Improved Closure Models for Fluid Moment Modeling of Capacitively Coupled Plasmas

Capacitively coupled plasmas (CCPs) are radiofrequency (RF) plasma sources that are widely used in industrial applications, including plasma etching and microfabrication. Single or multiple RF frequencies are used to ionize and sustain a plasma through an alternating electric field. The acceleration of electrons via the RF field is the primary driver for ionization and the sustainment of the plasma. The higher energy tail of the electron velocity distribution function (VDF) plays a critical role in this process. Conventional fluid models, which directly model macroscopic plasma properties assuming some form of the VDF, often Maxwellian, fail at capturing the effects of the high energy tail. Similarly, these models often assume heuristic formulas for the transport coefficients. The inclusion of more sophisticated closure models that capture the effects of non-Maxwellian deviations in the VDF is thus critical to model the operation of CCPs appropriately. Collisional terms for the electrons are derived using a modification of Grad’s method and implemented on the full-fluid moment (FFM) model on an RF setup similar to CCPs. This leads to a more accurate drag contribution and a conductive heat flux contribution that includes the Peltier effect and the effect of the density gradient. The results are compared to widely used fluid closures, such as the Bhatnagar-Gross-Krook (BGK) operator for drag and Fourier’s law for the conductive heat flux.