Self-Diffusion of Lead-210 in Single Crystals of Lead Selenide

Abstract

Self‐diffusion of Pb‐210 in lead selenide has been studied in an inert atmosphere as a function of temperature (over the range 400–800°C) and defect concentration introduced by doping. Diffusion measurements were performed on specimens of p‐type PbSe containing 10¹⁸ holes per cc and on specimens doped with ½ mole % Bi₂Se₃ to give n‐type material with 5×10¹⁹ electrons per cc or ½ mole % Ag₂Se which resulted in p‐type material containing 10¹⁹ holes per cc. Experimental results show that doping with Bi₂Se₃ decreased diffusivities as compared with undoped PbSe, whereas addition of Ag₂Se caused diffusion coefficients to be increased. The diffusion activation energies were 0.83 ev, 1.61 ev, and 0.55 ev for undoped PbSe, bismuth doped PbSe, and silver doped PbSe, respectively. From a consideration of the possible reactions for establishment of equilibrium between solid PbSe and the gas phase, C. Wagner has derived the following equations: $$\begin{array}{c}[{\mathrm{Pb}}^{\text{2+}}\mathrm{\hspace{0.17em}(}\mathrm{interstitial}{\mathrm{)]\propto \; p}}_{\mathrm{Pb}}\mathrm{/[}\mathrm{excess\; electrons}{]}^2,\\ [\mathrm{cation\; vacancy}\mathrm{]\propto [}\mathrm{excess\; electrons}{]}^2{\mathrm{/p}}_{\mathrm{Pb}},\end{array}$$ where the value of p_Pb is to be treated as a constant under the conditions of this experiment. From a consideration of the point defects introduced by doping and an evaluation of diffusion data applied to the above equations, it is concluded that Frenkel defects predominate in lead selenide and that diffusion of lead in this compound occurs predominantly by an interstitial mechanism under these conditions.