NUMERICAL-SIMULATION OF THE ION ETCHING PROCESS

Numerical techniques traditionally used in The simulation of compressi ble fluid dynamics are applied to the ion etching process. This proces s is governed by a non-linear hyperbolic conservation law describing t he evolution of the local slope of a surface. The hyperbolic nature of the equation allows discontinuities of slope to develop which are see n numerically and experimentally as cusps in the surface of the etched material. These discontinuities are analogous to shocks in fluid dyna mics. Initially, an essentially non-oscillatory (ENO) algorithm is use d to simulate the evolution of a single homogeneous material with fixe d boundaries and known flux function. The algorithm is then extended t o simulate the evolution of two different homogeneous materials which is more representative of a typical etching configuration. The two mat erials are assumed to be separated by an interface of known form. The additional mathematical and physical reasoning to describe the two-mat erial configuration is presented from which a new algorithm is develop ed. This algorithm requires the hyperbolic conservation law to be solv ed on a moving mesh since the interface between the materials is numer ically treated as a moving boundary. The nature of the two-material pr oblem is such that shocks and expansion waves can develop at this inte rface and thus special numerical treatment of the moving boundary is r equired; this is achieved by using a lower order approximation in this localised region. Finally, a more realistic method to calculate the f lux function is adopted which changes the nature of the governing equa tion since the flux function becomes dependent on the geometry of the surface as well as the local slope. The algorithm is extended to inclu de this flux calculation which allows the numerical simulation of the physically observed phenomena such as RIE lag and undercutting. (C) 19 94 Academic Press, Inc.