Electromagnetic Modeling of Plasma Etch Chamber for Semiconductor Microchip Fabrication

In the plasma etch chamber used to fabricate semiconductor microchips, maintain- ing the symmetry and uniformity of the electric fleld in the plasma discharge region is critical. Very-high-frequency (VHF) RF sources are attractive for such applications as they improve the e-ciency of plasma generation. Electromagnetic efiects become important at these frequencies, and etch chamber design requires careful investigation of the electromagnetic fleld spatial struc- ture in the chamber. In this paper, we apply the flnite-difierence time-domain (FDTD) method to examine various electromagnetic efiects in the plasma etch chamber and investigate strategies for improved chamber design. These efiects include the standing wave efiects and asymmetric fleld distributions that can be caused by asymmetric RF power feed conflgurations. The FDTD method is formulated in both cylindrical and Cartesian coordinate systems to facilitate modeling of rotationally symmetric chamber and asymmetric RF feed structures. The electric fleld dis- tribution generated by various RF feed conflgurations is studied at difierent VHF frequencies. Based on the FDTD simulations, we have been able to identify a variety of design approaches for ensuring electric fleld symmetry and uniformity. When the electromagnetic efiects become signiflcant, it is indispensable to fully understand the electrodynamic behavior of the RF flelds in the etch chambers because any nonuniformity of the electric flelds in the plasma region would directly have an impact on the etch uniformity and quality. In this paper, we apply the FDTD technique (2) to model the RF wave behavior in the chamber. We particularly pay attention to the electric fleld distribution at the wafer level and the corresponding electromagnetic efiects at very high frequency. The FDTD method is formulated in both cylindrical and Cartesian coordinate systems to facilitate modeling of rotationally symmetric chamber and asymmetric RF feed structures. We couple the FDTD formulation with the CPML (2) absorbing boundary conditions to accurately simulate the RF power delivery via a coaxial line. 2. COMPUTATIONAL METHOD DESCRIPTION To make the computational model conformal to the geometrical features in the cylindrical etching chamber, we formulate the FDTD method in the cylindrical coordinate system. In the cylindrical coordinate system, the Maxwell's curl equations for linear, isotropic, nondispersive materials can