Control of electromagnetic edge effects in electrically-small rectangular plasma reactors

Electromagnetic fields supported by rectangular reactors for plasma enhanced chemical vapor deposition are studied theoretically. Expressions for the fields in an electrically-small rectangular reactor with plasma in the chamber are derived. Modal field decompositions are employed under the homogeneous plasma slab approximation. The amplitude of each mode is determined analytically. It is shown that the field can be represented by the standing wave, evanescent waves tied to the edges, and an evanescent wave tied to the corners of the reactor. The impact of boundary conditions at the plasma edge on nonuniformity is quantified. Uniformity may be improved by placing a lossy magnetic layer on the reactor sidewalls. It is demonstrated that nonuniformity is a decreasing function of layer thickness.