High pressure core structures of Si nanoparticles for solar energy conversion

High pressure core structures of Si nanoparticles for solar energy conversion S. Wippermann, M. Vörös, D. Rocca, A. Gali, G. Zimanyi, G. Galli [Phys. Rev. Lett. 11, 4684 (213)] NSF/Solar DMR-135468 NISE-project 35687 Wi3879/1-1

Multiple Exciton Generation (MEG) Hot exciton relaxes by creating another electron-hole pair, instead of thermalizing to the band edges 2% effect in bulk semiconductors, but significantly more efficient in quantumconfined nanostructures M. Beard, JPCL 2, 1282 (211)

Multiple Exciton Generation (MEG) Hot exciton relaxes by creating another electron-hole pair, instead of thermalizing to the band edges 2% effect in bulk semiconductors, but significantly more efficient in quantumconfined nanostructures M. Beard, JPCL 2, 1282 (211) Key problem: Quantum confinement required for efficient MEG, but pushes electronic gap beyond solar spectrum

Multiple Exciton Generation (MEG) Hot exciton relaxes by creating another electron-hole pair, instead of thermalizing to the band edges 2% effect in bulk semiconductors, but significantly more efficient in quantumconfined nanostructures M. Beard, JPCL 2, 1282 (211) Key problem: Quantum confinement required for efficient MEG, but pushes electronic gap beyond solar spectrum Idea: MEG observed in Si: gap/wavefunction engineering possible? => look at high pressure phases

Phases of Si under pressure slow pressure release (~8 GPa) R8 (Si-XII) ambient pressure BC8 (Si-III) metal β-tin (Si-II) Eg = 1.1 ev pressure (~12 GPa) Eg =.24 ev semimetal annealing (47 K) hex. diam. (Si-IV) Si-I Eg =.95 ev

Phases of Si under pressure slow pressure release (~8 GPa) R8 (Si-XII) ambient pressure BC8 (Si-III) β-tin (Si-II) metal Eg = 1.1 ev pressure (~12 GPa) fast pressure release (<1ms) Eg =.24 ev Si-XIII, Si-IX only incomplete structural information known semimetal annealing (47 K) hex. diam. (Si-IV) Si-I Eg =.95 ev

Phases of Si under pressure slow pressure release (~8 GPa) R8 (Si-XII) ambient pressure BC8 (Si-III) β-tin (Si-II) metal Eg = 1.1 ev pressure (~12 GPa) fast pressure release (<1ms) Eg =.24 ev Si-XIII, Si-IX only incomplete structural information known (yet) hypothetical phases of Si semimetal annealing (47 K) hex. diam. (Si-IV) Si-I Ibam (Si-IX??) bct ST12 Eg =.95 ev

Phases of Si under pressure BC8 is a metastable phase of silicon, in analogy to diamond being a metastable phase of carbon R8 (Si-XII) slow pressure release (~8 GPa) ambient pressure BC8 (Si-III) β-tin (Si-II) metal Eg = 1.1 ev pressure (~12 GPa) fast pressure release (<1ms) Eg =.24 ev Si-XIII, Si-IX only incomplete structural information known (yet) hypothetical phases of Si semimetal annealing (47 K) hex. diam. (Si-IV) Si-I Ibam (Si-IX??) bct ST12 Eg =.95 ev

High pressure Si nanoparticles Si34H36 (R8) Si34H38 (BC8) Si42H48 (Ibam) Si35H36 (cd) Si39H4 (hd) Si46H52 (ST12) Si44H48 (bct)

Electronic properties: low gaps for BC8 BC8 is a semi-metal in the bulk,.3 ev direct overlap at the H-point Quantum confinement opens gap in BC8 nanoparticles BC8 NPs feature much smaller gaps than Si-I NPs

Electronic properties: low gaps for BC8 BC8 is a semi-metal in the bulk,.3 ev direct overlap at the H-point Quantum confinement opens gap in BC8 nanoparticles BC8 NPs feature much smaller gaps than Si-I NPs

Electronic properties: low gaps for BC8 GW calculations confirm trends observed at single particle level of theory* Si-BC8 NP GW gaps ideal for solar energy conversion in 4-8nm size range, where MEG is still efficient for Si-I NPs GW gaps provide upper estimate: reconstructions, excitonic effects further reduce gaps Si123H1 Si144H114 2.5 ev 1.1 ev 1.8 ev.5 ev *Fitting performed including known GW bulk gaps; theory: H.-V. Nguyen et al., PRB 85, 8111 (212)

Impact ionization: Si-BC8 wins over Si-I Impact ionization (II) is dominating contribution to MEG [1]; calculate II rates from first principles [M. Vörös, D. Rocca, G. Galli, G. Zimanyi, A. Gali, PRB 213 (accepted)] [1] A. Piryatinski et el., J. Chem. Phys. 133, 8458 (21); K. Velizhanin et al., Phys. Rev. Lett. 16, 2741 (211)

Impact ionization: Si-BC8 wins over Si-I Impact ionization (II) is dominating contribution to MEG [1]; calculate II rates from first principles [M. Vörös, D. Rocca, G. Galli, G. Zimanyi, A. Gali, PRB 213 (accepted)] [1] A. Piryatinski et el., J. Chem. Phys. 133, 8458 (21); K. Velizhanin et al., Phys. Rev. Lett. 16, 2741 (211)

Impact ionization: Si-BC8 wins over Si-I Impact ionization (II) is dominating contribution to MEG [1]; calculate II rates from first principles [M. Vörös, D. Rocca, G. Galli, G. Zimanyi, A. Gali, PRB 213 (accepted)] BC8 NPs feature lower activation threshold on absolute energy scale & order of magnitude higher impact ionization rate at same energies and same NP size! [1] A. Piryatinski et el., J. Chem. Phys. 133, 8458 (21); K. Velizhanin et al., Phys. Rev. Lett. 16, 2741 (211)

BC8 NPs discovered 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 (BC8) => Proof that BC8 NPs exist and can be prepared experimentally! M. Smith, E. Mazur et al., J. Appl. Phys. 11, 53524 (211)

Embedded high pressure phase Si NPs Experimental preparation of BC8 NPs requires kinetic trapping in host material After initial calculations on hydrogenated high pressure Si NPs, now investigating high pressure Si NPs embedded in amorphous Si Creation of accurate structural models by ab initio molecular dynamics Work in progress* Si-I in a-si Si-II (β-tin) in a-si Si-III (BC8) in a-si *regarding embedding see also: Complementary transport channels in Si-ZnS nanocomposites (4:18pm)

Summary (Metastable) high pressure phases of elemental semiconductors allow for gap engineering of nanoparticles (NPs), while retaining efficient multiple exciton generation (MEG) BC8 is a metastable phase of silicon, in analogy to diamond being a metastable phase of carbon Si-BC8 NPs predicted to feature efficient MEG within the solar spectrum NSF/Solar DMR-135468 NISE-project 35687 Wi3879/1-1

Thanks to our colleagues and don t miss our related talks! Session U38/W38, Thursday March 21st, room 347 12:3pm-12:15pm: Germanium nanoparticles for solar energy conversion 4:18pm-4:3pm: Complementary transport channels in Si-ZnS nanocomposites 12:39pm-12:51pm: Monte Carlo modeling of charge transport in nanocrystalline PbSe films

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)

Density functional theory (DFT): Hohenberg-Kohn theorem: E e [n] =T [n]+ 1 n(r)n(r ) drdr + 2 r r [Walter Kohn, Nobel Prize for chemistry in 1998] E XC [n] E LDA XC [n] = n(r) hom XC (n(r))dr n(r)v (r)dr + E XC [n] atomic positions interatomic forces 2 2 + Starting point: initial geometry external potential n(r ) r r dr + V (r)+ ELDA XC n(r) structurally relaxed ground-state Kohn-Sham self-consistent electron structure j (r) = j j (r) n(r) = occ. j j(r) 2 vibrational and thermal properties electronic properties spectroscopic and transport properties

Excited states (GW/BSE) DFT disregards screened e--e- interaction and e--h interaction for excited states => band gap underestimation, wrong distribution of spectral weights Perturbative approaches for including screening (GW) and e--h interaction (Bethe-Salpeter), starting from Quantum Liouville equation h dˆ (t) i = H (t), ˆ(t) dt Z i (r, r, t) = v (r, t) v (r, t) v single particle occ. orbitals H (r, r, t) (r, t)dr = + self-energy X Z 1 2 r + vh (r, t) + vext (r, t) 2 (r, t) time-dep. perturbation, (r, r, t) (r, t)dr i. e. electromagn. field statically screened 1 Bethe-Salpeter COH (r, r ) = (r r )Wp (r, r ) 2 X equation (BSE) SEX (r, r, t) = v (r, t) v (r, t)w (r, r ) screened Coulomb interaction v

Excited states (GW/BSE) To correct for DFT s band gap underestimation, quasiparticle energies can be obtained in GW approximation from GW (r, r ; i!) = 1 2 W (r, r )= Z Z G(r, r ; i(!! ))W (r, r ; i! )d! Screened Coulomb interaction required (in random phase (RPA) approx.) 1 (r, r )v c (r, r )dr Bottleneck: calculation, storage & inversion of dielectric matrix is very computationally demanding, involves large sums over empty states and is hard to converge Solution: spectral representation of RPA dielectric matrix; obtain matrix from directly calculating eigenvectors and eigenvalues = NX i=1 ṽ i i ṽ H i = NX i=1 ṽ i ( i 1)ṽ H i + I => no summation over empty states, no inversion, storage of eigenvector/-value pairs only!

How to calculate the screening Obtaining the eigenvectors/-values does NOT require explicit knowledge of the matrix; knowledge of the action of the matrix on an arbitrary vector is sufficient! in linear response: charge density response to perturbation of self-consist. field V SCF can be evaluated from density functional perturbation theory orthogonal iteration procedure to obtain eigenvectors/-values, using as trial potentials V SCF in RPA fast monotonous decay of dielectric eigenvalue spectrum single parameter numerical accuracy ( I) V SCF = v c n N eig n to control = NX i=1 ṽ i i ṽ H i = NX i=1 ṽ i ( i 1)ṽ H i + I [H. Wilson et al., PRB 79, 24516 (29); D. Rocca et al., J. Chem. Phys. 133, 16419 (21); H.-V. Nguyen et al., PRB 85, 8111 (212)]

Ab initio impact ionization (II) rates Exciton -> biexciton decay rate from Fermi s Golden Rule with RPA statically screened Coulomb interaction (Rydberg atomic units): W i =2 f X i W XX f 2 (E i E f ) Exciton (X i ) and biexciton (XX f ) states approximated as singly and doubly excited Slater determinants build up from the DFT orbitals + j =4 klc ( V lckj V kclj 2 + V lckj 2 + V kclj 2 ) [ j ( l c + k )] a =4 lbc ( V aclb V ablc 2 + V aclb 2 + V ablc 2 ) [ a ( b l + c )] ja = a + + j j ( l c + k ) 2 (E) = ja ja [( a j ) E] a ( b l + c ) 2 ja [( a j) E] a j E 1 [M. Vörös, D. Rocca, G. Galli, G. Zimanyi, A. Gali, PRB 213 (accepted)] 5 mev