Abstract
This paper presents an exact analytical theory for the inverse tunneling of free vacuum electrons through a triangular potential barrier into a metal. It is found that the inverse tunneling probability is the same as that of the field emission of electrons from metal into vacuum, for the same incident electron energy, metal properties (work function, Fermi energy), and applied electric field strength. For incident electrons with velocities not normal to the vacuum-metal interface, the three-dimensional (3D) oblique tunneling is equivalent to the one-dimensional (1D) normal tunneling, by considering only the longitudinal energy of the electrons normal to the vacuum-metal interface.
Highlights
The field emission heat engine (FEHE) is a novel thermionic converter to directly convert heat into electricity with high efficiency
In FEHE, an electric field is applied near the anode to suppress the thickness of the potential barrier, so that vacuum electrons with total energy less than the anode surface vacuum level can still enter the anode via quantum tunneling
This paper provides an exact 1D theory for inverse tunneling of vacuum electrons into a metal, and its straightforward extension to the more general three-dimensional (3D) model, where the electron travels at arbitrary direction with an oblique angle to both the front and the back of the potential barrier (Fig. 4)
Summary
The field emission heat engine (FEHE) is a novel thermionic converter to directly convert heat into electricity with high efficiency. The power density and efficiency of a thermionic converter is typically limited by the work function of the anode.[3] In FEHE, an electric field is applied near the anode to suppress the thickness of the potential barrier, so that vacuum electrons with total energy less than the anode surface vacuum level can still enter the anode via quantum tunneling. This process is similar to field emission in reverse, so is called “inverse tunneling”.2. This paper provides an exact 1D theory for inverse tunneling of vacuum electrons into a metal, and its straightforward extension to the more general three-dimensional (3D) model, where the electron travels at arbitrary direction with an oblique angle to both the front and the back of the potential barrier (Fig. 4)
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