Limits of the ratios of tracer diffusivities for diffusion by vacancy pairs: Application to compound semiconductors

Abstract

In this paper, the vacancy-pair diffusion mechanism in cubic materials is revisited with emphasis on the limits of the ratio of the tracer diffusion coefficients to demonstrate the operation of this mechanism. The vacancy-pair mechanism puts very strict upper and lower bounds on this ratio. Extensive high precision Monte Carlo simulation is used to calculate tracer correlation factor, ratios of tracer diffusivities, and percolation effects ͑in mixed compounds͒. The three major cubic lattices-NaCl, CsCl, and zinc blende structures-are analyzed, and correct limits for the ratio of the tracer diffusivities are found to be 5.6, 11.2, and 2.6, respectively. For the case of the CsCl structure correlation factors are redetermined using the matrix method to obtain good agreement with the Monte Carlo results. Self-diffusion in the compound semiconductors PbSe ͑NaCl structure͒ InSb, GaSb, CdTe, and HgCdTe ͑zinc blende structure͒ is reanalyzed. It is shown that the vacancy-pair mechanism is unlikely to contribute to self-diffusion in CdTe and HgCdTe but it remains a valid possibility for self-diffusion in PbSe, InSb, and GaSb.

The diffusivity of the Cd interstitial in CdTe

“…(5) The chemical self-diffusivity, (D ), in undoped CdTe is equal to 3D(Cd •• i ) for the temperature range 500-900 • C over which (D ) was measured. (6) In the temperature range 500-900 • C the (D ) data (table 4) can be fitted to a single expression which yields D(Cd •• i ) = 0.23 exp(−0.99 eV/kT) cm 2 s −1 .…”

“…The possibility of Schottky pairs, (V Cd V Te ), and Frenkel pairs, (Cd i V Cd ), also arises but current ideas do not regard them as having primary significance. However, Cd self-diffusion results above ∼650 • C, in undoped CdTe, show that the neutral pair (Cd i V Cd ) × is responsible for the constant diffusivity of the Cd tracer across the whole partial pressure range [6,7]. As Cd saturation is approached the otherwise constant Cd selfdiffusivity, D(Cd), tends to increase with Cd pressure which is indicative of a contribution from Cd i .…”

“…At Cd saturation this increase is ∼25% at 700 • C and ∼ 50% at 800 • C above the pressure-independent (Cd i V Cd ) × component [7]. The different behavior of Cd and Te self-diffusivities with Cd partial pressure, P Cd , precludes any role for (V Cd V Te ) in the self-diffusion of Cd and Te [6]. This paper is concerned with the interpretation of experimental results available in the literature which can lead to values for the diffusivity of the Cd interstitial.…”