Complete report - Donostia International Physics Center - Euskal ...

2010 DIPC Highlight
Many-body effects in the excitation
spectrum of a defect in SiC
M. Bockstedte, A. Marini, O. Pankratov, and A. Rubio
Physical Review Letters 105, 026401 (2010)
Researchers from the Donostia International Physics Center, the Center of Materials Physics
(CISC) and the universities of Rome (Italy) and Erlangen-Nuremberg (Germany) demonstrated
that the photophysics of the carbon vacancy in Silicon Carbide with two excitation channels involving
conduction and valence bands is controlled by many-body effects beyond standard density
functional theory through both the renormalization of the quasiparticle states and excitonic
effects. Their analysis reassigns the excitation mechanism at the excitation thresholds observed
in photoinduced paramagnetic resonance experiments.
In their full fledge GW+BSE calculations of the photophysics of the carbon vacancy the authors demonstrated
that experimental spectra cannot be interpreted correctly without the inclusion of many-body effects
beyond the density functional theory. Excitation spectra are red shifted by strong excitonic effects
(~0.23eV) and electron-electron repulsion is underestimated by 0.3eV. Among the two competing excitation
channels only the transition of defect electrons to the conduction band has photon energies in the
range compatible with the absorption thresholds observed in the experiments. The theoretical analysis
unambiguously rectifies the earlier experimental assignment of the excitation mechanism and assessment
of ionization levels. These are pivotal for the defect diffusion and for understanding the carrier compensation
in high purity semi-insulating SiC.
Optical spectra of solids are comprised of the excitations of the perfect crystal and of its omnipresent imperfections.
For instance in transparent metal oxides small abundances of point defects absorb light in
the visible range and thereby determine the color of the material. Defects recently came into focus as a
promising implementation of quantum bits for the realization of solid state quantum computers. The quantum
information stored in the defect spin state is read out via an optical excitation.
Point defects as sources and sinks of charged carriers are fundamental for semiconductor technology
without which modern world would not take place. In the investigation of novel materials for electronics,
experiments unravel the role of specific defects via electronic and optical defect signatures. Unambiguous
interpretation of the experiments and the assignment of microscopic defect models, however, requires
theoretical support. Quantitative defect theory with density functional theory as its work horse successfully
addressed the ground state defect physics and defect kinetics. Without being able to treat the excited
state this work horse also notoriously underestimates semiconductor band gaps, thus, also affecting the
prediction of defect level positions. Many-body perturbation theory is free from this error. The quantitative
prediction of absorption spectra of a wide class of systems from insulators to surfaces, to nanotubes and
polymers in this frame work became tractable only recently.
The international research team of the Donostia International Physics Center and the Center for Materials
Physics (CSIC), and Universities of Rome (Italy) and Erlangen-Nuremberg (Germany) addressed this problem
for a prototypical defect within the frame work of many-body perturbation theory by solving the Bethe-
Salpeter equation and accounting for the GW self-energy. They selected the carbon vacancy in silicon
carbide for its well-established identification and the extensive experimental investigation of the excitation
spectrum of the positively charged defect. For the accurate interpretation of the experiments at least two
competing excitation channels are relevant: electron transitions from valence bands to localized defect
levels as well as transitions of defect electrons to conduction bands. Defect excitations combine the manybody
effects in both extended and localized states. Electron insertion into defect states invokes on-site
correlation due to electron-electron repulsion (Hubbard U), and defect-to-band transitions involve an electron
and a hole (one in the localized state and the other in the extended state), thus adding excitonic effects.
Excitation channels of the positively charged carbon vacancy in SiC:
(a) geometry with sketch of spin density of the paramagnetic electron.
(b) defect levels within the band gap. In the ground state the a level is
occupied with one electron. Arrows indicate transitions form valence
bands (V→a/e, lower set) and to conduction bands (a→C, upper set).
(c) sketch of the total energy of the positive (V + C ) and neutral (V 0 C ) vacancies
vs. the atomic coordinates. The transition V→a transforms V+
C
into V 0 C with a bound hole in the valence band. The occupation of
the defect level implies additional relaxation (Franck-Condon shift). (d)
Absorption spectra with and without excitonic effects at the BSE and
RPA level extrapolated to high k-point densities and including the effect
of Franck-Condon shifts. The transitions to the conduction bands sets
in at lower photon energies than the transitions from the valence bands.
Excitonic red shifts and
efect electron correlation
are indispensible for
unraveling the effect
of competing defect
excitation channels.
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