2016-05-03_JMFROST_EMRS_CZTS

EMRS 2016 Lille, 12 minute contributed talk to session V, on modelling the Voc deficit in CZTS thin films.

Transcript

1. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Jarvist Moore Frost,Suzanne Wallace, Adam Jackson, Jonathan Skelton, Aron Walsh (University of Bath, UK) Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk Disorder and Recombination in CZTS
2. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016
3. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Voc loss → recombination 1) Bandgap fluctuation 2) Electrostatic Potential variation
4. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Quaternary - entropy driven substitional disorder
5. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Every inequivalent site → different chemistry X2 X1 X1
6. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Formation energy of defects in CZTS [Cu- Zn + Zn+ Cu ] antisite pair Minimum energy defect complex: ~ 0.4 eV Cu-on-Zn; Zn-on-Cu is lowest energy defect pair Chen, S., Yang, J.-H., Gong, X. G., Walsh, A., & Wei, S.-H. (2010). Intrinsic point defects and complexes in the quaternary kesterite semiconductor Cu_{2}ZnSnS_{4}. Physical Review B, 81(24), 245204. doi:10.1103/PhysRevB.81.245204
7. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 CZTS has a low dielectric constant → weak screening d+ Germanium 16.2 Silicon 11.7 Hybrid Halide Perovskite * 24 GaAs 12.9 CuZnSnS * ~ 7.0 / 9.0 AgZnSnSe * 11.9 (* PBESol DFT; Berry phase analysis, VASP code)
8. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Eris: Substitutional Site Disorder • On-lattice Monte Carlo • Written in the C programming language • Fast (cut-off) Evjen summations for electrostatics
9. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 [Cu- Zn + Zn+ Cu ] antisite pair in CZTS Cu S Zn Sn • Hybrid DFT Defect formation energies – (HSE06 Functional, VASP code, 25 % HF exchange) • 3 inequivalent antisite pairs • ‘Infinite’ distance defect pair → ~0.25 eV to produce a defect pair
10. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Point defect concentration
11. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Eris → Classical electrostatics with cut-offs
12. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 • Crystals are not 0K ◦ (But this is usually what we study with DFT ) • Phonons → Harmonic description ◦ Sample with Boltzmann statistics Phonons: APL Mater. 3, 041102 (2015); http://dx.doi.org/10.1063/1.4917044 Molecular Dynamics
13. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 • Ab-initio Molecular Dynamics → Fully anharmonic description, but costly to sample phase space ( Born-Oppenheimer ab-initio MD, PBESol functional, VASP, lightweight cut-offs ) Molecular Dynamics
14. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 POLARON POLARON Real space off-set in gap Real space potential fluctuations
15. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Real space recombination model:
16. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Sinusoidal potential variation...
17. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Recombination rates: Statistical Mechanics V h+ h+ h+ e- e- Recombination...
18. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Recombination energy: Quantum Mechanics V h+ h+ h+ e- e- Recombination... Requires a larger scale calculation that possible with KS DFT
19. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Boltzmann / mid-gap Fermi Dirac Fermi level
20. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
21. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Mobility (Boltzmann distribution of electrons, at 300 K) Simple thermal de- trapping model, with assumed percolation threshold.
22. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Conclusion ERIS: Custom codes for On-lattice MC Classical electrostatics, parameterized with hybrid DFT calculations Molecular dynamics (harmonic phonons, Born- Oppenheimer MD) Statistical Mechanics informed recombination Require a semi-empirical method to calculate delocalised electrons and holes
23. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 WMD Group, Bath Acknowledgments:- EPSRC - EP/K016288/1 EPSRC Archer - EP/L000202 University of Bath HPC http://go.bath.ac.uk/wmd Suzanne 'Suzy' Wallace
24. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 The backpages
25. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 R→ infinity value is the same as the Landau order (but SNR has increased by R^2 !) Define a radially-dependent autocorrelation function of the dipoles Ziman - Models of Disorder, 1979
26. Jarvist Moore Frost (University of Bath, UK) EMRS Spring 2016 - Lille Tue 3rd May 2016 Plan - 12 minutes • Voc Loss; at Voc all charges recombine • PL/EL ; Why EL (+ EQE) would be good • Dielectric constant - v. low for CZTS. Ag material - higher; ref Su Hei paper • Disorder:- ◦ Substititonal Disorder (Eris) ◦ Positional Disorder (Phonons, MD) • Eris - Code; early results • Positional disorder; MD vid, • Conclusion?