Modeling of Cu gettering in p- and n-type silicon and in poly-silicon

Based on experimental findings we set up calculations of numerical modeling of gettering efficiencies for Cu in various silicon wafers. Gettering efficiencies for Cu were measured by applying a reproducible spin-on contamination in the 10(12) atoms/cm(2) range, followed by a thermal treatment to redistribute the metallic impurity. Subsequently, the wafers were analyzed by a novel wet chemical layer-by-layer etching technique in combination with inductively coupled plasma mass spectrometry. We investigated p/p+ and n/n+ epitaxial wafers with different doping levels and different substrate-doping species. We have also investigated gettering efficiencies of phosphorus-diffused p- and n-type wafers. Heavily boron doped silicon exhibited a gettering efficiency of similar to 100%, while gettering by n+ silicon occurred for doping levels > 3 x 10(19) atoms/cm(3) only. In another set of experiments we investigated the dependence of the gettering efficiency of p-type wafers with poly-silicon back sides for different cooling rates and Cu spiking levels. A strong dependence on both parameters was found. Cu gettering in p/p+ epitaxial wafers was modeled by calculating the increased solubility of Cu in p+ silicon compared to non-doped silicon taking into account the Fermi-level effect, which stabilizes donors in p+ silicon, and the pairing reaction between Cu and B. Calculated gettering efficiencies were in very good agreement with experimental results. Gettering in n+ silicon was similarly modeled in terms of pairing reactions and the Fermi-level effect. But, for n-type silicon, many experimental uncertainties existed; thus, we applied our expressions to solubility data of Hall and Racette to obtain the unknown parameters. The empirical calculations were in good agreement even with results on n/n+ wafers. For phosphorus-diffused wafers we had to consider an excess vacancy concentration of 1.2-5.5 times the equilibrium concentration to explain the experimental findings by the model. Gettering by poly-silicon back sides was simulated by solving the time-dependent diffusion equation with boundary conditions that take into account different surface reaction rates of silicon point defects. Using this advanced model, the experimentally measured gettering efficiencies were reproduced within the uncertainty of the measurement.