A Study of Miram Curves in Thermionic Cathodes

The anode current vs. cathode temperature plot of a diode using a thermionic cathode is commonly known as the Miram [1] curve, and the transition from temperature to space charge limited flow is referred to as the `knee' in the curve. The physical reasons behind the shape of the knee are significant because a thermionic cathode is almost always operated in the vicinity of the knee to improve cathode life. This paper presents a novel analytic model, which solves the Poisson equation in 3D assuming an infinite axial magnetic field, including an arbitrary work function distribution on the cathode surface [2]. An earlier version that solves the Poisson equation in 2D yields excellent agreement with the corresponding MICHELLE code results [3]. Our model points to the deficiency of the customary Practical Work Function Distribution model [1], and demonstrates the necessity of a large fraction of non-emitting area to yield a Miram curve with a smooth knee, as often observed in experiments [1]. [1] M. Cattelino, G. Miram. Appl. Surf. Sci., vol. 111, pp. 90-95, 1997 [2] A. Jassem, D. Chernin, S. Ovtchinnikov, J. J. Petillo, Y. Y. Lau. Proc. IEEE Int. Vac. Electron Conf. (IVEC), Monterey, CA, USA, 2020. [3] D. Chernin et al. IEEE Trans. Plasma Sci., vol. 48, no. 1, pp. 146-155, 2020.