Thermal Equilibrium Concentrations and Effects of Ga Vacancies in n-TYPE GaAs

We have calculated the thermal equilibrium concentrations of the various Ga vacancy species in GaAs. That of the triply-negatively-charged Ga vacancy, % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwb % Waa0baaSqaaiaabEeacaqGHbaabaGaaG4maiabgkHiTaaaaaa!3C0B! $$V_{{\text{Ga}}}^{3 -}$$ , has been emphasized, since it dominates Ga self-diffusion and Ga-Al interdiffusion under intrinsic and n-doping conditions, as well as the diffusion of Si donor atoms occupying Ga sites. Under strong n-doping conditions, the thermal equilibrium % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwb % Waa0baaSqaaiaabEeacaqGHbaabaGaaG4maiabgkHiTaaaaaa!3C0B! $$V_{{\text{Ga}}}^{3 -}$$ concentration, % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaqGdb % Waa0baaSqaaiaadAfadaqhaaadbaGaae4raiaabggaaeaacaaIZaGa % eyOeI0caaaWcbaGaaeyzaiaabghaaaGccaGGOaGaaeOBaiaacMcaaa % a!413A! $${\text{C}}_{V_{{\text{Ga}}}^{3 -}}^{{\text{eq}}}({\text{n}})$$ , has been found to exhibit a temperature independence or a negative temperature dependence, in the sense that the % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaqGdb % Waa0baaSqaaiaadAfadaqhaaadbaGaae4raiaabggaaeaacaaIZaGa % eyOeI0caaaWcbaGaaeyzaiaabghaaaGccaGGOaGaaeOBaiaacMcaaa % a!413A! $${\text{C}}_{V_{{\text{Ga}}}^{3 -}}^{{\text{eq}}}({\text{n}})$$ value is either unchanged or increases as the temperature is lowered. This is contrary to the normal positive temperature dependence of point defect thermal equilibrium concentrations, which decreases as the temperature is lowered. This % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaqGdb % Waa0baaSqaaiaadAfadaqhaaadbaGaae4raiaabggaaeaacaaIZaGa % eyOeI0caaaWcbaGaaeyzaiaabghaaaGccaGGOaGaaeOBaiaacMcaaa % a!413A! $${\text{C}}_{V_{{\text{Ga}}}^{3 -}}^{{\text{eq}}}({\text{n}})$$ property provides explanations to a number of outstanding experimental results, either requiring the interpretation that % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0x % c9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwb % Waa0baaSqaaiaabEeacaqGHbaabaGaaG4maiabgkHiTaaaaaa!3C0B! $$V_{{\text{Ga}}}^{3 -}$$ has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect non-equilibrium phenomena. Furthermore, there exist also a few quantitative data which are in agreement with the presently calculated results.