Is Thermalization Due to Electronic Self-Trapplng?
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INTRODUCTION The standard interpretation [1,2] of low temperature photoluminescence (PL) in a-Si:H is that (i) After photogeneration of an electron-hole pair, the electron (e) and the hole (h) are rapidly trapped (picoseconds) to localized states. (ii) After initial trapping, e and h tunnel from localized state to localized state (thermalization phase), (iii) Thermalization is followed by radiative recombination of the e-h pair (radiative phase). The radiative phase of the process is generally assigned to radiative tunneling. Thus, if the eh pair separation is R, the radiative rate is: Vrad =
l/tPo exp[-2R / X],
(la)
where X is the localization length of the state, and lit. is the radiative prefactor. The thermalization phase is generally interpreted in two steps. First, (possibly) because of self-trapping, the hole is rapidly immobilized [3]. Second, the electron moves by non-radiative tunneling between localized states. The non-radiative hopping rate between two states r apart is:
1I
v ......ad = V0 exp[-2r / .]. lexp[-(Efi.,
-
Einitai ) / kT]
EinitiaI > Efinal E inita < E final
(b)
where Eidi, and E•.n, are the energies of the initial and final states, v0 is a rate prefactor, and T the temperature. Note that at equal r, transitions down in energy are more probable. At very low T, this in fact implies that the electron's energy continually decreases with time (thermalization). It also implies that the average hop distance increases with time, and that thermalization stops when the radiative tunneling rate becomes larger than the non-radiative rate. The radiative prefactor 1/Ytis usually taken to be a typical radiative prefactor, l/tc-~108s1. The non-radiative rate prefactor v. is usually taken to be of order a phonon frequency, vo-10' 2s'. Notice that vto>>; this implies that thermalization proceeds much faster than radiative recombination. This picture is very successful in qualitatively accounting for most aspects of low temperature, low generation rate, PL in a-Si:H [1]. For instance: 157 Mat. Res. Soc. Symp. Proc. Vol. 377 0 1995 Materials Research Society
1) The observed broad distribution of PL lifetimes. Because a-Si:H is disordered, thermalization creates a distribution of e-h pair separations R. Assuming that the PL lifetime is entirely determined by the radiative recombination phase, the exponential dependence of the lifetime on R implies that even a relatively narrow distribution of R results in a broad distribution of lifetimes. 2) The observed broad PL energy spectrum. Since a-Si:H is disordered, e-h pairs photogenerated at different positions see different atomic environments. Thus, they thermalize by different amounts of energy. This implies a distribution of photon energies. 3) Time-resolved studies of PL show that the energy spectrum shifts to lower energies with time (red shift). This is a manifestation of thermalization: a longer recombination time implies a larger amount of thermalization, thus a smaller photon energy. With only minor variations, this picture also explains very suc
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