A 3-dimensional model for inductively coupled plasma etching reactors: coil generated plasma asymmetries

Summary form only given. Inductively coupled plasma (ICP) reactors are being developed as high plasma density (10/sup 11/-10/sup 12/ cm/sup -3/), low gas pressure (<10 s mTorr) sources for etching and deposition of semiconductor materials. Although ICP plasma etching tools have been developed which have a high degree of plasma uniformity, it is not uncommon to find azimuthal asymmetries and side-to-side variations in etch rates and plasma density. These asymmetries have been correlated with azimuthal variations in input and pumping of gases, circuit issues related to transmission line matching to the coil, and particulars of the reactor configuration. In this paper, we describe a 3-dimensional, time dependent model for ICP reactors whose intent is to provide an infrastructure to investigate asymmetries in plasma etching and deposition tools. The model is a 3-dimensional extension of a previously described 2-dimensional simulation called the hybrid plasma equipment model (HPEM). HPEM-3D consists of an electromagnetics module (EMM), a Boltzmann-electron energy module (BEM) and a fluid-chemical kinetics simulation (FKS). The inductively coupled electromagnetic fields are produced by the EMM. Those fields are used in the BEM to solve the electron energy equation using transport coefficients derived from solution of Boltzmann´s equation, and fluxes obtained from the FKS. The electron energies and source functions obtained from the BEM are used in the FKS where the species densities are calculated and Poisson´s equation is solved. The EMM includes a transmission line circuit model for the coil which accounts for azimuthal variations in the coil current.