Hybrid model for the calculation of ion distribution functions behind a direct current or radio frequency driven plasma boundary sheath

A hybrid fluid dynamic/kinetic model is presented which describes the sheat h and the presheath regions of dc or rf driven low pressure gas discharges in a realistic and self-consistent way. The model assumes an infinite exten ded sheath parallel to the electrode, allowing a one-dimensional spatial de scription. It provides for the presence of multiple positive ion species an d their collisional interactions with the neutral background, and takes int o account the possibility of a nonharmonic modulation of the sheath potenti al and the application of an external dc bias; in this work, the model is a pplied to a two-species capacitively coupled argon and oxygen plasma. The i nput required by the model consists of the fluxes of the incoming ions, of the modulating current, and of the pressure, the composition, and the tempe rature of the background gas. On output, the model provides the values of t he electric field and of the particle densities within the sheath and the p resheath, the total voltage drop across the sheath, and also the energetica lly and angularly resolved distributions of the positive ions and the energ etic neutrals which impinge the material substrate at the boundary. In gene ral, the model is able to treat dc discharges as well as capacitively and/o r inductively coupled rf discharges, it thus covers most of the plasmas use d in very large scale integration microelectronics manufacturing and other surface modification techniques. Using the model, studies of the energy dis tributions of the incoming ions have been performed for a wide range of par ameters, and the effects of varying process conditions have been investigat ed. At low and intermediate pressures (p < 50 mTorr), the distribution func tions of rf driven discharges exhibit a characteristic bimodal structure; t his structure disappears with increasing pressure as ion-neutral collisions become significant. A comparison of calculated ion energy distributions wi th experimental measurements on capacitively coupled argon and oxygen disch arges shows excellent quantitative agreement. In addition to the ion energy distribution, the angular distributions of the incident ions at various en ergies are also discussed as a function of the neutral gas pressure. It tur ns out that the details of the angular distribution not only depend on the field structure of the sheath itself but also on that of the presheath. The results of the presented model are therefore more reliable than those of p revious models which restricted themselves to the sheath region. This high physical accuracy of the presented model, together with its flexibility and its high execution speed, allows its use as a tool for technology-oriented computer-aided design in the microelectronics industry. (C) 2001 American Institute of Physics.