Condensation of non-equilibrium charge carriers in semiconductors

General Density Functional Theory

“…We can also write Exe in the suggestive form (74) where R(rl) is an average range of the exchange-correlation hole iixe(rhr2) as function of (r2 -rl) in the sense (75) Of course, for an interacting, inhomogeneous system the functions hand fixe are not exactly known and approximations must be made. In this process the sum rules given in equation (67) and equation (73) The local density approximation corresponds LO (76) where ho(lr\ -r21; n) is the hole function for an interacting uniform electron gas of density n. For given rJ, by comparison with a uniform gas of density n = n(r\), we see that (76) satisfies the sum rule (73). It does not, however, satisfy the symmetry condition (66).…”

“…The form for Exn equation (70), suggests some other simple approximations which should be more accurate than the LDA, equation (76). We shall limit ourselves to approximations based on the exchange-correlation hole functions ho(r;n), which are directly obtainable from the pair correlation functions gA(r;n) of a homogeneous electron gas with interaction ,vlr\ -r21.…”

“…Experiments in germanium and silicon have revealed that at high densities optically pumped electrons and holes undergo a phase transition. (75)(76)(77)(78)(79) The new phase of the system, called electron-hole liquid (EHL), consists of interpenetrating and interacting electron and hole degenerate Fermi liquids.…”

CRITICAL CONCENTRATION FOR THE METAL-NON METAL TRANSITION IN n-TYPE GERMANIUM AND SILICON

“…If v is the number of conduction band minima (4 and 6 for Ge and Si, respectively) the kinetic energy is (see e. g. [24])…”

“…We simply believe that a delicate problem should be approached in as many ways as possible. [24]). We may understand the formation of an electron-hole plasma at T = 0 K in the following elementary way.…”