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Vacancy dependent nucleation curves were measured. They exhibit four maxima which all increase with increasing vacancy concentration. Even at 1000 {degree sign}C considerable nucleation takes place for high vacancy concentrations. The analysis of nucleation based on classical nucleation theory has shown that nucleation of oxide precipitates takes place at heterogeneous nucleation sites. These sites contain oxygen atoms and vacancies and it is assumed that these sites are VOn complexes with 2

The coherent agglomeration of interstitial oxygen into single-plane and double-plane plates can explain the two peaks in the M-shaped nucleation curves in Czochralski silicon. The density of nucleation sites for the double-plane plates corresponds to the VO2 concentration. Ab initio calculations have shown that the agglomeration of oxygen atoms in single-plane and doubleplane plates is energetically favorable. These plates are under compressive strain. VO2 agglomeration plays only a minor role for modeling the M-shaped nucleation curves because of prior homogenization treatments. It is of much higher impact if as-grown wafers are subjected to nucleation anneals because of the higher vacancy concentration which was frozen in during crystal cooling. This results in higher nucleation rates at higher temperatures. Because the oxygen diffusivity below 700 °C is important for the nucleation rate and many controversial results about the diffusivity in this temperature range were published, we have analyzed the data from literature. We have demonstrated that the effective diffusivity of oxygen at temperatures below 700 °C which corresponds to the quasi equilibrium dimer concentration is very similar to the extrapolation from oxygen diffusivity at high temperature. The high effective diffusivities from out-diffusion and precipitation experiments, and the somewhat lower effective diffusivities from dislocation locking experiments are the result of an ongoing formation of fast diffusing dimers because the equilibrium is disturbed as the result of the strongly increasing difference in the diffusion length between interstitial oxygen and the fast diffusing dimer with decreasing temperature.

We have investigated the impact of RTA induced vacancy supersaturation on oxide precipitation based on as much as possible experimental and theoretical values. Oxygen precipitation after RTA processing was found to be controlled by the initial concentration of interstitial oxygen in a sixth power dependency and frozen vacancies just in a cubic dependency. The formation of tensile strained nVO2 clusters seems to be the favored process for coherent nucleation of oxide precipitates. The reduction of interstitial oxygen can be accurately modeled for the temperature range from 1150 {degree sign}C to 1250 {degree sign}C using Ham's theory for precipitate growth and an empirical relation based on nucleation of oxide precipitates by agglomeration of VO2 complexes. During RTA treatments at temperatures {greater than or equal to} 1300 {degree sign}C vacancies seem to be consumed by other processes. Below RTA temperatures of 1150 {degree sign}C, oxide precipitation is dominated by shrunken as-grown precipitate nuclei because as-grown nuclei can be dissolved only at RTA temperatures {greater than or equal to} 1150 {degree sign}C.

In order to elucidate the influence of stress and in-diffused nitrogen on oxide precipitation after rapid thermal annealing (RTA), we carried out experiments with one-side and double-sided nitride layers accompanied by simulation models which help to understand the behavior of intrinsic point defects, nitrogen, and strain. We found that the presence of a nitride layer of any thickness, within the rage which we investigated, in direct contact with the silicon surface is sufficient to markedly change the precipitation behavior of interstitial oxygen after RTA at 1175 and 1250 °C. The presence of the nitride layer during the stabilization and growth of the oxide precipitates is not of any influence on the precipitation behavior. Therefore, the RTA of wafers covered with silicon nitride is the crucial step controlling the bulk microdefect (BMD) depth profiles. A 10 nm oxide between silicon substrate and nitride layer prevents any change of the BMD depth profile. Only in a direct contact with the nitride layers the vacancy supersaturation, which enhanced the oxide precipitation compared to wafers without nitride layers, was generated. Nitrogen peaks below the silicon surface generated by in-diffusion of nitrogen during RTA lead to an enhanced oxygen precipitation only for RTA at 1250 °C and not for RTA at 1175 °C. We propose a model based on very tiny coherent α-Si3N4 precipitates generated at nitrogen-vacancy (NV) complexes which can act as nucleation sites for oxygen precipitation. Because the stability of NV seems limited to temperatures above 1200 °C, it would not be effective for RTA at 1175 °C. RTA treatment of silicon wafers with one-sided nitride layers at 1250 °C leads to very sharp and small defect denuded zones in subsequent annealing and would be suitable for proximity gettering. The depth of the denuded zone is nearly independent of the thickness of the nitride layer.

We have investigated the impact of rapid thermal annealing (RTA) induced vacancy supersaturation on oxide precipitation based as much as possible on experimental and theoretical values. Oxygen precipitation after RTA processing was found to be controlled by the initial concentration of interstitial oxygen in a sixth power dependency and frozen vacancies just in a cubic dependency. The formation of tensile strained nVO 2 clusters seems to be the favored process for coherent nucleation of oxide precipitates. The reduction of interstitial oxygen can be accurately modeled for the temperature range from 1150 to 1250°C using Ham's theory for precipitate growth and an empirical relation based on nucleation of oxide precipitates by agglomeration of VO 2 complexes. During RTA treatments at temperatures ≥ 1300°C vacancies seem to be consumed by other processes. Below RTA temperatures of 1150°C, oxide precipitation is dominated by shrunken as-grown precipitate nuclei because as-grown nuclei can be dissolved only at RTA temperatures ≥ 1150°C.

The surface‐stress tensor is an important quantity entering the elastic theory of interaction between atomic steps on solid surfaces. For the clean Si(001) surface the difference between its diagonal elements, the surface stress anisotropy Δσ, comes out by about a factor of two smaller in experiment than compared to the value obtained from previous first‐principles calculations. This discrepancy was usually assigned to the presence of surface defects; as other plausible causes one could quote unrealistic atomic surface structures used for the calculations or even a failure of the local‐density approximation (LDA) on which the calculations were based. This constituted a serious deficiency in the understanding of the Si(001) surface. We demonstrate that, when first‐principles LDA calculations are carried out for the perfect Si(001) surface with the correct character of reconstruction, the calculated and measured Δσ agree within the experimental and numerical uncertainties. We conclude that standard LDA calc...

We discuss calculations from first-principles (using the local-density approximation for exchange and correlation) of defect total energies, vibrational modes, internal energies and entropies. Results are presented for the defect-induced distortion field of an arsenic impurity in silicon and for the vibrational entropy of a silicon vacancy. We also discuss the important role of electron and atom chemical potentials, presenting results for the Ga vacancy in the GaAs bulk and at the (111) surface.