chapter 4

Chapter 4

Photonic Sources

Contents

• Review of Semiconductor Physics• Light Emitting Diode (LED)

- Structure, Material,Quantum efficiency, LED Power, Modulation

• Laser Diodes

- structure, Modes, Rate Equation,Quantum efficiency, Resonant frequencies, Radiation pattern

• Single-Mode Lasers

- DFB (Distributed-FeedBack) laser, Distributed-Bragg Reflector, Modulation

• Light-source Linearity• Noise in Lasers

Review of Semiconductor Physics

a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band.The resultant free electron can freely move under the application of electric field.b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of electrons across the band gap

-123 JK 1038.1 Bk

Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

n-Type Semiconductor

a) Donor level in an n-type semiconductor. b) The ionization of donor impurities creates an increased electron concentration distribution.


p-Type Semiconductor

a) Acceptor level in an p-type semiconductor.

b) The ionization of acceptor impurities creates an increased hole concentration distribution


Intrinsic & Extrinsic Materials• Intrinsic material: A perfect material with no impurities.

• Extrinsic material: donor or acceptor type semiconductors.

• Majority carriers: electrons in n-type or holes in p-type.• Minority carriers: holes in n-type or electrons in p-type.• The operation of semiconductor devices is essentially based on

the injection and extraction of minority carriers.

)2

exp(Tk

Enpn

B

gi

ly.respective ionsconcentrat intrinsic & hole electron, theare && inpn

e.Temperatur is energy, gap theis TEg

2inpn

[4-1]

[4-2]

The pn Junction


Electron diffusion across a pn junction creates a barrier potential (electric field) in the depletion region.

Reverse-biased pn Junction


A reverse bias widens the depletion region, but allows minority carriers to move freely with the applied field.

Forward-biased pn Junction


Lowering the barrier potential with a forward bias allows majority carriers to diffuse across the junction.

Ek

kš /a–š /a

Ec

Ev

ConductionBand (CB)

Ec

Ev

CB

The E-k Diagram The Energy BandDiagram

Empty k

Occupied kh+

e-

Eg

e-

h+

h

VB

h

ValenceBand (VB)

The E-k diagram of a direct bandgap semiconductor such as GaAs. The E-kcurve consists of many discrete points with each point corresponding to apossible state, wavefunction k(x), that is allowed to exist in the crystal.The points are so close that we normally draw the E-k relationship as acontinuous curve. In the energy range Ev to Ec there are no points (k(x)solutions).

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

Direct Band Gap Semiconductors

Indirect Band Gap Semiconductors

E

CB

k–k

Direct Bandgap

(a) GaAs

E

CB

VB

Indirect Bandgap, Eg

k–k

kcb

(b) Si

E

k–k

Phonon

(c) Si with a recombination center

Eg

Ec

Ev

Ec

Ev

kvb VB

CB

ErEc

Ev

Photon

VB

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs istherefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced fromthe maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination ofan electron and a hole in Si involves a recombination center .


Semiconductor Device Fabrication

• Device fabrication requires a critical study of the crystal structure of the different materials

• Crystal structure is the periodic arrangement of atoms (Si or Ge) or group of atoms (GaAs or NaCl etc.)

• The spacing between the atoms or group of atoms is called lattice spacing or lattice constant

• To create a semiconductor device we need a crystalline base/ substrate for mechanical strength and electric contacts

• Thin layers of semiconductor materials are grown on the substrate which should have the same lattice structure as that of the substrate

• Lattice matching is required, means lattice constant should be the same

• Lattice matching is important as we want to avoid temperature dependent stresses or strain

• This is known as epitaxial growth (we can change the impurity level in the adjacent layers)

LED Structure

For use in the fiber transmission applications an LED must have

• High radiance output

Radiance is a measure , in watts, of the optical power radiated into a unit solid angle per unit area of the emitting surface. High radiances are necessary to couple sufficiently high optical power levels into a fiber.

• Fast emission response time

The emission response time is the time delay between the application of a current pulse and the onset of optical

emission. Time delay is responsible for limiting the band width with which the source is modulated.

• High quantum efficiency

Quantum efficiency is related to the fraction of injected electron-hole pairs that recombine radiatively

continued

To achieve high radiance and high quantum efficiency, the LED structure must provide a means to confine the charge carriers and the stimulated optical emission to the active region of the pn-junction where radiative recombination can take place

Carrier Confinement:

It is important to achieve the high level of radiative recombination in the active region of the device which yields a high quantum efficiency.

Optical Confinement:

It is important for preventing absorption of the emitted radiations in the surroundings.


Cross-section drawing of a typical GaAlAs double heterostructure light emitter. In this structure, x>y to provide for both carrier confinement and optical guiding. b) Energy-band diagram showing the active region, the electron & hole barriers which confine the charge carriers to the active layer. c) Variations in the refractive index; the lower refractive index of the material in regions 1 and 5 creates an optical barrier around the waveguide because of the higher band-gap energy of this material.

)eV(

240.1m)(

gE [4-3]

Surface-Emitting LED


• Active region is etched circular well.

• The circular active area have diameter 50μm and up to 2.5 μm thick.

• The emission pattern is almost isotropic with a 120o half-power beam width

• This pattern is called Lambertian Pattern i.e., the source is equally bright when viewed from any direction but the power diminishes as cosθ where θ is the angle between the viewing direction and the normal to the surface

• The power is half when θ = 60o so half power beam width is 120o

Edge-Emitting LED


Consists of an active junction region (source of incoherent light and two guiding layers).

• To match the core diameter, the contact strip is 50-70 m

• Length of active region range from 100 to 150 m

• The emission pattern is more directional.

• In the plane parallel to the junction, emitted beam is Lambertian with half power width 120o

• In the perpendicular plane half power width decrease to 25 – 35o

Light source Materials

• Material used in the active region should be a direct band gap material.

• In direct band gap material, radiative recombination is very high to maintain adequate level of optical emission.

• Single element semiconductors are not direct band gap materials.• III (e.g., Al, Ga, In)-V (e.g., P, As, Sb) compounds are direct band

gap materials. Few ternary and quaternary combinations of the binary compounds of III-V materials are also direct band gap materials.

• For operation in 800 -900 nm spectrum, the material used is the ternary alloy Ga1-x Alx As

• The ratio x will determine the band gap of the material or wavelength of the peak emitted radiation. The value of x for active region is chosen so that the emission spectrum should be 800 – 850nm

• For x = 0.8, peak is at 810nm

continued• At longer wavelengths, the quarternary alloy In1-x Gax Asy P1-y is

one of the premier candidate.

• By varying x and y I the active area, LED’s with peak power at any wavelength between 1.0 – 1.7μm

• E = h= hc/• The peak emission wavelength can be expressed as a function

of band gap energy Eg in eV by the equation

(μm) = 1.240/ Eg (eV)

Semiconductor Material Bandgap energy (eV)

Silicon 1.12

GaAs 1.43

Germanium Ge 0.67

InP 1.35

Ga0.93Al0.03As 1.51

Spectral width of LED types


Rate equations, Quantum Efficiency & Power of LEDs

• When there is no external carrier injection, the excess density decays exponentially due to electron-hole recombination.

• n is the excess carrier density,

• Bulk recombination rate R:

• Bulk recombination rate (R)=Radiative recombination rate + nonradiative recombination rate

/0)( tentn

lifetime.carrier :

densityelectron excess injected initial :0

n

n

dt

dnR

)1rate(ion recombinat venonradiati )1( rateion recombinat radiative

)1( rateion recombinatbulk

r nrnrr /τR/τR

/τR

With an external supplied current density of J the rate equation for the electron-hole recombination is:

regionion recombinat of thickness: electron; theof charge :

)(

dq

n

qd

J

dt

tdn

In equilibrium condition: dn/dt=0

qd

Jn

n is the steady state electron density in the active region when a constant Current is flowing through it.

rnrr

nr

nrr

r

RR

R

int

Internal Quantum Efficiency

region active in the efficiency quantum internal :int

The internal quantum efficiency in the active region is the fraction of electron-hole pairs that recombines radiatively

Where Rr and Rnr are the radiative and non radiative recombination rates

and nr = n / Rnr is the non radiative life time

Where is the bulk recombination life time and given as

nrr 111

q

hcIh

q

IP intintint

region active current to Injected :

power, optical Internal :int

I

P

Where Rr is the total number of photons generated per second and has energy h Optical power generated internally in the active region in the LED is:

Optical Power

In general r and nr are comparable for direct band gap materials so for simple homojunction LED quantum efficiency would b ½. However double heterostructures can have 60-80% efficiency

If the total current injected is I, then the total number of recombinations per second is Rr + Rnr = I/q, substituting this equation in quantum efficiencyeq. we get

Rr = int I / q

External Quantum Eficiency

• In order to calculate the external quantum efficiency, we need to consider the reflection effects at the surface of the LED. If we consider the LED structure as a simple 2D slab waveguide, only light falling within a cone defined by critical angle will be emitted from an LED.

photons generated internally LED of #

LED from emitted photons of #ext [4-10]

dTc

)sin2()(4

1

0

ext

221

21

)(

4)0(tCoefficienon Transmissi Fresnel :)(

nn

nnTT

211

ext2 )1(

11 If

nnn

211

intintext )1(

powr, optical emitted LED

nn

PPP

Modulation of LED• The frequency response of an LED depends on:

1- Doping level in the active region

2- Injected carrier lifetime in the recombination region, .

3- Parasitic capacitance of the LED• If the drive current of an LED is modulated at a frequency of

the output optical power of the device will vary as:

• Electrical current is directly proportional to the optical power, thus we can define electrical bandwidth and optical bandwidth, separately.

2

0

)(1)(

i

PP

[4-15]

i

current electrical : power, electrical:

)0(log20

)0(10log BW Electrical

Ip

I

)I(

p

)p(

[4-16]

)0(

)(log10

)0(

)(log10 BW Optical

I

I

P

P [4-17]


Some LED and Laser Diode Material Mixtures and their Characteristics

LASER

Light Amplification by the Stimulated Emission of

Radiation

Advantages:

Ideal laser light is single-wavelength only. This is not exactly true for communication lasers.

Lasers can be modulated (controlled) very precisely.

Lasers can produce relatively high power. Indeed some types of laser can produce kilowatts of power. In communication applications, semiconductor lasers of power up to about 20 mW are available

Because laser light is produced in parallel beams, a high percentage (50% to 80%) can be transferred into the fiber.

Disadvantages:

Lasers have been quite expensive by comparison with LEDs.Reason: Temperature control and output power control is needed.

The wavelength that a laser produces is a characteristic of the material used to build it and of its physical construction. Lasers have to be individually designed for each wavelength they are going to use.

Amplitude modulation using an analog signal is difficult with most lasers because laser output signal power is generally non-linear with input signal power

An Ideal Beam of LASER Radiation

LASER has three main characteristics:

Monochromatic

Coherent

Collimated

Properties of LASER

Radiation which occurs at a single wavelength or color.

Monochromatic

Properties of LASER

It means all waves vibrate in step, there by constructively reinforcing each adjacent wave.

Constructive interferenceCoherent light

Destructive interferenceIncoherent light

=

=

Coherent

A.

B.

OPTICAL INTERFERENCE

Properties of LASER

It means rays are travelling in the same direction on parallel paths.

Source

Target area

A

Source

Collimating lensCollimating lens

B

Collimated

Properties of LASER

LASER (Light Amplification by the Stimulated Emission of Radiation)

• Laser is an optical oscillator. It comprises a resonant optical amplifier whose output is fed back into its input with matching phase. Any oscillator contains:

1- An amplifier with a gain-saturated mechanism

2- A feedback system

3- A frequency selection mechanism

4- An output coupling scheme • In laser the amplifier is the pumped active medium, such as

biased semiconductor region, feedback can be obtained by placing active medium in an optical resonator, such as Fabry-Perot structure, two mirrors separated by a prescribed distance. Frequency selection is achieved by resonant amplifier and by the resonators, which admits certain modes. Output coupling is accomplished by making one of the resonator mirrors partially transmitting.

Pumped active medium• Three main process for laser action:

1- Photon absorption

2- Spontaneous emission

3- Stimulated emission


Lasing in a pumped active medium

• In thermal equilibrium the stimulated emission is essentially negligible, since the density of electrons in the excited state is very small, and optical emission is mainly because of the spontaneous emission. Stimulated emission will exceed absorption only if the population of the excited states is greater than that of the ground state. This condition is known as Population Inversion. Population inversion is achieved by various pumping techniques.

• In a semiconductor laser, population inversion is accomplished by injecting electrons into the material to fill the lower energy states of the conduction band.

Fabry-Perot Resonator

A

B

L

M1 M2 m = 1

m = 2

m = 8

Relative intensity

m

m m + 1m - 1

(a) (b) (c)

R ~ 0.4

R ~ 0.81 f

Schematic illustration of the Fabry-Perot optical cavity and its properties. (a) Reflectedwaves interfere. (b) Only standing EM waves, modes, of certain wavelengths are allowedin the cavity. (c) Intensity vs. frequency for various modes. R is mirror reflectance andlower R means higher loss from the cavity.


)(sin4)1(

)1(22

2

kLRR

RII inctrans

[4-18]

R: reflectance of the optical intensity, k: optical wavenumber

1,2,3,.. :modesResonant mmkL

Laser Diode• Laser diode is an improved LED, in the sense that uses stimulated

emission in semiconductor from optical transitions between distribution energy states of the valence and conduction bands with optical resonator structure such as Fabry-Perot resonator with both optical and carrier confinements.


Laser Diode Characteristics

• Nanosecond & even picosecond response time (GHz BW)• Spectral width of the order of nm or less• High output power (tens of mW)• Narrow beam (good coupling to single mode fibers)

• Laser diodes have three distinct radiation modes namely, longitudinal, lateral and transverse modes.

• In laser diodes, end mirrors provide strong optical feedback in longitudinal direction, so by roughening the edges and cleaving the facets, the radiation can be achieved in longitudinal direction rather than lateral direction.

DFB(Distributed FeedBack) Lasers• In DFB lasers, the optical resonator structure is due to the incorporation

of Bragg grating or periodic variations of the refractive index into multilayer structure along the length of the diode.


Laser Operation & Lasing Condition

• To determine the lasing condition and resonant frequencies, we should focus on the optical wave propagation along the longitudinal direction, z-axis. The optical field intensity, I, can be written as:

• Lasing is the condition at which light amplification becomes possible by virtue of population inversion. Then, stimulated emission rate into a given EM mode is proportional to the intensity of the optical radiation in that mode. In this case, the loss and gain of the optical field in the optical path determine the lasing condition. The radiation intensity of a photon at energy varies exponentially with a distance z amplified by factor g, and attenuated by factor according to the following relationship:

)()(),( ztjezItzI [1]

h

zhhgIzI )()(exp)0()(

1R 2R

Z=0 Z=L

)2()()(exp)0()2( 21 LhhgRRILI

2

21

21 t,coefficien absorption effective :

tcoefficiengain :g factor,t confinemen Optical :

nn

nnRα

1n

2n

Lasing Conditions:

1)2exp(

)0()2(

Lj

ILI

[2]

[3]

[4]

Previous eq. gives us the information related to the resonant frequencies of Fabry-Perot cavity.

Condition for Threshold:

The condition to just reach the lasing threshold is the point at which the optical gain is equal to the total loss αt, in the cavity.

Using the condition for threshold and eqs. [2] and [3] we will get the relation for threshold gain

Continued

Threshold gain & current density

endth

tth

g

RRLg

21

1ln

2

1

thgg :iff lase"" tostartsLaser

[4-23]

For laser structure with strong carrier confinement, the threshold current Density for stimulated emission can be well approximated by:

thth Jg [4-24]

onconstructi device specificon dependsconstant :

Where αend is the mirror loss in the lasing cavity. Thus

Optical output vs. drive current


Semiconductor laser rate equations• Rate equations relate the optical output power, or # of photons per unit

volume, , to the diode drive current or # of injected electrons per unit volume, n. For active (carrier confinement) region of depth d, the rate equations are:

emission stimulatedionrecombinat sspontaneouinjectionrateelectron

lossphoton emission sspontaneouemission stimulatedratePhoton

Cnn

qd

J

dt

dn

RCndt

d

sp

phsp

[4-25]

densitycurrent Injection

timelifephoton

mode lasing theintoemission sspontaneou of rate

process absorption &emission optical theofintensity theexpressingt Coefficien

:

:

:

:

J

R

C

ph

sp

Threshold current Density & excess electron density

• At the threshold of lasing:

• The threshold current needed to maintain a steady state threshold concentration of the excess electron, is found from electron rate equation under steady state condition dn/dt=0 when the laser is just about to lase:

0 ,0/ ,0 spRdtd

thph

ph nC

nCn

10/ 25]-[4 eq. from [4-26]

sp

thth

sp

thth nqdJ

n

qd

J

0 [4-27]

Laser operation beyond the threshold

• The solution of the rate equations [4-25] gives the steady state photon density, resulting from stimulated emission and spontaneous emission as follows:

thJJ

spphthph

s RJJqd

)( [4-28]

External quantum efficiency

• Number of photons emitted per radiative electron-hole pair recombination above threshold, gives us the external quantum efficiency.

• Note that:

)mA(

)mW(]m[8065.0

)(

dI

dP

dI

dP

E

q

g

g

g

th

thiext

[4-29]

%40%15 %;70%60 exti

Laser Resonant Frequencies• Lasing condition, namely eq. [4-22]:

• Assuming the resonant frequency of the mth mode is:

,...3,2,1 ,2L2 1)2exp( mmLj

n2

1,2,3,... 2

mLn

mcm

LnLn

cmm 22

2

1

[4-30]

[4-31]

Spectrum from a laser Diode

widthspectral: 2

)(exp)0()(

20

gg [4-32]

Laser Diode Structure & Radiation Pattern

• Efficient operation of a laser diode requires reducing the # of lateral modes, stabilizing the gain for lateral modes as well as lowering the threshold current. These are met by structures that confine the optical wave, carrier concentration and current flow in the lateral direction. The important types of laser diodes are: gain-induced, positive index guided, and negative index guided.

(a) gain-induced guide (b)positive-index waveguide (c)negative-index waveguide

Laser Diode with buried heterostructure (BH)

Single Mode Laser

• Single mode laser is mostly based on the index-guided structure that supports only the fundamental transverse mode and the fundamental longitudinal mode. In order to make single mode laser we have four options:

1- Reducing the length of the cavity to the point where the frequency separation given in eq[4-31] of the adjacent modes is larger than the laser transition line width. This is hard to handle for fabrication and results in low output power.

2- Vertical-Cavity Surface Emitting laser (VCSEL)

3- Structures with built-in frequency selective grating

4- tunable laser diodes.

Frequency-Selective laser Diodes: Distributed Feedback (DFB) laser

k

neB

2 [4-33]

Frequency-Selective laser Diodes: Distributed Feedback Reflector (DBR) laser

Output spectrum symmetrically distributed around Bragg wavelength in an idealized DFB laser diode

)2

1(

2

2

mLn ee

BB

[4-35]

Frequency-Selective laser Diodes: Distributed Reflector (DR) laser

Modulation of Laser Diodes

• Internal Modulation: Simple but suffers from non-linear effects.• External Modulation: for rates greater than 2 Gb/s, more

complex, higher performance.• Most fundamental limit for the modulation rate is set by the

photon life time in the laser cavity:

• Another fundamental limit on modulation frequency is the relaxation oscillation frequency given by:

thph

gn

c

RRLn

c

21

1ln

2

11 [4-36]

2/1

11

2

1

thphspI

If

[4-37]

Relaxation oscillation peak

Pulse Modulated laser

• In a pulse modulated laser, if the laser is completely turned off after each pulse, after onset of the current pulse, a time delay, given by:

dt

)(ln

thBp

pd III

It

current Bias :

amplitude pulseCurrent : timelifecarrier :

B

p

I

I

[4-38]

Temperature variation of the threshold current

0/)( TTzth eITI

Linearity of Laser

Information carrying electrical signal s(t)

LED or Laser diodemodulator

Optical putput power:P(t)=P[1+ms(t)]

Nonlinearity

...2coscos)(

cos)(

210

tAtAAty

tAtx

x(t) Nonlinear function y=f(x) y(t)

Nth order harmonic distortion:

1

log20A

An

Intermodulation Distortion

nmmn m,ntnmBty

tAtAtx

,21

2211

2,...1,0, )cos()(

coscos)(

Harmonics:

21 , mn

Intermodulated Terms:

,...2,2, 212121

Laser Noise

• Modal (speckel) Noise: Fluctuations in the distribution of energy among various modes.

• Mode partition Noise: Intensity fluctuations in the longitudinal modes of a laser diode, main source of noise in single mode fiber systems.

• Reflection Noise: Light output gets reflected back from the fiber joints into the laser, couples with lasing modes, changing their phase, and generate noise peaks. Isolators & index matching fluids can eliminate these reflections.

chapter 4

Documents

intrinsic semiconductor

lattice structure

acceptor type semiconductors

majority carriers

conduction band

valence band

diode led structure

electron diffusion