Presentation on early stages of Monte Carlo model for Cu-Zn disorder in PV material CZTS.

1. Metal Disorder in Cu2ZnSnS4
(CZTS) from Multi-Scale
Simulations
Suzanne K. Wallace, Jarvist M. Frost and Aron Walsh
Centre for Sustainable Chemical Technologies
University of Bath, UK
15th March 2016
APS March Meeting 2016

2. Cu2ZnSnS4 (CZTS) Solar Cells

3. Cu2ZnSnS4 (CZTS) For Thin-Film PV
• Kesterite mineral structure
• Space group I4
• Tetragonal crystal structure
 High optical absorption coefficient
> 104 cm-1
 Direct and sunlight matched band gap
1.5 eV (c.f. indirect in bulk Si)
 Earth abundant
 Non-toxic

4. Shockley-Queisser Efficiency Limit
CZTS
theoretical limit
28%
Green et al, Progress in Photovoltaics, 23, 1–9. (2015)

5. Shockley-Queisser Efficiency Limit
CZTS
record efficiency
8.5%
Tajima et al, Applied Physics Express, 8, 082303 (2015)

6. Origin of Low Solar Cell Efficiency
Low Open Circuit Voltage
• Low VOC (relative to band gap)
• Record efficiency device: VOC = 0.708 V
Green et al, Progress in Photovoltaics, 23, 1–9. (2015)

7. Origin of Low Solar Cell Efficiency
Low Open Circuit Voltage
• Low VOC (relative to band gap)
• Record efficiency device: VOC = 0.708 V
Green et al, Progress in Photovoltaics, 23, 1–9. (2015)
Formation of secondary phases
Disorder amongst Cu and Zn
Non-optimal electrical contacts
Possible explanations?

8. Origin of Low Solar Cell Efficiency
Low Open Circuit Voltage
• Low VOC (relative to band gap)
• Record efficiency device: VOC = 0.708 V
Green et al, Progress in Photovoltaics, 23, 1–9. (2015)
Formation of secondary phases
Disorder amongst Cu and Zn
Non-optimal electrical contacts
Possible explanations?

9. Kesterite-Structured Cu2ZnSnS4
Disorder in z = ¼ and z = ¾
planes  [Cu-
Zn + Zn+
Cu]
z = ¾
z = ¼

10. Point Defects in CZTS
Chen et al, Physical Review B, 81(24), 245204 (2010)
[Cu-
Zn + Zn+
Cu]
antisite pair
Low energy
defect complex:

11. Recent Evidence of Disorder
Disorder within Cu-Zn layers from
neutron powder diffraction data

12. Recent Evidence of Disorder
Using Raman intensity
as an order parameter
TC= 533 K

13. Recent Evidence of Disorder
Zn-rich domains
in atom probe
tomography

14. Photoluminescence Spectra & Band Tailing
Gokmen et al, Appl. Phys. Lett. 103, 103506 (2013)
Red shift of peak
B. Choudhury et al, Int.
Nano Lett., 201 3, 3, 25.
Band tailing

15. Origins of Band Tailing
1. Defect-induced mid-gap states
Shockley-Read-Hall
recombination
2. Band gap fluctuation
Regions of wide (Zn-rich)
and narrow gaps (Cu-rich)
3. Electrostatic fluctuation
Distribution of Cu+ and Zn++
ions in the lattice – localise
carriers
Gokmen et al, Appl. Phys. Lett. 103, 103506 (2013)

16. Origins of Band Tailing
1. Defect-induced mid-gap states
Shockley-Read-Hall
recombination
2. Band gap fluctuation
Regions of wide (Zn-rich)
and narrow gaps (Cu-rich)
3. Electrostatic fluctuation
Distribution of Cu+ and Zn++
ions in the lattice – localise
carriers
Gokmen et al, Appl. Phys. Lett. 103, 103506 (2013)
Shallow defect states

17. Origins of Band Tailing
1. Defect-induced mid-gap states
Shockley-Read-Hall
recombination
2. Band gap fluctuation
Regions of wide (Zn-rich)
and narrow gaps (Cu-rich)
3. Electrostatic fluctuation
Distribution of Cu+ and Zn++
ions in the lattice – localise
carriers
Gokmen et al, Appl. Phys. Lett. 103, 103506 (2013)

18. Methodology
Defect Formation Energy: [Cu-
Zn + Zn+
Cu]
Hybrid density functional theory (DFT)
• HSE06 functional
• 25% Hartree-Fock exchange
• Band gaps closer to exptl values
for CZTS
64 atom supercell
Defect formation energy:
Cu S Zn Sn
Zhang and Northrup, 1991; Van de Walle et al., 1993
Defect X in
charge state q

19. Methodology
Defect Formation Energy: [Cu-
Zn + Zn+
Cu]
Hybrid density functional theory (DFT)
• HSE06 functional
• 25% Hartree-Fock exchange
• Band gaps closer to exptl values
for CZTS
64 atom supercell
Defect formation energy:
Cu S Zn Sn
Zhang and Northrup, 1991; Van de Walle et al., 1993
total energy of
supercell with
defect X
total energy of
perfect crystal
using
equivalent
supercell

20. Methodology
Dilute Defect Limit
~ 4% defect
concentration
at 550K
< 1% for dilute limit
Equilibrium defect concentration:

21. Methodology
Dilute Defect Limit
~ 4% defect
concentration
at 550K
< 1% for dilute limit
Equilibrium defect concentration:

22. Methodology
Dilute Defect Limit
~ 4% defect
concentration
at 550K
< 1% for dilute limit
Equilibrium defect concentration:
Effective charges on
antisite pairs result
in a Coulombic
attraction and bond
length reduction
3.84  3.82 Å

23. Methodology
Monte Carlo Simulations of On-Lattice Disorder
Custom on-lattice
disorder code: ERIS
Cu
S
Zn
Sn
Mapping CZTS onto a lattice
• Two interpenetrating FCC lattices
• Neglect anion sub-lattice
• Use a ‘gappy’ lattice to map FCC
onto SC
• Immobilise Sn ions  simulate
disorder amongst Cu & Zn only
Scale interaction energies in classical Hamiltonian using hybrid-DFT
 Much larger system sizes than DFT
(approach dimensions of thin-film)
 Thermodynamics of Cu-Zn disorder in
CZTS
DFT Parameterisation

24. Cu-Zn Disorder with T:
Cu
Zn
Sn
Disorder in
Cu/ Zn
layers
(c.f. neutron
diffraction data)
Preliminary Results
Electrostatic
Potential with T:
Next Steps:
• Longer simulation times – allow
distribution of accepted moves to
converge to a Boltzmann distribution
• Larger systems – reduce finite size
effects and study domain formation

25. species potential
Band Tailing Due to Cu-Zn Disorder

26. Band Tailing Due to Cu-Zn Disorder
species potential

27. From preliminary simulations of Cu-Zn disorder:
• Preferential disorder amongst Cu-Zn layers
• Substantial fluctuation in electrostatic potential with T
On-going and future work:
• Simulating larger systems to reduce finite-size effects
• Developing long- and short-ranged structural order
parameters
• Extend study to non-stoichiometric systems
Conclusions