Theory of static structural properties, crystal stability, and phase transformations: Application to Si and Ge

Abstract

We demonstrate that not only the static structural properties but also the crystal stability and pressure-induced phase transformations in solids can be accurately described employing an ab initio pseudopotential method within the local density-functional formalism.Using atomic numbers of constituent elements and a subset of crystal structures as the only input information, the calculated structural properties of Si and Ge are in excellent agreement with experiment.-1--2- I. INTRODUCTIONIn this paper, we present an ab initio microscopic study of the static structural properties and other important structural properties including crystal stability and phase transformation of Si and Ge. Part of the results have been 1 previously reported. The method is based on a pseudopotential approach and uses the local density-functional approximation 2 which has also been used in all-electron calculations of static 3 structural studies of metals.We choose Si and Ge as our prototypes since they are the most studied semiconductors experimentally.Both have the (cubic) diamond structure and are found to undergo a semiconductor-4 metal phase transformation under pressure.Using the xray diffraction technique, the transformed phases have been and 100 kbar for Ge. 9In addition to the diamond and B-tin phases, a hexagonal diamond phase has been made lO for Si at room temperature and atmospheric pressure using a sequence of high-pressure and high-temperature treatments. This phase is semiconducting and has the same density as the (cubic) diamond phase. The Since this form has not been found in nature and no large crystals have been prepared,10 it is ~etastable with respect to the diamond phase. A similar structural form has not been found in Ge.There are other metastable phases of Si and Ge 10 11 (a bcc form,with 16 atoms per unit cell for Si and Ge and ,-.. 12 a tetra gonal form with 12 atoms per unit cell for Ge )i these will not be considered in the present study.There are interesting relations between the general phase transformation in semiconductors and other crystalline properties.Jamieson has related 5 the transition pressure (P t ) and the ;..../ atomic volume change (~V) in the phase transformation to the fundamental 'energy gap (E g ), and he ,obtained an empirical rule -of P t ~V = Eg/2 for Group IV elements and iso-row III-V compounds. Although this rule is less accurate when later refined experimental data is considered, the trend is still correct. This is consistent with the physical picture that the bigger the energy gap is, the more stabilized the structure is. Phillips13 has suggested that ionicity may be an important parameter in characterizing the phase transformation. He noted that the rocksalt structure becomes more favorable as the highpressure phase with increasing ionicity. The covalent counterpart ' ;:. of the rocksalt structure, that is, the simple cubic structure, is included in the present study.Pressure-induced phase transformations in tetrahedrally coordinated semiconductors have previously been ...

The martensitic transformation in silicon—III. comparison with other work

“…It seems that only the slightly more localized charge distribution in dh Si makes this phase less stable than the de phase [22]. Their results also show that dh Si is not a thermodynamically stable phase and de silicon cannot transform to dh silicon at equilibrium under any pressure.…”

Trends in the properties and structures of the simple metals from a universal local pseudopotential

“…To find the r s which characterizes zϭ4 silicon, it is only necessary to perform an all-electron or nonlocal pseudopotential calculation for this element in a hypothetical fcc structure, as in Ref. 63 (r s ϭ1.8 bohr).…”

The electron distribution in silicon. A comparison between experiment and theory

“…see Fig. 2 of Yin & Cohen (1982)]. Jacobi fits to these and the corresponding canonical orbital scattering factors for first-and second-row atoms have been reported by van der Wal & Stewart (1984).…”