Chapter 4 Optical SourceChapter 4 Optical Source -- OutlineOutline

4.1 Semiconductor physics4.1 Semiconductor physics-- Energy band Energy band -- Intrinsic and Extrinsic MaterialIntrinsic and Extrinsic Material-- pn Junctionspn Junctions-- Direct and Indirect Band Gaps Direct and Indirect Band Gaps

4.2 Light Emitting Diodes (LED)4.2 Light Emitting Diodes (LED)-- LED structureLED structure-- Light source materialsLight source materials--Quantum Efficiency and powerQuantum Efficiency and power-- Modulation of LEDModulation of LED

4.3 Laser Diodes4.3 Laser Diodes-- Laser diodes modes and thersholdLaser diodes modes and thershold-- Rate EquationsRate Equations-- External Quantum EfficiencyExternal Quantum Efficiency-- Resonant FrequenciesResonant Frequencies-- Single mode lasersSingle mode lasers-- Laser modulationLaser modulation

4.1 Semiconductor physics4.1 Semiconductor physics -- Energy bandEnergy band

Semiconductor: Conduction properties lies somewhere between those of conductor (metal) and insulator

Intrinsic Semiconductor: Pure crystal (such as Si, Ge) group IV

I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac** Rf Db Sg Bh Hs Mt Uun Uuu Uub Uuq Uuh Uuo

Lanthanides * Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Actinides ** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

Carrier: electrons / holes

Energy-band diagram:- conduction band EC- valence band EV- band gap Eg= EC - EV

4.1 Semiconductor physics4.1 Semiconductor physics -- Energy bandEnergy band

- free electron concentration n- hole concentration p- intrinsic carrier concentration ni

Concentration :

exp( ) (4.1)2

gi

B

En p n K

k T= = = − 2 3/2 3/42(2 / ) ( )B e hK k T h m mπ=

4.1 Semiconductor physics4.1 Semiconductor physics -- Energy bandEnergy band

Doping: Conduction can be greatly increased by adding traces of impurities from Group V or Group III

Doping Group V donor impurity (P, As, Sb; 5 electrons) free-electrons n-type material

Doping Group III acceptor impurity ( Al, Ga, In, Boron ) free-holes p-type material

Semiconductor physicsSemiconductor physics -- Intrinsic and Extrinsic Material Intrinsic and Extrinsic Material

Intrinsic material : A perfect material containing no impurities is called ~.Extrinsic material : Doped semiconductor is called ~.

Thermal generation produce electron-hole pairs( for intrinsic material: equal concentration n = p = ni )

Majority carriers : refers to electrons in n-type material, and holes in p-type material.Minority carriers: refers to holes in n-type material, and electrons in p-type material

Recombination : a free electron releases its energy and drops into a free hole in the valence band.

For extrinsic material: concentration of p and n is different, and follow the mass-action law: 2

ipn n= ni : intrinsic carrier concentration

Semiconductor physicsSemiconductor physics -- Intrinsic and Extrinsic Material Intrinsic and Extrinsic Material

Example 4-2Consider an n-type semiconductor which has been doped with a net concentration of ND donor impurities. Find electron and hole concentrations (nN, pN).

Let nN and pN be the electron and hole concentrations, respectively, where the subscript N is used to denote n-type semiconductor characteristics.

Total hole concentration pN (only from thermal excitation):

N D Nn N p= +

Np

Total electron concentration nN (from doped and thermal excitation):

2N N in p n⋅ =Mass-action law: 2( )D N N in p p n+ =

2 22 24

( 1 1 4 / )2 2

D D i DN i D

N N n Np n N− + −

= = − + − i Dn n2 /N i D

N D

p n nn n

Semiconductor physicsSemiconductor physics -- pn Junctionpn Junction

Doped n- or p-type semiconductor material by itself serves only as a conductor.

Only pn junction is responsible for the useful electrical characteristics of a semiconductor device

Barrier potential : prevents further movement of chargesDepletion region :

Reverse–biased for application in photodiodeForward–biased for application in laser diode

External battery can be connected to the pn junction, by reverse-biasor forward bias.

, /g ghf W hc Wλ= =Operating Wavelength:

Semiconductor physicsSemiconductor physics -- pn Junctionpn Junction

Forward-biased pn junction:Creates barrier potential, which prevent holes and electrons to move to junction region, but when pn junction is applied forward voltage, if eV >= Wg, the electrons and holes will move into junction region, and recombine, which will create Photons.

Reverse-biased pn junction:The width of the depletion region will increase on both the n side and p side. (will talk in next chapter for photodiode)

Note: for direct bandgap material

Semiconductor physicsSemiconductor physics -- Direct and Indirect Band GapsDirect and Indirect Band Gaps

Direct band gap material:no change of wavevector

efficientFor example: GaAs

Indirect band gap materialwith change of wavevector

LightLight--Emitting DiodesEmitting Diodes -- LED StructureLED Structure

Carrier (electron or hole ) confinement- bandgap difference of adjacent layer

Put fig. 4-8 here

The most effective structure: Double heterojunction (it could provide carrier and optical confinements.)

To achieve high radiance, high quantum efficiency, carrier confinement and optical confinement are necessary.

Structure:- homojunctions: same material (Wg)- single and double heterojunctions :

difference bandgap materials

Optical confinement- index difference of adjacent layer

Two basic LED configuration- Surface emitters - Edge emitters

Surface emitters /lambertian pattern

unsymmetric radiationParallel plane: Lambertian pattern Perpendicular plane: there is beam confinement(better coupling)

Edge emitters

LightLight--Emitting DiodesEmitting Diodes -- Laser Source MaterialsLaser Source Materials

III-V materials (Al, Ga, In III group; P, As, Sb V group

- Ternary alloy Ga1-xAlxAs, spectrum at 800 – 900 nm- Quaternary alloy In1-xGaxAsyP1-y , spectrum at 1.0 – 1.7 μm

Ternary and quaternary combinations

Spectrum, full-width-half-maximum (FWHM)- x, y Lattice constant

LightLight--Emitting DiodesEmitting Diodes -- Laser Source MaterialsLaser Source Materials

Relationship between energy E and frequency ν :

)(240.1)(eVE

m

hchE

g

=

==

μλ

λν

Relationship between lattice constant (x, y) and band-gap

- For Ga1-xAlxAs : 21.424 1.266 0.266 (4 4)gE x x= + + −

21.35 0.72 0.12 (4 5)gE y y= − + −- For In1-xGaxAsyP1-y :

Example 4-3Consider a Ga1-xAlxAs laser with x=0.07. Find the diode emission wavelength.

Example 4-4Consider the alloy In1-xGaxAsyP1-y (i.e., x = 0.26 and y =0.57), find diode emission wavelength.

LightLight--Emitting DiodesEmitting Diodes -- Internal quantum efficiency Internal quantum efficiency

τ/0

tenn −=τn

qdJ

dtdn

−=

J current density in A/cm2

q electron charged thickness of recombination region

Thermal generationCurrent

injection

rate equation

qdJn τ

=

equilibrium condition

nrr

nrnrrr

rnrrnrr

r

RnRnRR

R

τττ

ττττ

ττη

111//

/11

int

+=

==

=+

=+

=

ληνη

qhcIh

qIP intintint ==

Rr : radiative recombination rateτr : radiative recombination lifetime Rnr : nonradiative recombination rateτnr nonradiative recombination lifetime

When carrier injection stops, carrier density decays: For constant current flow into LED, an equilibrium condition will be established.

Internal Quantum efficiency ηint :

Pint : internal optical power

LightLight--Emitting DiodesEmitting Diodes -- Internal quantum efficiency Internal quantum efficiency

Example 4-5A double-heterojunction InGaAsP LED emitting at a peak wavelength of 1310 nm has radiative and nonradiative recombination times of 30 and 100 ns, respectively. The drive current is 40 mA. Compute internal quantum efficiency and internal optical power.

LightLight--Emitting DiodesEmitting Diodes -- External quantum efficiency External quantum efficiency External quantum efficiency

Emitted power

2

1( 1)ext n n

η ≈+

For n1=n, n2=1

0

1 ( )(2 sin )4

c

ext T dφ

η φ π φ φπ

= ∫

221

21

)(4)0(

nnnnT

+=

Incidental angle

critical angle

Fresnel transmissivityfor normal incidence

φ1

2 1/ 2 sin ( / )c c n nφ π θ−

= − =

n

Example 4-6Assuming a typical value of n=3.5 for refractive index of an LED material, calculate the ηext .

2int

int )1( +==

nnPPP extext η

LightLight--Emitting DiodesEmitting Diodes -- Modulation Modulation

Modulated output power

02

( ) (4.18)1 ( )i

PP ωωτ

=+

P0 power emitted at DCω modulation frequencyτi carrier lifetime

• Optical 3-dB modulation bandwidth : 21

)0()( 3 =

PP dBω

• Detected current is linearly proportional to optical power :( ) ( )(0) (0)

P IP I

ω ω=

• Detected electric power : 2( ) ( )p I Rω ω=

• Therefore, 3-dB electrical loss corresponds to 1.5-dB optical loss; in other words, 3-dB optical loss corresponds to 6-dB electrical loss.

3 3 31( ) ( ) 0.707 ( )2dB dB dBf electrical f optical f optical− − −= =

Laser DiodesLaser Diodes -- PrinciplesPrinciples

Types of Laser : lasing medium gas, liquid, solid state (crystal), semiconductor.

Laser action is the result of 3 key process: photon absorption, spontaneous emission, and stimulated emission.

Photon absorption: When a photon of energy hν12 impinges on the system, an electron in ground state E1 can absorb the photon energy and be excited to state E2.Spontaneous emission : The electron in state E2 falls down to state E1 by itself quite spontaneously, and emits a photon of energy hν12 in random direction.

Stimulated emission : The electron in state E2 falls down to state E1, induced by a coming photon of energy of hν12, and emits a photon of energy hν12 in the same direction.

Laser DiodesLaser Diodes -- PrinciplesPrinciples

In thermal equilibrium : The density of exited electron is very small

Population inversion : Population of excited states > that of the ground state stimulated emission will exceed absorption

Pumping techniques : obtain population inversionFor a semiconductor laser, population inversion can be achieved by injecting electrons, or another pumping laser for solid state laser (crystal)

Laser Diodes Laser Diodes -- ModesModes

Modes: Longitudinal mode; Lateral mode; Transverse mode- spectral characteristics (resonant frequencies) / longitudinal modes - spatial characterisitics depend on / lateral and transverse modes

Laser cavity : to convert the device into an oscillator and provide optical feedback to compensate the optical loss in the cavity- Fabry-Perot (FP) laser: : mirrors, mirrors, cleaved facets- Distributed feedback (DFB) laser : Bragg reflector

Laser Diodes Laser Diodes -- Threshold conditions Threshold conditions --1 1

( )( , ) ( ) j t zI z t I z e ω β−=I(z) optical field intensityω optical radian frequencyβ propagation constant

with

Optical field intensity in longitudinal direction

Γ optical confinement factorg gain coefficient depended on optical frequencyα effective material absorption coefficient

[ ( ) ( )]( ) (0) g h h zI z I e ν α νΓ −=

Ra Rb

z0 L

n1 n2

Fabry-Perot laser cavity

Gain medium

Reflecting mirror

Amplitude during one round trip))()((2)0()2( ναν hhgL

ba eRRILI −Γ=Ra Rb mirror Fresnel reflection coefficients 2

21

21 )(nnnnR

+−

=

Phase condition2 1j Le β− =

Decided by laser cavity dimension !

Amplitude conditionPhase condition

endba

th

hhgLba

RRLg

eRR

ILI

ααα

ναν

+=+=Γ

=

=−Γ

)1ln(21

1

)0()2())()((2

Amplitude condition

cavitythresholdgain

cavityMaterialloss

cavimirrloss

Laser condition: Laser occurs when the gain is sufficient to exceed the optical loss during one round trip

Laser Diodes Laser Diodes -- Threshold conditions Threshold conditions --2 2

)0()2( ILI =

- spontaneous radiation below threshold- threshold current

Example 4-7For GaAs, R1=R2=0.32 for uncoated facets (i.e. 32% of the radiation is reflected at a facet) and . This yields for a laser diode of length .

110cmα − 133cmthg −Γ =500μmL =

Optical power vs. drive current

thth Jg β=Threshold current density

β constant depended on device construction

Jth Threshold current densitygth Threshold gain

/th thJ I A=Ith Threshold current A Area

01≥−

ph

Cnτ

Laser Diodes Laser Diodes -- Rate equation -1

0

0

→

≥Φ

spRwithdtd

thnnwithdtdn

==Φ

=

0

0qdJn th

sp

th =τ

phth C

nnτ1

=≥

Photon density should be in increasing mode towards lasing with negligible spontaneous emission

If electron density is at threshold level, injected electrons are just fully consumed by spontaneous recombination without light emission

Electron density must exceed a threshold value in order for photon density to increase

spph

d Cn Rdt τΦ Φ

= Φ + −

Φ : photon densityC coefficient for optical absorption and emission interactionsRsp rate of spontaneous emission into lasing modeτph photon lifetime

rate equation for photon density

stimulatedemission

spontaneousemission

photonloss

Φ−−= CnnqdJ

dtdn

spτ

rate equation for electron density

injection spontaneousrecombination

stimulatedemission

J injection current densityτsp spontaneous recombination lifetime

Relationship between optical power and drive current can be determined by two rate equations: For photon density Φ ; For electron density n

Laser Diodes Laser Diodes -- Rate equation -2

0sth s sp

ph

d Cn Rdt τ

ΦΦ= Φ + − =

Steady-state solution for rate equations

0=Φ−−= sthsp

th CnnqdJ

dtdn

τ

Φs steady-state photon density

+

qdJn th

sp

th =τ

spphthph

s RJJqd

ττ

+−=Φ )(

Spontaneously generatedphotons

Photons resultingfrom stimulated emission

Laser Diodes Laser Diodes -- EExternal quantum efficiency

(1 ) (4.37)ext ithg

αη η= −

External quantum efficiency

ηi internal quantum efficiency~ 0.6-0.7 at room temperature

gth gain coefficient at threshold

)()()(8065.0

mAdImWdPm

dIdP

Eq

gext μλη ==

Achieved experimentally

Εg band-gap energy λ emitted wavlength

External quantum efficiency ηext is defined as the number of photons emitted per radiative electron-hole pair recombination above threshold.

Laser Diodes Laser Diodes -- Resonant frequenciesResonant frequencies

If many modes are allowed for lasing under the gain spectral profile, it is a multi-mode laser e.g. Fabry-Perot laser

Phase condition for lasing

2 1j Le β− =

Optical resonant frequencies(or longitudinal modes)

Frequency or wavelength spacing between modes(or free spectral range FSR)

These modes describe the possible resonant optical frequency, if lasing really happen at these frequencies or not, still depends on the laser gain profile.

2

1 1

or 2 2

cn L n L

λν λΔ = Δ =

122 2L n L m

cπνβ π= =

12cmn L

ν =

Laser Diodes Laser Diodes -- Resonant frequenciesResonant frequencies

Laser spectral gain profile

2

20

2)(

)0()( σλλ

λ−

−= egg

g(0) maximum gain proportional to population inversionλ0 wavelength at the spectrum centerσ spectral width of the gain

Example, 4-12A GaAs laser operating at 850 nm has a 500 μ m length and a refractive index n=3.7. What are the frequency and wavelength spacings. If, at the half-power point, λ – λ 0 = 2 nm, what is the spectral width σ of the gain ?

Laser Diodes Laser Diodes -- Single mode lasersSingle mode lasers

- reduce cavity length L to increase frequency interval (FSR) between modesuntil there is only one mode falls within the laser gain bandwidth (not practical due to its dimension and low optical power)

)21(

2

2

+±= mLn ee

BB

λλλ

kne

BΛ

=2λ

k order of the gratingne effective refrative index of the modeΛ period of corrugation

n1 n2

DFB laser cavity

Anti-reflectioncoating

- distributed-feedback (DFB) laser- two 0-order modes will be degenerated to single mode due to imperfect AR coating

Laser Diodes Laser Diodes -- ModulationModulation

Internal (direct, current) modulation ; External modulation

Ip+ IBIB I

P

td

Laser injection current

Laser output power

Laser carrier density

1 1 12 thsp ph

IfIπ τ τ

= −

Fig. 4-30 Example of the relaxation-oscillation peak o a laser diode

Modulate the laser above the threshold- Spontaneous radiative lifetime τsp ~ 1 ns- Stimulated carrier lifetime τst ~ 10 ps- photon lifetime τph ~ 2 ps sets the upper limit to the direct modulation capacityModulation frequency also can not be larger than the frequency of the relaxation of laser field f

P195, 4-9a) A GaAlAs laser diode has a 500 μ m cavity length which has an effective

absorption coefficient of 10 cm-1. For uncoated facets the reflectivities are 0.32 at each end. What is the optical gain at the lasing threshold ?

b) If one end of the laser is coated with a dielectric reflector so that its reflectivity is now 90 percent, what is the optical gain at the lasing threshold ?

c) If the internal quantum efficiency is 0.65, what is the external quantum efficiency in cases of (a) and (b)?

P196, 4-12A GaAs laser emitting at 800 nm has a 400 μ m cavity length with a refractive index n=3.6. If the gain g exceeds the total loss α t throughout the range 750 nm < λ < 850 nm, how many modes will exist in the laser ?

P195, 4-15For laser structures that have strong carrier confinement, the threshold current

density of stimulated emission Jth can to a good approximation be related to the lasing-threshold optical gain gth by gth = β Jth, where β is a constant that depends on the specific device construction. Consider a GaAs laser with an optical cavity of length 250 μ m and width 100 μ m . At the normal operating temperature, the gain factor β = 21x10-3 cm/A and the effective absorption coefficient α =10 cm –1.

a) If the refractive index is 3.6, find the threshold current density and the threshold current Ith. Assume the laser end facets are uncoated and the current is restricted to the optical cavity.

b) What is the threshold current if the laser cavity width is reduced to 10 μ m ?