Optically Induced Condensation of Impurity Excitations in Transparent Solids
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At a certain density of excitations the electron system is condensed. We can consider this condensation as a non-equilibrium metal-insulator transition so that the condition of this transition looks like the Mott criterion. The condensed phase produced is an analogue of the well-known electron-hole liquid in semiconductors. However the phase transition has a non-pure electronic character in contrast to the metal-insulator transition in the electron-hole system of semiconductors. This is because impurities are rigidly fixed in the lattice structure of a solid. Since the equilibrium concentration of excitations in the condensed state can be different from the actual concentration, mechanical stresses will arise. Thus a new type of interaction of radiation with transparent solids occurs. OPTCALLY INDUCED IMPURITIY EXCITATIONS A transparent solid contains a certain concentration Co of optically active impurities. Let us consider that these impurities are donor type impurities. The excitation spectrum of a given impurity can be, for example, hydrogen-like. The impurities are excited as a result of interaction with optical radiation. The higher the intensity of radiation, the higher the concentration C. Nevertheless the concentration of excited impurities C is smaller or equal to Co. When the concentration of excited impurities C is not large enough to exhibit any overlapping of excited
303 Mat. Res. Soc. Symp. Proc. Vol. 588 © 2000 Materials Research Society
states, one can consider these impurities as independent centers. The situation qualitative changes when wave functions of excited impurities overlap. The critical concentration C, when the overlapping is significant can be easily estimated from the average radius of an impurity in the given excited state r,,, where n is the level of excitation: 3
C0 =3/47r rn
In the case when the actual concentration of excited impurities C 2! C•, one shall consider a collective (condensed) state of excited impurities. CONDENSATION OF EXCITATIONS Let us find the equilibrium parameters of a condensed state of excited impurities. We will use the approximation of an almost homogeneous electron liquid, which is true for not-very-high excitations. In order to find the energy of the system one can use perturbation theory on the pseudopotential of electron-ion interaction. The perturbation parameter in this approach is the ratio of Fourier components of the pseudopotential in the nets of the reciprocal lattice Vg(n) to the
Fermi energy of electrons:
4(n)= Vg(n)/F
[3]. For the electron-ion pseudopotential we will use the
Ashcroft empty-core model when the pseudopotential of an individual excited impurity is assumed equal to zero inside of a sphere with a given radius R, and the Coulomb potential out of this sphere. This pseudopotential is based on the so-called compensation theorem: if the radius R, is close to the radius of the inner shell the pseudopotential inside of the sphere is practically equal to zero. The radius Rn is found from the energy terms of a real impurity. Conside
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