Diffusion, Solubility, and Electrical Properties of Copper in Indium Antimonide

Abstract

Radiotracer and sheet resistivity measurements show four distinct mechanisms of the diffusion of Cu in InSb: (A) Rapid diffusion as an interstitial atom with a diffusion coefficient of approximately ${10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec. No electrical activity of interstitial Cu is observed. (B) Dissociative diffusion due to reaction of interstitial Cu with vacancies diffusing in from the surface. This process has an activation energy of 1.08\ifmmode\pm\else\textpm\fi{}0.08 eV and a ${D}_{0}$ between ${10}^{\ensuremath{-}4}$ and ${10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{2}$/sec. (C) Diffusion due to reaction of interstitial Cu with vacancies inherited in dislocation-free crystals during growth. It is possible to free low-dislocation density crystals from such vacancies by a low-temperature heat treatment. The reaction of vacancy aggregates with diffusing interstitial Cu is analyzed as an example of a mechanism which explains the observed behavior. (D) The diffusion due to interstitial Cu reacting with vacancies supplied through dislocations. Diffusion in crystals containing ${10}^{5}$ dislocations ${\mathrm{cm}}^{\ensuremath{-}2}$ is 5 orders of magnitude faster than in dislocation-free and annealed InSb crystals. The solubility of substitutional Cu in InSb is expressed by the relation ${C}_{s}(T)=1.5\ifmmode\times\else\texttimes\fi{}{10}^{22}\mathrm{exp}(\ensuremath{-}\frac{0.76}{\mathrm{kT}})$. The solubility of interstitial Cu is approximately 50 times lower. From the Cu-labeling technique suggested by mechanism (C), the equilibrium In-vacancy concentration at the melting point is estimated to be 1.0\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, corresponding to an activation energy of 1.0 eV. The activation energy for the self-diffusion of indium in InSb is calculated to be 1.84\ifmmode\pm\else\textpm\fi{}0.14 eV, in excellent agreement with Eisen and Birchenall's measured value of 1.81\ifmmode\pm\else\textpm\fi{}0.25 eV. However, the diffusion coefficients calculated are one order of magnitude lower than their measured values, presumably because they were measured in high-dislocation density material.