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[1] 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[2]. In
addition, metastable phases can be obtained either by pressure decrease
from the metallic phases[3] or by chemical leaching of
lithium from Li 
Ge 
[4]. Very recently, it has been
found that small regions of metallic silicon can be obtained by
nanoindentation[5].
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.[6]
Silicon has been an ideal material for combining experiment and total
energy calculations. In their groundbreaking paper, Yin and
Cohen[7] 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[12]. 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[13]. 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[14]. Upon rapid release of pressure from the metallic
state, two tetragonal phases have been obtained[15]. 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[16]. Slow pressure decrease results in the
formation of diamond and ST12[17] 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.