Modeling of plasma etch profiles with ions and reactive neutrals

The simulation of plasma etch profiles of semiconductor trenches in the wafer processing of integrated circuits is developed in a mixed analytic/numerical approach. The main contributions of this study are the derivation and use of explicit analytical expressions for the etch rates and the computation of the etch profiles by standard computer packages. The computation of the etch profiles is efficient, is used as a benchmark for more complex numerical computer codes and illuminates the parameter dependence.;The etch rate due to the ions is assumed proportional to the ion energy flux as suggested by experimental evidence. The shadowing due to the mask is included in the simplified derivation of the ion energy flux in cylindrical velocity coordinates for a two-temperature ion drifting Maxwellian. Neutrals with varying sticking coefficients are modeled by interpolation between the etch rate for shadowed neutrals with unity sticking coefficients and isotropic neutrals. The etch profiles are determined by the method of characteristics from the nonlinear evolution equation for the etch profile surface. Standard Matlab packages for the graphics and integration of the ordinary differential equations for the characteristics make the computation of etch profiles more efficient and more transparent than many complicated computer codes.;The SEM images for trenches etched in silicon in a SF6 plasma in a RIE reactor are modeled by the simulation method for etch profiles. The etch rate is a linear combination of the etch rates of ions and neutrals in the ion flux-limited regime. Monte Carlo simulation of ion distribution functions in a chlorine plasma are fit by a simulated annealing procedure to a set of two-temperature drifting Maxwellians. The Monte Carlo simulations are noisy due to insufficient numbers of simulation particles. Smoothing of the distribution functions produces the expected bimodal ion distribution functions in the ICP reactor. The resultant etch profiles for the ion distribution functions have no numerical surface fluctuations.