ION-TRANSPORT ANISOTROPY IN LOW-PRESSURE, HIGH-DENSITY PLASMAS

Controlling ion transport is critical for controlling line profiles during the plasma etching of submicron structures for ultra-large-scale integrated circuits. Fortunately, the newest generation of plasma reactors are operated at low enough pressures that the sheath region separating the plasma from the wafer becomes collisionless. Under these circumstances, the ion angular distribution function at the wafer surface can be calculated from the sheath voltage and the ion velocity distribution function at the sheath edge. In this work, several limiting cases for the ion angular distribution function are considered. A good approximation for the angular distribution at the wafer surface is derived by assuming that the perpendicular velocity distribution is Gaussian, in agreement with experiment, while the parallel velocity distribution is a delta function with the magnitude of the parallel velocity simply given by the magnitude of the sheath voltage. Parallel velocity distributions with finite width at the sheath edge are shown to have only a small effect on the ion angular distribution function at the wafer surface. With these simple assumptions, the ion angular distribution function at the wafer surface is a function of only one parameter: the ratio of the sheath voltage to the perpendicular ion temperature.