Nonuniform radio-frequency plasma potential due to edge asymmetry in large-area radio-frequency reactors

Abstract

In small area capacitive reactors, the rf and dc components of the plasma potential can be assumed to be uniform over all the plasma bulk because of the low plasma resistivity. In large area reactors, however, the rf plasma potential can vary over a long range across the reactor due to rf current flow and the nonzero plasma impedance. A perturbation in rf plasma potential, due to electrode edge asymmetry or the boundary of a dielectric substrate, propagates along the resistive plasma between capacitive sheaths. This is analogous to propagation along a lossy conductor in a transmission line and the damping length of the perturbation can be determined by the telegraph equation. Some consequences are the following: (i) The spatial variation in sheath rf amplitudes causes nonuniform rf power dissipation near to the reactor sidewalls. (ii) The surface charge and potential of a dielectric substrate can be negative and not only positive as for a uniform rf plasma potential. The variation of sheath dc potential across a dielectric substrate causes nonuniform ion energy bombardment. (iii) The self-bias voltage depends on the plasma parameters and on the reactor and substrate dimensions—not only on the ratio of electrode areas. (iv) The nonuniform rf plasma potential in presence of the uniform dc plasma potential leads to nonambipolar dc currents circulating along conducting surfaces and returning via the plasma. Electron current peaks can arise locally at the edge of electrodes and dielectric substrates. Perturbations to the plasma potential and currents due to the edge asymmetry of the electrodes are demonstrated by means of an analytical model and numerical simulations.