Diffusion of lead and selenium in lead selenide

Abstract

New measurements of the radioactive tracer diffusion coefficients of selenium-75 and lead-2l 0 in PbSe, obtained using a vapor source diffusion technique, are reported. These measurements yield significantly lower values of the diffusion coefficients for both species than those previously reported by others. For selenium-saturated PbSe, D;e = 8.13 X 10-4 exp( -1.33 eV I k T) and D;b = 9.81 X 10-4 exp( -1.67 eV I k T), while for lead-saturated PbSe, D;e = 0.553 exp ( -2.22 eV I k T) and D;b = 3.74 X 10-2 exp( -2.05 eV I k T). An analysis of these results indicates that selenium atoms diffuse by means of interstitial defects in selenium-rich material and most probably through selenium vacancies in lead-rich material, and that lead atoms diffuse through lead vacancies in selenium-rich material and most probably through lead interstitials in lead-rich material. The tracer data are used in conjunction with a theoretical model of interdiffusion to predict values of the p-n junction diffusion coefficients in PbSe which are in excellent agreement with published experimental results. A similar comparison of the tracer data with n -p junction diffusion data shows good qualitative agreement. Quantitative discrepancies are observed which are explained by the theoretical model.The point-defect mechanisms to be considered are (i) diffusion of lead through lead vacancy sites, (ii) diffusion of lead through interstitial sites, (iii) diffusion of the chalcogen through chalcogen vacancy sites, and (iv) diffusion of the chalcogen through interstitial sites. The mechanisms (ii) and (iv) include either the interstitial or the interstitialcy mechanisms as subcases with minor modifications.The concentrations of the atomic point defects (vacancies or interstitials) associated with the above mecha-

Anomalous Diffusion Profiles of Ag in CdTe due to Chemical Self-Diffusion

“…Since the ratio Cd i = V Cd directly corresponds to the deviation from stoichiometry, the different Ag profiles reflect the variation of the deviation from stoichiometry of the CdTe crystal as a function of depth and time at the respective temperatures and external vapor pressures of Cd and Te. Consequently, the diffusion profiles of Ag should be the result of the so called chemical selfdiffusion in CdTe [10], which describes, using a diffusion coefficient D , the variation of the deviation from stoichiometry as a function of depth and time due to annealing under the respective external vapor pressures. Using the chemical self-diffusion coefficient D 5 exp ÿ1:12 eV=k B T cm 2 =s reported for CdTe, which was determined using high temperature electrical conductivity measurements [11], a value of 4:4 10 ÿ7 cm 2 =s at 800 K is obtained, yielding a diffusion length of 400 m after 60 min diffusion time.…”

Impurity Dopant Incorporation and Diffusion during Molecular Beam Epitaxial Growth of IV–VI Semiconductors

“…[16] would explain the 3 • 101~/cm 3 drop in n observed in undoped (PbSn)Te underneath highly Bi-doped material. However, an equally reasonable alternate explanation could be based on the incorporation of a small fraction of the Bi according to Eq.…”

“…We neglect the possibility of dopant substitution on VI sites which was suggested above for Sb and for Bi in (PbSn)Se, because there is no evidence of such behavior for Bi or Tl in (PbSn)Te, and it can be avoided for Bi and T1 in PbTe by the use of excess Te. The various mechanisms described above may be expressed symbolically for Bi incorporation as Bi(a) -~ Bi + (i) ~-e- [16] Bi(a) -p Vpb--~ e + -~ Bi + (s) -~ e- [17] Bi(a) -~ Bi+ (s) ~-Vie + ~-2e- [18] Bi ( Note that ~ varies from -p2 to --1 among the above ten mechanisms. We will now argue that many of these mechanisms are highly unlikely.…”

“…Therefore, it is most likely that Bi and T1 incorporation proceed by Eq. [20] and [25] involving substitution and displacement of Pb (and Sn) to the growth surface, although interstitial Bi (Eq [16]. ) cannot be ruled out either.…”

Limits of the ratios of tracer diffusivities for diffusion by vacancy pairs: Application to compound semiconductors

“…PbSe is a IVB-VIB compound semiconductor and takes the NaCl structure. The self-diffusivities of Pb and Se, D Pb and D Se , respectively, have been measured by Guldi et al 34 between 500 and 800°C at the Pb and Se saturated composition limits. At Pb saturation, D Pb ͑Pb sat͒ = 0.070 exp͑−2.07 eV/ kT͒ cm 2 s −1 and D Se ͑Pb sat͒ = 2.0 exp͑−2.30 eV/ kT͒ cm 2 s −1 while at Se saturation, D Pb ͑Se sat͒ = 1.78ϫ 10 −1 ϫ exp͑−1.73 eV/ kT͒ cm 2 s −1 and D Se ͑Se sat͒ = 1.50ϫ 10 −3 ϫ exp͑−1.41 eV/ kT͒ cm 2 s −1 .…”