Thermodynamics, Electronic Structure, and Vibrational Properties of Sn_n(S_1–xSe_x)_m Solid Solutions for Energy Applications

Abstract

The tin sulfides and selenides have a range of applications spanning photovoltaics and thermoelectrics to photocatalysts and photodetectors. However, significant challenges remain to widespread use, including electrical and chemical incompatibilities between SnS and device contact materials and the environmental toxicity of selenium. Solid solutions of isostructural sulfide and selenide phases could provide scope for optimizing physical properties against sustainability requirements, but this has not been comprehensively explored. This work presents a detailed modeling study of the Pnma and rocksalt Sn(S 1−x Se x ), Sn(S 1−x Se x ) 2 , and Sn 2 (S 1-x Se x ) 3 solid solutions. All four show an energetically favorable and homogenous mixing at all compositions, but rocksalt Sn(S 1−x Se x ) and Sn 2 (S 1−x Se x ) 3 are predicted to be metastable and accessible only under certain synthesis conditions. Alloying leads to a predictable variation of the bandgap, density of states, and optical properties with composition, allowing SnS 2 to be "tuned down" to the ideal Shockley−Queisser bandgap of 1.34 eV. The impact of forming the solid solutions on the lattice dynamics is also investigated, providing insight into the enhanced performance of Sn(S 1−x Se x ) solid solutions for thermoelectric applications. These results demonstrate that alloying affords facile and precise control over the electronic, optical, and vibrational properties, allowing material performance for optoelectronic applications to be optimized alongside a variety of practical considerations.

Lattice dynamics of Pnma Sn(S1–xSex) solid solutions: energetics, phonon spectra and thermal transport

“…We recently carried out a study of four Sn n (S 1-x Se x ) m alloys [26], including the Pnma and rocksalt monosulphides, by performing first-principles calculations on the full sets of symmetry-inequivalent structures formed by substituting chalcogen atoms in small supercells of the parent structures [28]. In this study we also confirmed the stability of the mixed Pnma Sn(S 1-x Se x ) alloys and further predicted the effect of alloying on the structural, electrical and optical properties [26].While many large-scale modelling studies make use of (semi-)local DFT methods to evaluate and compare energetics and electrical properties [29][30][31][32], modelling lattice dynamics and in particular thermal transport can be much more resource intensive, and there are thus comparatively fewer examples of screening studies focussing on these properties [33]. As a result, despite the widespread use of alloying to tune the performance of thermoelectric materials, there has been little theoretical investigation into how composition affects the dynamics and related properties.…”

“…However, the substantial difference in the mixing energy may be important in systems with competing phases. In our previous work [26,42], we predicted based on lattice energies that the energy difference between competing Pnma and rocksalt Sn(S 1-x Se x ) monochalcogenide solid solutions varies from 10.5 and 2.6 kJ mol −1 per F.U. between the SnS and SnSe endpoints [26].…”

“…The starting point for our calculations was the set of optimised structures in the Pnma Sn(S 1-x Se x ) solid solution model from our previous study [26]. In our previous work, the Transformer code [34] was used to enumerate the symmetry-independent structures formed by successively substituting the chalcogen atoms in a 32-atom 2×1×2 expansion of the Pnma SnS/SnSe structure, yielding a total of 2446 unique structures across seventeen compositions from x Se =0 (SnS) to x Se =1 (SnSe).…”

“…Due to the record-breaking high-temperature ZT of SnS, the Te-free Sn(S, Se) alloys are of particular interest, and experimental studies have demonstrated a reduction in the thermal conductivity of mixed compositions [12,14].Thermoelectricity is unique in that all four of the terms in the figure of merit ZT are amenable to calculation using first-principles electronic-structure methods such as density-functional theory (DFT) [18]. There have been a number of theoretical studies on existing and potential new single-component bulk thermoelectrics [6,[19][20][21][22][23], and there have recently been efforts to use high-throughput modelling to screen large numbers of compounds in a bid to identify new candidate thermoelectrics [24,25].Studying multicomponent alloy systems with first-principles methods is challenging, however, as building a realistic model requires calculations on a large number of configurations that for complex systems with lowsymmetry unit cells can easily approach the cost of a screening study [26]. Ektarawong and Alling used a firstprinciples cluster expansion method to study the Pnma Sn(S 1-x Se x ) system and confirmed the stability of the mixed phases at finite temperature [27].…”

“…Studying multicomponent alloy systems with first-principles methods is challenging, however, as building a realistic model requires calculations on a large number of configurations that for complex systems with lowsymmetry unit cells can easily approach the cost of a screening study [26]. Ektarawong and Alling used a firstprinciples cluster expansion method to study the Pnma Sn(S 1-x Se x ) system and confirmed the stability of the mixed phases at finite temperature [27].…”