Elementary framework for cold field emission from quantum-confined, non-planar emitters
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
For suitably small field emitters, the effects of quantum confinement at the emitter tip may have a significant impact on the emitter performance and total emitted current density (ECD). Since the geometry of a quantum system uniquely determines the magnitude and distribution of its energy levels, a framework for deriving ECD equations from cold field electron emitters of arbitrary geometry and dimensionality is developed. In the interest of obtaining semi-analytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the Jeffreys-Wentzel-Kramers-Brillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with non-planar geometries, ECD equations were derived for the normally unconfined cylindrical nanowire (CNW) and normally confined (NC) CNW emitter geometries. As a function of the emitter radius, the NC CNW emitter ECD profile displayed a strong dependence on the Fermi energy and had an average ECD that exceeded the Fowler-Nordheim equation for typical values of the Fermi energy due to closely spaced, singly degenerate energy levels (excluding electron spin), comparatively large electron supply values, and the lack of a transverse, zero-point energy. Such characteristics suggest that emitters with non-planar geometries may be ideal for emission from both an electron supply and electrostatics perspective.
- OSTI ID:
- 22402996
- Journal Information:
- Journal of Applied Physics, Vol. 117, Issue 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
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