E1and E2


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Assume a system of atoms in thermalequilibrium .

We can expect radiation similar to

black body radiation from such a

system

Radiation density per unit range ofspectral frequency centered about

( ) 1/exp/8 33

=

kTh

ch


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Population densities of atoms followBoltzmann statistics:

kTE

eN

:kT

E

eN1

1

andkT

E

eN2

2

( )

kT

EE

eN

N 21

2

1


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kTh

e

g

g

N

N

2

1

2

1 =

. g1and g2are called degeneracies of

levels 1 and 2Consider Rate of absorption due to

incident photonsOnly atoms in level E1will absorb the

photons


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Absorption rate depends on :1. Population in level 1

2.Radiation density of the incident

photons

112NBRa =

Result of absorption is emission:

spontaneous + stimulated


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Rate of spontaneous emission:221NAResp =

Rate of stimulated emission:

221NBRest=

Thus, 221221112 NBNANB +=

( ) 221221112 NANBNB =


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2121

2

112 ABe

ggB kT

h

=

21

21

2

1

21

12 1B

Ae

g

g

B

BkT

h

=

( )

1

/

2

1

21

12

2121

=

kT

h

egg

BB

BA


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Compare this result with

( ) 1/exp

/8 33

=

kTh

ch

(A21/B21) = 8h

3/c3

(B12/B21).(g1/g2)=1Above two equations are called Einsteins

equations


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Example: consider an incandescence lampT = 2000K emitting peak wavelength at

1.449 m. Find R

Ans: R = 7.02 x 10-3

Indeed very small. Spontaneous emission

will be most predominant in such cases.


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Threshold gain in laser diodesThreshold gain in laser diodesThreshold gain in laser diodesThreshold gain in laser diodes

Consider an optical cavity

Medium inside is the active regionIncident power PoAs the light propagates in z direction, itspower growsPz= Poexp [ g21.z]

. g21= gain coefficient for the system


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What started off as Po will end as PL at theother end of the cavity of length L

PL= Poexp [ g21.L]

There are also losses occurring in the path of

the light.Absorption losses, scattering losses, etc.

Consider net loss as a loss coefficient eff per

unit length

PL= Poexp [ (g21- eff).L]


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Consider the ends of the optical cavity to havereflectivity R1and R2respectively.

Fabry Perot Resonator Model

Supports a set of Characteristic Resonant

frequencies

Basically follows a model of an Oscillator

Amplifier with Feedback


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G = R2R1 Poexp [ (g21- eff).2L] / Po

This is the net gain over one pass

To sustain oscillation, the threshold conditionis:

G = 1 = R2R1 exp [ (gth- eff).2L]

Or, gth= eff+ (1/2L). ln [ 1/(R2R1)]


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Optoelectronic DevicesOptoelectronic DevicesOptoelectronic DevicesOptoelectronic Devices


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Devices that convert electricalDevices that convert electricalDevices that convert electricalDevices that convert electricalenergy to optical energy and viceenergy to optical energy and viceenergy to optical energy and viceenergy to optical energy and viceversaversaversaversaSemiconductors as PhotoconductorsSemiconductors as PhotoconductorsSemiconductors as PhotoconductorsSemiconductors as PhotoconductorsPPPP----n junctions can also be used asn junctions can also be used asn junctions can also be used asn junctions can also be used as

photodiodes.photodiodes.photodiodes.photodiodes.PhotodetectorsPhotodetectorsPhotodetectorsPhotodetectors

Solar CellsSolar CellsSolar CellsSolar CellsLight Emitting DiodesLight Emitting DiodesLight Emitting DiodesLight Emitting Diodes and Lasersand Lasersand Lasersand Lasers


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Consider a pConsider a pConsider a pConsider a p----n junction in reversen junction in reversen junction in reversen junction in reversebias.bias.bias.bias.If the pIf the pIf the pIf the p----n junction is uniformlyn junction is uniformlyn junction is uniformlyn junction is uniformlyilluminated by photons withilluminated by photons withilluminated by photons withilluminated by photons with h>EgThere is an added generation rateThere is an added generation rateThere is an added generation rateThere is an added generation rate

gopof EHPs/cmof EHPs/cmof EHPs/cmof EHPs/cm3333----s that cans that cans that cans that canparticipate in the current.participate in the current.participate in the current.participate in the current.


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p n

R V

Carriers are generated within the depletion region W.

AWgopcarriers generated within the depletion region W

In addition, the number of holes created within a diffusion

length Lpper second on the n-side: ALpgop

The number of electrons created within a diffusion length

Lnper second on the p-side: ALngop


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These electrons and holes are available due to the

diffusion of the optically generated carriers on either side.

Total contribution for current due to optically generated

carriers:

Iop= qAgop(Lp+ Ln+ W) directed from p to n

This current will be in addition to the reverse current that

flows in the junction:

I = Ith[exp(qV/kT)-1] - Iop

Note: I is directed from n to pWe can expand the above equation by writing the

expression for Ithand Iop


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( ) ( )WLLqAgenL

pL

qAI npopkTqVpn

nn

p

p

++

+= 1/

The I-V curve is thus lowered by an amount proportional

to gop

What happens when the device is shorted?

V = 0, the first term cancels, but not the second term.

There is a short circuit current Isc= -Iop


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When there is an open circuit, I = 0

( ) ( )WLLqAgenLpL

qA npopkTqV

p

n

nn

p

poc ++=

+ 1/

Voc= (kT/q). ln[(Iop/Ith) + 1]

( )

++

++

= 1.ln opp

n

nn

p

p

np

oc gn

Lp

L

WLL

q

kT

V


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In a symmetrical junction, pn= np, p= n

Also, pn/n= np/p= gthIf we neglect generation within W

Voc= (kT/q). ln(gop/gth)

Notice that gopshould be >> gth

As gopis increased, we should not expect Vocto increaseindefinitely.

More optically generated carriers means minority carrier

lifetime also reduces, gthincreases.

The appearance of Vocis called photovoltaic effect.


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Solar cell inventors at Bell Labs (left to right) Gerald Pearson,

Daryl Chapin and Calvin Fuller are checking a Si solar cell sample

for the amount of voltage produced (1954).


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If illumination is from one end


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TypicalI-Vcharacteristics of a Si solar cell. The short circuit current isIph

and the open circuit voltage isVoc. TheI-Vcurves for positive current

requires an external bias voltage. Photovoltaic operation is always in thenegative current region

V

I (mA)

Dark

Light

Twice the light

0.60.40.2

20

-20

0Voc

Iph


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Design of solar cells requires one to maximise the area of

illumination, increase absorption, decrease reflection at thesurface.

The maximum possible power that can be dissipated to a

load can be approximated to: Pmax= IscVoc

The ratio (ImVm)/( IscVoc) is called Fill Factor F

Figure of merit for a solar cell

Efficiency refers to how much of input light energy is

converted to electrical energy

Solar cells generally have about 10% efficiency


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LIGHT EMITTING DIODESLIGHT EMITTING DIODESLIGHT EMITTING DIODESLIGHT EMITTING DIODES


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(a) The energy band diagram of ap-n+

(heavilyn-type doped) junctionwithout any bias. Built-in potentialVoprevents electrons from diffusing

fromn+topside. (b) The applied bias reducesVoand thereby allows

electrons to diffuse, be injected, into the p-side. Recombination aroundthe junction and within the diffusion length of the electrons in the p-side

leads to photon emission.

h Eg

Eg

(b)

V

(a)

p n+

Eg

eVo

EF

p n+

Electron in CBHole in VB

Ev

Ec

Ev

EF

eVo

Electron energy

Distance into device

Ec


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Light output

pEpitaxiallayers

Substrate

n+

n+

A schematic illustration of one possible LED device structure. First n+isepitaxially grown on a substrate. A thinplayer is then epitaxially grown onthe first layer.


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(a) Photon emission in a direct bandgap semiconductor. (b) GaP isan indirect bandgap semiconductor. When doped with nitrogen thereis an electron recombination center atEN. Direct recombination

between a captured electron at ENand a hole emits a photon.

Ec

Ev

EN

Eg


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LASERS

LED is an incoherent light source generated

from spontaneous recombination of electronsand holes injected across a junction

In order to provide a coherent light source at aparticular wavelength, an LED needs to be

modified


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With a heavily doped p+-n

+ junction under

forward bias, population inversion is created


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Space charge region essentially exhibits

inversion phenomenon under forward bias with

injected carriers being made available by

forward bias.

Basic Semiconductor Laser:

What we need: Heavily doped direct band gap

semiconductor.


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Recombination of injected electrons and holes

in the junction results in the emission of non

coherent radiation as in an LED.

By building a resonant cavity, we can induceone photon to stimulate a radiative emission of

other e-h recombinations.

Di t bt d


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Semiconductor lasers have an optical cavity to build up the required

electromagnetic oscillations. In this example, one end of the cavity

has a Bragg distrubuted reflector, a reflection grating, that reflects

only certain wavelengths back into the cavity.

Optical cavity

DistrubtedBragg reflector

Diffractionlimitedlaser beam

Semiconductor

crystalPolished face

Current

Optical cavitycontainingactive layer

Corrugateddielectric structure

Distributed Braggreflector


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Double Heterostruture Laser

(a) A double heterostructure diode has two junctions which are

between two different bandgap semiconductors (GaAs and

AlGaAs).(b) Simplified energy band diagram under a large forwardbias. Lasing recombination takes place in the p-GaAs layer, the active

layer. (c) The density of states and energy distribution of electrons and

holes in the conduction and valence bands in the active layer

2 eV

Holes in VB

Electrons inCB

AlGaAsAlGaAs

1.4 eV

Ec

Ev

Ec

Ev

(a)

(b)

pn p

Ec

2 eV

(~0.1 m)

Stimulatedemissions

Energy

Ec

Ev

CB

VB

Density of states

Electrons in CB

EFn

EFp

(c)

ho

Holes in VB = empty states

GaAs


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n GaAs - p GaAs - p AlGaAs single

heterojunction


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Optoelectronic Detectors

Consider a reverse biased p-n junction:


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The response to an incident light is anoptically generated current whose value is

roughly proportional to the number of

incident photons.

( ) ( )WLLqAgenLpL

qAI npopkTqV

p

n

nn

p

p++

+= 1/

With large reverse bias,

( )WLLqAgnLpL

qAI npoppn

nn

p

p++

+=


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Optical absorption Coefficient

Optical incident power = Pin

Optical power entering thesemiconductor= Pin(1-R)

R = Fresnel reflection coefficient at theair-semiconductor interface.


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For e-h pairs to be produced, these

photons must be absorbed by the

material

Power absorbed over a length d of the

material ( Ln+Lp+W)Pabs= Pin(1-R).[1 exp(-d)]


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If the incident light is monochromatic

with wavelength =c/

Energy of each photon is hRate of photon absorption is

(Pabs/h) = (Pin(1-R)/h).[1 exp(-d)]

is strongly dependent on material.


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Assuming every photon absorbed results

in a EHP. The resulting photo current is

Ip= (Pin(1-R)q/h).[1 exp(-d)]

Quantum Efficiency:

= re/rp re=rate of electrons collected. re= (Pabs/h) Ip= q.re= q..rp

And rp= rate of photons incident.How to maximize ?


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Responsivity

R = Ip/ Pin (expressed in A.W-1)

Ip= q.re= q..rpAnd rp= rate of photons incident.

=Incident optical power/ Energy of photon= Pin/ h

Ip= q.re= q..rp = q.. Pin/ hR = Ip/ Pin = q./ h= q../ hc


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Long wavelength cut off

For the photo detector to absorb the

incident photons,Eph>>>>= Eg(= h= hc/)

The limiting value for wavelength ofincident photon = c= hc/Eg

Any wavelength greater than cwill not beabsorbed and detected


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Responsivity R for upto c

Responsivity R = 0 for above c

Ideal vs practical photodiode response


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c= hc/Eg

c(in m)= 1.24/Eg (in eV)

f


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Types of Photodetectors

Devices that measure light intensity.

Objective of design:

High sensitivity

High speed of response

For high sensitivity: Fill Factor, area A, gop

Are factors to consider

F hi h d


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For high speed:

Consider a series of light pulses 1 ns apart

During first pulse, photo generated minority

carriers are produced and detected.

But they must diffuse and be swept away in atime much less than 1 ns so that when the

second pulse arrives, it is detected accurately.

F thi l d l ti idth t j ti


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For this , large depletion widths at a junction

will help

The high electric field across a wide depletion

region will quickly drift away the carriers,

leaving only a thin region for the diffusion

process which can be completed within 1 ns.

One can also have a thick high resistive region

between p- and n- junction to form a p-i-nstructure.

p+

SiO2Electrode

Electrode


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(a) The schematic structure of an

idealizedpinphotodiode (b) The net

space charge density across the

photodiode. (c) The built-in field

across the diode. (d) Thepinphotodiode in photodetection is

reverse biased.

i-Si n+

net

eNa

eNd

x

(a)

(b)

W

x

E(x)

R

Eo

Iph

h>Eg

W

(c)

(d)

Vr

Vout

E

eh+

Wide W results in small C so the RC time


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Wide W results in small C, so the RC time

constant is small and speed of response is high

Avalanche Photodiode

Detects low level optical signals

Based on Avalanche multiplication effect


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OPTOELECTRONIC Sources & Detectors 7c-8

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