Rare Earths in Covalent Semiconductors: the Thulium-Gallium Arsenide System

Abstract

Solutions containing radioactive 170Tm were applied to the surface of GaAs wafers that were heated to 800°, 900°, or 1000°C for times up to 100 h. The solubilities and diffusion coefficients were obtained by fitting the experimental data with complementary error functions. The resulting surface concentration (cm−3) was taken as the equilibrium saturation solubility and is represented below the eutectic temperature of 1150°C by 6.7×1025 exp (−2.3 eV/kT), which gives Cmax=4×1017 cm−3. The atom size, defined as the single-bond radius, was found to be the dominant factor in limiting the solid-solution solubility of the rare earths in GaAs. Diffusion was faster at lower temperatures, and the diffusion coefficient D (cm2/sec) was 2.3×10−16 exp (1.0 eV/kT). This inverse temperature dependence of the diffusion coefficient may be explained by the effective D derived from the concept of simultaneous diffusion and chemical reaction. The resulting diffusion coefficient in intrinsic material is Dei=DiCii+/Cs0, where Di is the interstitial diffusion coefficient and Cii+/Cs0 is the ratio of singly ionized interstitial concentration to neutral substitutional concentration. The inverse temperature dependence of D may be ascribed to the more rapid increase of Cs0 with temperature than that of DiCii+.