lect11-semiconductor lasers and light-emitting diodes(2)

8/14/2019 Lect11-Semiconductor Lasers and Light-emitting Diodes(2)

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Electroluminescence in pn junctions

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ElectroluminescenceThe spontaneous emission of light due to the radiativerecombination from within the diode structure is known aselectroluminescence (EL) .

The term electroluminescence is used when the opticalemission results from the application of an electric field.

The light is emitted at the site of carrier recombination whichis primarily close to the junction , although recombinationmay take place through the whole diode structure as carriersdiffuse away from the junction region.

The amount of radiative recombination and the emission areawithin the structure is dependent upon the semiconductormaterials used and the fabrication of the device.

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depletion

Forming a p+-n+ junction in thermal equilibrium

p+

n+

---- --

-- +

+++ ++

++

p+

n+

x

E

W

position position

eV0

energy

Ecp

EvpEFp

Eg

Ecn

Evn

EFn

Eg

Ecp

EvpEFp

Eg

Ecn

Evn

EFn

Eg

eV0 > Eg


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Eg

EFv EFc

position

Eg

Heavily doped p+-n+ junction in thermal equilibrium

E l e c t r o n

e n e r g y eV0 > Eg

depletion


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Heavily doped p+-n+ junction under forward bias

he V > Eg

EFv

EFc

h

E l e c t r o n e n e r g y

position

e(V0-V)injection

injection

When a forward bias nearly equals or exceeding the bandgap

voltage there is conduction. (eV > E g) At high injection carrier density in such a junction there is anactive region near the depletion layer that containssimultaneously degenerate populations of electrons and holes. The injection carrier may be largely electrons injected into the p-nregion because of their larger mobility.

Active

EgEg


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Radiative recombination in a forward-biased p-n junction

The increased concentration of minority carriers in theopposite type region in the forward -biased p-n diode of

direct - bandgap materials leads to the radiative recombination of carriers across the bandgap.

The normally empty electron states in the conduction band of

the p-type material and the normally empty hole states in thevalence band of the n-type material are populated by injected carriers which recombine with the majority carriers across the bandgap.

The energy released by this electron-hole recombination isapproximately equal to the bandgap energy Eg.

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LED, SOA, LD

pn pn pn

Light-emitting diode SemiconductorOptical Amplifier

Laser Diode


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The light output of an LED is the spontaneous emission generated byradiative recombination of electrons and holes in the active region of the diode under forward bias.

The semiconductor material is direct-bandgap to ensure high

quantum efficiency , often III-V semiconductors. An LED emits incoherent, non-directional, and unpolarized spontaneous photons that are not amplified by stimulated emission .

An LED does not have a threshold current . It starts emitting light assoon as an injection current flows across the junction.

Light-emitting diodes (LEDs)


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Heavily doped p-n junction under forward bias

heV > Eg

EFv

EFch

E l e c t r o n e n e r g y

position

The internal photon flux : = int i/e

(injection electroluminescence)

int: int. quantum efficiency

e(V0-V)injection

injection

EgEg


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Internal quantum efficiency The internal quantum efficiency int of a semiconductor material:the ratio of the radiative electron-hole recombination coefficient to thetotal (radiative and nonradiative ) recombination coefficient.

This parameter is significant because it determines the efficiency of light generation in a semiconductor material.

Recall that the total rate of recombination = r n p [cm-3 s-1]

If the recombination coefficient r is split into a sum of radiative andnonradiative parts, r = r r + r nr , the internal quantum efficiency is

int = r r / r = r r / (r r + r nr )


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Define the radiative and nonradiative recombination lifetimes r and nr

1/ = 1/ r + 1/ nr

The internal quantum efficiency is then given by r r /r = (1/ r )/(1/ )

*Semiconductor optical sources require int to be large(in typical direct bandgap materials r nr ).

The internal quantum efficiency may also be written in terms of therecombination lifetimes as is inversely proportional to r.

int = / r = nr / ( r + nr )

Recombination lifetimes


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Order-of-magnitude values for recombination coefficientsand lifetimes

material r r (cm3 s-1) r nr int

Si 10-15 10 ms 100 ns 100 ns 10-5

GaAs 10-10 100 ns 100 ns 50 ns 0.5

The radiative lifetime for bulk Si is orders of magnitude longer than itsoverall lifetime because of its indirect bandgap (electron momentummismatched ). This results in a small internal quantum efficiency. For GaAs, the radiative transitions are sufficiently fast because of itsdirect

bandgap (electron momentum matched

), and the internal quantumefficiency is large.

*assuming n-type material with a carrier concentration n o = 1017 cm-3 and defect centers with aconcentration 1015 cm-3 at T = 300 K


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Electroluminescence in the presence of carrier injection

The internal photon flux (photons per second), generated within avolume V of the semiconductor, is directly proportional to the carrier-

pair injection rate R (electron-hole pairs/cm3-s).

The steady-state excess-carrier concentration n = R , where

is the total recombination lifetime (1/ = 1/ r + 1/ nr ). The injection of RV carrier pairs per second therefore leads to thegeneration of a photon flux = int RV photons/s.

= int RV = int V n/ = V n/ r

Or = int V (i/e)/V = int i/e


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Enhancing the internal photon flux

n/ r => Need higher n, shorter r

1. The excess carriers in a LED with homojunction (same materials onthe p and n sides ) are neither confined nor concentrated but are spread by carrier diffusion .

The thickness of the active layer in a homojunction is normallyon the order of one to a few micrometers , depending on the diffusion

lengths of electrons and holes.

2. There is no waveguiding mechanism in the structure for opticalconfinement. It is therefore difficult to control the spatial mode

characteristics (essential for laser diode ).


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A p+-n+ homojunction under forward biash

x

x

x

E x c e s s c a r r

i e r

d i s t r i b u t i o n

R e f r a c t

i v e

i n d e x

p r o

f i l e

O p t

i c a l

f i e l

d


EFv

EFc

~ 1 - few m

Eg Eg

carriers diffuse

homostructure

no waveguiding

Photons generatedcan be absorbed outside the activeregion


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Double heterostructures Very effective carrier and optical confinement can be simultaneouslyaccomplished with double heterostructures . A basic configuration can

be either P-p-N or P-n-N (the capital P, N represents wide -gap materials, p, n represents narrow -gap materials). The middle layer is a narrow-gapmaterial . (e.g. Ga1-yAlyAs-GaAs-Ga1-xAlxAs)

Almost all of the excess carriers created by current injection areinjected into the narrow-gap active layer and are confined within thislayer by the energy barriers of the heterojunctions on both sides of theactive layer .

Because the narrow-gap active layer has a higher refractive index thanthe wide-gap outer layers on both sides, an optical waveguide with the

active layer being the waveguide core is built into the doubleheterostructure.


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A P+-p-N+ double heterostructure under forward bias(GaAlAs/GaAs/GaAlAs)

h

x

x

x

E x c e s s c a r r

i e r

d i s t r

i b u t

i o n

R e f r a c

t i v e

i n d e x

p r o f i l e

O p t i c a l

f i e l d


EFv

EFc

~ 0.1 m

~few %

Ec

Ev

wide-gap outerlayers aretransparent to theoptical wave

carriers confined

Double

heterostructure

waveguiding


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Double heterostructures


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LED power

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e.g. The radiative and nonradiative recombination lifetimes of the minority carriers in the active region of a LED are 60 ns and

100 ns. Determine the total carrier recombination lifetime and the power internally generated within the device when the peak emission wavelength is 870 nm at a driving current of 40 mA. The total carrier recombination lifetime is given by

= r nr / ( r + nr ) = 37.5 ns

The internal quantum efficiencyint = / r = 0.625

=> Pint = int i/e (1240 eV-nm / 870 nm) = 36 mW!

( However, this power level is not readily out-coupled from the device ! )


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Output photon flux and efficiency The photon flux spontaneously generated in the junction active regionis radiated uniformly in all directions . However, the flux that emerges

from the device (output photon flux) depends on the direction ofemission.

p

n

A

l1c

B

Cactive region

e.g. Ray A at normal incidence is partially reflected. Ray B at obliqueincidence suffers more reflection. Ray C lies outside the critical angleand thus is trapped in the structure by total internal reflection .


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The photon flux (optical power) traveling in the direction of ray A(normal incidence) is attenuated by the factor

1 = exp(- l1)where is the absorption coefficient (cm-1) of the n-type material, and l1is the distance from the junction to the surface of the device.

For normal incidence, reflection at the semiconductor-air boundary permits only a fraction of the light to escape (see Fresnel reflection inLecture 2)

2 = 1 [(n-1)2/(n+1)2] = 4n / (n+1)2

where n is the refractive index of the semiconductor material.(For GaAs, n = 3.6,

2= 0.68. The overall transmittance for the

photon flux (power) traveling in the direction of ray A is A= 1 2)

reflectance


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The photon flux traveling in the direction of ray B has farther to travelsuffers a larger absorption;

a larger incident angle at the semiconductor-air interface=> a greater Fresnel reflection loss=>

B The output photon flux o = ext i/e=> ext is simply the ratio of the output photon flux o to the injectedelectron flux i/e.


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The LED output optical power Po:

Po = h o = ext h i/e

The internal efficiency int

for LEDs ranges between 50% and justabout 100%, while the extraction efficiency e can be rather low.

The external quantum efficiency ext of LEDs is thus typically low.

Output optical power


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Responsivity The responsivity R of an LED is defined as the ratio of the emitted optical power Po to injected current i, i.e. R = Po/i

R = Po/i = h o/i = ext h /e

The responsivity in W/A, when o is expressed in m,

R = ext 1.24/ o

The linear dependence of the LED output power Po on the injected current i is valid only when the current is less than a certain value(say tens of mA on a typical LED). For larger currents, saturationcauses the proportionality to fail.


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O u t p u

t o p t

i c a l p o w e r

P o ( m W )

Current i (mA)

*saturation at high injectioncurrent (droop --- the loss of efficiency at high power)

Optical power at the output of an LED vs. injection current

Slope = responsivity R = ext 1.24/


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Power-conversion efficiencyAnother measure of performance is the power-conversionefficiency (or wall-plug efficiency ), defined as the ratio of theemitted optical power Po to the applied electrical power .

c Po / iV = ext h /eV

where V is the voltage drop across the device

Note that c ext because h eV, where eV = EFc EFv ina degenerate (heavily doped) junction.


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Surface-emitting diodes radiate from the face parallel to the p-n junction plane.(The light emitted in the opposite direction can be reflected by ametallic contact .) Edge-emitting diodes radiate from the edge of the junction region.

Surface-emitting and edge-emitting

Multimodefiber


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Spatial pattern of surface-emitting LEDs The far-field radiation pattern for light emitted into air from a planar surface-emitting LED is given by a Lambertian distribution:

I( ) = Io cos

=> The intensity decreases to half its value at = 60o

Planar surface Io

I( ) Lambertian spatial pattern in theabsence of a lens

In contrast, the radiation pattern from edge-emitting LEDs (and laserdiodes) is usually quite narrow and can often be empirically described

by the function (cos )s, with s > 1.


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MM fiber SM fiber

The coupling efficiency couple (assuming Lambertian spatial pattern):

couple = I( ) sin d I( ) sin d 0

a

0

= sin2 a = NA2

surface-emitting edge-emitting

a: Fiber acceptance angle


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Transparent epoxy lenses of different shapes alter the emission patternin different ways (e.g. hemispherical vs. parabolic lenses)

Epoxy lenses can also enhance the extraction efficiency e a lenswith a refractive index close to that of the semiconductor reduces indexmismatch, and thus optimizes the extraction of light from thesemiconductor into the epoxy. (epoxy : semiconductor ~ 1.5 : 3.5 )

In practice, epoxy lenses can yield a factor of 2-3 enhancement in

light extraction .

Epoxy-encapsulated LED

LED chip


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Enhancing the extraction efficiency LED die geometry designs vs. simple planar-surface-emitting LEDs(limited by Fresnel reflection )

Roughen the planar surface - permitting rays beyond the criticalangle to escape via scattering

Contact geometry designs - Top-emitting LEDs make use of current-spreading layers , which are transparent conductive semiconductor layers(typically indium-tin-oxide (ITO)) that spread the region of lightemission beyond that surrounding the electrical contact.

Also include the use of reflective and transparent contacts ,transparent substrates ( flip-chip packaging allows light to be extracted through the substrate ), distributed Bragg reflectors, 2D photonic crystals,etc.


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Summary: LED efficiencies Internal quantum efficiency int - only a fraction of the electron-holerecombinations are radiative in nature

Extraction efficiency e only a small fraction of the light generatedin the junction region can escape from the high-index medium

External quantum efficiency ext = e int (can be measured fromthe responsivity R = Po/i)

Power-conversion (wall-plug ) efficiencyc efficiency of converting

electrical power to optical power ( c ext)

Coupling efficiency couple only a fraction of the light emitted from

the LED can be coupled (e.g. to an optical fiber)


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Spectral distribution The spectral intensity R sp( ) of light spontaneously emitted from asemiconductor in quasi-equilibrium (upon injection ) can be determinedas a function of the concentration of injected carriers n. The spectral intensity of the direct band-to-band injection-electroluminescence has precisely the same shape as the thermal-equilibrium spectral intensity , but its magnitude is increased by thefactor exp [(EFc EFv)/k BT], which can be very large in a presence of

injection. (assuming E Fc , E Fv within the bandgap for this simpleenhancement factor, eV = E Fc - E Fv)

1.2 1.3 1.4 1.5 1.6 1.7 h

Eg2k BT


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Spectral intensities vs. wavelength for LEDs

Wavelength m0.2 0.3 0.4 0.5 0.6 0.7

AlN: the largest III-nitride bandgap, emitting at 210 nmAlGaN: mid and near UVInGaN: violet, blue, and greenAlInGaP: yellow, orange, and red InGaAsP: near IR (1.3 1.55 m)

*LEDs arebroadband incoherent sources.


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Modulation


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Direct current modulation An LED can be directly modulated by applying the modulation signalto the injection current, an approach known as direct current-modulation .

There are two factors that limit the modulation bandwidth of an LED:the junction capacitance and the diffusion capacitance .

Because an LED is operated under a forward bias, the diffusion

capacitance is the dominating factor for its frequency response.

The diffusion capacitance is a function of the carrier lifetime , whichis the total carrier recombination lifetime (1/ = 1/ r + 1/ nr ), because it is associated with the injection and removal of carriers in thediffusion region in response to the modulation on the injection current .

The intrinsic speed of an LED is primarily determined by the lifetimeof the injected carriers in the active region .


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For an LED that is biased at a DC injection current level io and ismodulated at an angular frequency = 2 f with a modulation index m,

the total time-dependent current that is injected to the LED isi(t) = io + i1(t) = io (1 + m cos t)

In the linear response regime under the condition that m


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Normalized modulation response

-5

-4

-3

-2

-1

0

N o r m a l

i z e d m o d u l a t

i o n r e s p o n s e

R ( f ) / R ( 0 ) ( d B )

= 10 ns

0 5 10 15

Modulation frequency, f (MHz)

20

f 3dB = 1/2 = 15.9 MHz

*in electronics,f 3dB 0.35/rise time

=> rise time 2.2


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The spontaneous carrier lifetime is normally on the order of a few hundred to 1 ns for an LED.

The modulation bandwidth of an LED is typically in the rangeof a few megahertz to a few hundred megahertz .

A modulation bandwidth up to 1 GHz can be obtained with areduction in the internal quantum efficiency ( int = / r ) of the LED byreducing the carrier lifetime to the sub-nanosecond range .

Aside from this intrinsic response speed determined by the carrier lifetime, the modulation bandwidth of an LED can be further limited by parasitic effects from its electrical contacts and packaging, as wellas from its driving circuitry.

Modulation bandwidth


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Power-bandwidth productA 3-dB bandwidth f 3dB = 1/2

=> int f 3dB = ( / r ) (1/2 ) = 1/2 r One can obtain a certain internal-quantum-efficiency-bandwidth

product by choosing the semiconductor with a certain radiative lifetime .

At an injection current i, the output optical power and the small-signal modulation bandwidth of an LED have the following power- bandwidth product (i.e. a tradeoff between power and bandwidth):

Pof 3dB = e int (i/e) h (1/2 ) = e (i/e) h (1/2 r )At a given injection level , the modulation bandwidth of an LED is

inversely proportional to its output power . A high-power LED tends tohave a low speed, and vice versa . (P0f 3dB i)


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Semiconductor lasers

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Semiconductor as a gain medium Transition rates for semiconductors in quasi-equilibrium Rate equations Current pumping Laser threshold current Steady-state laser photon flux

Power output characteristics Spatial characteristics Spectral characteristics Typical laser diode specifications

Single-mode laser diode structures Wavelength-tunable laser diodes Direct modulation

Ref. Physics of Optoelectronics, Michael A. Parker, CRC Taylor and Francis, pp.47-78


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Semiconductor lasers*Some useful characteristics of semiconductor lasers:

1. Capable of emitting high powers (e.g. continuous wave ~ W).

2. A relatively directional output beam (compared with LEDs) permitshigh coupling efficiency (~ 50 %) into single-mode fibers.

3. A relatively narrow spectral width of the emitted light allowsoperation at high bit rates (~ 10 Gb/s), as fiber dispersion becomes

less critical for such an optical source.


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Laser diodes A laser diode (LD) is a semiconductor optical amplifier (SOA) thathas an optical feedback .

A semiconductor optical amplifier is a forward -biased heavily-doped p+-n+ junction fabricated from a direct -bandgap semiconductor material.

The injected current is sufficiently large to provide optical gain .

The optical feedback is usually implemented by cleaving thesemiconductor material along its crystal planes.

The sharp refractive index difference between the crystal (~3.5) andthe surrounding air causes the cleaved surfaces to act as reflectors.


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Electronenergy E Fc

E gE g

E Fvactiveregion(~ m)

h

Upon high injection carrier density in a heavily-doped p+

-n+

junction there exists an active region near the depletion layer, whichcontains simultaneously heavily populated electrons and holes population inverted!

Population inversion in a forward-biased heavily doped p+-n+ junction

P l i i i i P+ N+ d bl h d


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Population inversion in a P+-p-N+ double heterostructure under

forward bias (e.g. GaAlAs/GaAs/GaAlAs)

h

EFv

EFc

~ 0.1 m

Ec

Ev

activeregion

filled

The thin narrow-gap active region of a double heterostructurecontains simultaneously heavily populated electrons and holes in aconfined active region population inverted!


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Broadband optical gain

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k

EEFc

EFv

E2

E1

h

frequency

Opticalgain ( broadband )

FWHM = gain bandwidth

E g E FC - E FV


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Rate equations

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The rate equationsWe use the rate equations to describe how the gain , pump ,

feedback , and output coupler mechanisms affect the carrier and photon concentration in a device.

The rate equations manifest the matter-light interaction(emission, absorption) through the gain term.

The photon rate equation describes the effects of the outputcoupler and feedback mechanism through a relaxation termincorporating the cavity lifetime .

We will use the rate equations to determine the output optical power vs. input current (P-I curves ) and the modulationresponse to a sinusoidal bias current.


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Electron density and photon densityHere we denote the excess electron density (number ofelectrons per volume) by n

=> nVa represents the total number of excess electrons in theactive region of volume Va.

Also, let be the photon density (number of photons pervolume).

=> The total number of photons in the modal volume must be V and the total number of photons in the active regionmust be Va.


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Carrier rate equationThe carrier rate equation has the basic form (N: total numberof carriers)

dN/dt = Generation recombination

The carrier rate equation :

dN/dt = -(stimulated emission) + (absorption) + (Pump) (non-radiative recombination) (spontaneous

recombination)

This equation calculates the change in the number of carriersnVa in the active region.

Absorption and pumping increase the number while emissionand recombination decrease it.


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Spontaneous emission into the cavity modeThe number of photons in the lasing mode increases not onlyfrom stimulated emission but also from the spontaneousemission.

Excess electrons and holes can spontaneously recombine andemit photons in all directions.The wavelength range of spontaneously emitted photonsspans over the gain bandwidth.Some of the spontaneously emitted photons propagate inexactly the correct direction to enter the laser mode path.Of those photons that enter the laser mode path, a fraction ofthem have exactly the right frequency to match that of thelasing mode.

=> This small fraction of spontaneously emitted photons adds tothe photon density of the cavity.


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Spontaneous emission into the cavity modeThe rate of spontaneous emission into the cavity mode can bewritten as

V R sp = V r r n2

where r r is the radiative recombination coefficient (cm3 s-1),is the geometrical factor that gives the fraction of the totalspontaneously emitted photons that actually couple into thelaser mode. ( typically ranges from 10-2 to 10-5)The small fraction of spontaneous photons coupling into thecavity with the right frequency start the lasing process .

Above threshold , however, it wastes a significant fraction ofthe pump energy, thus raising the laser threshold current .


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Cavity optical lossThe total number of photons in the modal volume Vdecreases because of these optical losses.The number of photons lost from the cavity must depend onthe number of photons inside the cavity.Thus, a simple differential equation expresses the dynamicsin the absence of other sources or losses of photons

V d /dt = -V /

=> (t) = 0 exp (-t/ )

=> the initial photon density in the cavity decaysexponentially

All of the optical losses contribute to an overall relaxationtime --- the cavity lifetime (typically ~ 10-12 s ~ ps).


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Optical loss coefficientThe cavity lifetime describes a lumped device.

In order to include a spatial dimension , we define an optical

loss per unit length r [cm-1

].

r = 1/( vg) or 1/ = r vg

where vg represents the group velocity of the cavity light.Thus, the optical loss (per unit length) r gives the number of photons lost in each unit length of cavity.We picture the optical loss r as taking place along the lasercavity length.Suppose vg = c/ng ~ 108 m/s and ~ 10-12 s,then r ~ 104 m-1 or 102 cm-1


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Mirror lossHow to picture the mirror loss m as distributed along thelength d of the cavity?Assume that both mirrors have the same power reflectance R

(~0.34 for GaAs).The loss per mirror must be m/2.The rate of mirror loss can be written as(assume R = exp (- m/2 2d))

1/ m = vg m = (vg/d) ln (1/R)

The reciprocal of the cavity lifetime (total cavity decay rate) becomes

1/ = 1/ int + 1/ m = vg r = vg( int + m)

The internal loss and single mirror loss are typically on theorder of 30 cm-1.


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Stimulated emission or absorption rates


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pThe change in the total number of photons V in the modalvolume V due to gain and absorption must be proportionalto the number of photons present

R stim V = V d /dt V

R stim represents the net number of photons produced by

stimulated emission (R stim > 0) or absorbed (R stim < 0) in eachunit volume in each second (cm-3 s-1).

However, only those photons in the active region (volume

Va) can stimulate additional photons as the electron-hole pairs are confined to that region

R stim V = V d /dt Va

Temporal gain


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p gDefine the temporal gain gt (s-1)

R stim V = V d /dt = gt Va

R stim = d /dt = gt Va/V = gt

where = Va/V is the confinement factor.

The temporal gain gt must depend on the number of excessconduction-band electrons n per unit volume in the activeregion: gt = gt(n)The temporal gain gives exponential growth / decay of photon number density in time

= 0 exp ( gtt)

Material gain


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gWe define the material gain g (cm-1) in terms of the numberof photons produced in the medium in each unit of length foreach photon entering that unit length.

We can find the material gain from the temporal gain bychanging the units of gt from per second to those of thematerial gain g, namely per unit length.

Change of variables

d /dt = (d /dz) (dz/dt) = (d /dz) vg

=> d dz = (gt/vg) = gAgain, g = g(n) depends on the number of excess conduction- band electrons n per unit volume in the active region. (gt(n) =

vg g(n))


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Material gain in terms of stimulated rates


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R stim V = V d /dt = V (d /dz) vg = vg g Va

R stim = g ( Va) (vg/V

To account for frequency dependence , R stim then need torepresent the net number of photons produced by stimulatedemission (R stim > 0) or absorbed (R stim < 0) in each unitvolume in each second per unit frequency interval. (cm-3 s-1

Hz-1

or cm-3

)

Photon # inthe active region

Photon through each unitarea per unit time (cm-2 s-1)

Photon flux in the active region per unit area per unit time (cm-2 s-1)


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Peak gain coefficient as a function of current density for

the approximate linear model


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the approximate linear model

Note that J0 is directly proportional to the junction thickness l=> a lower transparency current density J0 is attained by using anarrower active-region thickness. (another motivation for usingdouble heterostructures where l is ~ 0.1 m or quantum wells )

Current density J (A cm-2)

P e a k g a i n c o e f

f i c i e n

t g p

( c m - 1 )

J0

-

gain

loss

*Net gain can be attained in asemiconductor junction only when J > J0.

J0 = (el/ int r ) n0


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The photon rate equation


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The photon rate equationThe photon rate equation

V d /dt = +(stimulated emission) - (absorption) (opticalloss) + (fraction of spontaneous recombination)

=> V d /dt = Vavgg V / + r r n2V

Using the optical confinement factor of = Va/V

=> d /dt = vgg / + r r n2

The rate equations


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Here we use the rate equations mainly to find the output power (also cavity power ) as a function of the bias current .We can also use them for a small-signal analysis of timeresponse of the laser beam to small changes in the biascurrent. Note that the laser rate equations are coupled (the electronequation depends on , the photon equation depends on n)and nonlinear as g is a function of n !In general the rate equations should be generalized to a

partial differential equation that includes a spatial coordinate.

dn/dt = -vgg + int (i/e)Va-1 r r n2

d /dt = vgg / + r r n2

Electron rate equation:

Photon rate equation:


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Power outputcharacteristics

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Photon density vs pump-current number densityWe solve the rate equations for the t d t t photon


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Photon density vs. pump current number densityWe solve the rate equations for the steady-state photondensity inside the laser cavity as a function of the steady-state pump-current number density int(i/e)Va-1.

The rate equations aredn/dt = -vgg(n) + int(i/e)Va-1 r r n2

d /dt = vgg(n) / + r r n2

A system attains steady state when all of the time derivatives become zero.

We assume that the laser has been operating for a long timecompared with the time constants (~ ps) and (~ ns).We define the effective carrier lifetime = 1/(r r n), assuminglarge excess carrier density.


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The photon-current relation below lasing threshold Thus the photon current relation


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106

Thus, the photon-current relation

= int(i/e)Va-1

This is the spontaneous emission photon density in the cavity .

The photon density is linear in the pump-current numberdensity int(i/e)Va-1 (or linear in the bias current i ).

The factor accounts for the geometrical factor describingthe coupling of spontaneous emission to the cavity mode.


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The steady-state laser equationsThe steady-state laser equations become


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108

The steady state laser equations become

0 = -vgg(n) + int(i/e)Va-1 r r n2

0 = vgg(n) /

The steady-state photon density equation can be solved forvgg(n)

vgg(n) = 1/(

Recall that the material gain g(n) and the temporal gain gt(n)are related vgg(n) = gt(n)

Steady-state temporal gain gt(n) = 1/(

Threshold carrier density

Th t d t t t l i ( ) i t t 1/( ) d


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109

The steady-state temporal gain gt(n) is a constant 1/( ) andindependent of n.

=> this requires the steady-state n to be a constant !

The threshold carrier density nth represents the approximatevalue of the carrier density n to produce steady-state laseroscillation n nth=> The steady-state carrier density remains fixed regardlessof the magnitude of the current above lasing threshold !

Below lasing threshold , the approximation n nth does nothold as the device produces mostly spontaneous emission=> the spontaneous emission term in the photon rateequation cannot be ignored.

Steady-state gain equals the loss At steady state above lasing threshold, the value of the

l i h f b i


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110

temporal gain therefore can be written asgt(nth) = 1/

If we write the cavity lifetime in terms of the loss coefficients(cm-1)

1/ = vg r

The steady-state material gain (cm-1) can be written as

g(nth) = gth = r

The gain equals the loss (and remains approximately fixed atg(nth) for currents larger than the threshold current) when the

laser oscillates.

(The gain condition !)


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Steady-state carrier density and photon density as

functions of injection current n


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112

current

S t e a d y - s

t a t e

c a r r i e r d e n s i

t y

ith

nth clamped at nth

currentith

P h o t o n

d e n s

i t y

Below threshold , the laser photon density is zero ; any increase inthe pumping rate is manifested as an increase in the spontaneous-emission photon flux, but there is no sustained oscillation .

Above threshold , the steady-state internal laser photon density isdirectly proportional to the initial population inversion (initial injected carrier density ), and therefore increases with the pumping rate, yetthe gain g(n) remains clamped at the threshold value ( g(nth)).

(additional carriersrecombine immediatelyunder the effect ofstimulated emissionand feedback )

Gain at threshold Above threshold , the gain does not vary much from gth = g(nth).


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113

g y gth g( th)Recall the differential gain is the slope of the gain g(n)

g0(n) = dg(n)/dn

For lasing, the differential gain is evaluated at the thresholddensity nth.The lowest order Taylor series approximation centered on thetransparency density n0 is

g(n) g0(n n0).

=> The gain at threshold must be

gth = g(nth) g0(nth n0)


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Remarks on threshold current density The threshold current density Jth is a key parameter in characterizing


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115

y th y p gthe laser-diode performance: smaller values of J th indicate superior

performance.

Jth can be minimized by (Jth J0):

maximizing the internal quantum efficiencyint

;

minimizing the resonator loss coefficient r ,

minimizing the transparency injected-carrier concentration n0,minimizing the active-region thickness l(key merit of using double heterostructures and quantum wells )


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Evolution of the threshold current density of semiconductor lasers

10000


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117Zhores Alferov, Double heterostructure lasers: early days and future perspectives,IEEE Journal on Selected Topics in Quantum Electronics, Vol. 6, pp. 832-840, Nov/Dec 2000

10

100

1000

10000

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

J t h

( A / c m

2 )

Year

4.3 kA/cm2(1968)

900 A/cm2(1970)

160 A/cm2(1981)

40 A/cm2(1988) 19 A/cm

2

(2000)

Impact of double heterostructures

Impact of quantum wells

Impact of quantum dots

Power output from two cavity mirrors

Now we convert the basic concepts (photon and current


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118

Now we convert the basic concepts (photon and currentnumber densities) into measurable quantities like optical power (Watts) and bias current (Amps) using simple scalingfactors.

Dimensional analysis for the power passing through bothlaser mirrors (assume equal reflectivity )

Power out both mirrors = Po = Energy / sec

= (energy/photon photons/volume modal volume) /m

= (hc/ V vg m

P-I below threshold We can find the output power from both mirrors as a functionf h bi i f l i b l h h ld i


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119

of the bias current i for a laser operating below threshold i Po = (hc/ ) ( int(i/e)Va-1) V vg m

Recall the cavity lifetime in terms of the mirror loss m and

the internal scattering / free-carrier absorption losses int

1/ = 1/ m + 1/ int = vg ( m + int)

P-I below threshold The P-I below threshold


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120

Po = (hc/ ) ( int(i/e)Va-1) V vg m

= ( int/ ) (hc/e ) ( m/( m+ int)) i

=> the output power below threshold is linear in the biascurrent i.

The modal coupling coefficient causes the output power to be of smaller magnitude than the power for the same laserabove threshold.

P-I above threshold Now we find the output power from both mirrors as afunction of the bias current i for a laser operating above


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121

function of the bias current i for a laser operating abovethreshold i > ith.Using the photon and carrier number density relation

= ( int(i/e)Va-1 r r nth2)

Po/[(hc/ )V vg m] = [( int(i/e)Va-1 int(ith/e)Va-1)]

Po = int (hc/e ) ( m/( int + m)) (i ith)

The P-I relation above threshold represents a straight line

with an intercept of ith.The mirror loss and the internal loss determine the slope ofthe line.Smaller mirror reflectivity gives larger loss m and thereforelarger output power .

The internal laser power above threshold:Power output of injection lasers


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122

P = int (hc/e ) (i ith) = (hc/ ) int (i ith)/e

Only part of this power can be extracted through the cavity mirrors,and the rest is dissipated inside the laser resonator.

Po = int (hc/e ) (i ith) (1/d) ln(1/R) / r

= e int (hc/e ) (i ith) = ext (hc/e ) (i ith)

The output laser power if the light transmitted through both mirrorsis used (assume R = R 1 = R 2 => total mirror loss m = (1/d)ln(1/R))

external differentialquantum efficiency

extractionefficiency ( m/ r )

External differential quantum efficiency The external differential quantum efficiency ext is defined as


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123

ext = d(Po/(hc/ ) / d(i/e)

=> dPo/di = ext hc/e = ext 1.24/ R (W/A)

Drive current i (mA) O u t p u

t o p t i c a l p o w e r P

o ( m W )

ith

slope R is known as the differential responsivity(or slope efficiency) --- we can extract ext from measuring R

e.g. InGaAsP/InGaAsP:

o: 1550 nm

ith: 15 mAext: 0.33

R: 0.26 W/A

e.g. Efficiencies for double-heterostructure InGaAsP laser diodesConsider again an InGaAsP/InP double-heterostructure laser diode with

= 0 5 = 59 cm-1 = 118 cm-1 and i = 38 mA


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124

int = 0.5, m = 59 cm , r = 118 cm , and ith = 38 mA.

If the light from both output faces is used, the extraction efficiency ise = m/ r = 0.5

The external differential quantum efficiency isext = e int = 0.25

At o = 1300 nm, the differential responsivity of this laser is

R = dPo/di = ext 1.24/1.3 = 0.24 W/A

For i = 50 mA, i ith = 12 mA and Po = 12 0.24 = 2.9 mW

P-I characteristics

w e r

)


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125

L i g h t o u

t p u t ( p o w

Current

Incoherentemission

Coherent

emission(Lasing)

Threshold current ith

much steeper than LED

(typically few 10 mAsusing double heterostructures)

Comparison of LED and LD efficiencies and powers When operated below threshold , laser diodes produce spontaneousemission and behave as light-emitting diodes


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126

emission and behave as light emitting diodes.

There is a one-to-one correspondence between the efficienciesquantities for the LED and the LD.

The superior performance of the laser results from the fact that theextraction efficiency e for the LD is greater than that for the LED .

This stems from the fact that the laser operates on the basis ofstimulated emission , which causes the laser light to be concentratedin particular modes so that it can be more readily extracted.

A laser diode operated above threshold has a value of ext (10s of %)

that is larger than the value of ext for an LED (fraction of %).

Power-conversion efficiency The power-conversion efficiency (wall-plug efficiency ):


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127

c Po/iV

c = ext [(i ith)/i] (h /eV)

Laser diodes can exhibit power-conversion efficiencies in excess of 50%, which is well above that for other types of lasers. The electrical power that is not transformed into light is transformed

into heat. Because laser diodes generate substantial amount of heat they areusually mounted on heat sinks, which help dissipate the heat and stabilize the temperature.

@ i = 2ith => c = ( ext/2) (h /eV) < ext

Typical laser diode threshold current temperature dependence

outputpower

60oC50403020T =


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128

Threshold current: ith exp (T/To)

(To ~ 40 75 K for InGaAsP)

power(mW)

current (mA)

Threshold current increaseswith p-n junction temperature

ith1 = ith2 exp[(T1 T2)/T0]

ith1ith2x ~2 ~3

(empirical)

More on temperature dependence of a laser diode

As the temperature increases, the diodes gain decreases , and so more


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129

current is required before oscillation begins (threshold current increases

by about 1.5%/o

C) Thermal generated minority carriers , holes in the n layer and electronsin the p layer recombine with majority free electrons and holes in the

doped regions outside the active layer, reducing the number of chargesreaching the active layer, thereby reducing gain .

Reducing in gain leads to an increase in threshold current .


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Spatial characteristics

130


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Lateral modes However, w is usually larger than o => the waveguide will supportseveral modes in the direction parallel to the plane of the junction.


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132

Modes in the direction parallel to the junction plane are called lateral

modes . The larger the ratio w/ o, the greater the number of lateral modes possible.

Optical-intensity (near-field ) spatial distributions for the laserwaveguide modes (p, q) = (transverse, lateral) = (1, 1), (1, 2) and (1, 3)

wl


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Far-field radiation pattern A laser diode with an active layer of dimensions l and w emits coherentlight with far-field angular divergence o/l (radians) in the plane

di l h j i d / ( di ) i h l ll l


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134

perpendicular to the junction and o/w (radians) in the plane parallel

to the junction. The angular divergence determines the far-field

radiation pattern . Due to the small size of its active layer, the laser diode is characterized by an angular divergence larger than that of most other lasers.

o/l

o/we.g. for l = 2 m, w = 10 m,and o = 800 nm, the divergenceangles are 23o and 5o.

*The highly asymmetric ellipticaldistribution of laser-diodelight can make collimating it tricky!

Elliptical beam


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Laser spectrum

135

Laser spectrumThe basic difference between a semiconductor laser and other classes oflasers, such as fiber lasers, is that a semiconductor laser has a very short


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cavity and a high optical gain .

Thus, a semiconductor laser has a larger longitudinal mode spacing and alarger linewidth than most other lasers.A semiconductor laser typically has a cavity length in the range of 200-500 m with a corresponding longitudinal mode spacing in the range of 100-200 GHz.Because the gain bandwidth of a semiconductor is typically in the rangeof 10-20 THz, a multimode semiconductor laser easily oscillates in 10-20longitudinal modes.The linewidth of each longitudinal mode is typically on the order of 10MHz, but can be as narrow as 1 MHz or as broad as 100 MHz.The linewidth narrows, but the number of oscillating modes increases, asthe laser is injected at a current level high above its threshold.

136

Laser spectrumIn many applications, a laser oscillating in a single frequency isdesired


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desired.There are many different approaches to making a semiconductorlaser oscillates in a single longitudinal frequency.E.g. The use of a very short cavity , as is the case of a vertical-cavity surface-emitting laser (VCSEL), and the use of a frequency-selective grating , as is the case of the distributed Bragg reflector(DBR) laser.For these single-frequency lasers, the linewidth is still in the typicalrange of 1-100 MHz.It is possible to obtain single-frequency output with a linewidth onthe order of 100 kHz or less by injection locking with a narrow-

linewidth, single-frequency master laser source or by using ahighly frequency-selective external grating as one optical-feedbackelement.

137

Spectral characteristics The spectral width of the semiconductor gain coefficient is relativelywide (~10 THz) because transitions occur between two energy bands.


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138

Simultaneous oscillations of many longitudinal modes in suchhomogeneously broadened medium is possible (by spatial hole burning ).

The semiconductor resonator length d is significantly smaller than

that of most other types of lasers.

The frequency spacing of adjacent resonator modes = c/2nd istherefore relatively large. Nevertheless, many such modes can still fitwithin the broad bandwidth B over which the unsaturated gain exceedsthe loss .

=> The number of possible laser modes is M B/


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Growth of oscillation in an ideal homogeneously broadened medium

go( )g( )


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140

r g( )

Immediately following laser turn-on , all modal frequencies for whichthe small-signal gain coefficient exceeds the loss coefficient begin to

grow, with the central modes growing at the highest rate. After a shorttime the gain saturates so that the central modes continue to grow whilethe peripheral modes, for which the loss has become greater than the gain,are attenuated and eventually vanish. Only a single mode survives .

Homogeneously broadened medium Immediately after being turned on, all laser modes for which theinitial gain is greater than the loss begin to grow.

> h fl d i i d i h M d


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141

=> photon-flux densities 1, 2,, M are created in the M modes.

Modes whose frequencies lie closest to the gain peak frequency growmost quickly and acquire the highest photon-flux densities.

These photons interact with the medium and uniformly deplete the gainacross the gain profile by depleting the population inversion .

The saturated gain :g( ) = go( )/[1 + j/ s( j)]

where s( j) is the saturation photon-flux density associated with mode j. j=1

M

Homogeneously broadened medium Under ideal steady-state conditions, the surviving mode has thefrequency lying closest to the gain peak and the power in this preferredmode remains stable, while laser oscillation at all other modes vanishes.


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142

Semiconductors tend to be homogeneously broadened as intraband

scattering processes are very fast (~0.1 ps). [So it does not matter whichoptical transitions (modes) deplete the gain, the carrier distribution withinthe band quickly, within ~0.1 ps, return to quasi-equilibrium, and the whole gain

profile is uniformly depleted .] => Suggesting single-mode lasing

In practice , however, homogeneously broadened lasers do indeed oscillate on multiple modes because the different modes occupydifferent spatial portions of the active medium .

=> When oscillation on the most central mode is established, the gaincoefficient can still exceed the loss coefficient at those locationswhere the standing-wave electric field of the most central modevanishes .


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This phenomenon is known as spatial hole burning . It allows another mode, whose peak fields are located near the energy nulls of the

l d h i l

Spatial hole burning


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144

central mode, the opportunity to lase.

permits the simultaneous oscillation of multiple longitudinal modes ina homogeneously broadened medium such as a semiconductor.

Spatial hole burning is particularly prevalent in short cavities inwhich there are few standing-wave cycles.

=>permits the fields of different longitudinal modes, which aredistributed along the resonator axis, to overlap less , thereby allowing partial spatial hole burning to occur.

Multimode spectrum of a 1550nm laser diode


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145

3dB bandwidth~3 nm

Typical laser diode


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Typical laser diodespecifications

146

(AlGaAs laser diode)


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147

AlGaAs laser diode specificationsTemp.


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148

~4 nm linewidth multimode lasing

(InGaAsP laser diodes)


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149

InGaAsP Fabry-Perot laser diodes


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150


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Single-mode laser diodes

151

Single-mode laser diodes Essential for Dense-Wavelength-Division Multiplexing(DWDM) technology channel spacing is only 50 GHz in the 1550 nmwindow (i.e. 0.4 nm channel spacing or 64 channels within ~ 35 nm


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152

bandwidth of the C-band) Single-mode laser diodes: eliminate all but one of the longitudinalmodes

Recall the longitudinal mode spacing : =2

/ (2nd)

> the gain bandwidth => only the single mode within the gain bandwidth lases

But this either imposes very narrow gain bandwidth or very smalldiode size !

Multimode vs. singlemode laser spectra


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153

3-dB linewidth3-dB linewidth


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The most popular techniques for WDM

Distributed-feedback (DFB) laser diodes

p-contact


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155

The fabricated Bragg grating selectively reflects only one wavelength.

InGaAsP MQW active regionn-InP

p-InP

p-InGaAsP (grating)

AR coatingn-contact

Bragg grating provides distributed feedback

MQW: multiple quantum well

The grating in DFB lasers The laser has a corrugated structure etched internally just above (or below) the active region.

Th i f i l i h l i l fl li h


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156

The corrugation forms an optical grating that selectively reflects lightaccording to its wavelength.

This grating acts as a distributed filter , allowing only one of the

cavity longitudinal modes to propagate back and forth .

The grating interacts directly with the evanescent mode in the space just above (or below) the active layer.

The grating is not placed in the active layer , because etching in thisregion could introduce defects that would lower the efficiency of thelaser, resulting in a higher threshold current.


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DFB laser radiates only one wavelength B a single longitudinal mode

Anti-

d ~ 100 m

sub mSinglelongitudinal


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158

Active region

DFB laser

reflection(AR)

AR

For an InGaAsP DFB laser operating at B = 1.55 m, is about 220 nmif we use the first -order Bragg diffraction (m = 1) and n

eff ~ 3.2 3.5.

mode

B

Power-current characteristics of DFB laser diodes


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159

Different cavity lengths of 400, 600, 800, and 1200 m. The inset showsthe singlemode laser spectrum from a packaged 800- m long DFB laserat a fiber-coupled power of 150 mW @ 600 mA.

Funabashi et al.: Recent advances in DFBlasers for ultradense WDM applications,IEEE JSTQE, Vol. 10, March/April 2004

DFB laser modules


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160

Funabashi et al.: Recent advances in DFBlasers for ultradense WDM applications,IEEE JSTQE, Vol. 10, March/April 2004

DFB laser characteristics

Narrow linewidths (typically 0.1 0.2 nm), attractive for long-haulhigh-bandwidth transmission.


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161

Less temperature dependence than most conventional laserdiodes

The grating tends to stabilize the output wavelength, which varies withtemperature changes in the refractive index.

Typical temperature-induced wavelength shifts are just under 0.1 nm/oC,

a performance 3-5 times better than that of conventional laser diodes.

neff = m o/2

Vertical-cavity surface-emitting laser diodes

The vertical-cavity surface-emitting laser (VCSEL) was developed in the 1990s, several decades after the edge-emitting laser diode.


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162

This diode emits from its surface rather than from its side. The lasingis perpendicular to the plane defined by the active layer.

Instead of cleaved facets, the optical feedback is provided by Braggreflectors (or distributed Bragg reflectors DBRs) consisting of layerswith alternating high and low refractive indices.

Because of the very short cavity length (thereby a short gain medium),very high ( 99%) reflectivity are required, so the reflectors typicallyhave 20 to 40 layer pairs.

VCSEL schematic

Patterned or semitransparent metal electrodes

Circular-shaped laser beamoutput vertically


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163

active region

n

p

Metal electrodes

*The upper DBR is partially transmissive at the laser-outputwavelength.

DBR (20 40layer pairs)

DBR (20-40layer pairs)

short gain region

VCSEL merits Due to the short cavity length , the longitudinal-mode spacingis large compared with the width of the gain curve.

If the resonant wavelength is close to the gain peak , single-


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164

If the resonant wavelength is close to the gain peak , singlelongitudinal-mode operation occurs without the need for anyadditional wavelength selectivity.

VCSELs have short cavity lengths, which tend to decreaseresponse times (i.e. short photon cavity lifetimes ). Theresult is that VCSELs can be modulated at very high speeds .(e.g. 850 nm VCSELs can be operated at well above 10 Gb/s .)

The beam pattern is circular , the spot size can be madecompatible with that of a single-mode fiber, making thecoupling from laser to fiber more efficient (compared withthe elliptical beam from an edge-emitting diode laser ).

VCSEL applications VCSELs operating in the visible spectrum are appropriate as sourcesfor plastic optical fiber (e.g. for automotive) systems.

VCSELs are often selected as sources for short-reach datacom (LAN)


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165

VCS s a e o te se ected as sou ces o ( )networks operating at 850 nm. Applications include the high-speedGigabit Ethernet.

Longer-wavelength VCSELs (emitting in the 1300 and 1550 nmwavelengths) can be considered for high-capacity point-to-point fiber systems.

Because of the geometry, monolithic (grown on the same substrate)two-dimensional laser-diode arrays can be formed . Such arrays can beuseful in fiber optic-network interconnects and possibly in othercommunication applications (such as on-chip optical interconnects ).

Wavelength-tunable laser


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diodes

166

Wavelength-tunable laser diodes Sources that are precisely tunable to operate at specific wavelengths(e.g. in WDM systems, where wavelengths are spaced by fractions of anm) --- a wavelength tunable laser diode can serve multiple WDMchannels and potentially save cost, think using 64 fixed-wavelength


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167

p y , g gdiodes vs. a few wavelength-tunable laser diodes!

e.g. A DFB laser diode can be tuned by changing the temperature or

by changing its drive current. The output wavelength shifts a few tenths of a nanometer per degreeCelsius because of the dependence of the material refractive indexon temperature.

The larger the drive current, the larger the heating of the device.Tuning is on the order of 10-2 nm/mA. e.g. a change of 10 mA produces a variation in wavelength of only 0.1 nm (less than WDMchannel spacing).

Wavelength-tunable semiconductor lasersn Lm

m


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168

m = 2nL

=> = n/n + L/L m/m

Larry A. Coldren et al., Tunable semiconductor lasers: a tutorial, Journal of Lightwave Technology,Vol. 22, pp. 193 202, Jan. 2004

External-cavity tunable laser

Mode selection ( m)

Key mechanisms for semiconductor laser wavelengthtuning

By differential analysism = 2nL


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169

m + m = 2 n L + 2n L( m + m )/m = (2 n L + 2n L)/2nL

m/m + = n/n + L/L

= n/n + L/L - m/m

thermalor electricalinjection

cavitylengthtuning

mode selectionfiltering

=>

The tuning range is proportional to the change in the effectiverefractive index ( neff ), having cavity length and cavity mode fixed

Example: wavelength tuning by varying the refractiveindex


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170

/ = neff /neff

Consider the maximum expected range of variation in the effectiveindex is 1%. The corresponding tuning range would then be

= 0.01

For ~ 1550 nm, ~ 15 nm (This is quite decent as it covers abouthalf the C-band!)

Tunable Distributed-Bragg Reflector (DBR) laser diodes

p

Metal electrodes

IGain IPhase IBragg


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171

active region

nMetal electrodes

Gain Phase BraggA separate current controls the Bragg wavelength by changing thetemperature in the Bragg region. (need three separate electrodes !)

Heating causes a variation in the effective refractive index of the Braggregion, changing its operating wavelength .From the Bragg condition: neff = m o/2

neff /neff

Wavelength tunable VCSELs


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172

A tunable cantilever VCSEL. The device consists of a bottom n-DBR, a cavitylayer with an active region, and a top mirror. The top mirror, in turn, consists ofthree parts: a p-DBR, an airgap, and a top n-DBR, which is freely suspendedabove the laser cavity and supported via a cantilever structure. Laser drive currentis injected through the middle contact via the p-DBR. An oxide aperture isformed in the p-DBR section above the cavity layer to provide efficient currentguiding and optical index guiding . A top tuning contact is fabricated on the top n-DBR.

Connie J. Chang-Hasnain, Tunable VCSEL, IEEE Journal on Selected Topics in Quantum Electronics,Vol. 6, pp. 978 987, Nov/Dec. 2000


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Modulation characteristics

173

Laser diodes temporal response Laser diodes respond much faster than LEDs , primarily because therise time of an LED is determined by the natural spontaneous-emissionlifetime sp of the material.


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174

The rise time of a laser diode depends upon the stimulated-emissionlifetime .

In a semiconductor, the spontaneous lifetime is the average time thatfree charge carriers exist in the active layer before recombiningspontaneously ( from injection to recombination ).

The stimulated-emission lifetime is the average time that free chargecarriers exist in the active layer before being induced to recombine bystimulated emission.

Stimulated lifetime


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175

Otherwise, spontaneous recombination would occur before stimulatedemission could begin, decreasing the population inversion and inhibitinggain and oscillation.

The faster stimulated-emission process, which dominatesrecombination in a laser diode, ensures that a laser diode respondsmore quickly to changes in the injected current than a LED.

Typical LED rise time ~ 2 50 ns

Using 3-dB electrical bandwidth f 3dB = 0.35/rise time


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176

Stimulated emission from injection lasers occurs over a muchshorter period.

Rise times: ~ 0.1 1 ns3-dB bandwidth < 0.35 / (0.1 ns) = 3.5 GHz

=> 3-dB bandwidth < 0.35 / (2 ns) = 175 MHz

The modulation of a laser diode can be accomplished by changing thedrive current.This type of modulation is known as internal or direct modulation .Th i t it f th di t d i d l t d intensity modulation

Direct modulation


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177

The intensity of the radiated power is modulated - intensity modulation .

Drawbacks of direct modulation: (1) restricted bandwidth and (2) laser frequency drift (due to the phase modulation of thesemiconductor gain medium upon free-carrier density change ).

*Note: Laser diode direct modulation is now only used for relatively low-speed

modulation (below GHz).For GHz and beyond

, we typically employexternal

modulation , namely, running the diode laser at steady-state (continuous-waveoperation) and modulate the laser beam with an external modulator (which hasa bandwidth on the order of ten GHz).

Direct modulation

The coupled rate equations (given by the stimulated emission termvgg(n) ) => laser diode behaves like a damped oscillator (2nd -order ODEin d2 /dt2) before reaching steady state condition


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178

The direct modulation frequency cannot exceed the laser dioderelaxation oscillation frequency without significant power drop.(* Biasing above threshold is needed in order to accelerate the switching of a laserdiode from on to off .)

in d 2 /dt2) before reaching steady-state condition

Under a step-like electrical inputcurrent

thresholdsmall-signal bias


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179

time (ns)

Photondensity

relaxation osc. period

time (ns)

threshold (gain=loss)

gain clampingcondition @steady state

How fast can we modulate a laser diode?Low frequency (modulated under steady-state )

@ Relaxation frequency


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180

time (ns)

time (ns)

averaged pulse power

time (ns)

time (ns)

1st pulse power only (highestaverage power )

( )

> Relaxation frequency

Small-signal modulation behavior

Laser


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181

time (ns)

time (ns)

reduced average power

Laserdiode

LED

Relaxation oscillationfrequency

(LED does nothave the coupledstimulated emissionterm)

For sp ~ 1 ns, ~ 2 ps for a 300 m laser

Relaxation oscillation f ~ (1/2 ) [1/( sp )1/2] (i/ith 1)1/2

(i f ; f


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182

When the injection current ~ 2ith, the maximum modulation

frequency is a few GHz .

LED: f 3dB 1/2 sp ~ 100 MHz

LD: relaxation oscillation f

1/2 ( sp )1/2

~ GHz*For beyond GHz modulation, we usually use external modulation.

lect11-semiconductor lasers and light-emitting diodes(2)

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