Influence of a finite energy width on the hot electron double-slit ...

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4 and 5 are consistent with the expression Eq. 11 and Eq. 11 can be rewritten in a more explicit form for electrons in GaInAs as. EF in emitter. 8103 d2 nm2. meV.
Influence of a finite energy width on the hot electron double-slit interference experiment: A design of the emitter structure Hiroo Hongo,a) Yasuyuki Miyamoto,b) Michael Gault, and Kazuhito Furuya Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, 2–12–1 O-okayama, Meguro-ku, Tokyo 152, Japan

~Received 10 April 1997; accepted for publication 3 July 1997! The influence of electron energy width in the hot electron double-slit experiment is investigated quantitatively. The required condition on the Fermi level in the emitter and the slit-spacing is derived for the experiment. In order to achieve a coherent electron source, a single-barrier graded emitter structure is discussed and its characteristics are considered. For application to the hot electron double-slit experiment, the graded emitter diode is fabricated and the current–voltage relation is measured in a supplementary experiment. © 1997 American Institute of Physics. @S0021-8979~97!01720-9#

I. INTRODUCTION

Hot electron interference/diffraction phenomena by potential grating in a semiconductor has a potential of application to novel electron devices.1 In order to apply to a future electron device, an experiment of double-slit hot electron interference has been proposed.2 The proposed device structure is shown in Fig. 1.2 It consists of a buried double slit whose size is comparable with an electron wavelength and fine electrodes for detection. In this device structure, a single barrier emitter structure is formed underneath the double slit. Hot electrons are emitted from the bottom emitter to the slits and cause interference by passing through the two slits. Each peak and valley of the interference pattern is detected as the spatial distribution of currents. For example, the peak corresponds to a large current, the valley corresponds to a small current, etc. There are two important points to perform the observation experiment of hot electron double-slit interference: the first is the required size of the device structure, and the second is the effect of the energy width of incident hot electron waves. The former point is concerned with the finite phase relaxation of hot electron waves in semiconductors, and discussed in Ref. 2. The latter point is concerned with the finite energy distribution of electrons. Most of electron wave phenomena ~interference or diffraction! can be considered by analogy with light. However, there is a significant difference between the electron and the photon. The electron is a Fermi particle and any two electrons cannot occupy the same state. This means that the state of each electron is different from each other. The energy is related to the state, so in the case of the electron gas, it is impossible to realize a perfectly monochromatic energy distribution. This is the difference between the electron wave and the light wave. A finite energy distribution means a finite distribution of the direction of the wave number vector. As will be seen in Sec. III, a superposition of interferences caused by waves with various incident angles reduces the apparent interfera!

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J. Appl. Phys. 82 (8), 15 October 1997

ence. Therefore a small energy distribution is important to observe interference effects. In Ref. 3, the effective wavefront spread of electrons from a planar emitter was studied. However, the physical meaning of the dependency of the wavefront spread on various parameters in Ref. 3 is not clear, or the explicit requirement on an emitter source and the device parameter for hot electron interference/diffraction experiment has not been discussed. In this paper, we consider how the energy distribution affects the obtained interference pattern. By using a qualitative discussion, a requirement on the relation between the slit-spacing ~center to center! and the Fermi level in the emitter is derived. A simple numerical simulation confirmed this requirement. To realize the required hot electron energy distribution, a graded emitter structure is considered. In order to apply the graded emitter to the double-slit experiment, an experiment of the graded emitter diode is performed. The current–voltage characteristics of the graded emitter is calculated, and the measured current is analyzed. This graded emitter structure is employed in the double-slit experiment under a magnetic field reported in Ref. 4. In Sec. II, a brief discussion of an ideal case of monochromatic energy distribution is given. Then in Sec. III, the effect of the finite energy width on the double-slit interference is discussed. In order to apply to the experiment, the graded emitter structure is considered in Sec. IV and the experiment of the graded emitter diode is presented. Finally, the conclusion is given in Sec. V.

II. MONOCHROMATIC ENERGY CASE

Before we discuss the influence of a finite energy width of the electron wave to the double-slit experiment, a case of monochromatic energy is considered. In the next section, we extend the discussion to the case of a finite energy width. If we assumed spherical waves with point sources from each slit, the interference pattern on the electrode layer is e ikr 1 e ikr 2 1 , r1 r2

~1!

where k is the electron wave number, and r 1 and r 2 are the 0021-8979/97/82(8)/3846/7/$10.00

© 1997 American Institute of Physics

FIG. 1. Proposed device structure for hot electron interference by double slit.

distances from each slit to the point on the electrode layer. Then the intensity of the interference pattern at a point x on the electrode layer becomes 212 cos

kdx L

r2

~2!

,

or 2 p dx 212 cos Ll r2

,

~3!

where L is the distance from the slit layer to the electrode layer, d is the slit spacing, l is the electron wavelength, and r5 AL 2 1x 2 . Then the period of the interference pattern from the peak to the valley is Ll/2d. In order to detect the peaks and the valleys of the interference pattern, the electrode spacing ~center to center! T electrode and the slit spacing d must satisfy the following relation: T electrode