G. Hobler

Monte Carlo simulation of two-dimensional implanted dopant distributions at mask edges

Abstract Two-dimensional implanted dopant distributions at mask edges are studied using the Monte Carlo code IMSIL. The models implemented in the program are reviewed. An empirical model of electronic stopping describes correctly the range of channeled B, P, and As ions in a wide energy range. The damage model takes defect recombination into account but does not require the simulation of recoil cascades. Two-dimensional dopant distributions are calculated by randomly selecting the starting points of the ions between two positions defining a mask opening. The simulation results show that the penetration below the mask is larger than expected and that a Gaussian function is inappropriate to describe the lateral distribution function. The discrepancy increases with decreasing implantation energy. The dependence of the two-dimensional profiles on mask edge orientation, tilt angle, and ion species, and the influence of a screening oxide are investigated.

Two-dimensional modeling of ion implantation induced point defects

An analytical model for the description of ion-implantation-induced damage profiles is presented. The model is based on extensive Monte Carlo simulations of B-, P-, As-, and Sb-implantations in Si. One-dimensional profiles are described by a Gaussian function and an exponential function joined together continuously with continuous first derivatives. The two-dimensional model has previously been developed by the authors for dopant profiles and is demonstrated to apply well to point defect distributions. Parameters have been obtained for the four ions by fitting the model to the Monte Carlo results, and they are provided in the form of tables for the energy range of 10-300 keV (for the 1D model 1-300 keV). The Monte Carlo simulations are based on the binary collision approximation, the assumption of a random target, and the validity of the linear collision cascade theory. The importance of energy transport by recoils is pointed out. >

Full three-dimensional simulation of focused ion beam micro/nanofabrication

2D focused ion beam simulation is only capable of simulating the topography where the surface shape does not change along the third dimension, both in the final result and during processing. In this paper we show that a 3D topography forms under the beam even though the variation in the final result along the third direction is small. We present the code AMADEUS 3D (advanced modelling and design environment for sputter processes), which is capable of simulating the surface topography in 3D space including angle-dependent sputtering and redeposition. The surface is represented by a structured or unstructured grid, and the nodes are moved according to the calculated sputtering and redeposition fluxes. In addition, experiments have been performed on nanodot formation and box milling for a case where a 3D temporary topography forms. The excellent agreement validates the code and shows the completeness of the model.

Current density profile extraction of focused ion beams based on atomic force microscopy contour profiling of nanodots

An approach to the profile extraction of nanoscale focused ion beams is presented. It is based on contour profiling of dots patterned at various ion doses by focused ion beam exposure. While the surface contour depends on the spatial variation of the beam-solid interaction, at no single ion dose the contour reflects the current density profile of the beam itself, due to effects such as target swelling, redeposition, and angle-dependent sputtering yield. Instead, we monitor the surface deviation relative to the unimplanted case as a function of dose for the radial positions of interest, and determine scaling factors for the dose such that the scaled curves coincide for all radial positions in the regions of small milling depths. We apply the method to beam shape determination of 10 and 50 keV focused ion beams using silicon and GaAs as targets and atomic force microscopy as a contour profiling technique. Despite the different irradiation response of silicon and GaAs, the beam profiles evaluated on these su...

Boron channeling implantations in silicon: Modeling of electronic stopping and damage accumulation

Channeling implantations of 20 keV boron into silicon have been performed with doses between 1013 and 1016 cm−2 in the [100], [110], and [211] direction, and parallel to a (111) plane. Simulations using an empirical electronic stopping model agree very well with the experimental results. The model has been obtained considering a large number of random and channeling implantations published in the literature. It contains a nonlocal and an impact parameter dependent part with the nonlocal fraction increasing with energy. Moreover, a computationally efficient damage accumulation model is presented which takes point defect recombination into account. It is found that due to interactions within a recoil cascade only 1/8 of the generated damage is stable, and that damage saturation takes place at a concentration of 4×1021 cm−3. Comparison of simulations and experiments indicates that displaced atoms reside on random positions rather than on tetrahedral interstitial sites in the silicon lattice.

Simulation of ion beam induced micro/nano fabrication

The shrinking critical dimensions of modern technology place heavy requirements on optimizing feature shapes at the micro and nano scale. Ion beams are increasingly used for technology development in the nano-scale world. In recent years, many approaches and research results have indicated that re-deposition of sputtered target atoms is the most serious problem in fabricating micro and nano devices. A simulation tool is essential to reduce unnecessary time and efforts spent in process development. In this paper, we present two-dimensional string-based simulation software for ion milling and focused ion beam direct fabrication, AMADEUS-2D (advanced modeling and design environment for sputter processes). We discuss the numerical model for considering sputtering and re-deposition fluxes. In addition, we investigate sputtering yield and sputtered atom distributions as obtained from several binary collision simulation codes. The newly developed simulation code is validated by comparison with experimental data on single-pixel hole milling, on the width and dose dependence of trench formation and on the effective sputtering yield as a function of scan speed.

Comparison of Transmission Electron Microscope Cross Sections of Amorphous Regions in Ion Implanted Silicon with Point‐Defect Density Calculations

The width of the amorphous zone in the near-surface region of (100) silicon and polycrystalline silicon formed during high-dose silicon, phosphorus, or arsenic implantation is measured by cross-sectional transmission electron microscopy. Various technologically important examples were selected for this study. Comparison with point-defect density calculations yields a critical point-defect density for the crystalline-to-amorphous transition of 1.15.10 22 cm -3 for all implantations. The width of the amorphous zone may be predicted for Si + , P + and As + ilmplants with an accuracy of less than 5 %

Monte Carlo simulation of ion implantation into two- and three-dimensional structures

Until now, rigorous Monte Carlo simulations of ion implantation into 3-D structures have been prohibited by the large amount of computer time required, and 2-D simulations have been restricted to simple structures like linear mask edges or rectangular trenches. Methods are presented which made 2-D simulations with arbitrary geometries as well as 3-D simulations with simple geometries feasible. First, an auxiliary grid is used to reduce the time required to check whether an ion crosses a boundary. Second, each ion trajectory is used several times to determine the history of ions entering the target at different positions. The methods are demonstrated by three examples: implantation into a rectangular trench, implantation into a 2-D trench with nonplanar sidewalls, and implantation into a 3-D trench with quadratic cross section. >

Computer Simulation of Oxygen Precipitation in Czochralski‐Grown Silicon during HI‐LO‐HI Anneals

A model is presented which describes statistically the growth and dissolution of oxygen precipitates and stacking faults by a set of rate equations (RE) and a Fokker-Planck equation (FPE). The REs allow an accurate description of very small precipitates and stacking faults while the FPE allows an efficient treatment of the large ones. The influences of interstitial oxygen diffusion, precipitate stress, and point defects are considered in the model. The system of nonlinear coupled partial differential equations (PDE) formed by the REs, FPEs, and the continuity equations of interstitial oxygen and of the point defects is solved by a numerical method especially suited for the structure of this system. The model is applied to the simulation of HI-LO-HI anneals which are typically performed by wafer manufacturers to produce a defect-free zone and internal gettering (IG) sites. The results are verified by comparison with experimental data reported in the literature.

Monte Carlo simulations of defect recovery within a 10 keV collision cascade in 3C–SiC

A kinetic lattice Monte Carlo (KLMC) model is developed to investigate the recovery and clustering of defects during annealing of a single 10 keV cascade in cubic silicon carbide. The 10 keV Si cascade is produced by molecular dynamics (MD), and a method of transferring the defects created by MD simulations to the KLMC model is developed. The KLMC model parameters are obtained from MD simulations and ab initio calculations of defect migration, recombination, and annihilation. The defects are annealed isothermally from 100 K to 1000 K in the KLMC model. Two distinct recovery stages for close Frenkel pairs are observed at about 200 and 550 K, and the growth of complex clusters is observed above 400 K. These simulation results are in good agreement with available experimental results.