Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives

A (2+1)D kinetic Monte Carlo (KMC) code was developed for coarse-grained as well as atomic-scale simulations that require detailed consideration of complex surface-reaction mechanisms associated with electrodeposition of copper in the presence of additives. The physical system chosen for simulation is similar to that used by the microelectronics industry to fabricate on-chip interconnects, where additives are used to tailor shape evolution. Although economically significant, such systems are often designed in an empirical manner that would be greatly enhanced by improved understanding of the additive mechanism gained through simulations. By comparing simulated results at atomic as well as coarse-grained scales with theoretical results obtained analytically for various limiting cases of behavior, the validity of the KMC code was tested. It was found that the surface roughness at a specified length scale can be accurately simulated by using a coarse-grained KMC code with lattice spacing of 1/10 or smaller than that of the specified length scale—a result that is particularly useful for comparing experimental data on surface roughness with numerical simulations. For second-order homogeneous surface reactions, it is shown that the KMC-simulated surface coverage approaches the analytical surface coverage as surface mixing is increased by increasing the surface diffusion rate. The results verified the numerical accuracy and the reduced computational cost of the coarse-grained KMC approach for simulating complex chemical and electrochemical mechanisms.

[1]  Paul Shewmon,et al.  Diffusion in Solids , 2016 .

[2]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[3]  A. Voter,et al.  Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). , 1986, Physical review. B, Condensed matter.

[4]  Kobayashi,et al.  Stochastic simulation of molecular-beam epitaxial growth of a model compound semiconductor: Effects of kinetics. , 1989, Physical review. B, Condensed matter.

[5]  W. H. Weinberg,et al.  Theoretical foundations of dynamical Monte Carlo simulations , 1991 .

[6]  Landau,et al.  Monte Carlo simulation and dynamic scaling of surfaces in MBE growth. , 1994, Physical review. B, Condensed matter.

[7]  Manipulation of nucleation by growth rate modulation , 1995 .

[8]  W. Steckelmacher.  Molecular gas dynamics and the direct simulation of gas flows , 1996 .

[9]  James E. Butler,et al.  A kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition: Application to diamond , 1997 .

[10]  M. Kotrla,et al.  Theory and simulation of crystal growth , 1997 .

[11]  Alan C. West,et al.  Copper Deposition in the Presence of Polyethylene Glycol II. Electrochemical Impedance Spectroscopy , 1998 .

[12]  D. L. Ma,et al.  Optimal model-based experimental design in batch crystallization , 2000 .

[13]  John C. Shelley,et al.  Computer simulation of surfactant solutions , 2000 .

[14]  David V. Baxter,et al.  A kinetic Monte Carlo simulation of chemical vapor deposition: non-monotonic variation of surface roughness with growth temperature , 2000 .

[15]  G. Henkelman,et al.  Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table , 2001 .

[16]  K. Hebert.  Analysis of Current-Potential Hysteresis during Electrodeposition of Copper with Additives , 2001 .

[17]  M. Kushner,et al.  Trench filling by ionized metal physical vapor deposition , 2001 .

[18]  Linda J. Broadbelt,et al.  Generic Monte Carlo Tool for Kinetic Modeling , 2001 .

[19]  M. Klein,et al.  Computer simulation studies of biomembranes using a coarse grain model , 2002 .

[20]  R. Ferrando,et al.  Collective and single particle diffusion on surfaces , 2002 .

[21]  Haydn N. G. Wadley,et al.  Kinetic Monte Carlo simulation of heterometal epitaxial deposition , 2002 .

[22]  Mark J. Kushner,et al.  Monte Carlo Simulation of the Electrodeposition of Copper II. Acid Sulfate Solution with Blocking Additive , 2002 .

[23]  M. Kushner,et al.  Monte Carlo Simulation of the Electrodeposition of Copper I. Additive-Free Acidic Sulfate Solution , 2002 .

[24]  Per Linse,et al.  Effect of spatially distributed hydrophobic surface residues on protein-polymer association , 2003 .

[25]  Timothy O. Drews,et al.  Evolution of Surface Roughness during Copper Electrodeposition in the Presence of Additives Comparison of Experiments and Monte Carlo Simulations , 2003 .

[26]  Markos A. Katsoulakis,et al.  Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles , 2003 .

[27]  Andrew J. Majda,et al.  Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems , 2003 .

[28]  George Stephanopoulos,et al.  Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties , 2003 .

[29]  R. Braatz,et al.  Parameter Sensitivity Analysis of Monte Carlo Simulations of Copper Electrodeposition with Multiple Additives , 2003 .

[30]  M. D. Rooij,et al.  Electrochemical Methods: Fundamentals and Applications , 2003 .

[31]  David L. Ma,et al.  Coupled mesoscale—continuum simulations of copper electrodeposition in a trench , 2004 .