Leonard Borucki

General model for mechanical stress evolution during electromigration

A model is presented for the development of stress during electromigration. Formally similar to a thermal stress model, it provides a method of calculating all of the components of the stress tensor and clearly couples vacancy transport and stress evolution with the boundary conditions that apply to the metal. Analytic solutions are discussed for electromigration either normal or parallel to a plate. The solution parallel to a plate is used to reinterpret x-ray microdiffraction experiments from the literature. We find that the effective charge for vacancies in pure polycrystalline aluminum at 533 K is about 0.84. Using parameters that were either measured or calculated with the embedded atom method, our model displays good agreement with both transient electromigration data and drift data.

Multiple scale integrated modeling of deposition processes

The ability to predict feature profile evolution across wafers during processing using equipment scale operating conditions is one important goal of process engineers. We present an integrated approach for simulating the multiple length scales needed to address this problem for thermal chemical vapour deposition (CVD) processes. In this approach, continuum models on the reactor scale and mesoscopic scales are coupled tightly with ballistic transport models on the feature scale to predict micro and macro loading effects in a transient environment. As an example of this approach, the transient simulation results for thermal deposition of silicon dioxide from tetraethoxysilane (TEOS) are presented. The efficiency of the approach presented and extensions to more complex systems are briefly discussed.

A Multiscale Simulator for Low Pressure Chemical Vapor Deposition

An integrated simulator for chemical vapor deposition is introduced. In addition to reactor scale and feature scale simulators, it includes a mesoscopic scale simulator with the typical length scale of a die. It is shown that the three-scale integrated simulator used is a proper extension of two-scale deposition simulators that consist of reactor scale and feature scale simulation models. Moreover, it is demonstrated that information is provided on a new length scale, for which no information is available from the two-scale approach, as well as important corrections to the simulation results on the reactor scale. This enables, for instance, studies of microloading. Thermally induced deposition of silicon dioxide from tetraethyoxysilane is chosen as the application example. The deposition chemistry is modeled using six gaseous reacting species involved in four gas-phase and eight surface reactions.

A theory of pad conditioning for chemical-mechanical polishing

Statistical models are presented to describe the evolution of the surface roughness of polishing pads during the pad-conditioning process in chemical-mechanical polishing. The models describe the evolution of the surface-height probability-density function of solid pads during fixed height or fixed cut-rate conditioning. An integral equation is derived for the effect of conditioning on a foamed pad in terms of a model for a solid pad. The models that combine wear and conditioning are then discussed for both solid and foamed pads. Models include the dependence of the surface roughness on the shape and density of the cutting tips used in the conditioner and on other operating parameters. Good agreement is found between the model, Monte Carlo simulations and with experimental data.

Mathematical modeling of polish-rate decay in chemical-mechanical polishing

A model is presented for polish-rate decay in chemical-mechanical polishing based on the Greenwood-Williamson theory of contact between a smooth surface (a wafer) and a rough surface (the polishing pad). The model assumes that polishing causes pad asperities to wear, with high asperities wearing faster than low asperities. Model predictions of the time dependence of polish-rate decay compare favorably with experiments.

Effect of Slurry Flow Rate on Tribological, Thermal, and Removal Rate Attributes of Copper CMP

cFujimi Incorporated, Kagamigahara, Gifu Prefecture 509-0108, Japan Chemical mechanical polishing of copper is examined experimentally and theoretically as a function of slurry flow rate and the product of applied wafer pressure and relative sliding speed ( p 3 V). It is observed that under constant tribological conditions, the removal rate at any fixed value ofp 3 V generally decreases as slurry flow rate increases. The increased cooling of the wafer surface, as a result of increased slurry flow rate, is used to explain this reduction in the reaction rate. At a fixed flow rate, it is further observed that removal rate does not necessarily increase monotonically with p 3 V. The rate instead depends on the particular values of pressure and velocity, regardless of the fact that they may result in the same value of p 3 V. This dependence is shown to be caused by changes in the coefficient for convective heat-transfer between the wafer and the slurry, as well as the heat partition factor, which determines the fraction of the total frictional power that heats the wafer. Results further indicate that trends in copper removal rate can be adequately explained with a Langmuir-Hinshelwood kinetics model with both mechanical and chemical rate components.

Topography simulation for the virtual wafer fab

Abstract We introduce modeling and simulation of topography evolution during processes used in the fabrication of integrated circuits. After an overview, the presentation is divided into three major sections. In the first section, we consider thermal processes. The first process considered in this section is the chemical vapor deposition (CVD) of SiO 2 from TEOS (tetraethoxysilane). We discuss the use of film profile information to help decide between, and to help refine, kinetic models. The second example deals with thin film flow of doped glasses for planarization applications, and demonstrates model calibration. The second major section demonstrates the state of topography simulation for plasma processes. We demonstrate the use of physically motivated models that require calibration using experimental data for a given set of operating conditions. We first consider the plasma-enhanced chemical vapor deposition (PECVD) of silicon dioxide from TEOS and oxygen mixtures (PETEOS). We then consider ionized physical vapor deposition (IPVD) of copper, incorporating results of new calculations on the interactions of gas phase-species with the surface. As the last example in this section, we discuss a reactive ion etch (RIE) model. The last major section presents four applications. First, programmed rate CVD is discussed in some detail, in order to demonstrate how feature scale modeling can be used in process development. Next, the RIE model is used to demonstrate aspect ratio-dependent etching, and to show how simulations can be used to develop engineering relationships. The third example shows how topography simulations can be used to aid process integration studies, and involves PETEOS, etching and reflow simulations. The final example uses the model for PETEOS to demonstrate the roles of ‘3d/2d’ and ‘3d/3d’ (transport dimensionality/surface dimensionality) topography simulators in ‘virtual wafer fabs’.

Defect generation and diffusion mechanisms in Al and Al–Cu

A defect generation mechanism, namely, the grain-boundary Frenkel pair model, and corresponding diffusion mechanisms during electromigration are developed using atomic simulation techniques in Al and Al–Cu. We contend that large numbers of interstitials and vacancies exist at grain boundaries and both contribute to mass transport. Cu preferentially segregates to the interstitial sites at grain boundaries via a Frenkel pair generation process and reduces the overall grain-boundary diffusivity due to the stronger Al–Cu binding. Predictions from our models are in excellent agreement with available experimental data and observations.

Revisiting the Removal Rate Model for Oxide CMP

This study seeks to explain removal rate trends and scatter in thermal silicon dioxide and PECVD tetraethoxysilane-sourced silicon dioxide (PE-TEOS) CMP using an augmented version of the Langmuir-Hinshelwood mechanism. The proposed model combines the chemical and mechanical facets of interlevel dielectric (ILD) CMP and hypothesizes that the chemical reaction temperature is determined by transient flash heating. The agreement between the model and data suggests that the main source of apparent scatter in removal rate data plotted as rate versus pressure times velocity is competition between mechanical and thermochemical mechanisms. A method of visualizing removal rate data is described that shows, apart from any particular interpretative theory, that a smooth and easily interpretable surface underlies the apparent scatter.

A new, general model for mechanical stress evolution during electromigration

A new model is presented for the development of stress during electromigration. Formally similar to a thermal stress model, it provides a method of calculating all of the components of the stress tensor and clearly couples vacancy transport and stress evolution with the boundary conditions that apply to the metal. Analytic solutions are discussed for electromigration either normal or parallel to a plate. The latter is similar to the metallization in experiments by Wang et al., permitting us to reinterpret these experiments. We find that the effective charge for vacancies in pure polycrystalline Al at 533 K is about 1.3. Using parameters that were either measured or calculated with the Embedded Atom Method, our model displays good agreement with both transient electromigration data and drift data.