Fernando A. PonceDepartment of Physics and Astronomy

Arizona State UniversityTempe, Arizona, USA

Luminescence Imaging and Spectroscopy with High Spatial Resolution

Arizona State University

Lecture 4

Determination of the optical properties with high spatial resolution and

correlation with the crystal structure

With contributions by S. Srinivasan and A. Bell

• Luminescence in semiconductors

• Excitons

• Measuring light emission with high spatial resolution

• Correlation with the crystal structure

Light emission in semiconductors

hν

Light emission in semiconductors is a result of three processes:

• Generation on electron-hole pairs

• Relaxation and/or diffusion of carriers

• Recombination

Applications:

• Light emitting diodes

• Laser diodes

• Phosphors

Light emission in semiconductors

hν

Excitation source:

Light (laser) Photoluminescence

Electron Cathodoluminescence

Electric field Electroluminescence

Chemical reaction Chemiluminescence

Relaxation:

Phonon emission 10-15 seconds

Carrier migration 10-12 seconds

Exciton formation 10-12 seconds

Recombination 10-9 seconds

Ability to focus to

very small spots

Topics for this Lecture

• Luminescence in semiconductors

• Excitons

• Measuring light emission with high spatial resolution

• Correlation with the crystal structure

Pure Semiconductor at 0K

Ec

Ev

Valence band is full of electrons

Conduction band is empty

Ground State

EF

Ec

Ev

Excited StateElectrons in conduction band

Holes in valence band

Generation of electron-hole pairs

EF

Light EmissionEc

Ev

EFhν

• The excited state is unstable and has a finite lifetime.

• Electron hole pairs recombine to give light.

• The energy of the emitted light is approximately equal to the band gap. (Why?)

UV, Blue, Green

Yellow-Red

Red-IR

Wavelength rangeBandgap (eV)Material

3.42 eVGaN

2.78 eVGaP

1.52 eVGaAs

Light Emission in SolidsThe emission of light can be classified as spontaneous and stimulated.

Spontaneous emission occurs without the need of any other type of stimulus. The lifetime of excited states is relatively short, of the order of a few nanoseconds. It is accompanied by the emission of a photon and/or the dissipation of heat. This mechanism is also called luminescence or fluorescence.

Some materials have higher lifetimes, of the order of microseconds or milliseconds, in which case the process is called phosphorescence.

Spontaneous light emission is incoherent (the phase of light waves is random), nearly isotropic (it has a broad angular emission), and polychromatic (over a range of wavelengths).

Stimulated emission: Under special conditions, light can be produced by stimulation with an external means. This results in the emission of a highly coherent and monochromatic radiation. This phenomenon is used in lasers.

Light Emission in SolidsThe spontaneous emission rate for radiative transitions between two levels is determined by the Einstein A coefficient. If the upper level has a population N at time t, the radiative recombination rate is given by:

ANdtdN

radiative

−=

The rate equation gives:

)/exp()0()exp()0()( RtNAtNtN τ−=−=

where is the radiative lifetime of the transition.1−= ARτ

Light Emission in SolidsThe luminescence intensity at frequency ν is:

)()()( 2 factorsoccupancylevelxhgMhI υν ∝

where the “level occupancy factors” give the probabilities that the relevant upper level is occupied and the lower level is empty. M is the matrix element for the transition, and g(ν) is the density of states for the transition. The latter determine the quantum mechanical transition probability by Fermi’s golden rule.

Lattice vibrations and traps can generate non-radiative relaxation paths. In their presence, the luminescence efficiency ηR can be calculated as:

)11(NRRNRRtotal

NNNdtdN

ττττ+−=−−=

Light Emission in SolidsWhere the radiative and non-radiative recombination rates are included.

)/1()/1/1( NRRNRRR

AN

ANττττ

η+

=+

=

where we have used the fact that 1−= RA τ

When , then ηR approaches unity, and the light emission is very efficient.

NRR ττ <<

Interband Luminescence

Direct gap materials

Interband Luminescence

Indirect gap materials

Interband Luminescence

Photoluminescence

Topics for this Lecture

• Luminescence in semiconductors

• Excitons

• Measuring light emission with high spatial resolution

• Experimental determination of bandgap

What is an exciton?

e- h+

An exciton is like a hydrogen atom!!

Electron orbits the hole.

As a pair they are free to move around the lattice.

This is called a free exciton.

An exciton is a two-particle system.

When the solid is excited electron-hole pairs are generated.

Electron is negative and hole is positive

So there is Coulombic attraction and they bind to each other.

Excitonic recombination

xg EEh −=ν

222

4* 12 nh

qmE rx ε=

Ex is the energy of the exciton,

The energy of the light emitted is not exactly equal to the bandgap.

It is less by an amount equal to the exciton energy, Ex

Value of Ex depends on the material

Ex, meV

60ZnO

25GaN

5GaAs

Typical values of Ex

Excitonic recombination

An exciton is not spatially localized.

This means that it is highly localized in k-space.

Electron and hole have the same velocity.

For a radiative recombination they must have the same momentum.

So excitons are usually found near the Γ-point (k=0)

Excitonic recombination usually results in a very sharp peak, because the dispersion is fairly small.

Bound excitons

where Ei is the exciton binding energy of the impurity,

The exciton is not always free

One of the carriers can be trapped at an impurity atom, and the other orbits it.

This is called a bound exciton

Different impurities give rise to different bound-exciton peaks.

ixg EEEh −−=ν

GaN spectrum at 4K

B. Monemar “Bound excitons in GaN” J. Phys.:Condens. Matter. 13, 7011 (2001).

Topics for this Lecture

• Luminescence in semiconductors

• Excitons

• Measuring light emission with high spatial resolution

• Experimental determination of bandgap

Luminescence Studies

Excitation

Spectrometer(wavelength)

Detector(Intensity)

PL uses a laser for excitation

For higher spatial resolution we use an electron beam.

This is called cathodoluminescence (CL)

It is convenient to classify the luminescence process by means of the excitation source:

Light PhotoluminescenceElectrons CathodoluminescenceElectric field Electroluminescence

CathodoluminescenceCL electron in, photon out

Ec

Ev

hνe-

Sample

Primary Electrons

Secondary Electrons

Backscattered ElectronsAuger Electrons

X-rays

Cathodoluminescence

EBIC

e-

hν

JEOL JSM 6300 SEM

Gatan monoCL2 spectrometer

CL System at ASU

CL System at ASU

Cathodoluminscence

Local Spectra Line Scans Area Scans (Imaging)

CL enables microscopic study of light emission characteristics with high spatial resolution.

Electron beam can be controlled easily. So properties can be studied as a function of position.

350 400 450 500 550

x = 0.17

CL

Inte

nsity

(cou

nts)

Wavelength (nm)

λ = 444nm

λ = 497nm1.0 µm

Low [In] InGaN

High [In] InGaN

Mapping Indium Composition in InGaN

S. Srinivasan et al., Appl. Phys. Lett. 80, 550 (2002).

Spatial variation of luminescence

390 395 400 405 410 415

∆λ = 4 nm dislocation matrix

norm

. CL

Inte

nsity

(cou

nts)

Wavelength (nm)

Variations in local emission wavelength can be probed with a spatial resolution of <100 nm

395 nm

401 nm

300 320 340 360 380 400

323nm UV-LED

CL

Inte

nsity

Wavelength (nm)

318.3nmAl0.27Ga0.73N328.4nmAl0.21Ga0.79N334.4nmAl0.17Ga0.83N338.0nmAl0.14Ga0.86N

• Different aluminum incorporation on the inclined facet and the vertical facet

Evolution of Crystal Growth

Threading Dislocations in GaN

0 100 200 300 400 500 600

4.6

4.8

5.0

5.2(b)

REH

Pote

ntia

l (V)

Distance (nm)

2 mµ

(a)

300 400 500 600 700 800 900

(b) RCL

CL

Inte

nsity

(cou

nts)

Distance (nm)

J. Cai, F. A. Ponce, Physica Status Solidi A, 192 (2002)

Ec

Ev

Misfit dislocations in InGaNStrain Relaxation by generation of misfit dislocations1.08% misfit strain from composition

0.14% strain relaxed from dislocation distance

Plan-view TEM for x=0.1. dislocation distance~230nm

S. Srinivasan et al, Appl. Phys. Lett. 83, 5187 (2003).

Stacking Fault Emission in GaN

500 nm500 nm500 nm

1234

5

6 7 8

9

1234

5

6 7 8

9

1234

5

6 7 8

9

355 360 365 370 375 380

3.30 eV

3.414 eV

3.471 eV

C

L In

tens

ity (a

.u.)

Wavelength (nm)

CL Microscopy allows probing of optical properties at a high spatial resolution.

We can directly correlate optical properties with crystal defects.

TEM

CL 363 nm

CL 376 nm

Non-polar a-plane epitaxy

Growth of GaN on r-plane sapphireC-plane is normal to growth directionNo piezoelectric field along growth directionAnisotropy observed in +c and -c directionsStacking faults are generated for growth along -c

direction.Highly localized emission peaks are observed.

R. Liu, A. Bell, F. A. Ponce, C. Q. Chen, J. W. Yang, and M. A. Khan. Appl. Phys. Lett. 86, (2005).

g=11-20

Stacking faults in a-GaN

3.20 3.25 3.30 3.35 3.40 3.45 3.50

3.34

0eV

3.32

2eV

3.28

8eV

3.413eV

3.474eV

CL

Inte

nsity

(arb

. uni

ts)

Energy (eV)

Stacking faults emit at 3.41eVBasal plane stacking fault jogs via prismatic a-plane stacking faults withemission at 3.33eV. Partial dislocations emit at 3.29 eV

Stacking faults are likely to occur in non-polar epitaxy on a-GaN. Complex emission spectra is directly related to the microstructure.

R. Liu, A. Bell, F. A. Ponce, C. Q. Chen, J. W. Yang, and M. A. Khan. Appl. Phys. Lett. 86, (2005)

bce d

Stacking faults and partial dislocation emission

a-plane stacking faults are associated with the 3.33 eV emission.Partial dislocations terminating the c-plane SFs are associated with the 3.29 eV emission.

R. Liu, A. Bell, F. A. Ponce, C. Q. Chen, J. W. Yang, and M. A. Khan. Appl. Phys. Lett. 86, (2005)

Time-resolved Cathodoluminescence

Using carrier dynamics to study the effects of piezoelectric fields in quantum wells

Light emission in semiconductors

hν

Excitation source:

Light (laser) Photoluminescence

Electron Cathodoluminescence

Electric field Electroluminescence

Chemical reaction Chemiluminescence

Light emission in semiconductors is a result of three processes:

• Generation on electron-hole pairs

• Relaxation and/or diffusion of carriers

• Recombination

Applications:

• Light emitting diodes

• Laser diodes

• Phosphors

Luminescence in diodes

F. A. Ponce and D. P. Bour, Nature 386, 351 (1997)

Quantum wells

A quantum well is formed by sandwiching a narrow bandgap semiconductor in between two layers of a wider bandgap semiconductor

Advantages of using a quantum well:

• Improved carrier confinement

• Greater recombination probability

• Improved device efficiencies

Sapphire

4 µm GaN

3 nm InGaN100 nm GaN

hν

Effect of piezoelectric fields

• Electric fields tilt the bands

• Quantum well becomes somewhat triangular

Special case of nitrides:

Non-centrosymmetric structure

+ Highly strained interfaces

= Piezoelectric fields

Quantum-confined Stark effect

• Piezoelectric fields tilt the bands in the quantum well.

• Electrons and holes sit at opposite ends of the well

• Energy difference between electron and hole levels is decreased.

• Light emission from quantum well is red-shifted (i.e. shifted to a longer wavelength).

• Wavefunction overlap is reduced

Internal quantum efficiency

350 400 450 500 550 600 650 700

400 nm 460 nm 500 nm 520 nm 590 nm 630 nm

CL

Inte

nsity

(cou

nts)

Wavelength (nm)

Increasing [In]

As [In] is increased, strain increases. So piezoelectric fields increase. Wavefunction overlap reduces. Internal quantum efficiency goes down.

Time-resolved CLExcitation

Time

Time

Onset

Luminescence

Steady State

Decay

Inte

nsity

Excitation and luminescence as a function of time

(a)

(b)

Time-resolved CLProbing the time evolution of opticalexcitation and de-excitation in InGaN quantum wells using time resolved cathodoluminescence

400 450 500 550 6000

50

100

150

200

250

300 Decay 1 Decay 2

Rec

ombi

natio

n Li

fetim

e (n

s)

Nominal Wavelength (nm)

Recombination lifetimes

0 200 400 600

400 nm 460 nm 500 nm 520 nm 590 nm

C

L In

tens

ity (a

.u.)

Time (ns)

Low Indium High Indium

Localization

• Blue-shift of luminescence peak with increasing excitation densitydue to band filling

• Red-shift after pulsed excitationdue to band emptying

• Stokes shift (shift between luminescence peak and absorption edge)• Broad luminescence line-width• S-shape temperature dependence of peak positionS. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, “Spontaneous emission of localized excitons in InGaN single and multiquantum well structures” Appl. Phys. Lett. 69 (1996).

Evidence

Fields

A. Hangleiter, J.S. Im, J. Off, and F. Scholz “Optical Properties of Nitride Quantum Wells: How to Separate Fluctuations and Polarization Field Effects” Phys. Stat. Sol. (b) 216, 427 (1999).

• Blue-shift of luminescence peak with increasing excitation densityDue to screening of fields

• Red-shift after pulsed excitationDue to “de-screening” of fields

Evidence

Increasing QW thickness

Narrow quantum wellOverlap of wave functionsEfficient radiative recombination

Wider quantum wellCarrier separation, lower emission ratesscreening of PE fields, blue shift.

Spectrally resolved transients

375380

385390

395400

0.1

1

10

100

1000

10

20

3040

50

CL

Inte

nsity

(a.u

.)

Time (ns)

Wavelength (nm)

0 20 40

τ = 1.4 ns

CL

Inte

nsity

(a.u

.)

Time (ns)

Time-delayed spectra - 6nm thick QW

-100 0 100 200 300 400 500 600 700412

414

416

418

420

422

424

426

428

Q6 13% 6nm

Beam offBeam on

Wav

elen

gth

(nm

)

log

(Nor

mal

ized

CL

Inte

nsity

)

Time (ns)

1001021041061091111131161181211231261291311341371401431461491521551591621651691721761801841871911952002042082132172222262312362412462512572622682732792852912973033103163233303373443513593663743823903984074154244334424524614714814915025125235345455575695815936066186316456586726877017167317477627797958128298478658839019219409609801001

412 414 416 418 420 422 424 426 428

784 ns

22 ns-121 ns

Norm

aliz

ed C

L In

tens

ity

Wavelength (nm)

400 420 440

Q6 13% 6nm CW pulsed

N

orm

aliz

ed C

L In

tens

ity

Wavelength (nm)

-100 0 100 200 300 400 500 600 7001E-3

0.01

0.1

1

Q6 13% 6nm

412nm413nm414nm415nm416nm417nm418nm419nm420nm421nm422nm423nm424nm425nm426nm427nm428nm

CL

Inte

nsity

(cou

nts)

Time (ns)

Time-delayed spectra - 8nm thick QW

426 428 430 432 434 436 438 440 442 444

786 ns

24 ns-118 ns

Norm

aliz

ed C

L In

tens

ity

Wavelength (nm)

380 400 420 440 460 480

Q7 13% 8nm CW pulsed

N

orm

aliz

ed C

L In

tens

ity

Wavelength (nm)-100 0 100 200 300 400 500 600

426

428

430

432

434

436

438

440

442

444

Beam on Beam off

q7_lt_cl.opj

Q7 13% 8nm

Time (ns)

Wav

elen

gth

(nm

)

log

(Nor

mal

ized

CL

Inte

nsity

)

1001021051071101131151181211241271301331371401431471501541581621651691741781821871911962002052102152212262312372432492552612672742802872943013093163243323403483563653743833924024124224324424534644754874995115235365495625765906046196346496656816977147327497687868058258458658869089309539769991024104810741100

-100 0 100 200 300 400 500 6001E-3

0.01

0.1

1

Q7 13% 8nm

425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445

CL

Inte

nsity

(cou

nts)

Time (ns)

Time-delayed spectraTime-resolved cathodoluminescence studies indicate:

• Localization effects dominate in thin wells (widths < 6 nm)

• Screening of fields dominate for thick wells (widths > 8 nm)

• LEDs have wells < 6 nm (typically 2.5 nm), so localization effects

should be dominant in such devices

The effect of temperature has also been studied.

Temperature affects the localization of excitons.