"Phase field" model of electrodeposition. (News Briefs).

NIST metallurgists have for the first time applied the phase field method to the modeling of electrochemical processes. This method employs a phase-field variable, a function of position and time which describes whether the material at a certain location is a particular phase, such as liquid or solid. The behavior of this variable is coupled to the relevant transport equations for the material during electrodeposition of metals, such as copper for the wiring in integrated circuits. Interfaces between phases are described by smooth, but highly localized, changes of this variable. This approach avoids the mathematically difficult problem of applying boundary conditions at an interface whose location is part of the unknown solution. The phase field technique has been developed and applied with great success over the last decade, both by NIST researchers and others around the world. The range of problems addressed includes the time evolution of complex solidification morphologies related to the casting of metals, the behavior of crystalline dislocations under stress, and surface electromigration on metals.

This new model also predicts the behavior of electrical charges at the electrode-electrolyte interface. The resulting relationships between electrostatic potential and surface energy (electrocapillary curves), surface charge, and differential capacitance are completely consistent with the traditional sharp-interface models of electrochemical interfaces. This new phase field method provides advantages over existing sharp-interface models in that details of interfacial behavior can be readily explored on complex morphologies, such as within the narrow trenches used in microelectronic fabrication or the dendrites formed during battery recharging.

CONTACT: Jonathan Guyer, [phone]; [e-mail].