Probing the exciton density of states
through the phonon-assisted emission
in a GaN epilayer
Lucia Cavigli, Riccardo Gabrieli, Massimo
Gurioli and Anna Vinattieri
Dipartimento di Fisica e Astronomia, LENS,CNISM
Università di Firenze
Franco Bogani
Dipartimento di Energetica, Università di Firenze
Eric Feltin, Jean-François Carlin, Raphaël
Butté, and Nicolas Grandjean
Institute of Condensed Matter Physics, Ecole Polytechnique
Fédérale de Lausanne, Switzerland
GaN and related
nanostructures
New generation of opto-electronic devices, in particular Blue/UV emitters
Advantages
High tunability NUV-NIR
High radiative efficiency
Low maintenance cost
Main problems
Piezoelectricity
High content of defects
Poor control of doping
Recent advances in growing epitaxial GaN, with relatively low defect density
(down to 107 cm-2) give the opportunity to study fundamental optical processes
in a broad temperature range.
Our sample is a 3 µm thick non intentionally doped wurtzite GaN epilayer
grown by metal organic vapor phase epitaxy (MOVPE) on a c-plane
sapphire substrate characterized by a threading dislocation density lower
than 1x109 cm−2, provided by the group of Prof. Grandjean (EPFL,
Lausanne)
Exciton-phonon
interaction in GaN
Importance of the knowledge of electron–phonon interaction for improving the device
operation, since interactions of electrons with phonons affect the optical and electrical
properties of semiconductors.
In GaN the Fröhlich interaction of excitons with longitudinal optical (LO) phonons (a
Coulomb interaction between electrons and the longitudinal electric field produced by the LO
phonons) due to the ionic nature of III nitrides, causes the appearence of intense phonon
replicas (PRs) of the excitonic emission.
Under the assumption of a quasithermal exciton distribution
Phonon-assisted emission
0
D XA
92 meV
XA1S
is the energy-dependent probability that an
exciton with kinetic energy Ek recombines
emitting n phonons
XB1S
92 meV
XA-1LO
XA-2LO
is the exciton density of states
Zero-phonon line emission (ZPL)
3.30
10 K
3.35
3.40
3.45
Energy (eV)
3.50
B. Segall and G. D. Mahan, Phys. Rev. 171, 935 1968.
S. Permagorov, Excitons North-Holland, Amsterdam, 1982
Until now
For an ideal bulk sample, and a single
free exciton band in an isotropic threedimensional system:
the energy corresponding to the maximum
of the first and second phonon replica
depends linearly on T with a characteristic
slope:
Why not higher T ?
Etaloning
High quality thin (3 µm thick) GaN epilayer
interference effect in the transparent region
We compare LO-phonon emission with the corresponding reflectivity spectra
@ 10 K Low Temperature!!
5000
3000
20000
2000
10000
1000
3.375
1LO
3.400
3.425
0
Energy (eV)
30000
2000
20000
10000
1000
0
-10000
3.275
3.300
3.325
Energy (eV)
The reflectivity spectra exhibit a modulation with a
period much larger than the FWHM of the PR lines.
No extrinsic effects
3.350
Reflectivity (arb. un.)
3000
PL Intensity (arb. un.)
4000
Reflectivity (arb. un.)
PL Intensity (arb. un.)
40000
30000
-20000
2LO
Etaloning
10000
250
0
3.375
1LO
3.400
3.425
Energy (eV)
0
3.450
Different
colors
correspond to
different
points on
sample
30000
250
20000
10000
0
3.275
3.300
3.325
3.350
Energy (eV)
Reflectivity (arb. un.)
500
Reflectivity (arb. un.)
PL Intensity (arb. un.)
20000
750
PL Intensity (arb. un.)
@ 140 K
1000
0
3.375
2LO
Different PR lineshapes are found for different points in the sample, denoting a
spatially dependent nature of the PR structuring
extrinsic effects
Given the energy scale of the interference pattern, the modification of the PR
lineshape gets more important as T>80 K, when the PR band becomes broad.
Etaloning
Hence an appropriate correction is required before comparing the
experimental PR lineshape and PR energy peak position with the model in
the high-temperature range
Since the sample acts as a spectral filter for the
luminescence below the energy bandgap, we
introduce a transfer function TF(E) (proportional
to the transmittivity) between the
internal PL and the external measured PL
250
PL Intensity (arb. un.)
PL Intensity (arb. un.)
1000
750
500
250
0
3.375
3.400
3.425
Energy (eV)
1LO
3.450
200
150
100
50
3.275
3.300
3.325
3.350
3.375
Energy (eV)
Lucia Cavigli et al Physical Review B 2010 82 115208
2LO
Comparison of our
experimental data with model
185
90
1LO
2LO
EXA-E2LO (meV)
EXA-E1LO (meV)
• Red lines are linear fits to
the data.
• Black lines correspond to the
kBT dependence expected
model considering only the A
exciton band contribution
95
85
180
80
75
175
70
65
0
5
10
kBT (meV)
15
170
0
5
10
kBT (meV)
For the 1LO the best fit gives a slope of −1.4 ± 0.1, close to the
theoretical prediction of −1.5.
For the 2LO we find a slope of −0.70 ± 0.05, against an expected value
of −0.5. Clearly experimental data are largely off the theoretical
predictions.
Lucia Cavigli et al Physical Review B 2010 82 115208
15
0
10
20
30
Energy (meV)
160 K
80 K
34 K
ρ W2 (Arbitrary Units)
ρW1 (Arbitrary Units)
1LO
160 K
80 K
34 K
40
50
2LO
0
10
20
30
Energy (meV)
40
50
We analyze the quantity quantity ρWn, as obtained from experimental spectra divided by the
Boltzmann factor. The zero of the energy scale corresponds to the onset of the replica at the energy
EXA−nħωLO.
Different temperatures ⇒ same behavior!!! ⇒
validity of the exciton thermalization hypothesis
direct information on the intrinsic exciton-phonon interaction can be obtained from the
analysis of the PR lineshapes
Lucia Cavigli et al Physical Review B 2010 82 115208
0
10
20
30
Energy (meV)
160 K
80 K
34 K
ρW2 (Arbitrary Units)
ρ W1 (Arbitrary Units)
1LO
160 K
80 K
34 K
40
50
The common model predict:
2LO
0
10
20
30
Energy (meV)
1LO
2LO
40
50
Light blue
lines
We modified the expression of the density of states, including the contribution
of B exciton:
where α1=1 and α2=0, and cn=0.5 accounts for the different exciton masses in the A
and B bands.
With this expression we can reproduce the
experimental data!!! 2LO=DOS
Dark blue lines
in figures!
Lucia Cavigli et al Physical Review B 2010 82 115208
Conclusion
The simultaneous measurement of PL and R
spectra allows us to correct for etaloning effects
and to reconstruct the intrinsic PR lineshapes
The comparison with existing models to describe
the PR lineshape and intensity shows that the
complex nature of the exciton band in GaN has to
be considered to fully account for the PR energyshift, lineshape, and intensity
The analysis of 2LO band provides physical
information on the whole radiative and non
radiative exciton states