Various impurities are used in VLSI processes. The key factors for the selection of the impurities are their solid solubility and diffusion coefficient. B, As, P are commonly used as doping impurities due to their high solid solubility. In and Sb are sometimes used to realize shallow junctions due to their low diffusion coefficients. We briefly showwhere various impurities are used in two distinguished devices of bipolar transistors and MOS FET’s.

The interactions between incident ion and substrate atoms are classical physical subjects. Ions lose its initial accelerated energy through the interaction between electron cloud and nuclei. The process is described with fundamental atomic properties such as atomic number and mass. Therefore, the model accommodates any combination of incident atom as well as the substrate composed of various kinds of atoms. We show the detail derivation process of nuclei and electronic stopping power models.

The physics for the ion implantation can be directly implemented in Monte Carlo (MC) simulation, and hence MC simulation is widely used for predicting ion implantation profiles. Here, we compared MC simulation results with a vast database of ion implantation secondary ion mass spectrometry (SIMS), and showed that the Monte Carlo data sometimes deviated from the experimental data. We modified the electronic stopping power model, calibrated its parameters, and reproduced most of the database. We also demonstrated that the Monte Carlo simulation can accurately predict profiles in a low energy range of around 1 keV once it is calibrated in the higher energy region.

In the design of VLSI devices, accurate prediction of the doping profiles resulting from ion implantation, a standard method for doping impurities in VLSI (very-large-scale integrated circuit) processes, is essential. This is done by obtaining analytical expressions for the SIMS (secondary ion mass spectrometry) data of ion implantation profiles, and these analytical formulas are used to compile an ion implantation profile database. The profiles of arbitrary implantation conditions can be generated using interpolated parameter values. Various analytical models have been developed for expressing ion implantation profiles. The functions used to express these ion implantation profiles include Gaussian, joined half Gaussian, Pearson, and dual Pearson functions. In addition to these, a tail function was proposed. This tail function has fewer parameters than the dual Pearson function, and it is better able to specify an arbitrary profile using a unique set of parameters.

Pearson IV is one function among Pearson function family, where various Pearson functions exist. Each Pearson function is characterized by its related γ² β plane. The moments of real profiles frequently deviate from the plane for the Pearson IV function. Therefore, we need to extend the function to whole Pearson function family. We described the detail derivation of the functions.

Pearson function is commonly used to express ion implantation profiles based on its four moments. Pearson function is not the unique one that uses the given four moments. Edgeworth polynomial is a function that is also generated using the four moments or more. We explain the model in this section, and express some experimental data with this model.

Experimental data and Monte Carlo data provide data sources for constructing ion implantation profile database. We need to extract parameters for various analytical functions from the profile data. We showed that, for the expression of ion implantation profiles, there are many local minimum values sets for the third and fourth moment parameters of γ and β for the Pearson function that comprises the standard dual Pearson and tail functions. It was proposed to use a joined tail function as a mediate function to extract γ and β , and demonstrated that this enables us to extract the parameters uniquely. Other parameters associated with channeling phenomena can also be simply and uniquely extracted by the procedure.

An analytical model with lateral straggling parameters was developed to describe the tilt dependence of ion-implantation profiles. There are three parameters associated with depth-dependent lateral straggling into the model. On the basis of comparison between experimental and analytical data, a database of ion-implantation profiles that includes lateral-straggling parameters have established. The data with tilt 0° were evaluated using off angle substrates.

Ion implantation profiles are expressed by the Pearson function with first, second, third and fourth moment parameters of Rp , ΔRp , γ , and β. We can derive an analytical model for these profile moments by solving a Lindhard-Scharf-Schiott (LSS) integration equation using perturbation approximation. This analytical model reproduces Monte Carlo data which were well calibrated to reproduce a vast experimental database. The extended LSS theory is vital for instantaneously predicting ion implantation profiles with any combination of incident ions and substrate atoms including their energy dependence.

The moments associated with the peak region were evaluated with the extended Lindhard-Scharff-Schiott (LSS) theory. The theory was further extended to that for moments of profiles in crystalline substrates. The channeling length was related to the maximum range that is associated with electron stopping power only. The shape of the channeling tail and the channeling dose were expressed in an empirical way but with a universal form. The theory was successfully applied to the profiles in Si_1-xGe_x substrates.

The derivation of second-order extended Lindhard-Scharff-Schiott theory (E2LSS) has shown that it is possible to predict accurate ion implantation moment parameters for a projected range of Rp , a straggling parameter ΔRp , and a lateral straggling parameter pt ΔR . Starting from E2LSS theory, we divided the energy region and introduced the ratio r_s of the nuclear stopping power S_n to the total stopping power in each energy region, related S_n to energy straggling, and succeeded in obtaining a simplified analytical model. We showed that the range and the ratio r_s have a universal dependence on the energy, normalized with respect to the reference energy E₁ where S_n the electron stopping power at that energy equals. The simplified model can be applied to any combination of ion and substrate atoms, similarly to E2LSS. The simplified model reproduces E2LSS over a wide range of ion implantation conditions and can be used to generate Gaussian profiles easily and obtain physical intuition for ion implantation profiles.