9. Semiconductors Optics

•Absorption and gain in semiconductors

•Principle of semiconductor lasers (diode lasers)

•Low dimensional materials:

Quantum wells, wires and dots

•Quantum cascade lasers

•Semiconductor detectors

Semiconductors Optics

Semiconductors in optics:

•Light emitters, including lasers and LEDs

•Detectors

•Amplifiers

•Waveguides and switches

•Absorbers and filters

•Nonlinear crystals

One atom Two interacting atoms N interacting atoms

The energy bands

Eg

Insulator Conductor(metals)

Semiconductors

Doped semiconductor

n-type p-type

Interband transistion

gEh gEh

nanoseconds in GaAs

n-type

Intraband transitions

< ps in GaAs

UV

Optical fiber communication

GaAs InPZnSe

Bandgap rules

The bandgap increases with decreasing lattice constant.

The bandgap decreases with increasing temperature.

Interband vs Intraband

Interband:

Most semiconductor devices operated based on the interband transitions, namely between the conduction and valence bands.

The devices are usually bipolar involving a p-n junction.

Intraband:

A new class of devices, such as the quantum cascade lasers, are based on the transitions between the sub-bands in the conduction or valence bands.

The intraband devices are unipolar.

Faster than the intraband devices

C

V

C

E

k

cm

kkE

2)(

22

Conduction band

Valence band

Interband transitions

E

k

cm

kkE

2)(

22

Conduction band

Valence band

Examples:

mc=0.08 me for conduction band in GaAs

mc=0.46 me for valence band in GaAs

Eg

Direct vs. indirect band gap

k k

GaAsAlxGa1-xAs x<0.3ZnSe

SiAlAsDiamond

Direct vs. indirect band gap

Direct bandgap materials:

Strong luminescence

Light emitters

Detectors

Direct bandgap materials:

Weak or no luminescence

Detectors

Fermi-Dirac distribution function

1

1)(

/)( kTEE Fe

Ef

f(E)

E

10.5EF

Fermi-Dirac distribution function

1

1)(

/)( kTEE Fe

Ef

f(E)

E

10.5EF

For electrons

)(1 Ef For holes

kT

kT=25 meV at 300 K

Fermi-Dirac distribution function

1

1)(

/)( kTEE Fe

Ef

f(E)

E

10.5EF

For electrons

)(1 Ef For holes

kT

kT=25 meV at 300 K

E

Conduction band

Valence band

Em

E

StatesofDensity

c )2

(2

1)(

2

E

Conduction band

Valence band

Em

E c )2

(2

1)(

2

For filling purpose, the smaller the effective mass the better.

E

Conduction band

Valence band

Em

E c )2

(2

1)(

2

Where is the Fermi Level ?

Intrinsic

P-doped

n-doped

Interband carrier recombination time (lifetime)

~ nanoseconds in III-V compound (GaAs, InGaAsP)

~ microseconds in silicon

Speed, energy storage,

E

Em

E c )2

(2

1)(

2

Quasi-Fermi levels E E

Immediately after Absorbing photons

Returning to thermal equilibrium

Ef e

Ef h

Em

E c )2

(2

1)(

2

E

EF e

EF h

x =

fe # of carriers

gFvFcnet

absorptionemissionnet

cccvvemission

cccvvabsorption

EEER

RRR

EfEEfR

EfEEfR

)(

)()())(1(

))(1)(()(

E

EF c

EF v

Eg

Condition for net gain >0

P-n junction

unbiased

EF

P-n junction

Under forward bias

EF

Heterojunction

Under forward bias

Homojunction

hv

N p

Heterojunction

waveguide

n

x

Heterojunction

10 – 100 nm

EF

Heterojunction

A four-level system

10 – 100 nm

Phonons

E

Eg

gEE

g

Absorption and gain in semiconductorE

Conduction band

Valence band

Em

E c )2

(2

1)(

2

Eg

Eg

Absorption (loss)

g

g

Eg

Gain

Eg

g

Eg

Gain at 0 K

Eg

EFc-EFv

Density of states

EFc-EFv

E=hv

gEE

g

Eg

Gain and loss at 0 K

EF=(EFc-EFv)

E

gEE

g

Eg

N2 >N1N1

Gain and loss at T=0 K

at different pumping rates

EF=(EFc-EFv)

E

gEE

g

Eg N2 >N1N1

Gain and loss at T>0 K

laser

E

gEE

g

Eg N2 >N1N1

Gain and loss at T>0 K

Effect of increasing temperature

laser

At a higher temperature

Larger bandgap (and lower index ) materials

Substrate

Smaller bandgap (and higher index ) materialsCleaved facets

w/wo coating

<0.2mp

n

A diode laser

<1 mm

<0.1 mm

Wavelength of diode lasers

• Broad band width (>200 nm)

• Wavelength selection by grating

• Temperature tuning in a small range

Wavelength selection by grating tuning

<0.2mp

n

A distributed-feedback diode laser

with imbedded grating

Grating

Typical numbers for optical gain:

Gain coefficient at threshold: 20 cm-1

Carrier density: 10 18 cm-3

Electrical to optical conversion efficiency: >30%

Internal quantum efficiency >90%

Power of optical damage 106W/cm2

Modulation bandwidth

>10 GHz

Semiconductor vs solid-state

Semiconductors:• Fast: due to short excited state lifetime ( ns)• Direct electrical pumping• Broad bandwidth• Lack of energy storage• Low damage threshold

Solid-state lasers, such as rare-earth ion based:• Need optical pumping• Long storage time for high peak power• High damage threshold

Strained layer and bandgap engineering

Substrate

3-D (bulk) EE )(

E

Density of states

Low dimensional semiconductors

When the dimension of potential well is comparable to the deBroglie wavelength of electrons and holes.

Lz<10nm

2- dimensional semiconductors: quantum well

)(EE

constant

Example: GaAs/AlGaAs, ZnSe/ZnMgSe

Al0.3Ga0.7As

Al0.3Ga0.7As

GaAs

,....2,12 2

222 n

LmnE

zcn

E1

E2

For wells of infinite depth

2- dimensional semiconductors: quantum well

,....2,12 2

222 n

LmnE

zenc

E1v

E2c

,....2,12 2

222 n

LmnE

zhnv

E1c

E2v

2- dimensional semiconductors: quantum well

E1v

E2c

E1c

E

(E)

E2v

2- dimensional semiconductors: quantum well

E1v

E2c

E1c

E2v

g

N0=0

N1>N0N2>N1

T=0 K

2- dimensional semiconductors: quantum well

E1v

E2c

E1c

E2v

g

N0=0

N1>N0N2>N1

T=300K

E=hv

2- dimensional semiconductors: quantum well

E1v

E2c

E1c

E2v

g

N0=0

N1>N0N2>N1

E=hv

Wavelength : Determined by the composition and thickness of the well and the barrier heights

3-D vs. 2-D

E2v

g

T=300K

E=hv3-D

2-D

Multiple quantum well:coupled or uncoupled

1-D (Quantum wire)

gEEE

1)(

E

Eg

Quantized bandgap

0-D (Quantum dot)

An artificial atom

)()( iEEE

E

Ei

Quantum cascade lasers