The linear theory of acoustoelectric oscillators with arbitrary static field distributions

Abstract

General formulae are derived for the growth rate and frequency shift from acoustic resonance for an arbitrary mode of an acoustoelectric oscillator. The formulae are valid to first order in the electromechanical coupling constant for arbitrary DC field distributions and AC electrical boundary conditions. They are used to calculate the growth rates of the low frequency mode of short oscillators in the zero diffusion limit for DC field distributions with three different dependences on distance from the cathode: uniform, square root and hyperbolic tangent. Mode 1 has a negative growth rate in all cases and it is rigorously shown that this is necessarily so under open circuit conditions whenever the electronic transit time is less than the acoustic transit time. For a uniform field the mode dependence of the growth rate has a small modulation due to space-charge waves. For the square root distribution, which describes a space-charge limited diode, the growth rate varies rapidly with mode number in both magnitude and sign. For a hyperbolic tangent distribution, with a rise length of 10 mu m in the vicinity of the cathode, the calculated growth rates are in good qualitative and quantitative agreement with the characteristic 'mode 3' behaviour observed in short oscillators for all oscillator lengths in the range 15-30 mu m and a wide range of bias conditions.