Simulation of surface topography evolution during plasma etching by the method of characteristics

Abstract

Application of the method of characteristics to the general case of ion or plasma etching is reviewed, yielding a topography evolution algorithm which is simultaneously accurate, flexible, and efficient. The behavior of initial slope discontinuities is computed by mapping the characteristic locus in the region of the discontinuity and removing any closed loops which appear in the locus. The new method is shown to produce profiles which satisfy the required entropy and jump conditions for any given variation of etching rate with surface slope, while allowing the use of longer integration time steps than conventional methods. Previously published “string” algorithms [W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, and M. O’Toole, IEEE Trans. Electron Devices ED-26,717 (1979); A. R. Neureuther, C. Y. Liu, and C. H. Ting, J. Vac. Sci. Technol. 16, 1767 (1979)] are compared to the new method, and are shown to be capable of generating correct profiles only under limited conditions, i.e., for specific etching behaviors or if slope discontinuities are artificially removed. © 1994, American Vacuum Society. All rights reserved.