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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.
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