Diffusion and Point Defects in Silicon Materials

Abstract

This chapter aims to provide a basic understanding on the complex diffusion behavior of self-, dopant-, and selected metal atoms in silicon (Si). The complexity of diffusion in Si becomes evident in the shape of self-and foreign-atom diffusion profiles that evolves under specific experimental conditions. Diffusion studies attempt to determine from the diffusion behavior not only the mechanisms of atomic transport but also the type of the point defects involved. This information is of pivotal interest to control the diffusion and activation of dopants during the fabrication of Si-based devices and, from a more fundamental scientific point of view, for comparison to the predictions of theoretical calculations on the properties of point defects in Si. In general, diffusion research relies both on experimental methods to accurately determine diffusion profiles established under well-defined conditions. The analysis of diffusion profiles that can be based on either analytical or numerical solutions of the considered diffusion-reaction equations provides first information about possible diffusion mechanisms. To identify the mechanisms of diffusion, studies under different experimental conditions have to be performed. This chapter on diffusion in Si starts with an introduction on the significance of diffusion research in semiconductors to determine the properties of atomic defects. Diffusion in solids is treated from a phenomenological and atomistic point of view. Experiments designed to investigate the diffusion of self-and foreign atoms are presented and typical self-and foreign-atom profiles obtained after diffusion annealing under specific conditions are illustrated. The mathematical treatment of diffusion-reaction mechanisms is introduced to understand the shape of diffusion profiles and the meaning of the diffusion coefficient deduced from experiments. Modeling of self-, dopant-, and metal-atom diffusion is described that aims at a consistent interpretation of atomic transport processes in Si based on unified properties of the native point defects involved. Finally, till unsolved questions on the properties of point defects in bulk Si and on the diffusion behavior in threedimensional confined Si structures are addressed.

Concentrations and diffusion coefficients of thermal equilibrium point defects in silicon crystals

“…The dependences of fractional deviations (Δ) on 10 4 /T. Circles and triangles correspond to our data D SD (S-I-Y) 5) and Bracht group's data D SD (N), 37) respectively. A solid line and a dashed line are drawn for the eye's guide.…”

“…We calculated the fractional deviations (Δ) for many data sets. Figure 3 shows the fractional deviations of our data 5) (given by circles: D SD (S-I-Y) = 0.90exp (-4.30 eV/k B T) + 6.9 × 10 2 exp(-4.8 eV/k B T)) and those of Bracht group's data 37) [triangles: D SD (N) = 0.5 × 2.7exp(-4.24 eV/k B T) + 0.7273 × 3.00 × 10 3 exp(-4.95 eV/k B T)], where 0.5 and 0.7273 are the correlation factors of a vacancy and an interstitial, respectively. Nakamura 33) adopted data from the Bracht group.…”

Density Functional Theory Study of the Stress Impact on Formation Enthalpy of Intrinsic Point Defect around Dopant Atom in Ge Crystal

“…They showed that the diffusion coefficient was decreased to about 70% by the hydrostatic pressure of 0.5 GPa in intrinsic Ge between 876-1086 K. It is well accepted that the self-diffusion in Ge crystals proceeds by a vacancy mechanism. 20 Here, we evaluate the thermal equilibrium V concentration, and compare the results with their experiment by assuming that only the change of V concentration by σ ex contributes to the change of self-diffusion coefficient in intrinsic Ge.…”

Ion-Beam-Induced Atomic Mixing in Ge, Si, and SiGe, Studied by Means of Isotope Multilayer Structures

“…The high energy deposition by incident ions causes concentrations of defects X that are several orders of magnitude higher than their concentrations under thermal equilibrium. Self-diffusion in solids is controlled by the product of defect concentration and its diffusivity (cf., e.g., [ 36 ]). This shows that only mobile defects can contribute to IBIESD.…”