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

2. Outline Background Experimental Computational aspects Conclusions
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

3. 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!

4. Defects in semiconductors
Defects may occur either as point defects or defect complexes
Vacancy
Self interstitial
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!

5. 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

6. Defects in semiconductors
stable vs metastable Dn
Dn-1
Total (electronic+elastic) energy
a) Ordinary defect
a) Large lattice relaxation defect
c) Metastable defect in one charge state
d) Metastable defect in both charge states
Defect configuration coordinate

7. 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 identify the DLTS peaks associated with the B-V centre and observe metastability

8. Properties of the B-V complex

9. Experimental background: DLTS

10. Experimental observations
Zangenberg et al. Appl. Phys. A 2005
DLTS after annealing at 215 K under
Zero bias
Reverse bias
Zero bias (again)
Stable configurations
Configuration A: Zero bias
Configuration B: Reverse bias

11. 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.

12. 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

13. 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

14. Results: Formation energies as a function of Fermi level.

15. 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

16. Results: Comparison between DLTS energy levels and calculated transition levels
Configuration
Experiment
Theory
C1 (B)
EV eV
EV eV (+/0) [shallow]
EV eV (0/-)
C2 (A)
EV eV
EV eV
EV eV (+/0)
EV eV (0/-)

17. 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.

18. AHSANTE SANA!!!!!