Instability of the Electron-Hole Plasma and its Possible Relation with Melting
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INSTABILITY OF THE ELECTRON-HOLE PLASMA AND ITS POSSIBLE RELATION WITH MELTING
MONIQUE COMBESCOT, JULIEN BOK Groupe de physique des solides de l'Ecole Normale Supgrieure, 24 rue Lhomond, 75005 Paris, France
ABSTRACT We show that the softening of the T.A. phonon mode produces an instability in the electron-hole plasma of a silicon-like semiconductor and suggest that this instability can be the mechanism for melting of this type of material. This allows us to estimate the characteristics of a laser pulse which are necessary to modify the usual melting, i.e. which would lead to a substantial decrease of the melting temperature.
The interest of laser-annealing in the manufacturing of semiconductor devices of submicronic size has produced a large amount of work on that subject. A few years ago Van Vechten [I( has suggested that, as the energy is transferred from the laser beam to the lattice via the creation of electron-hole (e-h) pairs, those pairs may modify, if their density is large enough, the lattice stability, and lead to a melting at a temperature T lower than Tm % 17000 K. This idea is in fact directly related to previous work by Heine and Van Vechten [2], who explained the decrease of the band gap Eg of silicon-like semiconductors, by the softening of the T.A. phonon mode in the presence of a large density of e-h pairs. We came back [3] to this original idea, now well accepted for the variation Eg(T) at low temperature and considered first the simple heating, in a furnace for example, of Si or Ge, without an extra energy source such as the absorbed photons in laser annealing. In this simplest case, we follow Heine and Van Vechten, and calculate the total free energy F of a silicon sample at temperature T, having Na atoms and N e-h pairs in a volume V. F is composed of an atomic part Fa(Na, V, T), a plasma part Feh(N, V, T) and a phonon part Fph(Na, N, V, T) which depends on both the atom and the e-h pair density due to the change in the phonon frequency with n = N/V. Considering only the T.A. phonons, as done by Heine and Van Vechten, and for which the frequency dependence can be written, in a first approximation as (1
(1)
-(-)
0 where no = 5xlO22 cm-3 is the density of Si atoms and a is phonon free energy reads
-*0i
F
ph
E= kT Ln(l - e
kT) , kT E Lni
a constant,
the
oii
kT
""Nan0kT Ln(1 - atn-) + terms independent of n At constant T and V, the e-h pair number Jadjusts for an isolated system, that the e-h pair chemical potential p =- 3 3N NA,V,T is zero.
Mat. Res. Soc. Symp. Proc. Vol. 13 (1983) @ Elsevier Science Publishing Co.,
Inc.
(2) such
42
•N ;F==Eo E -
p(n,T)
1-an kT no
+ Pe
+ Ph
(3)
EG is the band gap at T = 0 and Pe and Ph are the free electron and hole at large n). chemical potential (We '-kT Ln n at low density and Pe 'u n Considering only the low T case, where c0-0
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