Frank Wirbeleit

Non-Gaussian Diffusion of Phosphorus and Arsenic in Silicon with Local Density Diffusivity Model

In the light of published phosphorus and arsenic diffusion profiles [1,2] a non-Gaussian mathematical diffusion model is developed in this work based on separate forward and reflected impurity diffusion flows and called local density diffusion (LDD) model. The LDD model includes the rational function diffusion (RFD) model published in [3] and represents an improvement for near surface and tail concentration profile slope approximation by introducing just one single empirical fit parameter “r”. This single fit parameter is related to the given combination of impurity species (phosphorus: r=0.18; arsenic: r=0.43) in the applied host lattice system (silicon), but does not vary while approximating different experiments with different impurity surface concentrations and penetration depths [1,2]. Based on the LDD approximation in this work a surface enhanced diffusivity for phosphorus and a tail decelerated diffusion for arsenic is suggested in comparison to RFD model approximation only. The local density diffusivity is found to be non-linear along the penetration path and reaches its maximum at a distance LLDD from the surface.

Local Density Diffusivity (LDD-) Model for Boron Out-Diffusion of In Situ Boron-Doped Si0.75Ge0.25 Epitaxial Films Post Advanced Rapid Thermal Anneals with Carbon Co-Implant

Boron in silicon has presented challenges for decades because of clustering and so-called transient enhanced diffusion [1-2]. An understanding of boron diffusion post rapid thermal annealing in general, and out of in situ doped epitaxially grown silicon-germanium films in particular, is essential to hetero junction engineering in microelectronic device technology today. In order to model boron diffusion, post-implantation, the local density diffusion (LDD) model has been applied in the past [3]. Via mathematical convolution of the diffusion model slope and the initial boron concentration profile, these former results were transferred to this work. In this way, non-diffusing boron was predicted to exist in the center of the presented in situ boron-doped films. In addition, boron diffusion control by co-implanted carbon was demonstrated and the applied LDD model was completed and confirmed by adapting A. Einstein’s proof [4] for this purpose.

Non-Gaussian Local Density Diffusion (LDD-) Model for Boron Diffusion in Si- and SixGe1-x Ultra-Shallow Junction Post-Implant and Advanced Rapid-Thermal-Anneals

Boron diffusion after implant and anneal has been studied extensively in the past, without de-convoluting the Boron diffusion behavior by the initial post implant Boron concentration profile, which is done in this work first time. To support the de-convolution approach, the local density diffusion (LDD) model is selected, because this model is based on just one single arbitrary diffusion parameter per atomic species and host lattice combination. The LDD model is used for Phosphorus and Arsenic diffusion so far and an extension to simulate Boron diffusion in presence of Boron clusters is presented here. As the result, maximum Boron penetration depth post different rapid thermal anneals and the quantification of diffusing and clustering (non-diffusing) Boron in silicon and silicon-germanium host lattice systems are given.