Scott T. Dunham

Consistent quantitative model for the spatial extent of point defect interactions in silicon

The silicon point defect properties which control the spatial extent of their interactions (e.g., interstitial diffusivity) have been calculated by many researchers. However, large discrepancies exist in the reported values of these parameters, and it is essential to have a consistent set of parameters for use in process simulation. To meet this need, we present here a model which includes important interactions which have been ignored in previous analyses, specifically bulk recombination of interstitials with vacancies and segregation of interstitials to surface oxide films. We assess the effectiveness of the model in predicting the spatial extent of point defect interactions by comparing simulation results with a wide range of experimental data. Although this same experimental data previously gave large differences in calculated parameter values, we obtain a single set of model parameters which can account for the full range of data in a consistent manner.

A Quantitative Model for the Coupled Diffusion of Phosphorus and Point Defects in Silicon

In this paper, we develop and analyze models for the coupled diffusion of dopants and point defects, since such models have been observed to display the qualitative aspects of high concentration phosphorus diffusion profiles such as the characteristic «kink and tail.» We begin by describing a general model for phosphorus diffusion via dopant/defect pairs assuming local equilibrium for electronic processes, but not for chemical processes. Using this system, along with parameters based on experimental data previously reported in the literature, we test common model assumptions

Interactions of silicon point defects with SiO2 films

Interactions of point defects with SiO2 films play a central role in integrated circuit fabrication processes. In this work, a model is developed for the Si‐SiO2 system that considers the segregation of excess silicon between the oxide and the silicon substrate and diffusion and reaction of that excess silicon in SiO2. The model is able to explain a broad range of experimental observations under both oxidizing and nonoxidizing conditions in a consistent manner including: the variation of interstitial supersaturation with oxidation rate in steam and dry O2 ambients, oxidation enhanced and retarded diffusion results in 〈100〉 and 〈111〉 silicon, the large interstitial supersaturation resulting from the nitridation of SiO2, the reduction of SiO2 in argon and the corresponding decrease in interstitial concentration, contradictory calculations of effective interstitial diffusivity, and the greatly reduced effective recombination velocities for nitrided oxides relative to capped oxides.

A predictive model for transient enhanced diffusion based on evolution of {311} defects

It has been observed that {311} defects form, grow, and eventually dissolve during annealing of Si-implanted silicon wafers. The fact that for subamorphizing silicon implants {311} defects initially contain the full net dose of excess interstitials, and that the time scale for dissolution of these defects is about the same as the time scale of transient enhanced diffusion (TED) leads to the conclusion that {311} defects are a primary source of interstitials under TED conditions. We describe a comprehensive model which accounts for the evolution of these defects during ion implant annealing, and in combination with point defect parameters from previous work also correctly predicts TED behavior.

ATOMISTIC MODELS OF VACANCY-MEDIATED DIFFUSION IN SILICON

Vacancy‐mediated diffusion of dopants in silicon is investigated using Monte Carlo simulations of hopping diffusion, as well as analytic approximations based on atomistic considerations. Dopant/vacancy interaction potentials are assumed to extend out to third‐nearest neighbor distances, as required for pair diffusion theories. Analysis focusing on the third‐nearest neighbor sites as bridging configurations for uncorrelated hops leads to an improved analytic model for vacancy‐mediated dopant diffusion. The Monte Carlo simulations of vacancy motion on a doped silicon lattice verify the analytic results for moderate doping levels. For very high doping (≳2×1020 cm−3) the simulations show a very rapid increase in pair diffusivity due to interactions of vacancies with more than one dopant atom. This behavior has previously been observed experimentally for group IV and V atoms in silicon [Nylandsted Larsen et al., J. Appl. Phys. 73, 691 (1993)], and the simulations predict both the point of onset and doping depe...

Moment expansion approach to calculate impact ionization rate in submicron silicon devices

A method to calculate the impact ionization rate in submicron silicon devices is developed using both an average energy and an average square energy of electrons. The method consists of an impact ionization model formulated with the average energy and conservation equations for the average square energy in the framework of an energy transport model. Parameters for the transport equations are extracted in such a way that calculated moments based on these equations match Monte Carlo simulation results. The impact ionization generation rate in an n+nn+ structure calculated with this method agrees well with the results obtained from Monte Carlo simulation. The new method is also applied to a submicron n‐MOSFET. The calculated distribution of the generation rate is found to be quite different from the results based on a conventional method.

Investigation and Modeling of Fluorine Co-Implantation Effects on Dopant Redistribution

A comprehensive model is developed from ab-initio calculations to understand the effects of co-implanted fluorine (F) on boron (B) and phosphorus (P) under sub-amorphizing and amorphizing conditions. The depth of the amorphous-crystalline interface and the implant depth of F are the key parameters to understand the interactions. Under sub-amorphizing conditions, B and P diffusion are enhanced, in contrast to amorphized regions where the model predicts retarded diffusion. This analysis predicts the F effect on B and P to be entirely due to interactions of F with point-defects.

A simple continuum model for boron clustering based on atomistic calculations

Boron exhibits anomalous diffusion during the initial phases of ion implant annealing. Boron transient enhanced diffusion is characterized by enhanced tail diffusion coupled with an electrically inactive immobile peak. The immobile peak is due to clustering of boron in the presence of excess interstitials which also enhance boron diffusion in the tail region. We present a simple model for the formation of immobile boron interstitial clusters and associated point defect interactions derived based on atomistic calculations.

Modeling of the Kinetics of Dopant Precipitation in Silicon

In heavily doped silicon, dopant aggregation leads to a reduction in the electrically active concentration. For thermal cycles typical of very large scale integrated circuit fabrication, the kinetics of this precipitation process can play a critical role in determining the active doping levels and thus device electrical characteristics. In this work, we develop a general kinetic precipitation model which explicitly considers the time evolution of the precipitate size density, and is thus able to account for a broad range of behavior. We compare our model to previously published experimental data for arsenic and phosphorus activation/deactivation in silicon over a wide temperature range (300 to 800°C), and find that it can account accurately for the experimental observations, including reverse annealing following a temperature step.

Growth kinetics of disk‐shaped extended defects with constant thickness

In this work, we derive a simple analytic expression for the growth rate of disk‐shaped extended defects which maintain their thickness as they grow. The analysis includes both the interface reaction and solute diffusion as limiting the growth rate. We consider both the surface energy and the matrix strain energy and assume a toroidal capture surface around the periphery of the disk in determining the rate of the interface reaction. We utilize a series of spheres to approximate a torus and thereby are able to derive a simple expression for the solute concentration near the periphery of the disk as a function of solute diffusivity and defect size.