The modelling of surface evolution during growth and erosion

Abstract

AbstractWhen the erosion or growth of a surface that occurs in semiconductor device processing can be considered as everywhere continuous in space and time, the equations of motion of the surface may be specified and determined numerically using a kinetic model of surface evolution. In this review the fundamental concepts of the kinematic model of surface evolution are discussed. Detailed consideration of the theory of characteristics reveals its limitations which are overcome by recent theoretical development based on the Huygens principle of wavefront reconstruction. Correct interpretation of the nature of the basic wavelet, coupled with contemporary ideas of surface and edge propagation, form the essence of a new numerical algorithm. Numerical analysis and consequent numerical procedures derived from the generalized kinematic model are presented. Examples of surface evolution, with particular reference to ion beam induced erosion are given to show the advantages and potential of the method as opposed to existing models and theoretical prediction.When evolution processes are discontinuous and localized, other approaches, particularly those that use numerical modelling, are required. Such approaches are also reviewed here.