Stability and Polaronic Motion of Self-Trapped Holes in Silver Halides: Insight through DFT+UCalculations

Abstract

Polarons and their associated transport properties are a field of great current interest both in chemistry and physics. In order to further our understanding of these quasi-particles, we have carried out first-principles calculations of self-trapped holes (STH) in the model compounds AgCl and AgBr, where extensive experimental information exists. Our calculations confirm that the STH solely stabilizes in AgCl but with a binding energy of only 165 meV, an order of magnitude smaller than that found for the Vk center in KCl. Key contributions to this stabilization energy come from the local relaxation along breathing (a1g) and Jahn-Teller (eg) modes in the AgCl6 4-unit. In order to study the transfer of the STH among silver sites we (i) use first-principles calculations to obtain the hopping barrier of the STH to first and second neighbors, involving eight distinct paths, using firstprinciples and (ii) construct a simple model, based on Slater-Koster parameters, that highlights the similarity of polaron transfer with magnetic superexchange. This allows one understanding why the movement of STH to second neighbors is highly enhanced with respect to closer ones. In agreement with experimental data and the model, the present calculations prove the existence of a dominant mechanism of polaronic motion that corresponds to the displacement of the STH to the next nearest sites in the <100> direction and a small barrier of 37 meV. This mechanism is dominated by the covalency inside a AgX6 4-complex (X:Cl;Br) thus explaining why the STH is not stabilized in AgBr following the increase of covalency due to the ClBr substitution. The present calculations confirm that ~10% of the charge associated with the STH in AgCl is lying outside the AgCl6 4-complex. This fact is behind the differences between optical and magnetic properties of the STH in AgCl and those observed in KCl:Ag 2+ .2

Wide‐Bandgap Double Perovskites with Multiple Longitudinal‐Optical Phonon Scattering

“…[ 38 ] The excitonic recombination process is accompanied by a lattice distortion, [ 37 ] which is generally referred to as the Jahn–Teller distortion (Figure 4b). [ 39 ] Multiphonon peaks superimposed on a continuous band are the product of the multiphonon transitions caused by lattice relaxations. In the distorted lattice field of the alloyed double perovskites, a bound exciton is trapped as a polaron due to a strong exciton–phonon coupling effect; thus, the electron–phonon coupling plays a crucial role in the self‐trapped exciton formation.…”

Electronic band structure of cuprous and silver halides: An all-electronGWstudy

“…The results from PBE and HSE06 are consistent with the previous findings in the literature. 23,27 For GW band gaps, we find that including HLOs in the LAPW basis leads to remarkable improvement for the band gap prediction for cuprous and silver halides. With the default LAPW basis, G 0 W 0 gives an average quasi-particle correction to the band gap as 0.72 and 0.89 eV for CuX and AgX, respectively.…”

“…the phase transition of CuI at high temperature, 18,19 the extraordinarily large excitonic binding energy of CuX, 4,20 and the electronic dynamics within AgX in the latent image formation. [21][22][23] Nowadays, first-principles electronic structure calculations are being practiced routinely to predict electronic and optical properties of materials. Among different methods, Kohn-Sham (KS) density functional theory (DFT) in the local density approximation or generalized gradient approximation (LDA/GGA) is most widely used for its efficiency and accuracy.…”

“…Previous work confirmed that the band gaps predicted for cuprous and silver halides by LDA/GGA are typically smaller than experimental values by 1-2 eV, 4,[24][25][26] and the problem is only partly remedied when using the hybrid functional approximation. 23,27 The many-body perturbation theory based on Green's function in the GW approximation has proven to be able to accurately predict electronic band structure of typical semiconductors, [28][29][30] and it has been applied in attempt to resolve the band-gap problem in cuprous and silver halides. 4,27,[31][32][33] However, LDA/GGA-based G 0 W 0 calculations generally give underestimated band gaps for these materials.…”

Jahn–Teller and Non-Jahn–Teller Systems Involving CuF64– Units: Role of the Internal Electric Field in Ba2ZnF6:Cu2+ and Other Insulating Systems

“…The Jahn–Teller (JT) effect has been widely invoked in the last 50 years for explaining the properties of systems involving d 9 , d 7 , and d 4 cations under octahedral coordination. Accordingly, experimental results on Cu 2+ systems like superconducting copper oxides or copper oxyfluorides and on silver­(II) fluorides have often been analyzed assuming the existence of a JT effect. − Nevertheless, this assumption implies that there exist a high symmetry reference conformation possessing an orbitally degenerate electronic state, but this crucial condition has not been proved in all cases. , So, while it is fulfilled for the polaron in AgCl − and d 9 impurities in cubic lattices without any close defect, − doubts have been raised analyzing the experimental and theoretical results for CuF 6 4– complexes in the tetragonal K 2 ZnF 4 lattice. ,− Indeed, the ground state in K 2 ZnF 4 :Cu 2+ is certainly unusual when compared to cubic fluoride ,− or chloride lattices − doped with d 9 ions displaying a static JT effect. In the latter systems the hole is always in the b 1g (∼ x 2 – y 2 ) level while it surprisingly resides in the a 1g (∼3 z 2 – r 2 ) level for K 2 ZnF 4 :Cu 2+ . ,, Furthermore, the optical properties of CuF 6 4– complexes in K 2 ZnF 4 cannot be quantitatively explained considering only the isolated CuF 6 4– unit at the equilibrium geometry derived for K 2 ZnF 4 :Cu 2+ . , Nevertheless, in a previous study it was found that both the d–d transitions and the unusual ground state of K 2 ZnF 4 :Cu 2+ are reasonably explained merely adding in the calculation the internal electric field, E R ( r ), that the rest of ions, belonging to the tetragonal lattice, create on the complex where active electrons do reside. , These results also imply that due to the action of E R ( r ) there is a gap, Δ 0 , between b 1g (∼ x 2 – y 2 ) and a 1g (∼3 z 2 – r 2 ) levels of CuF 6 4– units in K 2 ZnF 4 when the complex is perfectly octahedral …”