Upper bound of photovoltaic efficiency of imperfect crystals. & Sunghyun Kim Dept. of Materials, Imperial College London [email protected] | frssp.github.io | frssp | 0000-0001-5072-6801 2020 CPE Seminar What a computational [ Physicists ] can do about it.
We have/know (almost) everything. But, can we predict something? 9 Theory Experiment SQ limit SRH statistics MPE process Efficiency lifetime Capture cross-section Empirical parameters? η = max η(Eg , NT , ET , Cn/p ,…) ?
If we can remove extrinsic impurities, the native defects remain. 10 Trap Limited Conversion Efficiency η = max η(Eg , NT , ET , Cn/p ,…) ! Maximum photovoltaic efficiency of a material containing equilibrium concentrations of native defects Equilibrium concentration of defects is a balance between enthalpic cost and entropic gain. Defect concentration Energy Enthalpy: ΔH Entropy: −TΔS Free energy: ΔG = ΔH −TΔS Gain from more configurations Cost of Breaking bonds NT at equilibrium!
13 S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889 If only we have known the limit before we spend too much time and money… C p C n E gap VB CB E gap Energy Configuration coordinate p 0 n 0 ΔE f E F E F E T N V p 0 +Δn n 0 +Δn DOS N C μ A μ B B AB A E F,p qV E F,n J V C n : Electron capture C p : Hole capture V B + V A − V B VA E F h+ e− J SC J 0 rad(eqV/k B T−1) qR SRH W η max Band structure E gap N C N V ro t condition μ ormation energy E f , E T Configuration coordinate Capture coe cient C n/p Se consistent ermi e e E F N T n 0 p 0 SRH recom ination rate R SRH Radiati e imit J SC J 0 rad SC 0 SRH 1 1 2 2 3 3 4 5 6 6 7 7 8 5 5 4
Two Common Characteristics of “Killer” Centers Deep level Large lattice relaxation “… So-called killer centers, with fast nonradiative transitions, … we list four examples: … 2. Defect with favorable vibrational properties, that is, with large- amplitude modes promoting the transitions, and large-energy modes to take up the electronic energy …” - A. M. Stoneham in Defects and Defect Processes in nonmetallic Solids 17 Park, J.-S., Kim, S., Xie, Z. & Walsh, A., Nat. Rev. Mater. 3, 194 (2018) Which defects exhibit both deep levels and large laBce relaxaCon? Lone-pairs!
Redox Activity of Cation Lone-pairs Large lattice relaxation Inert-pair effect: ineffective screening by d and f orbitals The large ionization energy for ns orbitals leads to a deep donor levels. Deep level [Kr] 4d10 5s0 5p0 R = 71 pm [Kr] 4d10 5s2 5p0 R = 112 pm The reduction and oxidation may lead to a large change in the structure of defect Sn(IV) Sn(II) The defects involving the oxidation and reduction of lone-pairs can act as killer centers.
Deep Donor Levels of VS, SnZn , and Complexes 20 Energy (eV) a b c d 0.0 0.5 1.0 1.5 (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (0/ ) V e n n V e n n n n n n V E F (0/ ) (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (+/ ) V n n V n n n n n n V E F (0/ ) (+/0) (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (0/ ) V e e n V e n e n n n n V E F (0/ ) (+/0) (2+/+) (+/0) (+/0) (+/0) (2+/0) (0/ ) (0/ ) (0/+) (0/ ) V e n n V e g n n n g n n g g n V g E F / E F e e e The formaCon of lone-pair in Sn-related defects introduces deep levels. S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Large lattice distortion 2 4 6 −2 0 2 4 6 −2 0 Sn Zn 2++h++e− Sn Zn 1++h+ Sn Zn 2+ Ge Zn 2++h++e− Ge Zn 1++h+ Ge Zn 2+ 0 2 1 Q (am 1 2 Q (am 1 2 ne (e a b E b E b (QHUJ\ H9 1HXWUDO WUDS 5HSXOVLYH WUDS *LDQW WUDS 9 6 &X =Q 9 6
6Q =Q
6Q =Q
&X 6Q í 7 . ıQ FP
í í í í í í í D E The lone-pair leads to large lattice distortions and large capture cross-sections. J. Mater. Chem. A 7, 2686 (2019) S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Phase diagram 23 ZnSe is too stable with respect to the formation of CZTSe. μSn (eV) −1 −2 0 o Zn-rich Additional Zn forms ZnSe. o Sn-poor The Cu-rich secondary phases are conductive. o hole poor (n-type) The acceptor (CuZn ) are too many. Ag 8 SnSe 6 Ag Ag 2 SnSe 3 ZnSe SnSe SnSe 2 Se CuSe Cu 2 Se Cu Cu 2 SnSe 3 Se ZnSe SnSe SnSe ₂ μSn μZn μ Cu 0 −2 −2 − − − −2 0 0 μSn μZn μ Ag 0 −2 −2 − − − −2 0 0 Se Se a b S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889 (eV) (eV)
Trap Limited Conversion Efficiency 2 4 6 −2 0 2 4 6 −2 0 Sn Zn 2++h++e− Sn Zn 1++h+ Sn Zn 2+ Ge Zn 2++h++e− Ge Zn 1++h+ Ge Zn 2+ 0 2 1 Q (am 1 2 Q (am 1 2 ne (e a b E b E b 25 Energy (eV) a b c d 0.0 0.5 1.0 1.5 (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (0/ ) V e n n V e n n n n n n V E F (0/ ) (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (+/ ) V n n V n n n n n n V E F (0/ ) (+/0) (+/0) (+/0) (2+/+) (+/0) (0/ ) (0/ ) (0/+) (0/ ) V e e n V e n e n n n n V E F (0/ (+/0 (2+/+) (+/0) (+/0) (2+/0) (0/ ) (0/ ) (0/+) V e n n V n n n g g n V g 0 0.4 0.8 0 50 40 30 20 10 SQ limit N d = 1020 cm–3 w/o doping a Current den it (m /cm2) Voltage (V) NT Cn ET SnZn : high concentration, deep level, and high capture coefficient Nonradiative Loss T = 300K W = 2µm 31.6% 20.3% S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Bad News: All Kesterites are not good. E g (eV) E g (eV) 0 20 40 60 J SC (mA/cm2) a b c d 0.5 1.0 1.5 2.0 V OC (V) 0.5 1.0 1.5 2.0 0 25 50 75 100 FF (%) 0.5 1.0 1.5 2.0 0 10 20 30 PCE (%) CZGSe AZTSe CZTSSe SQ lim i SQ limi SQ limi SQ lim i E g High concentration of recombination centers limits the open-circuit voltage and efficiency of kesterite solar cells S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
To p or Not To p, That is the Question! 28 p-type: High hole concentration promotes the formation of native donors. not p-type: Low hole concentration reduces the p-type conductivity. S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Codoping in Kesterites 30 Low hole concentration: Low donor concentration Post annealing in a H-free environment: High hole concentration S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Effect of H-doping E g (eV) E g (eV) 0 20 40 60 J SC (mA/cm2) a b c d 0.5 1.0 1.5 2.0 V OC (V) 0.5 1.0 1.5 2.0 0 25 50 75 100 FF (%) 0.5 1.0 1.5 2.0 0 10 20 30 PCE (%) CZGSe AZTSe CZTSSe SQ lim i SQ limi SQ limi SQ lim i E g J.-S. Park, S. Kim, Z. Xie, and A. Walsh, Nat. Rev. Mater. 3, 194 (2018) S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889 To access the true limits of solar cells, we need to take into account of thermodynamics of light, electron, and crystal.
I’m developing the first- principles method to calculate the theoretical maximum photovoltaic efficiency of real materials without empirical parameters. The simulations can complement the experiments and bridge the gap between macroscopic properties of materials and microscopic processes underneath. J.-S. Park, S. Kim, Z. Xie, and A. Walsh, Nat. Rev. Mater. 3, 194 (2018) S. Kim, J. A. Márquez, T. Unold and A. Walsh, arXiv:1912.07889
Making Good Solar Cells: a No-win Scenario. Do not go gentle into that good night Dylan Thomas Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the dying of the light. Though wise men at their end know dark is right, Because their words had forked no lightning, they Do not go gentle into that good night. … 33
“I don’t believe in the no-win scenario.” Do not go gentle into that good night Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the nonradiative recombination. Though wise men at their end know dark is right, Because their words had forked no lightning, they Do not go gentle into that good night. … 34 - James T. Kirk
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