T. M. Makhviladze

Influence of electrical current on the stability of a conducting film surface

In this paper, a model of the influence of electromigration induced by current flow on the development of instability of the free surface of a conducting film on a substrate is developed. The dependence of the conditions for the appearance of the instability on the value and the direction of the electric field applied to the film and on the value and character of mechanical stress on the boundary with the substrate is obtained and studied analytically.

Characteristics of the kinetics of periodic structures CMP for a nonlinear pressure dependence of the polishing rate

For the kinetics of the chemical mechanical polishing (CMP) of wafers containing periodic metal–dielectric structures, a model is developed and theoretically investigated with the use of contact mechanics methods for the nonlinear pressure dependences of the polishing rate. In the steady-state regime, expressions for the dishing effect, which is characterized by the difference in the depths of the polishing metal and dielectric strips, are analytically derived and investigated. The specific characteristics of this effect, which are observed for different kinds of nonlinearities of the polishing rate depending on the pressure and the relative rotation velocity of the pad and wafer, are analyzed. Particularly, it is shown that, under certain conditions, the steady-state regime may be nonunique (the bistability effect).

Advanced atomic-scale simulation of silicon nitride CVD from dichlorosilane and ammonia

The work is devoted to atomistic-scale modeling of chemical vapor deposition (CVD) of silicon nitride thin films from dichlorosilane (DCS) and ammonia (NH3). Within the framework of extended chemical mechanism that essentially extends the chemical reactions scheme developed earlier to include DCS catalytic decomposition reactions, selfconsistent model of CVD at atomistic scale has been elaborated. The extended chemical mechanism has been built up and studied by means of ab initio quantum chemistry methods. It allowed us to describe adequately the gas phase kinetic processes over a typical range of temperature, pressure and DCS: NH3 ratio. The effective kinetic model has been developed for the extended set of possible reactions. It enabled us to calculate the reaction rates and concentrations of gas mixture components as well as to carry out sensitivity analysis of kinetic equations. The surface mechanism of film growth for the extended reactions scheme has been investigated with the use of non-empirical methods based on the cluster model. Reactions of additional gas mixture components with active surface centers were calculated by quantum chemistry methods, and thermodynamic analysis of surface coverage by various chemisorbed groups has been performed.

Electromigration theory and its applications to integrated circuit metallization

The theory of electromigration-induced nano- and microprocesses that terminate in failure of thin-film conductors is given. These processes determine operational reliability of IC metallization system. The physical foundations of degradation and lifetime of interconnects are analyzed. The various mechanisms of their deformations and failures that are of practical importance for different types of multilevel arrangement and microstructure are studied. The full 3D theory developed considers the electromigration failures as a set of processes occurring at the nano-, micro- and mesoscale. We reduced the general equations in order to describe specific conducting systems, developed the methods of their numerical modeling, and created software packages. It allows carrying out the simulation of electromigration failures and performing the lifetime analysis for various interconnect systems that are of prime practical significance as regards the operation of IC metallization, the modeling being over a wide range of material, geometrical, structural, and operational parameters. Some examples of the reliability analysis and of the analysis of the most likely failure locations in dependence on the current density, parameters of multilevel metallization, temperature, and polycrystalline grain microstructure of interconnects are represented. We also put forward an approach to modeling the electromigration in conductors containing impurities.

Modeling of the interfacial separation work in relation to impurity concentration in adjoining materials

On the basis of the general thermodynamic approach developed in a model describing the influence of point defects on the separation work at an interface of solid materials is developed. The kinetic equations describing the defect exchange between the interface and the material bulks are formulated. The model have been applied to the case when joined materials contain such point defects as impurity atoms (interstitial and substitutional), concretized the main characteristic parameters required for a numerical modeling as well as clarified their domains of variability. The results of the numerical modeling concerning the dependences on impurity concentrations and the temperature dependences are obtained and analyzed. Particularly, the effects of interfacial strengthening and adhesion incompatibility predicted analytically for the case of impurity atoms are verified and analyzed.

Simulating the Effects of Internal Mechanical Stresses on the Decomposition Kinetics of a Supersaturated Oxygen Solution in Silicon

We justify and exactly formulate a method for simulating the effect of mechanical stresses induced in a system silicon matrix–oxygen precipitate (SiO2) on the rates of fundamental processes determining the kinetics of precipitation. The developed model is based on the classical theory of kinetics of the first-order phase transitions with regard to the observed features of the SiO2 particle growth in silicon (two-stage precipitation) and the main relations of the theory of elasticity. The proposed approach is used to establish and analyze the dependences of the main kinetic parameters describing the variations in the number of critical nuclei of the precipitate phase on the characteristics of the interfacial mechanical stresses induced and developed during the postcrystallization cooling of silicon wafers.

Electromigration-Induced Instability of the Interface between Solid Conductors

A model has been developed to describe the influence of vacancy electromigration in the bulk of joined conducting materials under applied electric current on the shape stability of a flat interface between them. A system of equations is formulated and solved to describe the relationship between changes in the interface profile and mechanical stresses arising in it due to ion and vacancy fluxes, induced by a small spatially periodic perturbation of the interface. Criteria of the perturbation amplitude growth with time, i.e., the shape instability conditions for the interface, are determined. A more detailed analysis and estimation are performed for two special cases: in the first case the interface is between two similar materials, and in the other the mobility of ions and vacancies in one of the materials can be neglected. Perturbation wavelength ranges are determined and studied analytically for these cases; within the intervals the bulk vacancy electromigration is the main factor that leads to the growth of perturbation amplitude and mechanical stresses along the interface with time. Conditions for the existence of such ranges and dependences of their boundaries on the current direction and current density are determined. Particular wavelength and current density ranges of the interface instability are estimated. The estimates show that the interface instability due to bulk electromigration is possible under reasonable (experimentally and practically) conditions in terms of temperature (∼100°C), current density (∼1010 − 1012 A/m2), and perturbation wavelength (∼101 − 103 μm). The obtained results may be useful, e.g., for improving the reliability and lifetime of micro- and nanoelectronic components.

Nonempirical simulation of chemical deposition of silicon nitride films in CVD reactors

This work is devoted to the atomistic simulation of chemical vapor deposition (CVD) of thin silicon nitride films from the mixture of dichlorosilane (DCS) and ammonia in CVD reactors. The earlier developed chemical mechanism is substantially extended by including the reactions of catalytic decomposition of DCS, and a self-consistent atomistic model of a CVD process is developed. An extended chemical mechanism is constructed and analyzed that allows one to adequately describe kinetic processes in a gas phase within the ranges of temperature, pressure, and the DCS: NH3 ratio of original reactants, that are characteristic of silicon nitride deposition. An effective kinetic model is developed that involves the calculation of the rate constants and the concentrations of the gas mixture components. A thermodynamic analysis of the surface coverage by various chemisorbed groups is carried out, and equilibrium surface concentrations are obtained for the main chemisorbed groups. Practically significant conclusions are made about the character of the deposition process and, in particular, about the role of the extended chemical mechanism.

A thermodynamic model of the influence of atomic impurities on the adhesion strength of interfaces

A model which describes the influence of point defects on the work of separation of interfaces of solid materials is developed based on the thermodynamic approach. The model is used to analyze the situation where the joined materials contain the point defects in the form of impurity atoms. The dependence of the work of separation of joined solid materials on the concentration of atomic impurities in their bulks is numerically modeled for different temperatures and in a wide region of parameters. The results show that in certain regions of the parameters, it is possible to strengthen or weaken the interface. The interface can also turn out to be in a state where its spontaneous separation is more favorable. These effects can be applied to control the adhesion properties of multilayered systems.

Thermodynamic theory of interfacial adhesion between materials containing point defects

Thermodynamical models allowing to find the surface tension and the separation work of the interfaces of joined materials as functions of lattice defect concentrations in the materials are developed. The models are applied to the cases when the defects are vacancies, vacancy clusters, and impurity atoms. As a result it is obtained that at certain defect concentrations the interfacial surface tension and separation work can be made vanish and become negative.