Anomalous Field Enhancement in Planar Semiconducting Cold Cathodes from Spontaneous Ordering in the Accumulation Region
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Anomalous Field Enhancement in Planar Semiconducting Cold Cathodes from Spontaneous Ordering in the Accumulation Region Griff L. Bilbro1 and Robert J. Nemanich2 1 Department of ECE, NC State University, Raleigh, NC 27695-7911 2 Department of Physics, NC State University, Raleigh, NC 27695-8202 ABSTRACT Wide band gap semiconductors exhibit a low electron affinity and may prove suitable for cold cathode applications. We introduce a simple closed-form analytic approximation for the stability of electrons in the electron accumulation layer of planar Low Electron Affinity (LEA) semiconducting cathodes. This analysis extends our previous results, which used Runge-Kutta numerical integration of the linearized equations of motion for the electric potential and quasi Fermi level. The model shows conditions in which the electrons in the accumulation layer form a two dimensional array of regions of higher and lower electron density. This instability could lead to field enhancement without surface roughness and could account for observed electron emission at low applied fields. INTRODUCTION Wide band gap semiconductors such as diamond, AlN, or BN can exhibit negative electron affinities depending on surface termination. However, n-type doping of these materials is difficult. In contrast, Al1-xGaxN alloys (x~0.5) can be doped n-type and can exhibit a low electron affinity of ~1 eV [1]. LEA-coated cold cathodes may lead to vacuum electron devices (VEDs) with unprecedented versatility and performance [2]. Robust electron emission with high current density has been predicted for graded aluminum gallium nitride that is undoped [3] or doped [4]. LEA cathodes that require neither field enhancement nor high temperature may lead to VEDs with micrometer grid-to-cathode distances, picosecond transit times, and terahertz operating frequencies. In this paper we provide simple closed-form expressions for our previous numerical prediction that LEA cathodes may be unstable against certain three-dimensional perturbations of the electron accumulation layer [5]. The instabilities may lead to ordered regions of higher or lower electron densities, and these regions would result in field enhancement without surface morphology. Our effort is motivated by recent characterizations of planar cathodes which emit more electrons at lower voltages than can be readily explained without field enhancement [6] according to the usual equilibrium theory [7]. MODEL In a Cartesian coordinate system, consider a uniform n-type semiconductor filling the region x ≤ 0 with vacuum in the region x>0 as shown in Figure 1.
R6.4.1
Figure 1. Coordinate system at the semiconductor/vacuum interface of a semiconductor filling the half space x < 0. The anode (not shown) is parallel to the interface at some x>0 in the vacuum.
Assuming complete ionization and Maxwell-Boltzmann statistics, the electron density for x ≤ 0 is n = NC exp{ (EFn - EC) / kBT } where NC is the effective density of states of the conduction band and EFn is the quasi Fermi level for electrons. EFn differs f
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