SPATIAL VARIATIONS OF RADIO-FREQUENCY PLASMA-DENSITY CAUSED BY A STEP-CHANGE OF SECONDARY-ELECTRON EMISSION COEFFICIENT

A two-dimensional analytical model for the effect of a nonuniform secondary electron emission coefficient (γ) on the powered electrode of a radio frequency plasma was developed. The nonuniformity was a step change in the value of γ. The ambipolar diffusion equation, including ionization by thermal and secondary electrons, took the form of a Helmholtz equation for which the solution by separation of variables was a series of cosine functions. The discontinuity of γ on the electrode engendered substantial nonuniformity of plasma density. For example, the nonuniformity at the sheath edge of an Ar plasma (50 mTorr, 200 V) was 40% for a substrate having a γ of 0.027 and resting on a platen having a γ of 1.00. © 1995 American Institute of Physics.