A Unified Treatment of The Thermal Donor Hierarchies in Silicon and Germanium*
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A UNIFIED TREATMENT OF THE THERMAL DONOR HIERARCHIES IN SILICON AND GERMANIUM* JEFFREY T. BORENSTEIN and JAMES W. CORBETT Physics Department, SUNY/Albany, Albany NY 12222,
USA.
ABSTRACT The hierarchies of thermal donor binding energies produced by annealing oxygen-containing silicon or germanium at ca. 450 0 C are explained by using a generalized perturbation model which involves a standard repulsion parameter for the interaction between agglomerating oxygen atoms and the shalThis model is capable of fitting the low donor electrons. ground state ladders for both charge states of the thermal donors in both Si and Ge, sin-ce differences between the two ladders can--ee explained entirely by the change in the electron-effective-mass and dielectric constant of the host. INTRODUCTION Recent infrared electronic absorption studies have revealed a ladder of progressively shallower double donor defects in Czochralski-silicon [1-4] and oxygen-doped germanium [5,6] annealed at ca. 4500 C for periods of hours. Kinetic studies of the annealing behavior of thermal donors in silicon have indicated that the defects arise from oxygen agglomerates [4,7-8], with a donor core which has as yet not been determined. As the annealing time increases, the shalThe silicon thermal dolower levels become more dominant. nors have been shown experimentally to contain differing numbers of oxygen atoms [4], and kinetic arguments indicate that the same is true in the case of germanium [9]. Kinetic models [7,8] have argued that the thermal donor formation process proceeds by the successive incorporation Followof oxygen interstitials into a thermal donor core. ing this model Corbett et. al. [10] and Borenstein et. al. (11] have explained the-li-eir--chy of successively sh-a-lower levels in silicon by assuming that the agglomerating oxygen atoms introduce a repulsive interaction with the shallow donor electrons, which repulsion grows in size with each additional oxygen atom. This repulsion is treated as a perturbation to the Coulombic attraction of the defect core, and its effect is to lower the binding energies of the elecIn this paper we will trons and increase their orbit sizes. show that the perturbation model is capable of reproducing the ladder of successively shallower binding energies for both charge states of the thermal donors in both silicon and The repulsion strength, initially treated as a germanium. free parameter, is shown to scale by the dielectric constant so that the ground state ladders in both materials may be explained by a single mechanism.
Mat. Res. Soc. Symp. Proc. Vo. 59. -1986 Materials Research Society
Downloaded from https://www.cambridge.org/core. University of Arizona, on 21 Jul 2018 at 08:32:58, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1557/PROC-59-159
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PERTURBATION MODEL The potential exerted by a shallow impurity in a semiconductor can be expressed as: V = -Z e 2,/
(c r)
(1)
for distances r>d, where d is the lattice parameter and c is t
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