We treat analytical models for two-dimensional profiles in patterned substrates. It is shown that the doses in the scaled MOSFET’s gates become significantly smaller that the doses in the large gate. We should therefore be careful about ion implantation conditions in scaled devices considering the two-dimensional effects. We further evaluated the relationship between vertical and lateral junction depth using the model.

Two-dimensional profile model for ion implantation at high tilt angle was derived, in order to describe the pocket ion implantation of MOSFETs. Then we can generate two-dimensional profile of ion implantation for the full MOS process neglecting diffusion of dopants, in order to predict electrical characteristic of MOSFETs.

We first simplify the existing model for two-dimensional profiles without losing accuracy. Then, a geometrical appreciation is given to the model. Next, a R_p line concept is generated from the simplified model. We can generate three-dimensional ion implantation profiles related to the R_p line for various device structures, and demonstrate that this procedure is applied to three-dimensional ion implantation profiles in FinFET. Furthermore, the models are extended to make Pearson function available.

It is important to predict ion implanted profiles in substrates comprised of different materials, where related moment parameters are different. We describe two procedures to generate profiles in multi-layers by using data for each layer, that is, dose matching method, and R_p normalized method, where R_p is the projected range. We show the process in which the methods are applied to multi-layers. Dose matching method is a simple and effective method. However, it provides unstable results sometimes, while R_p normalized method provides stable results.

Ion implanted impurity also plays a role for sputtering substrate atoms. The profiles are influenced by the sputtering. The database for the sputtering has also been developed. We described a model for the profiles where sputtering phenomenon is included. The model predicts the profile becomes invariable when the dose exceeds a certain value.

A parameter of thorough dose, Φ_a/c is introduced to express continuous amorphous layer thickness. Φ_a/c is defined by the dose of ions that pass through the amorphous/crystal interface, and the thickness of amorphous layer d_a is expressed by Φ_a/c combined with parameters for ion implantation profiles. Φ_a/c is independent of ion implantation conditions but depends on impurities. Φ_a/c for Ge, Si, As, P, B, In, and Sb were evaluated. Consequently, we can predict d_a over wide ion implantation conditions.

We summarize effects of impurity concentration, kinds of impurity and crystal orientation on solid phase epitaxy (SPE) of silicon from amorphous layers created by ion implantation. SPE speed is significantly low for the wafer orientation of (111) and high for (100) orientation. The SPE speed is significantly enhanced by doping impurities, such as B, As, and P. N, O, and F retard the growth rate by one order, and the speed is almost zero for Ar and Xe. Random nuclear growth is a competing mechanism with SPE, and polycrystalline layer is formed where random nuclear growth rate is comparable with SPE.

It is found that impurities are redistributed during solid phase epitaxy, which cannot be explained by normal diffusion theory. A model is proposed, where the driving force of the redistribution is the phase transition from amorphous and crystalline forms. The model has parameters of a segregation coefficient m, which is between amorphous and crystalline Si, and an introduced parameter of reaction length l, that is, the distance where impurities are exchanged. The model reproduces various experimental data by using corresponding parameter values with the same theoretical framework.

Solid solubility is not a limiting factor for the maximum activation of impurities during solid phase epitaxial recrystallization (SPER). However, activation is limited to the maximum value of about 2x10²⁰ cm^-3 during SPER. A concept of the isolated impurity that has no neighbor impurities with a certain lattice range is introduced. The impurities react with neighbor impurities to form clusters, and only the isolated impurities can be active. The isolated impurity concentration has the maximum concentration at the total impurity concentration of about 10²¹ cm^-3, and it decreases with a further increase in total impurity concentration.