The diffusion of self-atoms and $n$-type dopants such as phosphorus, arsenic, and antimony in germanium was studied by means of isotopically controlled multilayer structures doped with carbon. The diffusion profiles reveal an aggregation of the dopants within the carbon-doped layers and a retarded penetration depth compared to dopant diffusion in high-purity natural Ge. Dopant aggregation and diffusion retardation are strongest for Sb and similar for P and As. In addition, the shape of the dopant profiles changes for dopant concentrations in the range of ${10}^{20}{\text{cm}}^{-3}$ mainly due to the formation of dopant-vacancy complexes, which is more significant at high concentrations. Accurate modeling of the simultaneous self-diffusion and dopant diffusion is achieved on the basis of the vacancy mechanism and additional reactions that take into account the formation of neutral carbon-vacancy-dopant and neutral dopant-vacancy complexes. The stability of these complexes is compared to theoretical calculations published recently and to additional calculations presented in Part II. The overall consistency between the experimental and theoretical results supports the stabilization of donor-vacancy complexes in Ge by the presence of carbon and the dopant deactivation via the formation of dopant-vacancy and carbon-vacancy-dopant complexes.

We report the diffusion of boron, arsenic, and phosphorus in silicon isotope multilayer structures at temperatures between $850°\mathrm{C}$ and $1100°\mathrm{C}$. The diffusion of all dopants and self-atoms at a given temperature is modeled with the same setting of all native-point-defect-related parameters. The evaluation of the relative contributions of charged native-point defects to self-diffusion enables us to determine the defect energy levels introduced by the native-point defects in the Si band gap. Making allowance for the fact that the band gap and the energy levels change with temperature, an energy-level diagram of the native-point defects is obtained that shows a reversed level ordering for the donor levels of the self-interstitials. In accord with the general state of knowledge, the diffusion of boron is mainly mediated by self-interstitials whereas the properties of both vacancies and self-interstitials are important to model arsenic and phosphorus diffusion. The simultaneous diffusion of phosphorus and silicon requires the existence of a singly positively charged interstitial phosphorus. It is the diffusion of this defect that strongly affects the shape of the phosphorus diffusion tail and not entirely the supersaturation of self-interstitials argued so far. Taking into account the mechanisms of dopant diffusion and the properties of native-point defects determined from the simultaneous diffusion experiments, let us describe accurately dopant profiles given in the literature. Altogether, this work provides overall consistent data for modeling dopant and self-diffusion in Si for various experimental conditions. A comparison of experimentally and theoretically determined activation enthalpies of self- and dopant diffusion shows excellent agreement for self-interstitial-mediated diffusion but significant differences for vacancy-mediated diffusion in Si. This disagreement either reflects the deficiency of first-principle calculations to accurately predict the energy band gap of Si or points to a still-remaining lack in our understanding of diffusion in Si.

Diffusion of silicon (Si) and germanium (Ge) in silicon-germanium ${\text{Si}}_{1-x}{\text{Ge}}_x$ -isotope heterostructures with Ge contents $x=0$ , 0.05, 0.25, 0.45, and 0.70 was investigated in a temperature range between 690 and $1270°\text{C}$ . The concentration profiles of the stable Si-isotopes and Ge-isotopes were recorded by means of time-of-flight secondary ion mass spectrometry. Analysis of the experimental profiles shows that the Si and Ge diffusion coefficients in elemental Si agree within experimental accuracy. However with increasing Ge content the diffusion of Ge gets increasingly faster compared to that of Si. An Arrhenius type temperature dependence of diffusion is observed for all compositions with slightly lower values for the activation enthalpy of Ge compared to Si. The more pronounced Ge diffusion indicates that with increasing Ge concentration the diffusional jumps of Ge atoms become more successful compared to those of Si. This trend is explained with an increasing contribution of vacancies to self-diffusion in ${\text{Si}}_{1-x}{\text{Ge}}_x$ with $x$ . In contrast to earlier results the composition dependence of the activation enthalpy of self-diffusion reveals an upward bowing. A similar composition dependence is reported for the arsenic (As) and antimony (Sb) diffusion in SiGe and is predicted theoretically for the stability of phosphorus-vacancy and arsenic-vacancy pairs in SiGe. The nonlinear behavior seems to be a general trend and accordingly mainly a consequence of the SiGe alloy system.

We have studied the mobilities of calcium and sodium ions in silicate glasses of compositions xNa₂O·(3 − x)CaO·4SiO₂ with x = 0.0, 0.1, 0.3, 1.0 and 3.0 by means of radiotracer diffusion, electrical conductivity measurements, and dynamic mechanical thermal analyses. In glasses containing sodium oxide, the Na⁺ ions are much more mobile than the Ca²⁺ ions, and are, therefore, governing the electrical conductivity. In the pure calcium silicate glass, the activation energy of Ca²⁺ diffusion is higher than the activation energy of the electrical conductivity. This provides strong evidence that the electrical conductivity of this glass is not determined by the migration of Ca²⁺ ions, but by impurity charge carriers, which are most likely Na⁺ ions. We sketch the composition-dependent mobilities of Na⁺ and Ca²⁺ ions in soda-lime silicate glasses with variable Na₂O and CaO content. Our results indicate that the coordination environment of Ca²⁺ ions remains unchanged when CaO is replaced by Na₂O which is consistent with recent results of molecular dynamic simulations. Moreover, our results confirm the formation of dissimilar Na–Ca pairs which lead to a non-random mixing of the cations in the glass. The formation of such pairs was recently deduced from nuclear magnetic resonance spectra of soda-lime silicate glasses.

Dopant diffusion experiments in semiconductors yield the mobility of the element of interest and information about the possible mechanisms of atomic diffusion. In many cases the diffusion is described on the basis of Fick’s law of diffusion, but this treatment is often too simple. In this paper, dopant diffusion in semiconductors is treated systematically on the basis of diffusion-reaction equations. Predictions on the shape of dopant-diffusion profiles that develop under specific experimental conditions are derived. It is illustrated that the charge states of the point defects involved in the diffusion process strongly affect the shape of the dopant profile under electronically extrinsic conditions. The relation between the shape of the dopant profile and the underlying mechanism of atomic diffusion, and between the apparent dopant diffusion coefficient and the point defect mediating the diffusion process is explained. With the advance in epitaxial deposition techniques and the availability of isotopically enriched elements, semiconductor isotope heterostructures can be grown, which are highly appropriate for studying the impact of dopant diffusion on self-diffusion. The modeling of the simultaneous diffusion of self- and dopant atoms in semiconductor isotope heterostructures is described and the advances resulting from this new diffusion approach compared to conventional diffusion studies that treat self- and dopant diffusion separately, are highlighted. This paper aims to serve as a useful guide to understand and accurately model the diffusion of dopants and their impact on self-diffusion in semiconductors.