PowerPointPrsentation

1
Nonparabolicity and excitons in optical
absorption of InN
Friedhelm Bechstedt Friedrich-Schiller-Universität
Jena Germany
2
Optical absorption
critical points

extraordinary (E c) ordinary (E ?
c) a-plane on a-plane GaN/AlN
on r-plane sapphire (MBE) R. Goldhahn et al.,
Superlattices Microstructures 36, 591 (2004)
E
6.05 eV
2
E
8.6 eV
4
E4.88 eV
E
7.87 eV
3
E
5.35 eV
1
onset
plateau
Photon Energy (eV)
3
Low-energy optical transitions
plateau
transition near 1.3 1.4 eV
onset (Eg 0.7 eV)
F. Bechstedt et al., phys. stat. sol. (a) 195,
628 (2003)
4
Onset (Gap)
(i) band calculation in DFT-LDA with and
without effects of d electrons
accuracy 0.1 eV (ii) extrapolated pd
repulsion accuracy 0.1 eV
(iii) quasiparticle gap opening
accuracy 0.1 0.1 0.2 eV
In4d screening Result Eg
(0.8 ? 0.4 ) eV
Other results All-electron self-consistent GW Eg
? 0 eV ( T. Kotani, SCC 121, 461 (2002)) Exact
exchange Eg ? 1.4 eV ( M. Städele, PRL 79, 2089
(1997))
5
Low-energy optical absorption
ordinary dielectric function
Spectral region below 4 eV ? dramatic effects due
to nonparabolicity of bands ? k?p theory
Kane model (cubic, h? gt Eg)

• plateau for h? gt Eg
• square-root for
• energy-dependent interband mass

• spectral ellipsometry R. Goldhahn et al.
• calculation (independent-quasiparticle approach)
  
• F. Bechstedt et al.

6
High-energy optical absorption
ordinary dielectric function
many peaks in 4 10 eV energy region trials to
relate to interband transitions
7
van Hove singularities
in principle impossible since several k-point
regions may contribute to one peak
D. Fritsch et al., PRB69, 165204 (2004)
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Problem Excitons(more general electron-hole
interaction)
Electron-hole pair Hamiltonian
with quasiparticle energies
9
Independent-KS particles, independent
quasiparticles, and Coulomb-correlated
electron-hole pairs Optical absorption of Si
... quantitative agreement with experiment
Aspnes, Studna,
PRB27, 985 (1983)
W.G. Schmidt et al., PRB67, 085307 (2003)
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Influence of excitons(example extraordinary
dielectric function)

• drastic effects
• broadening of electron-hole pairs,
• here 0.2 eV (smearing of fine
• structure due to density of states)
• red shift of high-energy
• transitions by 0.6 eV due to
• electron-hole attraction
• weak effect
• plateau uninfluenced
• advantages/disadvantages
• 6 ordinary / 3 extraordinary
• structures

Problems (i) convergence (4500 k points in BZ
not enough) (ii) lattice polarizability,
free-electron effect? (iii) pd repulsion
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Optische anisotropy

• anisotropy intrinsic effect due to
• band structure
• absorption of light for h? lt 7 eV
• is weaker for ordinary polarization
• perpendicular to c axis (in
• agreement with measurements)
• drastic effect for peak around 5
• eV (exp. 5.35 eV) due to matrix
• elements

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Summary / Conclusions

• characteristic lineshape (onset, plateau, peaks
  due to band-to-band transitions)
• versus increasing photon energy
• low-energy region
• high-energy region

• dominated by optical transitions around ? point
  (upper valence bands into
• first conduction band)
• onset plateau express nonparabolicity of
  conduction band
• weak excitonic effects

• dominated by optical transitions at k points in
  several parts of the Brillouin
• zone
• influence of excitons on peak positions and of
  lifetimes on spectral structures

13
Collaborations/Acknowledgements
Computations J. Furthmüller L.K. Teles M.
Ferhat P. Hahn K. Seino
Experiments R. Goldhahn ... O. Ambacher ... C.F.
Mc Conville ... W.J. Schaff
Grants DFG German group-III nitride
initiative 1994 2002 EU RTN NANOPHASE 2001
04 NoE NANOQUANTA 2004 08
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Dielectric function of InN
15
Optical anisotropy
a-plane InN on a-plane GaN/AlN on r-plane
Sapphire grown by MBE
(d670 nm, n6x1018 cm-3, ?250 cm2/Vs)
16
Parameterfree calculations of semiconductor gaps
two steps (i) ground-state calc. density
functional theory (DFT) local density
approximation (LDA) Kohn-Sham bands
??(k) (ii) excitation aspect XC
self-energy in GW, parturbation th.
quasiparticle shifts ??(k) ? gaps
with accuracy of 0.1 eV
KS gap QP effect QP gap AlN 3.9
1.9 5.8 eV GaN 2.3 1.2
3.5 eV
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InN Why difficult?
(i) shallow In4d electrons (15 eV below VBM) ?
15 bonding ? overestimation of pd repulsion in
DFT-LDA/GGA negative ?1 - ?6
distance (ii) non-perturbative treatment of
quasiparticle effects to solve band gap problem
F. Bechstedt et al., J. Cryst. Growth 246, 315
(2002) phys. stat.
sol. (a) 195, 628 (2003)
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Polarization anisotropy of absorption edge

• ? an intrinsic property of wurtzite InN and not
  of metallic In inclusions
• spin-orbit splitting clearly visible
• ? magnitude only for band-to-band transitions

R. Goldhahn et al., Superlattices
Microstructures 36, 591 (2004)
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Level scheme near fundamental gap
F. Bechstedt in B. Gil, Low-dimensional nitride
semiconductors I. Vurgaftman/J.R. Meyer, JAP 34,
3675 (2003) B.E. Foutz et al., JAP 85, 7727 (1999)
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Chemical trend in band structures
21
Optical transitions
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Problem In4d electron
pd repulsion (Wei/Zunger (88))
Important In4d as valence electrons ?
correct lattice constant But 4d electrons too
shallow 13.5 eV (experimental 14.9 or
16.7eV) ? overestimation of pd
repulsion
Gaps and GW shifts (eV) Polytype LDA
LDA GW QP
QP (with 4d)
(without 4d) correction (with
4d) (without 4d) wurtzite
-0.19 0.58 0.93
0.74 1.50 zinc blende
-0.36 0.43 0.87
0.52 1.31
full
no
perturbation-theory argument for pd Eg 0.81
(0.59) eV wurtzite (zinc blende)
0.89 (0.67)