The study of the pressure and temperature phase diagram of semiconductors has continued for several decades now using powerful experimental techniques such as x-ray and neutron diffraction and light scattering. The high pressure polymorphism, as yet, is neither fully known nor completely understood. This is due to the extreme complexity and to large hysteresis observed on release of pressure. Silicon is known to display at least eleven different crystalline phases at pressures up to 248 GPa some of which can be recovered as complex metastable phases at atmospheric pressure. In germanium transitions to the -Sn structure, hexagonal close-packed (hcp) and distorted-hcp have been observed up to 125GPa. In addition, metastable phases can be obtained either by pressure decrease from the metallic phases or by chemical leaching of lithium from Li Ge . Very recently, it has been found that small regions of metallic silicon can be obtained by nanoindentation.
For carbon it is impossible to perform experiments on phases with higher density than diamond because of the huge pressures involved. Indeed, in most pressure experiments, carbon diamond-anvil cells are used to produce the required pressure. In view of the existence of a covalently-bonded diamond phase, it seems reasonable to investigate whether the phase diagram may be similar to Si and Ge. Calculations of metallic phases in carbon do, however, suggest that these are not significantly denser than diamond.
Silicon has been an ideal material for combining experiment and total energy calculations. In their groundbreaking paper, Yin and Cohen predicted that the -Sn phase would transform to hcp at 43GPa. In searching for this transition, experimental results revealed another phase, simple hexagonal, which Yin and Cohen had not examined. On repeating the calculation the stability of the simple hexagonal structure was confirmed. Similar calculations have been carried out in germanium and carbon, examining both stable and metastable phases[6, 8, 9].
Ab initio total energy calculations are sufficiently accurate to have a predictive capability, and certainly their success in reproducing many experimental features of condensed matter is impressive.
As illustrated by the above example, however, it is often important to know what to expect before beginning the calculation, so that all reasonable possibilities are examined. However, the calculation of intermediate stages of these first order phase transition is much more complicated. This is because the rate at which first order phase transitions occur varies enormously, so that the lifetimes of some metastable phases is essentially infinite because of the large kinetic barrier to transition. Since the transition path is seldom known, the lifetime of metastable phases cannot be readily calculated.
Metastable phases of the group IV elements have long been of great practical and theoretical interest. The hardness of diamond has been utilized since ancient times, while more recently amorphous silicon has found numerous uses. With pressure treatment it is also possible to create high-density phases of Si and Ge which are long-lived under normal conditions. These complex structures have been shown to be useful models in exploring the effect of increasing short range disorder on optical properties and have provided a vital insight into the nature of the amorphous phase of these materials[10, 11]. A thorough study of these metastable phases: BC8 and ST12, both in silicon and germanium has been carried out, where they have been observed experimentally, and also in carbon. In addition to revealing the structural stability and nature of the bonding, the results will be a useful guide in determining the degree to which simple empirical models can account for the structural trends.
Silicon BC8 and germanium ST12 phases are reasonably easy to synthesize. Under a pressure of about 12.5GPa diamond Si transforms to the -Sn phase. This is a massively first order phase transition in which the structure transforms from fourfold to sixfold coordination and the material itself transforms from semiconductor to metal. There is no easy kinetic path for this transition, and on depressurization there is considerable hysteresis. Eventually, at about 8GPa the -Sn phase transforms back, not to diamond, but to the BC8 phase. The lifetime of BC8 silicon under ambient conditions seems to be indefinite.
The nature and number of metastable phases formed on depressurization appears to depend upon the temperature and rate of depressurization. Slow decompression from crystalline ( -Sn phase) Si at ambient temperature gives a mixture of amorphous silicon, diamond and BC8. Upon rapid release of pressure from the metallic state, two tetragonal phases have been obtained. It appears that once converted to any metallic form by application of pressure, silicon reverts to BC8 and the diamond form cannot be recovered, even by heat treatment and recrystallization where the Lonsdaleite structure (hexagonal diamond) is formed.
The polymorphism of germanium is similarly complex. Pressure increase from the cubic diamond structure results in the -Sn structure at 10.6GPa. Slow pressure decrease results in the formation of diamond and ST12 germanium at 7.6GPa. A metastable form of germanium in the BC8 structure has also been observed on pressure decrease[18, 19].
In carbon no phases with higher density than diamond have been made.
The discovery of the BC8 phase, its identification as a semimetal (with resistivity about a thousand times lower than the semiconducting diamond form and a hundred times higher than the -Sn form), and the crystallographic structural solution have been reported previously[20, 21, 22, 23, 24, 25]. There have also been some total energy calculations on the BC8 phase in silicon[6, 9, 10, 26], and in carbon[6, 9] where it has been predicted to be stable over a range of very high pressures. This has not been experimentally verified, and for obvious reasons is impossible with conventional diamond anvil pressure cells.