Transcript Slide 1

Metastability of the boron-vacancy complex
(C center) in silicon: A hybrid functional study
Cecil Ouma and Walter Meyer
Department of Physics, University of Pretoria
Outline
• Background
– Defects and metastable defects
– B-V Centre
• Experimental
– DLTS
– Observed properties of the B-V centre
• Computational aspects
– Formation energies
– Transition levels
– Comparison with experiment
• Conclusions
Defects in semiconductors
• The electronics industry is ever expanding and so is the
research in device design in applications
• Defects in semiconductors play an essential role
• Required for doping
• Side effect of fabrication –> detrimental -> limit and remove
• Beneficial properties -> understand, use and control -> Model!
Defects in semiconductors
• Defects may occur either as point defects or defect
complexes
Self
interstitial
Vacancy
Substitutional
impurity
Interstitial
impurity
A fundamental
understanding of defect
properties is important in
device engineering &
applications
• Defects can be beneficial or detrimental in a
semiconductors -> Need to understand!
Defects in semiconductors
• Defects may either be:
• Stable : A defect which has a single fixed atomic
configuration for a given charge state and their properties do
not depend on the history of the sample.
• Metastable (Bistable) : A defect that, in at least one charge
state, has two stable configurations.
Stable defects have been and are extensively
Metastable defects provide an opportunity to test a variety of
aspects of the capabilities of simulation techniques
Defects in semiconductors
Total (electronic+elastic) energy
• stable vs metastable
Dn
Dn
Dn-1
Dn-1
c) Metastable defect in one charge state
Dn
a) Ordinary defect
Dn
Dn-1
Dn-1
d) Metastable defect in both charge states
a) Large lattice relaxation defect
Defect configuration coordinate
Boron-vacancy complex
• Watkins 1976: Tentatively associated the Si-G10 EPR
spectrum to the Bs-V complex in silicon
• Sprenger et al. 1987: Tentatively associated the Si-G10 EPR
spectrum to the Bs-V complex in silicon (ENDOR)
• Londos 1992, Bains et al. 1985, Zangenberg et al. 2005
identify the DLTS peaks associated with the B-V centre and
observe metastability
Properties of the B-V complex
•
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Experimental background: DLTS
•
DLTS signal
S = C(t1) – C(t2)
T
(i)
(ii)
(iii)
Increasing
temperature
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
C
t1
t
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t2
(a)
(b)
Experimental observations
Zangenberg et al. Appl. Phys. A 2005
DLTS after annealing at 215 K under
a) Zero bias
b) Reverse bias
c) Zero bias (again)
Stable configurations
Configuration A: Zero bias
Configuration B: Reverse bias
Computational background
DFT with LDA and GGA functionals has a number of successes,
but:
•
Band gaps of semiconductors are significantly under-estimated.
–
•
•
E.g. Ge is a metal.
Kohn-Sham states do not represent individual electron wave
functions
Very unreliable in predicting DLTS levels.
DFT with hybrid potentials correctly predict band gaps.
Calculation of formation energies according to Zhang & Northrup.
Calculate thermodynamic transition levels from Fermi-level
dependence.
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Computational details
MedeA-VASP package
•64 atom supercell
•K-mesh: 2✕2✕2 MP
•Ecut = 500 eV
•Functionals: HSE06
•Formation energy calculated according to Zangh & Northrup
E f ,q (BV ) = ED,q - E p + 2mSi - mB + q(EF + EV + DV)
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Results: Calculated formation energies
(with Fermi level at valence band)
Configuration
q = -1
q=0
q = +1
C1
5.14
4.99
4.96
C2
5.78
5.08
4.60
C3
5.94
5.32
5.02
C4
5.86
5.23
4.77
Results: Formation energies as a function
of Fermi level.
Results: Theoretical predictions and
comparison with experiment
Zero bias:
Charge state: q=+1
Stable configuration: C2
High temperature Peaks
Two peaks observable
Reverse bias:
Charge state: q=-1
Stable configuration: C1
Low temperature Peaks
Only one peak observable
Configuration B  C1
Configuration A  C2
Results: Comparison between DLTS
energy levels and calculated transition
levels
Configuration
Experiment
Theory
C1 (B)
EV + 0.105 eV
EV + 0.03 eV (+/0) [shallow]
EV + 0.15 eV (0/-)
C2 (A)
EV + 0.31 eV
EV + 0.37 eV
EV + 0.48 eV (+/0)
EV + 0.70 eV (0/-)
Conclusions
• DFT with hybrid functionals may successfully be used to model the
electronic properties of the metastable B-V complex in silicon.
• The thermodynamic charge transition levels obtained were
consistent with previous experimental observations.
• There was correct qualitative prediction of the observed changes in
the DLTS spectrum due to the metastability of the defect complex.
AHSANTE SANA!!!!!
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