Ion dynamics model for collisionless radio frequency sheaths

Full scale reactor model based on fluid equations is widely used to analyze high density plasma reactors. It is well known that the submillimeter scal e sheath in front of a biased electrode supporting the wafer is difficult t o resolve in numerical simulations, and the common practice is to use resul ts for electric field from some form of analytical sheath model as boundary conditions for full scale reactor simulation. There are several sheath mod els in the literature ranging from Child's law to a recent unified sheath m odel [P. A. Miller and M. E. Riley, J. Appl. Phys. 82, 3689 (1997)]. In the present work, the cold ion fluid equations in the radio frequency sheath a re solved numerically to show that the spatiotemporal variation of ion flux inside the sheath, commonly ignored in analytical models, is important in determining the electric field and ion energy at the electrode. Consequentl y, a semianalytical model that includes the spatiotemporal variation of ion flux is developed for use as boundary condition in reactor simulations. Th is semianalytical model is shown to yield results for sheath properties in close agreement with numerical solutions. (C) 2000 American Institute of Ph ysics. [S0021-8979(00)02810-3].