MOMENTUM TRANSFER THEORY OF ELECTRON TRANSPORT IN × FIELD

Requirements for an electron transport theory which can serve as the basis for rf discharge modeling are increasingly complex and represent the main obstacle in achieving global plasma processing device modeling. In case of inductively coupled plasma (ICP) modeling1, additional complication arises from the need to describe the effect of magnetic field and it requires non-linear equations of motion. Development of a simple, reasonably accurate kinetic theory, which on the other hand can describe all the relevant processes, is a desirable option to numerically intensive models. A very good example of great benefits from a simple analytical or semi-analytical theory is application of the non-local theory of Tsendin and Kortshagen2. In this paper we develop another aproach to developing a simple kinetic theory which can be used universally. It is the Momentum Transfer Theory (MTT) which has been used in physics of electron and ion swarms to provide physical insight into kinetic phenomena through development of analytical relations3. In this paper we restrict ourselves to application of MTT to charged particle transport, electrons in particular. MTT basically consists of applying Taylor expansion to the rate coefficients at the appropriately determined value of the mean energy. Regardless of its simplicity it allows a reasonably small uncertainty of the calculated data of the order of 10%. While early developments relevant to MTT date back to the work of Wannier 4, 5 and Mason 6 the MTT has been mostly developed by Robson and coworkers. MTT has been applied to test the validity of Blanc’s law for charged particle transport in mixtures of gases having only elastic processes6, 7, 8. Inelastic collisions have been included in the single gas MTT and corresponding equations for energy, drift velocity and relationship between the mobility and components of the diffusion tensor were developed. Reactive collisions were included in addition to inelastic and the corresponding effects of attachment, annihilation10 and ionization 11 on t ranspor t coefficients were discussed. MTT was also applied to electron transport in crossed electric and magnetic fields for a case of a single gas with non-reactive collisions12. Recently, however, MTT has been developed for a general case of gas mixtures that