0

Introduction to

Semiconductor Lasers:

Guy Verschaffelt

Vrije Universiteit Brussel, guy.verschaffelt@vub.ac.be

Based on semiconductor lasers chapters in the “Lasers” course, Interuniversity

Master in Photonics, Geert Morthier, Guy verschaffelt

1

SEMICONDUCTOR LASERS

Laser:

Gain medium

Pump

Resonator

→ Semiconductor

Advantages:

Mass-fabrication → low production cost

Direct electrical pumping

Small

Low threshold current and power dissipation

High efficiency

High modulation bandwidth

Integration with other optical components

2

SEMICONDUCTOR MATERIAL

Crystalline solid

Energy

Energy bands Band filling

Electron

Hole

Metal Semi-

conductor Isolator

Conduction

band

Valence

band

Energy

3

SEMICONDUCTOR LASERS

Source: Laser Focus World

4

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

5

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

6

HOMOJUNCTION LASER DIODE

First pulsed demonstration in 1962 by Robert N. Hall

(homojunction laser diode)

7

HOMOJUNCTION LASER DIODE

Lasing is possible, but with very high threshold current density (1000 A/cm2 at

77 K, 100 000 A/cm2 at 300 K)

→ Solution: double heterostructure

8

DOUBLE HETEROSTRUCTURES

First CW laser diode operating at room temperature was demonstrated

in 1970 by Zhores Alferov (double heterostructure laser diode)

9

LASER DIODE GEOMETRY

TYPICAL GEOMETRY BURIED RIDGE LASER

bond wire

x (transverse)

y (lateral)

z (longitudinal)

p-ohmic metal

dielectric

p-InP InGaAsP

active layer n-InP

n-InP substrate

n-ohmic metal

10

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Tunable lasers

■ Packaging

■ Summary

11

DIRECT VS. INDIRECT SEMICONDUCTORS

Band diagram:

Direct, e.g. GaAs Indirect, e.g. Si

Notice: k = k-vector of electron or hole

Real band diagrams normally depend on direction of k

Laser or LED requires direct material, photodetector not!

12

MATERIALS

Bandgap (eV)

Lattice

constant

(nm) l/(µm)

0 1 2 3

3. 2. 1.5 1 0.8 0.6

0.60

0.54

InAs

Ge GaAs

Si GaP AlP

AlAs

AlSb GaSb

InSb

InP l[mm]=1.24/Eg[ev]

13

DOUBLE HETEROSTRUCTURES

Band edge diagram:

Refractive index profile:

Stimulated emission is only possible for photon energies slightly above Eg

Materials have to be lattice matched

Ec

Ev

Active

layer

cladding cladding

Bulk material

Undoped: N=P

14

Conduction and valence bands

dE)]E;E(f1)[E(P

dE)E;E(f)E(N

Fvv

Fcc

Semiconductor in equilibrium: single Fermi level Ef

Non-equilibrium:

dE)]E(f1)[E(P

kT

E-Eexp1f(E) with dE)E(f)E(N

v

1

fc

15

Low dimensional structures

Bulk Quantum well Quantum wire Quantum box

g(E)

E E E E

g(E) g(E) g(E)

Density of

states:

QUANTISATION OF ACTIVE LAYER

16

DOUBLE HETEROSTRUCTURES

Band edge diagram:

Refractive index profile:

Ec

Ev

Active

layer

cladding cladding

Bulk material QW material

Ec

Ev

Active

layer cladding cladding

Undoped: N=P

17

QUANTISATION IN 1, 2 and 3 DIMENSIONS

dEE-E~(E)dE ,dkk~(k)dk

m2

kkkEE :.B.C

c

2

c

2

z

2

y

2

x

2

c

xn

c

2

z

2

y

2

nc

L decreasingfor increases E

dE~(E)dE kdk,(k)dk

m2

kkEEE :.B.C

Ec

Ev

Quantum

well

barrier barrier

E1

E2 Bulk:

QW:

QWire:

….

Lx< 10 nm

yxmn,

c

c

2

z

2

nmc

L,L decreasingfor increases E

dEE-E

1~(E) dk,~(k)dk

m2

kEEE :.B.C

18

ABSORPTION VS. STIMULATED RECOMBINATION

Absorption (= optical loss)

Ec

Ev

hn hn 2hn

Stimulated Recombination (= optical gain)

Absorption rate Stimulated Recombination rate

nIEfEfBR cv )(1)( 211212 nIEfEfBR cstim )(1)( 1v22121

)(2112 EinsteinBBB

Net amplification

inversion)n (populatio )(E)( 0 12 vc

vc

fEfif

IffB

n

E2

E1

E2

E1

19

EINSTEIN COEFFICIENTS

Spontaneous emission Ec

Ev

hn

Emission rate

E2

E1

)(1)( 122121 EfEfAR vcspont

Thermal equilibrium spontstim RRR 212112

Number of photons (per unit energy and per unit volume) photphot nEEI 1212 n

2112

12

211212

12

21

1exp

expBB

TkE

BTkEB

E

A

B

B

phot

20

ABSORPTION VS. STIMULATED RECOMBINATION

Energy levels involved in interband transitions:

kkkk

m

kE

m

kEBC

vphv

v

vv

c

cc

cc

v*

22

1

c*

22

2

k k

hole) of momentum :(k 2

E :V.B.

electron) of momentum:(k 2

E :..

2/1

2/3

22

2

4

1)( with )( g

rcvcvvc

g

EEm

EEffv

Bgain

r

g

vc

g

m

kE

mm

kEEE

2

11

2

22

**

22

12

21

GAIN CALCULATION

qVEEEE if )E(f)E(f fvfcg1v2c [Condition of Bernard and

Duraffourg]

gmax = A.N - B

22

GAIN CALCULATION

More accurate gain calculations need to consider

• Energy bands are only approximately parabolic

• Band mixing effects due to strain

• Gain in two-level system has a Lorentzian shape

• Excitonic effects near band gap

• Gain nonlinearity, e.g. due to spectral hole burning

En

erg

y

Electron density

Ec

Equilibrium

distribution

in

in

SEDensity of

states

in : intraband relaxation

SE: stimulated emission

23

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Tunable lasers

■ Packaging

■ Summary

24

LASER DIODE WAVEGUIDES

n2 n1

Index guiding: n1>n2

Fundamental waveguide mode:

propagation constant b,

b=kneff with n2<neff<n1

Fraction of power in active layer

: confinement factor

Change Dn1 in n1 and Dn2 in n2:

Dneff=Dn1+(1-) Dn2

25

a-factor

BNAgdA

ctedN

dN

N

N

i

r

andKK from''

)'( and

dg

dn4

0

r

a

l

a

For QW active region For 2-level system (e.g. gas laser)

gain

l

A is asymmetric around llasing

a ≠ 0

gain, and also differential gain,

is symmetric around llasing

a ≈ 0

From: S. F. Yu,, Analysis and

Design of Vertical Cavity Surface

Emitting Lasers

26

COMPLEX REFRACTIVE INDEX

Complex effective index due to carrier density N:

k2

gjN

dN

dg

k2)E(nn int

0,effc,eff

a

a

a-factor or linewidth enhancement factor

Material dependent

Wavelength dependent

Current dependent

27

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

28

CAVITY RESONANCE

L

facet

x

z

Fabry-Perot

Cavity

Resonance means : For Fabry-Perot cavity :

1

gain roundtrip

λN,L

rλN,R

r

condition) (amplitude

2R

1R

1ln

2L

1

passαΓ1

actΓαNΓg

condition) (phaseinteger m ,m

2L

n

λ

r

passive cladding active layer passive cladding

L

facet R

facet R

r

r

a

g(N), aact

a

pas

pas

R

L

1

2

29

CAVITY RESONANCE

Jth

power

threshold

current

power

spectrum Dl

l

Dl

l

l n

L

r

2

l

roundtrip gain

λN,.rλN,r RL

30

FACET REFLECTIVITY

■ TE-mode has higher reflectivity than TM-mode

laser emission is mainly TE

■ Facet reflectivity can be modified with coatings

AR-coating: R down to 0,01%, HR-coating: R up to 100%

TM ±30%

R TE

d/l

31

FAR FIELD (ANGULAR RADIATION PATTERN)

■ wide transverse beam divergence

■ elliptic beam

■ in some lasers: astigmatic beam

2wx

2wy

2qx

2qy

y

y

x

x

w

w

lq

lq

32

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

33

RATE-EQUATIONS

Simplest dynamic model to describe lasers

ΔNdN

dG

2

α

dt

dφΔω

V NR βτ

SSN,R

dt

dS

V

SN,RNR

qV

I

dt

dN

spont

p

stim

stimspont

Carrier equation:

Photon equation:

Phase equation:

S: Number of photons in the mode, N: carrier density in active layer [cm-3], φ: phase of the field

nspont τNNR

SG S Ng vΓSN,R gstim

BANNg

spontaneous recombination rate [cm-3 s-1]

stimulated emission rate [s-1]

gain [cm-1]

carrier lifetime [s]

photon lifetime [s]

spontaneous emission coupling factor (typically 10-4)

volume of active layer [cm3]

nτ

pτ

β

V

34

For phase-dependent coupling: often easier to start from

instead of the rate-equations for S, f and N

RATE-EQUATION FOR THE COMPLEX FIELD E

2

1

2

1

EV

GN

qV

I

dt

dN

EGj

dt

dE

n

p

a

35

RATE-EQUATIONS

Photon rate equation: simple derivation from field propagation

)exp()()( tjtStE Field:

After one roundtrip in cavity: ]exp[)()( tjtStE

SRRL

vvgv

dt

dStStS

RRLg

RRLg

LjknLgRRtEtE

g

gg

eff

21

int

21

int

21

int

int21

1ln

2

)()(

1ln)(21S(t) )S(t

1ln)(2S(t)exp)S(t

)2exp()(exp.).()(

a

a

a

a

36

DIFFERENCE WITH OTHER LASERS

■ Carrier lifetime very short: of order ns or sub-ns

■ Linewidth enhancement factor a (0 in other lasers)

■ Short cavities high mirror losses

+ “Low” facet reflectivities

■ High differential gain

37

STEADY STATES AND LINEAR STABILITY

Steady state:

1) S=0 solution

2) Non-zero solution

0 and 0 dt

dN

dt

dS

Vq

IN

S

n

0

th

p

p

IIq

S

G

1

N

I

S

I

N

I

S

I I = Ith

G(N) = 1/τp

38

DYNAMIC OPERATION: IM AND FM MODULATION

Thermal FM Carrier FM

Modulation frequency (Hz)

(GHz/mA)

1 1K 1M 1G

1

0.1

ID

nD

Modulation frequency (Hz)

(mW/mA)

1 1K 1M 1G

1

0.1

I

P

D

D

Carrier IM

I t I0 DI cos mt

D

D

D

D

)(cos

distortionorder 3rd3cos

distortionorder 2nd2cos

cos

0

33

22

0

FMtt

tP

tP

IMorAMtPPtP

vm

pm

pm

pm

f

f

f

f

39

POWER SPECTRUM and PHASE NOISE

Power spectrum:

Phase noise: spontaneous emission

ftjdtSfSE f

2exp2

exp )(

2

D

tat D )(2f

Lorentzian spectrum:

2

2

2)2(

)(

a

f

aSfSE

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Po

we

r [a

.u.]

Frequency [MHz]

Dn 21

22

1

2a

n D

S

Ra sp

40

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

41

Fabry-Perot Laser Diodes

Mirrors = Cleaved facet

Active layer: double

heterostructure

Iactive

Disadvantages:

• No longitudinal mode selection:

• More than one mode

• Mode hoppping

Power

spectrum

l

SMSR (e.g.10 dB

or less)

42

DFB and DBR Laser Diodes

Distributed Feedback (DFB) laser diode

Distributed Bragg Reflector (DBR) laser diode

gain

section

bragg

section

Ip Ig Ib

phase

section

grating

Active layer

Passive waveguide

Ia

43

Reflectivity of Passive Grating

R

1

l lB

IMPORTANT PARAMETERS

lB 2nr

L ( : grating coupling coefficient in 1 / cm)

waveguide

power flux

L

Dl

44

Roundtrip gain of DFB laser

0.9

0.92

0.94

0.96

0.98

1

1.02

-4

-3

-2

-1

0

1

2

3

4

1.535 1.54 1.545 1.55

Am

plit

ud

e

Wavelength [ mm]

Ph

ase

F-P laser vs. DFB laser

0

0.2

0.4

0.6

0.8

1

1.2

-4

-2

0

2

4

1.557 1.559 1.561 1.563 1.565 1.567

Wavelength [ mm]

Am

plit

ud

e

Ph

ase

[rad

.]

45

VCSELs

Advantages:

• compact

• low threshold

• wafer testable

• cheaper

• dense 2D arrays

• circular beam

• single longitudinal mode

Difficulties:

• high reflectivity mirrors

• series resistance in mirror

• current confinement

46

Semiconductor ring lasers

Advantages:

• no DBR mirros

• integrable

• all-optical directional switching

Difficulties:

• moderate output power

• no longitudinal mode selection

• increased bending loss in

small devices

SRL

Couplers

Trigger pulse1

Trigger pulse2

CCW

CW

47

QUANTUM DOT LASER DIODES

■ Advantages: - low to zero a-factor

- very broad gain bandwidth (due to spread in

dimensions): tunable lasers and amplifiers

SEM-picture of self-organized InAs quantumdots

on a GaAs-surface grown with MBE.

48

QUANTUM CASCADE LASERS

Different type of gain layer based on intra-band transitions

Conduction

band

Valence

band

Conduction

band

Interband laser Intersubband transition Multiple cascades

in series

Advantages

Long wavelength laser (mid- to far-infrared wavelength range, THz generation)

Large wavelength span with one material system

49

OUTLINE

■ Introduction

■ Structure of semiconductor lasers

■ Gain

■ Refractive index and a-factor

■ Laser resonance

■ Rate-equation description and linewidth

■ Different types of semiconductor lasers

■ Packaging

■ Summary

50

LASER PACKAGING

TO package

Butterfly package

DIL package

51

LASER PACKAGING

LASER PACKAGE MAY CONTAIN

photodiode monitoring back side emission

Peltier cooler and temperature sensor

fiber coupling

high bandwidth modulation access

optical isolator: laser diodes are very sensitive to external

reflections (e.g. from fiber tip)

change in P

increase in intensity and phase noise

chaos

52

Summary/Conclusions

Semiconductor lasers

Overview of operating principles

Different structures/materials for optimized performance in

different applications

New wavelength ranges and new laser types are under

development

Highly efficient, compact sources