Semiconducting nano-composites for solar energy conversion: insights from ab initio calculations. S. Wippermann, G. Galli

Transcription

1 Semiconducting nano-composites for solar energy conversion: insights from ab initio calculations S. Wippermann, G. Galli ICAMP-12, 08/10/2012

2 Search for materials to harvest light: Desperately seeking silicon Nanoparticles (NPs): light emission and absorption Interplay between quantum confinement, defects and surface structure? Differences between colloidal and matrixprecipitated NPs? S. Huang et al., J. Appl. Phys. (2009) Light absorption in dots and rods Can we optimize absorption in functionalized Si-rods and use them as photo-cathodes for solar cells? Multiple exciton generation (MEG) More efficient in nanoparticles? Origin and dependence on preparation conditions? [1] Space-separated quantum cutting with Si nanocrystals for photovoltaic applications, D. Timmerman et al., Nature Photon 2, 105 (2008) [2] Multi-exciton generation in semiconductor quantum dots, A. J. Nozik et al., Chem. Phys. Lett. 457, 3 (2008) [3] Energy-conversion properties of vapor-liquid-solid-grown silicon wire-array photocathodes, S. Boettcher et al., Science 327, 185 (2010) Motivation embedded NPs advanced theory MEG 01/20

3 Realistic models of nanoparticles (NPs) SixO1-x Devise structural model Informed assumptions Realistic & complex environments Growth & kinetic processes T. Li (GWU) D. Donadio (MPI, Mainz) Precipitate nanoparticles in a matrix from the melt, following prescriptions borrowed from simulations of nucleation processes Forward Flux Sampling of rare events [R. J. Allen et al., 2005 & 2009], coupled to MD simulations with Langevin thermostat [2] T. Li, D. Donadio, L. Ghiringhelli, G. Galli, Nature Mat. (2009) & JCP (2009) [1] A. Puzder, A. J. Williamson, N. Zaitseva, G. Galli, L. Manna, A. P. Alivisatos, Nanoletters (2004) Motivation embedded NPs advanced theory MEG 02/20

4 Motivation embedded NPs advanced theory MEG 03/20 Si NPs embedded in nitride/oxide matrices We have used accelerated MD simulation techniques - similar to those employed to study nucleation in supercooled liquid Si - to precipitate Si nanoparticles in silicon nitride & oxide amorphous matrices - at present only possible with semi-empirical potentials We have investigated interfaces and computed electronic properties using ab initio techniques (semi-local DFT) T. Li (GWU) F. Gygi (UCD) QBox code: electrons, 800,910 basis functions for tens of picoseconds for several samples Si! SixO1-x [1] L. Dal Negro, J. H. Yi, J. Michael, L. C. Kimerling, S. Hamel, A. Williamson, G. Galli, IEEE Nanophotonics 12, 1151 (2006) [2] L. Dal Negro, J. H. Yi, L. C. Kimerling, S. Hamel, A. Williamson, G. Galli, Appl. Phys. Lett. 88, (2006)

5 !! Motivation embedded NPs advanced theory MEG 04/20 Electronic states of embedded nanoparticles matrix density type of nano-heterojunction ρ = ρ0 Si Si ρ > ρ0 SiO2 Si The relative position of the matrix and nanoparticle energy levels depends on the matrix density

6 !! Motivation embedded NPs advanced theory MEG 05/20 Electronic states of embedded nanoparticles matrix density type of nano-heterojunction size-dependence & localization of energy levels ρ = ρ0 ρ > ρ0 Si Si SiO2 Si!! Si-HOMO: size-dependent position and strain-induced localization Si-LUMO: size-insensitive & delocalized The relative position of the matrix and nanoparticle energy levels depends on the matrix density

7 Electronic states of embedded nanoparticles HOMO interface state; LUMO delocalized over cluster Control of optical properties not only through nanoparticle size but also through strain and matrix density T. Li, F. Gygi, G. Galli, Phys. Rev. Lett. (2011) T. Li (GWU) S. Wippermann (UCD) Motivation embedded NPs advanced theory MEG 06/20

8 Motivation embedded NPs advanced theory MEG 07/20 Si nanoparticles in ZnS: strong gap reduction In atomic layer deposition (ALD) processes, sulfides are used to embed NPs Our ab initio MD simulations show that S is drawn from the matrix and the Si surface is terminated by sulfur The electronic gap of the NP is substantially lowered Cause? S. Wippermann, G. Zimanyi (UCD)

9 Motivation embedded NPs advanced theory MEG 08/20 Si nanoparticles in ZnS: lone pairs at interface S atoms at NP surface are typically 3-fold coordinated, due to valence electronic structure: 1 S-Si bond, 2 Zn-S bonds => lone pairs at interface lone pairs fall energetically into NP gap NP-HOMO is now an interface state, involving the S lone pairs NP-HOMO sulfur lone pairs

10 Si nanoparticles in ZnS: spatial separation of states near band edges valence band edge: interface & matrix states conduction band edge: localized in NP extremely small Si-ZnS lattice mismatch (0.3%); type II interface at equilibrium density interface chemistry & matrix density dominate NP properties at small NP sizes Motivation embedded NPs advanced theory MEG 09/20

11 Motivation embedded NPs advanced theory MEG 10/20 Extract nanoparticles and use higher level of theory embedded extracted Surgery: NP extracted with a surface shell as determined in the matrix, exhibits very similar electronic properties Time-dependent density functional theory i (r,t)= is the theory good enough? apple 1 2 r2 + v H (r,t)+v xc (r,t)+v ext (r,t) i(r,t)

12 Semiconducting nanoparticles: light absorption and emission from many-body perturbation theory Comparison between many-body perturbation theory (BSE) and TD-DFT (LDA or PBE) Larger differences for smaller nano-dots Important qualitative differences in Si nanowires up to ~600 electrons D. Rocca, Y. Ping (UCD) strength of excitonic effect depends on surface structure ~1nm Si NW Motivation embedded NPs advanced theory MEG 11/20

13 Semiconducting nanoparticles: light absorption and emission from many-body perturbation theory Developed algorithms and codes to compute optical spectra of materials and nanostructures scalable to large systems: no calculation of empty states, no storage and inversion of dielectric matrices emission and absorption spectra C87H76 D. Rocca, H.-V. Nguyen, T. A. Pham (UCD) D. Rocca, D. Lu, G. Galli, JCP (2010); D. Rocca, Y. Ping, R. Gebauer, G. Galli, PRB (2012); Y. Ping, D. Rocca, D. Lu, G. Galli, PRB (2012); T. A. Pham, D. Rocca, G. Galli, PRB-RC (2012) Motivation embedded NPs advanced theory MEG 12/20

14 Motivation embedded NPs advanced theory MEG 13/20 Silicon great for MEG, but: gaps just don t match the solar spectrum hν > 2Eg hot exciton Multiple exciton generation (MEG) in Si NPs Single high energy photon creates several excitons Silicon: High carrier multiplication yield, low relative activation threshold Problem: quantum confinement increases gap! => MEG activation energy beyond solar spectrum same problem with other materials e - -phonon, Auger rec. MEG => Need to bring down the gap in Si NPs without sacrificing MEG efficiency single exciton multi-exciton

15 Motivation embedded NPs advanced theory MEG 14/20 Idea: look at silicon high pressure phases β-tin (Si-II) metal pressure (~12 GPa) R8 (Si-XII) slow pressure release (~8 GPa) fast pressure release (<100ms) Eg = 0.24 ev Si-XIII, Si-IX only incomplete structural information known ambient pressure semimetal hex. diam. (Si-IV) BC8 (Si-III) annealing (470 K) Si-I Eg = 1.1 ev BC8 is semimetal and stable at ambient conditions => strong candidate! Eg = 0.95 ev

16 Motivation embedded NPs advanced theory MEG 015/20 Si NPs with high pressure core structures Si34H36 (R8) Si34H38 (BC8) Si42H48 (Ibam) Si35H36 (cd) Si39H40 (hd) Si46H52 (ST12) Si44H48 (bct)

17 Motivation embedded NPs advanced theory MEG 16/20 Electronic properties Si-I ST12 BC8 BC8 NPs feature smallest electronic gaps of all Si NPs with high pressure cores ST12 has increased bulk gap, smaller increase by quantum confinement & by far highest EDOS of all Si phases

18 Motivation embedded NPs advanced theory MEG 16/20 Electronic properties Si-I ST12 BC8 BC8 NPs feature smallest electronic gaps of all Si NPs with high pressure cores ST12 has increased bulk gap, smaller increase by quantum confinement & by far highest EDOS of all Si phases

19 Optimum gap for MEG in 4-8nm BC8 NPs Si123H100 Si144H ev 1.1 ev 1.8 ev 0.5 ev GW calculations up to d=1.6nm (Si144H114) confirm trends observed in LDA Optimum gap for PV cells employing MEG (Eg = ev) [4] found for BC8 NPs within typical experimental size range of d = 4-8 nm (extrapolation of GW gaps) [4] M. Hanna, A. Nozik, J. Appl. Phys. 100, (2006) Motivation embedded NPs advanced theory MEG 17/20

20 MEG: Strong gain for BC8 on absolute scale impact ionization rate Impact ionization (II) is dominating contribution to MEG [5]; calculate II rates ab initio BC8 NPs feature lower activation threshold on absolute energy scale & order of magnitude higher impact ionization rate at same energies and same NP size! [5] A. Piryatinski et el., J. Chem. Phys. 133, (2010); K. Velizhanin et al., Phys. Rev. Lett. 106, (2011) Motivation embedded NPs advanced theory MEG 18/20

21 MEG: Strong gain for BC8 on absolute scale impact ionization rate Impact ionization (II) is dominating contribution to MEG [5]; calculate II rates ab initio BC8 NPs feature lower activation threshold on absolute energy scale & order of magnitude higher impact ionization rate at same energies and same NP size! [5] A. Piryatinski et el., J. Chem. Phys. 133, (2010); K. Velizhanin et al., Phys. Rev. Lett. 106, (2011) Motivation embedded NPs advanced theory MEG 18/20

22 BC8 NPs found in black silicon Black Silicon discovered by E. Mazur in 1999, very low reflectance, sub Si bandgap optical absorption fs-laser irradiation in SF6 or Se atmosphere creates nanopillars on Si surface laser-induced recoil pressure waves create BC8 & R8 Si NPs in a-si regions within core of nanopillars [6] (BC8) BC8 NPs can also be created by nanoindentation => Si high pressure NPs exist! [6] M. Smith, E. Mazur et al., J. Appl. Phys. 110, (2011) Motivation embedded NPs advanced theory MEG 19/20

23 Summary Embedded NPs in SiO2: tuning of optical & electronic properties not only by size, but also matrix density ZnS: strong gap reduction due to interface chemistry; at band edges electrons in NP core, holes at NP surface & inside matrix => possibly improved hole conductivity MEG in Si NPs with high pressure core structures Si-I: high carrier multiplication yields & low relative activation thresholds, but quantum confinement increases gap beyond solar spectrum Si NPs with BC8 core structures feature optimum gap range of Eg = ev at size range d = 4-8 nm Order of magnitude higher impact ionization rates for BC8 NPs compared to standard Si-I NPs at same size on absolute energy scale Si BC8 NPs can be created in amorphous Si ( black silicon, nanoindentation) S. Wippermann, M. Vörös, D. Rocca, A. Gali, G. Zimanyi, G. Galli (submitted) Motivation embedded NPs advanced theory MEG 20/20

24 Motivation embedded NPs advanced theory MEG 21/25 Additional Slides

25 Si nanoparticles embedded in solid matrices for solar energy conversion Interface between Si-nanoparticle and a-zns Si atoms 4-fold coordinated Zn/S atoms in matrix mostly 4-fold coordinated S atoms at interface mostly 3-fold coordinated => S lone pairs on NP-surface Occasional ZnS dimer/chain formation on Si-NP surface bond configurations 1/2 3/2 1/2 3/2 1/2 2 3/2 3/2 S Zn 1/ Si NP-surface Si => Look at electronic properties Motivation Si-NPs in a-zns Si high-pressure phases Summary 22/25

26 Motivation embedded NPs advanced theory MEG 23/25 Idea: silicon high pressure phases Ibam structure recently proposed as Si-IX (APS 2012 [2]) bct & ST12 phases predicted for Si, but not (yet) observed experimentally bct ST12 Ibam (Si-IX)?? [2] B. Malone, M. Cohen, Phys. Rev. B 85, (2012)

27 Motivation embedded NPs advanced theory MEG 24/25 Optical properties (TD-DFT RPA) red-shifted optical absorption onset for high density phases (BC8, R8, Ibam) less pronounced for ST12 and low density phases (bct, hd)

28 Motivation embedded NPs advanced theory MEG 25/25 cubic diamond vs. ST12 II i = 2 ~ X f = 2 ~ W i eff hx i W XX f i 2 (E i E f ) 2 TDOSi cubic diamond: NP size increase reduces Coulomb interaction Weff, trion DOS almost constant => impact ionization rate drops ST12: Weff reduced as for cubic diamond, but TDOS increases => impact ionization rate remains almost constant with increasing size