Characterization of ZnSe:N Using Screening Effects
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1. INTRODUCTION It has long been known that dielectric screening will reduce (in absolute values) the energy levels of impurities in semiconductors [1,2]. Such screening will include both free carrier and impurity ion contributions. The free carrier contribution is treated by the standard theory [3]. Ionic screening may originate from several phenomena: a) from ionic motion until the ions become "frozen" into the lattice[2], b) from preferential ion neutralization due to preferential carrier capture at impurities surrounded by more favorable configurations of other impurities (e.g [4]), c) fluctuation of the ionic potential due to fluctuations in the random distribution of the ions (where this latter effect is important primarily for high degrees of compensation and is neglected here). These approaches, as far as we know, have so far been applied only to materials in the dark [2,4]. In the present paper, we consider the case of optical excitation as well as the "dark" case, specifically analyzing data for a material of high interest, N doped ZnSe. We show that literature data [5] which was interpreted as showing that the N acceptor was located interstisially can, instead, be explained by screening. Moreover, we show that a well-known discrepancy between optical and thermal activation energies is very likely due, at least in part, to screening. A further modification of past work is an improved method of evaluating results from the screened Schrodinger equation, which is valid for impurities with sufficiently small Bohr radii. In the next section we introduce our modified solution of the Schrodinger equation. This is then applied to the case of dark carrier concentrations in ZnSe:N (Section 3a), and to the optical case in Section 3b. 2. THEORY It is well known that the potential (U) of a hydrogenic impurity in semiconductors can be described by the screened Coulomb potential [6]: 443 Mat. Res. Soc. Symp. Proc. Vol. 406 0 1996 Materials Research Society
U
=
e +--exp(-qr)
(1)
where q is the inverse screening length, - is the dielectric constant, e is the electron charge, and r is the spatial coordinate. Let us consider the inverse screening length, for a moment, as a parameter of the problem. Let us define H 0 as the Hamiltonian for the "infinitely dilute" system (where q=O) (see, for example, [7]). Then the Schr6dinger equation is: 2
{H 0 +
(I - exp[-qr]) Vf(r)) = EA I'(r))
(2)
where EA is the energy in the screened case. N in ZnSe gives a relatively deep acceptor (-110112 meV) and the Bohr radius (aB) is, therefore, relatively small (5 - 6 A [8]). Thus, for all r's where the probability of finding the hole bound to the acceptor is not vanishingly small, the product qr is much less than 1. Hence, we can expand the exponent in Eq.2 into series, keeping only the first order terms: 2
{H 0 + -- q}~l V(r)) = EA I11(r))
(3)
.6
After bringing the second term on the right side to the left side, Eq.3 will have the form of the "infinitely dilute" Schrodinger equation, so that the ground state energy can be writte
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