Atomic transport of trivalent impurities in silicon: diffusion, isotope effects, activation volumes

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Abstract
Tracer diffusion coefficients, and their dependence on temperature, pressure and isotope mass, have been determined for B and Ga as impurities in (111) oriented silicon single crystals. The measurements were evaluated with stable isotopes by means of secondary ion mass spectrometry. The diffusivities, measured between 850 and 1150 °C, are found to be represented, in cm2 s–1, by the expression: DB–Si= 33.7 exp[–(3.93 ± 0.10)eV/kBT] and DGa–Si= 6.5 exp[–(3.59 ± 0.10)eV/kBT]. The mean values of the isotope effects between 850 and 1150 °C are EB–Si= 0.39 ± 0.03 and EGa–Si= 0.51 ± 0.04. The relative volumes of activation are (V*/Ω)B–Si=+0.27 ± 0.13 (mean in the range 1050–1230 °C) and (V*/Ω)Ga–Si=–0.7 ± 0.1 (at 1053 °C). These results, and their comparison with earlier data on diffusion in elemental semiconductors, suggest a predominantly interstitial diffusion mode for group III impurities in Si. The behaviour is not in all parts reconcilable with a conventional interstitialcy mechanism, but rather suggests what has been introduced in the literature as a ‘kick-out’ mechanism.