Comment on “Towards Direct-Gap Silicon Phases by the Inverse Band Structure Design Approach” In the Letter of Xiang et al. [1], a novel, metastable cubic silicon phase Si20-T was theoretically predicted by the modified particle swarm optimization method CALYPSO

In the Letter of Xiang et al. [1], a novel, metastable cubic silicon phase Si20-T was theoretically predicted by the modified particle swarm optimization method CALYPSO [2]. The optical absorption of this phase was computed and compared to that of diamond silicon. Si20-T exhibits a quasidirect gap of 1.55 eV and has a stronger absorption in the visible compared to diamond silicon, which makes it a candidate as a solar energy absorber. However, we have strong reasons to believe that this phase cannot be experimentally synthesized via strong compression or decompression or through molecular encapsulation as proposed by the authors [3]. According to our density functional theory calculations with the Perdew-Burke-Ernzerhof functional, and in agreement with the data reported in Ref. [1], the energy differences at ambient conditions of Si20-T with respect to diamond silicon and to the type II silicon clathrate are 286 and 233 meV=Si, respectively. In fact, Botti et al. [4] predicted a plethora of energetically much more favorable silicon polymorphs, some of which are equally well suited for photovoltaic applications, by employing the minima hopping method [5,6]. In view of that, even in the unlikely case that Si20-T could be synthesized, its stability is highly questionable since it would quickly and highly exothermically decay to some more favorable metastructure, such as those of Ref. [4]. Furthermore, the configurational density of states increases with energy and essentially explodes [7] when amorphous silicon becomes accessible at roughly 290 meV=Si above silicon diamond [8]. A huge number of structures therefore compete thermodynamically with Si20-T such that a crystallization in this phase is very unlikely. To address the above issues, Botti et al. [4] systematically rejected all phases with higher energies than 150 meV=Si above diamond silicon. Although compression or expansion of silicon is a valid and promising approach to synthesize novel silicon polymorphs, we are convinced that this approach is not applicable to obtain Si20-T. Xiang et al. [1] conclude that Si20-T can be synthesized at cell volumes below 15.6 Å=Si or above 37.0 Å=Si by boldly comparing its energy=atom curve as a function of volume=atom with respect to diamond silicon alone, ignoring all other lowerenergy metastable polymorphs. This complete neglect of the complex phase diagram of silicon, which undergoes several phase transitions as a function of pressure, is the origin of their erroneous conclusions. The energies of the various silicon phases as a function of atomic volume are shown in Fig. 1. With the full phase diagram in mind, we can clearly see that the β-tin phase is by far energetically favored over Si20-T at 16 Å =Si (170 meV=Si), while silicon clathrates are favored in the high volume range (156 meV=Si at 37.0 Å=Si). Note that at this high volume, which corresponds to a negative pressure of -1.8 GPa, our calculations show that Si20-T silicon is dynamically unstable, making it therefore irrelevant to propose the synthesis beyond 37.0 Å=Si. Xiang et al. [1] also proposed molecular encapsulation to synthesize Si20-T with intercalated CH4. Again, the authors neglected the energetically more favorable silicon clathrates in their comparison. By inserting CH4 in the clathrate’s polyhedra the cell volume expands by merely 1.6%, compared to 8.3% volume expansion in Si20-T, resulting in a significantly stronger strained structure. Therefore it is not surprising that, according to our calculations, the clathrate with encapsulated CH4 is favored by 458 meV=Si. In conclusion, optimizing a single physical property alone when designing novel functional materials is by no means sufficient to predict promising structures, but a rigorous study of the thermodynamic stability is essential when evaluating their synthesizablity.