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The effects of substrate bias on microwave plasma etching have been theoretically analyzed, and the potentials at the surface of the semiconducting and the insulating materials being etched under a substrate bias have been derived. The computed results indicate that the etch rate increases with increasing impinging ion energy which depends strongly on the magnitude and the frequency of the substrate bias voltage. The theory correlates well with the experimental results on the electron cyclotron resonance microwave plasma etching of semiconducting Si and insulating Si3N4 films under radio frequency (107 Hz) substrate bias voltages.