The document summarizes research on photoferroic materials for solar cell applications. It discusses computational studies of the electronic and optical properties of three candidate photoferroic minerals: enargite, stephanite, and bournonite. The studies show they have suitable bandgaps and absorption properties. Rashba splitting was also found in bournonite. The document then discusses how defects could be tolerated in these materials through shallow defect levels related to their electronic structure. Finally, methods for further computational investigation of defects and spontaneous polarization are presented.
Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b
NREL PV seminar
1. Centre for Sustainable Chemical Technologies
Accelerating the development
of photoferroic solar cells
Suzanne K. Wallace
Supervisor: Prof Aron Walsh
3rd October 2017
2. Centre for Sustainable Chemical TechnologiesPhotoferroic materials for solar cells
Bulk photovoltaic effect (BPE)
photocurrents measured in single crystals (p-n or p-i-n junctions not needed)
Anomalous photovoltaic effect (APE)
measured photovoltages >> band gap
trieste.nffa.eu/areas/theory/ferroelectric-properties/
photoferroic = photoactive ferroelectric
K. T. Butler, J. M. Frost and A. Walsh, Energy Environ. Sci., 2015, 8, 838–848.
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1. Ferroelectric domains
Enhanced carrier separation [1]
2. Large dielectric constant
Defect-tolerant carrier transport [2]
3. APE in MAPI
Measured photovoltage of ~12 V [3]
CH3NH3PbI3 (MAPI)
methylammonium lead iodide
Design principles inspired by MAPI
[1] J. M. Frost et al, Nano Letters, 2014, 14, 2584–2590
[2] R. E. Brandt et al. MRS Commun., 2015, 5, 265–275
[3] Yuan et al. Science Advances, 2017, vol. 3, no. 3, e1602164
DOI:10.1038/nature12509
5. Centre for Sustainable Chemical TechnologiesChemically stable
~200 naturally
occurring
minerals
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~200 naturally
occurring
minerals
Chemically stable
Dark streak
colour
Eg in visible range
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~200 naturally
occurring
minerals
Chemically stable
Dark streak
colour
Eg in visible range
Polar crystal
structure
Potential ferroelectric
Candidate
photoferroic
minerals
8. Centre for Sustainable Chemical TechnologiesCandidate photoferroics: Sulfosalt minerals
Cu Ag Pb Sb S As
Enargite Cu3AsS4 Stephanite Ag5SbS4
Bournonite CuPbSbS3
9. Centre for Sustainable Chemical TechnologiesCandidate photoferroics: Sulfosalt minerals
Cu Ag Pb Sb S As
Enargite Cu3AsS4 Stephanite Ag5SbS4
Bournonite CuPbSbS3
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1. Magnitude of the band gap
Sunlight-matched (~ 1.0-1.7 eV)
2. Strength of optical absorption
• Direct band gap
• Abrupt of absorption edge
• c.f. SLME metric [4]
3. Light charge-carrier effective-mass
Better carrier mobility and long diffusion length
[4] Yu, L.; Zunger, A. Phys. Rev. Lett. 2012, 108 (6), 68701
DOI: 10.1126/science.aad4424
Standard PV design principles
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4. Rashba splitting: may reduce radiative
recombination rate and contribute to long
carrier lifetimes in MAPI [5, 6]
[5] P. Azarhoosh et al, APL Materials, 2016, 4, 091501
[6] Wang et al, Energy Environ. Sci., 2017, 10, 509-515
[7] R. E. Brandt et al, MRS Communications, 2015, 5(2), 1–11
5. Possible indicators of defect tolerance
• Active ns2 lone pairs: character of band extrema implies
shallow defects are likely [7]
• Large dielectric constant: enhanced charge screening [7]
More novel PV design principles
13. Centre for Sustainable Chemical TechnologiesDefect tolerance
1. Shallow defects
• Reduction in SRH e--h+ recombination
• Possible link to character of band extrema [7-9]
Host material with antibonding upper VB and
bonding lower CB
Dangling bond defects repelled into continuum
bands instead of band gap
2. Reduced scattering
• Carrier transport less hindered by presence of
charged defects
• Long diffusion lengths in defective materials
• Linked to large dielectric constant [7]
DOI: 10.1021/jz5001787
[7] R. E. Brandt et al, MRS Communications, 2015, 5(2), 1–11
[8] S. B. Zhang et al, Phys.Rev. B, 1998, 57, 9642–9656
[9] A. Zakutayev et al, Phys. Chem. Lett., 2014, 5, 1117–1125
14. Centre for Sustainable Chemical TechnologiesComputational methods
• HSE06+SOC
• Default ‘tight’ settings for basis set
Geometry optimisation
• Lattice parameters fixed to high-quality XRD
data from the ICSD
• Internal coordinates relaxed to within a
tolerance of 1x10-3 eV/ Å
• 4x4x4 gamma-centred k-point grid
Band structure calculations
• 8x8x8 k-point grid
Optical dielectric function, 𝜺 𝝎
• Random phase approximation
• Bournonite: 8x8x8 k-point grid
• Enargite and stephanite: 10x10x10 k-point grid
Absorption co-efficient, 𝜶(𝝎)
All-electron electronic
structure code
Numeric atom-centred
orbital basis sets
15. Centre for Sustainable Chemical TechnologiesOptoelectronic properties for PV
Enargite
Cu3AsS4
Stephanite
Ag5SbS4
Bournonite
CuPbSbS3
1.24 eV
1.37 eV 1.42 eV
1.59 eV
Enargite Stephanite Bournonite
me
cond 0.21 0.33 0.45
mh
cond 0.49 0.86 0.94
16. Centre for Sustainable Chemical TechnologiesRashba splitting for PV
Bournonite (CuPbSbS3)
- with SOC
- without SOC
No SOC
direct gap
SOC
Rashba split
18. Centre for Sustainable Chemical TechnologiesDefect tolerance from electronic structure
Bonding character of VBM
Bournonite
CuPbSbS3
Enargite
Cu3AsS4
Stephanite
Ag5SbS4
Cu d-orbital
S p-orbital
Ag d-orbital
S p-orbital
Cu d-orbital
S p-orbital
19. Centre for Sustainable Chemical TechnologiesSpontaneous lattice polarisation
Katrine Svane
[10] R. Wahl, D. Vogtenhuber and G. Kresse, Phys. Rev. B, 2008, 78, 104116
[11] H. H. Wieder, Phys. Rev., 1955, 99, 1161–1165
[12] I. Grinberg and A. M. Rappe, Phys. Rev. B, 2004, 70, 220101
[10]
[11]
[12]
Computational details
• 500 eV cut-off energy
• 2x2x2 k-point grid
• HSE06 functional
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DOI: 10.1039/c7se00277g
1. Optoelectronic properties for PV
• Sunlight-matched optical band gap
• m* < 1me
• Strong absorption
• Rashba splitting in bournonite
2. Strong lattice polarisation of
enargite and stephanite
Conclusion (part one of two!)
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1. Predict suitable device architectures
VOC losses linked to misalignment of bands with
contact materials
Poor epitaxy from lattice mismatch
2. Investigate defect physics of the materials
Likely impact of defects on PV performance
Predicting and tuning impact?
Will they grow up to be solar cells?
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Python script: https://github.com/keeeto/ElectronicLatticeMatch
1. Predictions for device architecture
Screen by necessary conditions for a good contact
Keith Butler: k.t.butler@bath.ac.uk
1. Electronic matching
Optimal band offsets
Screen by IP and EA
Minimise VOC loss across junction
2. Lattice strain
Match crystal lattices
Minimal for good epitaxy
DOI: 10.1039/c5tc04091d
23. Centre for Sustainable Chemical TechnologiesDefect-tolerant p-n junctions?
DOI: 10.1063/1.4953820
p-type
CB
VB
n-type
−Δ𝐸 𝐶𝐵
e-
Type II ‘cliff’ CBO
p-type
CB
VB
n-type
+Δ𝐸 𝐶𝐵
e-
Type I ‘spike’ CBO
h+ h+
24. Centre for Sustainable Chemical TechnologiesDefect-tolerant p-n junctions?
p-type
CB
VB
n-type
−Δ𝐸 𝐶𝐵
e-
Type II ‘cliff’ CBO
p-type
CB
VB
n-type
+Δ𝐸 𝐶𝐵
e-
Type I ‘spike’ CBO
h+ h+
• Create a h+ barrier at the
interface
• Not enough h+ present for e--h+
recombination at interface
defect states
Optimal CBO spike:
0.1 eV ≤ ∆EC ≤ 0.3 eV
Barrier too large: ∆EC ≥ 0.4 eV
Cliff CBO: ∆EC < 0
Allows h+ in high concentrations at
interface
Allows for e--h+ recombination at
defect trap states
Inhibits e- transport across interface
25. Centre for Sustainable Chemical Technologies2. Defect physics
DOI: 10.1038/nmat4973
Defect ‘flavours’
• Doping/ conductivity promoting
• Charge-scattering
• Killer, deep, charged recombination centres
Good
Bad
26. Centre for Sustainable Chemical Technologies2. Defect physics
DOI: 10.1038/nmat4973
Defect ‘flavours’
• Doping/ conductivity promoting
• Charge-scattering
• Killer, deep, charged recombination centres
Good
Bad
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Predict
concentration of
deep vs. shallow
defects
DOI: 10.1002/adma.201203146
n = N exp
−∆𝑮
𝒌 𝑩 𝑻
Equilibrium defect concentration
Defect transition levels
no. of lattice sites
defect
formation
energy
Predicting impact
Frenkel (1925); Jost (1933); Mott & Littleton (1938)
28. Centre for Sustainable Chemical TechnologiesTuning impact
F. A. Kröger “Chemistry of Imperfect Crystals” (1964)
Defect free energy of formation,
∆𝑮 𝝁𝒊, 𝑬 𝑭
Fermi level
(function of n, p, T)
Atomic chemical potentials
(growth and annealing conditions)
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𝝁i during synthesis
Using accessible 𝜇
range
Increase energy for
deep defects
DOI: 10.1002/adma.201203146
Tuning impact
F. A. Kröger “Chemistry of Imperfect Crystals” (1964)
∆𝑮 𝝁𝒊, 𝑬 𝑭
Defect free energy of formation, Fermi level
(function of n, p, T)
Atomic chemical potentials
(growth and annealing conditions)
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DOI: 10.1038/nmat4973
Tuning impact
Benign defect complexes
Encourage formation of defect pairs to ‘clean up’ the band gap?
D+ = donor
A- = acceptor
Defect-defect interactions
Form charge-neutral complex
Remove deep levels
e.g. InCu
2+ + 2VCu
- (InCu + 2VCu)0 in CuInSe2
S. B. Zhang, et al, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57
31. Centre for Sustainable Chemical TechnologiesConclusion (part two of two!)
Acknowledgements
Duke University: Volker Blum, David Mitzi, Will Huhn, Tong Zhu
University of Bath: Katrine Svane, Keith Butler, Jonathan Skelton
Imperial College London: Aron Walsh
NREL: Stephan Lany, Jie Pan, Prashun Gorai, Anuj Goyal
Thanks for listening!
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Electronic band structures with FHI-aims
FHI-aims: all-electron electronic structure code based on numeric
atom-centred orbital basis sets
Geometry optimization
• Initial structures taken from high-quality XRD data from the icsd
• Default ‘tight’ settings
• HSE06+SOC
• 4x4x4 gamma-centred k-point grid
• Lattice parameters fixed to unit cell from high quality XRD data
• Internal coordinates relaxed to within a tolerance of 1x10-3 eV/ Å
Band structure calculations
• HSE06+SOC
• 8x8x8 k-point grid
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Absorption co-efficients with FHI-aims
Optical dielectric function, 𝜺(𝝎)
• Random phase approximation (RPA)
• HSE06+SOC
• 10x10x10 k-point grid for enargite and stephanite
• 8x8x8 k-point grid for bournonite
Absorption co-efficient, 𝜶(𝝎)
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Spontaneous lattice polarisation with VASP
VASP: plane-wave electronic structure code using PAW pseudopotentials
• Using Berry-phase formalism
• Polarisation only allowed along z-axis for all 3 materials (based on
symmetry)
• Only differences in polarisation are meaningful
• Optimise +PS structure
• Invert to obtain structure with opposite polarisation, -PS
• Calculate polarisation difference between two structures, 2PS
• To verify that change in polarisation is continuous, calculate P of a
number of configurations connecting the +PS and -PS structures
VASP calculation settings:
• 500 eV cut-off energy for plan-wave basis set
• 2x2x2 k-point grid
• HSE06 functional
K. L. Svane and A. Walsh, The Journal of Physical Chemistry C, 2016.