Derive an expression for the fime it takes a positive ion to traverse the cathode sheath assuming collision-free motion in a uniform electric field. Calculate this time for an Ar ion if the sheath thickness is 0.4 mm and the target voltage is 800V. Why is the energy of ion bombardment of the cathode expected to be higher for DC rather than high frequency operation? (a) An electron-beam gun with a filament anode spacing of 0.5 cm operates at 10kV and delivers a current of 1A. For areactive evaporation process the vacuum chamber contains oxygen at a pressure of 107 torr. If the first ionization potential of O, is 12.1V what is the probability of ionizing O, in the vicinity of the electron gun? (b) Electrons pass through electrodes that are spaced 5 cm apart and support a voltage difference of 1000V. At what O, pressure will 50% ionization occur? A simple approximation by Sigmund (Eq 3-1) for the sputter yield when the projective energy is below for particle energies of less than 3 keV. The relation holds when 1/5