第四讲-激子与发光课件

课程内容绪论经典传播带间吸收激子发光半导体量子阱、自由电子、分子材料发光中心123第四讲

ExcitonsThe

concept

of

excitonsFree

excitonsFree

excitons

at

high

densityFrenkel

excitonsThe

concept

of

excitonsIn

semiconductors

and

insulators:

photon

absorption

→

electrons

in

the

conductionband

and

holes

in

the

valenceband.Exciton:

bound

electron

–

hole

pair

by

Coulomb

interactionTwo

types

ofexcitons:Stable

excitons

will

onlybeformed

if

the

attractiveenergy

>>kBT

(0.026eV

atroom

temperature)Free

excitons

are

stable

atcryogenic

temperature.Tight

bound

excitons

arestable

at

roomtemperature.Wannier激子（自由激子）

•Frenkel激子

（束缚激子）:Observedsemiconductors;radius;

delocalizedinlargestates;move

freely;

binding

energy~

0.01

eVObserved

in

insulators

and

molecularcrystals;

smaller

radius;

localizedstates

;

less

mobile

and

hoping

;binding

energy

~

0.1

-1

eV.4The

concept

of

excitonsFree

excitonsFree

excitons

at

high

densityFrenkel

excitons5第四讲

ExcitonsBinding

energy

and

radius

of

free

excitonsFree

excitons:

weakly

boundelectron-hole

pair;

a

hydrogenic

systemApplying

the

Bohr

model

to

the

exciton,

considering

dielectric

constant

r

of

themedium

and

the

reduced

mass

of

electron

and

hole.The

energy

of

the

nth

level

relative

to

the

ionizationlimitRH

is

the

Rydberg

constant

of

the

hydrogen

atom(13.6

eV).

RX:exciton

Rydbergconstant.The

radius

of

the

electron-hole

orbit:aH

is

the

Bohrradius

of

the

hydrogenatom(5.29

×

10-11m)

andax

is

theexcitonBohr

radius.ground

state

with

n

=

1

has

the

largest

binding

energy

and

smallest

radius.n>1:

less

strong

binding

energy

and

larger

radius.x

rBiding

energy

tends

to

decrease

and

a to

increase

as

increase.6Rx

tends

to

increase

and

ax

todecrease

as

Eg

increases.Causes:

r

tends

to

decrease

and

to

increase

as

the

band

gapincreases.In

insulators

with

band

gaps

greater

than

about

5

eV,

ax

becomescomparableto

the

unit

cell

size,

and

the

Wannier

model

is

no

longer

valid.narrow

gap

semiconductors:

RH

is

so

small

thatexciton

effectsis

hard

toobserve.(Eg=1-3eV,

free

excitons

behavioris

best

observed)7Exciton

absorptionelectric

field

and

tend

to

ionize

excitons.8Exciton

creation:

electron-hole

pairsand

same

velocities.The

group

velocity

of

an

electron

or

hole

in

a

band

is

given

by:Free

excitons

are

typically

observed

in

direct

gap

semiconductors.

(hard

toobserve

in

the

absorption

spectra

of

indirect

semiconductor)At

the

Brillouim

zone

centre

of

direct

semiconductor:

k

=0

and

zero

gradient.Eectron-hole

pairs

created

by

direct

transition

and

have

the

same

velocities.Therefore,

strong

excitons

occur

in

the

spectral

region

close

to

the

fundamentalband

gap.The

energy

of

exciton

absorption

is:Band

edge

absorption

spectrum

for

a

direct

gapsemiconductor

with

excitonic

effects

included.

The

dashedline

shows

the

expected

absorption

when

the

excitoniceffects

are

ignored.Free

excitons

can

only

be

observed

in

very

pure

samples.Impurities:

screening

the

Coulomb

interaction

in

the

excitonand

thereby

strongly

reduce

the

binding

forces;

generatingExperimental

data

for

free

excitons

in

GaAsExciton

absorption

of

ultrapure

GaAs

at

1.2

K.hydrogen-like

energy

spectrumof

the

exciton

in

the

vicinity

ofthe

band

gap.E1=1.5149

eV,

E2=1.5180eV,E3=1.5187eVEg=l.5191

eV,

agree

with

othermeasurements.9The

experimental

Rx=4.2

meV

is

in

good

agreement

with

thecalculated

value.10The

concept

of

excitonsFree

excitonsFree

excitons

at

high

densityFrenkel

excitons第四讲

ExcitonsLow

density,

the

exciton-excitoninteractions

are

negligible

;

the

exciton

wavefunctions

begin

to

overlap

at

high

density

and

the

interaction

will

becomesignificant.Mort

densityNmott:the

densityatwhich

the

exciton-excitondistance

is

equal

tothe

exciton

diameter:High

density

is

achievable

with

a

focussed

laserbeam.11The

exciton

density

can

be

controlled

by

tuning

the

laserpowerDensity

Effects:121.electron-hole

plasmaweakening

and

broadening

ofthe

exciton

absorption

line

isobserved

(absorptionsaturation,

nonlinear

effects).Biexcitons

(exciton

molecules)equivalent

process

to

the

formation

of

an

H2

molecule;

new

feature

linecan

be

found.electron-

hole

dropletsBroad

feature

line

at

lower

energy

than

the

free

excitonBose-Einsteincondensation(Stotal=0

or1)13The

concept

of

excitonsFree

excitonsFree

excitons

at

high

densityFrenkel

excitons第四讲

ExcitonsFrenkel

excitonsoccurring

in

large

band

gap

materials

with

smalldielectric

constants

and

large

effective

masses.small

radii

and

large

binding

energies,

0.1

eV

toseveral

eV,

stable

at

roomtemperature.propagating

through

the

crystal

by

hopping

.Localized

on

the

atom

site,

may

therefore

be

considered

as

excited

states

of

theindividual

atoms

or

molecules,

especially

for

n=1exciton

energy

.Theoretical

treatment

of

Frenkel

excitons

is

more

complicated.14Rare

gas

crystalsCrystallize

at

cryogenic

temperatures.Large

band

gap,

Neon has

thelargestband

gap

innature.Exciton

transitions

all

occur

in

thevacuumultraviolet

spectral

rangeBinding

energies

are

very

large.15A

close

correspondence

between

the

n=1

exciton

energies

in

the

crystalsand

the

optical

transitions

of

the

isolated

atoms

(For

Xenon5p6→5p56s).The

radius

increases

with

n,

delocalized,

correspondence

gets

weaker.Alkali

halidesLarge

direct

band

gaps

(5.9

eV

13.7

eV)LiF

has

the

widest

band

gap

of

any

practicalopticalmaterial.Eg

and

exciton

binding

energy

tends

to

increase

withdecreasing

anion

and

cation

size.The

excitons

are

localized

at

the

negative

(halogen)ions.16Strong

excitoneffects

at

RTbecause

of

largebinding

energy(0.8eV

and1.9eV)17Principles

of

luminescenceInterband

luminescencePhotoluminescenceElectroluminescent第五讲

Interband

Luminescence发光的定义固体中的电子受到外界能量的激发，从基态跃迁到激发态，这是一种非平衡态。 处于激发态的电子具有一定的寿命，以一定几率回落到基态，并把多余的能量以各种形式释放出来。如果以光能的形式释放，称为发光过程。任何物体在一定温度下均有热辐射（热发光）。为了区分其它发光形式和热发光，严格的固体发光概念不包含热发光。发光现象有两个主要特征：

发光为固体吸收外界能量后，所发出总辐射超出热发射的部分。（发光的定义，指出了与热辐射的区别）

外界激发源对物体的作用停止后，发光现象会持续一段时间。（发光与散射、反射等现象的区别）18发光的分类依据激发方式不同，固体发光可分为以下几种形式：光致发光：如荧光灯，PDP。电致发光：如LED。阴极射线发光：CRT。高能射线或粒子（X射线，

射线，

粒子等） 发光：如医学胸透。化学发光：如荧光棒。生物发光：如萤火虫。机械发光：摩擦发光。19Light

emission

in

solidsτR=1/A，radiative

lifetime

of

transitio2n0Injected

electron

or

holeRelax

to

the

minimum

energy

stateThe

photon

is

emitted

when

anelectron

in

an

excited

state

dropsdown

into

an

empty

state

in

theground

stateband---Luminescence.If

the

upper

level

has

a

population

N

at

time

t,

the

radiativeemissionrate

is

given

by:A:

Einstein

coefficient.21Photon

absorptionPhoton

emissiontransitions

which

have

large

absorption

coefficients

also

have

high

emissionprobabilities

and

short

radiative

lifetimes.photons

can

be

absorbed

to

any

state

within

the

excited

state

band,

nomatterhow

far

it

is

above

the

bottom

of

the

band.Electrons

and

holes

relax

rapidly

to

the

lowest

levels

of

excited

state,

and

thelight

will

therefore

only

be

emitted

within

a

narrow

energy

range

from

thelowest

levels

in

the

excited

state

band.Normally,

the

absorption

and

emission

spectra

are

not

same.The

luminescent

intensity

at

frequency

ν

:The

matrix

element

M:

Fermi’s

golden

ruleThe

joint

density

of

state

g(hν)the

occupancy

factors

give

the

probabilities

that

the

relevantupper

level

is

occupied

and

the

lower

level

is

empty.22光致发光的效率辐射跃迁并不是激发态电子回到基态的唯一途径。另一途径：无辐射跃迁，发射声子（吸收光能转变为热）。消弱发光。设无辐射跃迁寿命为

NR，同时考虑辐射跃迁和无辐射跃迁，激发态电子数变化速率：发光效率ηR定义为辐射跃迁速率/总跃迁速率：高效发光材料要求辐射跃迁寿命

R远小于无辐射跃迁寿命

NR

。2324Principles

of

luminescenceInterband

luminescencePhotoluminescenceElectroluminescent第五讲

Interband

LuminescenceInterband

luminescenceInterband

luminescence:

in

a

semiconductor,

an

electron

that

has

beenexcited

into

the

conduction

band

drops

back

to

the

valence

band

by

theemission

of

a

photon.

Corresponding

to

the

annihilation

of

an

electron-hole

pair

(electron-hole

recombination

).1.

Direct

gap

materialsThe

optical

transitions

are

dipole-allowed

and

havelarge

matrix

elements.radiative

lifetime:10

-8

-10

-9

s;

luminescent

efficiency

ishigh.injected

electrons

and

holes

relax

very

rapidly

to

thelowest

energystates.electron

and

hole

that

recombine

must

have

the

same

kvector,

downward

vertical

arrow.No

matter

how

we

excite

the

electrons

and

holes

in

thefirst

place,

luminescence

at

energies

close

to

the

bandgap

is

alwaysobtained.25Luminescence

spectrum

and

absorptionof

a

GaN

epilayer

at

4

K.

Thephotoluminescence

(PL)

was

excited

byabsorption

of

4.9

eVphotons.The

emission

spectrum

consist

of

a

narrow

emission

line

at

3.5

eVclose

to

the

band

gap

energy,

while

the

absorption

shows

the

usualthreshold

at

Eg

with

continuous

absorption

for

ħω

>

Eg.The

emission

and

absorption

spectra

are

not

the

same,

even

thoughthey

are

determined

by

the

same

matrix

element.

The

band

gapcorresponds

to

the

threshold

for

optical

absorption,

but

to

theenergy

of

the

optical

emission.262.

Indirect

gapmaterialsRequiring

emitting

both

aphonon

and

a

photon

duringthetransition.a

second-order

process,with

asmall

transition

probability.longer

radiative

lifetime,

smallerluminescent

efficiency.The

indirect

gap

materials

such

as

silicon

and

germaniumare

generally

bad

light

emitters.2728Principles

of

luminescenceInterband

luminescencePhotoluminescenceElectroluminescent第五讲

Interband

LuminescencePhotoluminescence

in

a

direct

gap

semiconductor:

interbandluminescence

excited

by

a

photon

with

energy

greater

than

Eg.Photons

absorption

from

anexcitation

source

(

laser

or

lamp),electrons

(in

conduction

band)

andholes

(in

valence

band)

are

created.hvL>EgThe

electrons

and

holes

rapidly

relaxto

the

bottom

of

their

bands

byExcitation

and

relaxation-13phonon

emission

(~10

s

)

beforerecombining

by

emitting

a

photon

(

~10-9s).occupancy

factors

shown

by

the(

a)

Schematic

diagram

of

the

processesoccurring

during

PL

in

a

direct

gapsemiconductor

after

excitation

atfrequency

L

.

(b)

Density

of

states

andlevel

occupancies

for

the

electrons

andholes

after

optical

excitation.shading

can

be

calculated

by

applyingstatistical

physics

to

the

electron

andholedistributions.29Low

carrier

densitiesAt

low

carrier

densities,

the

occupancy

of

the

levels

is

small

and

+1

factor

inf

e(

E

)

can

be

ignored.

The

electron

and

hole

distribution

will

be

described

byclassical

statistics.Fermi

Boltzmann

distribution

:The

luminescent

intensity

at

frequency

ν

:Assuming

that

the

matrixelement

is

independent

offrequency.Arising

from

the

joint

density

of

statesArising

from

the

Boltzmannstatistics

of

the

electrons

andholes.30PLspectrum

of

GaAs

at

100K.

Theexcitation

source

was

a

helium

neonlaser

operating

at

632.8

nm

(1.96

eV)

.The

spectrum

shows

a

sharprise

at

E

g

due

to

the

(

hν

-

Eg)1/2

factor.Then

falls

off

exponentiallydue

to

the

Boltzmann

factor.31The

full

width

at

halfmaximum

of

the

emission

lineis

very

close

to

~

kBTPhotoluminescence

spectroscopyPhotoluminescence

(PL)

spectra:The

sample

is

excited

with

a

laser

or

lamp

with

photon

energygreater

than

the

band

gap.

The

spectrum

is

obtained

by

recording

theemission

as

a

function

ofwavelength.Photoluminescence

excitation

spectroscopy

(PLE):The

luminescence

intensity

at

the

peak

of

the

emission

is

measuredas

the

excitation

wavelength

is

scanned.32GaN:Zn:

excitation

and

emission

spectra3334Principles

of

luminescenceInterband

luminescencePhotoluminescenceElectroluminescent第五讲

Interband

Luminescence35General

principles

of

electroluminescent

devicesElectroluminescence

is

the

process

by

which

luminescence

is

generated

while

anelectrical

current

flows

through

an

optoelectronic

device.Two

main

types

of

devices:Light

Emitting

Diodes

(LED)

and

Laser

Diode

(LD).Structure:

epitaxial

layer;

p-

and

n-type

region;

active

region.Mechanism:

operated

in

forward

bias;

electron

s

and

holes

injection

andrecombination

in

active

region.

Be

same

as

the

photoluminescence

and

band

gapdetermining

the

emission

spectra

(line

emission

at

Eg

with

band

width

of~kT).Commercial

electroluminescent

devices

are

therefore

made

from

direct

gapcompounds.

Three

factors

for

the

choice

of

materials:1.

band

gap

size;

2.

lattice

matching;

3.p-typedoping.36Band

gap

of

selected

III-V

semiconductors

vs

lattice

constant“lattice

matching”

between

theepitaxiallayers

and

the

substrate:

ifnot,

the

formed

dislocation

willdegrade

the

optical

quality.

Nitride?AlxGa1-xAs:

630-870nm,red

andinfrared

LED;

perfect

latticematching.GaxInl-xAsyPl-y:0.92~1.65

m,

aslight

source

for

optical

fibercommunication

(

operated

at1.55and

1.3

m)Gax

In

1-x

N:

The

emission

wavelength

varied

from

360

to

650nm,

green

and

blueLED;Latticematchingandp-dopingproblems;p-type

doping

in

wide

band

gap

semiconductor

will

result

in

deep

acceptor

levels.And

then

the

low

hole

density

gives

the

layers

a

high

resistivity,

which

causesohmic

heating

when

the

current

flows

and

hence

devicefailure.This

a

common

problem

for

most

of

wide

gap

semiconductors.At

forwa