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Japanese Journal of Applied Physics

Wavefront Spread of Hot Electrons Generated by Planer Tunnel Emitters

Hiroshi Matsuura, Kazuhito Furuya

Published Jul 1, 1995• 8 citations
Publisher

Abstract

For realization of quantum coherent devices which use the wavefront of the electron wave, the wavefront spread is important. To investigate the wavefront spread, the double-slit diffraction of hot electrons from a planer tunnel emitter is analyzed. Due to the statistical spread of the transverse momentum of electrons in the emitter electrode, the visibility of the diffraction pattern is less than unity. The wavefront spread is defined as the maximum spacing of the double-slit which provides visibility higher than 1/e. Dependencies of the wavefront spread on various parameters are derived. It increases when the temperature and/or the Fermi energy decreases. For example, when the Fermi energy is 5 meV, spread is 60 and 27 nm at 4 and 77 K, respectively.

DOI
10.1143/jjap.34.3589

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For realization of quantum coherent devices which use the wavefront of the electron wave, the wavefront spread is important. To investigate the wavefront spread, the double-slit diffraction of hot electrons from a planer tunnel emitter is analyzed. Due to the statistical spread of the transverse momentum of electrons in the emitter electrode, the visibility of the diffraction pattern is less than unity. The wavefront spread is defined as the maximum spacing of the double-slit which provides visibility higher than 1/e. Dependencies of the wavefront spread on various parameters are derived. It increases when the temperature and/or the Fermi energy decreases. For example, when the Fermi energy is 5 meV, spread is 60 and 27 nm at 4 and 77 K, respectively.
We have carried out Young's double-slit experiment for the hot-electron wave in man-made semiconductor structures with a 25-nm-space double slit in an InP layer buried within GaInAs, a 190-nm-thick GaInAsP hot-electron wave propagation layer, and a collector array of 80 nm pitch. At 4.2 K, dependences of the collector current on the magnetic field were measured and found to agree clearly with the double-slit interference theory. The present results show evidence for the wave front spread of hot electrons using the three-dimensional state in materials, for the first time, and the possibility of using top-down fabrication techniques to achieve quantum wave front control in materials.
This is a detailed description of the first definite observation of the double-slit interference of a hot electron in a solid. The observation has been achieved by fabricating a double-slit with a 12 nm opening and a 25 nm center-to-center distance and a detection electrode with a 40 nm width. Various inspections are made theoretically to confirm the double-slit diffraction/interference. This achievement will open the door to the creation of solid-state devices with new functions based on the wave nature of electrons.
We propose a trajectory density formulation of the double-slit interference pattern that reproduces observed fringe intensities without wave superposition. The intensity at screen position x is the weighted density of particle trajectories arriving there, suppressed exponentially by the deflection cost in energy space: I(x) = V_{Trit}(KE) \times \sum_n w_n \cdot \delta\!\left(x - \frac{n\lambda L}{d}\right) \cdot e^{-k|n|} where k = dθ_eff/λ_dB is the coherence parameter set by the effective illumination semiangle θ_eff, and V_Trit(KE) = 2γβ/(1+γ²β²) is a new energy-dependent visibility factor from the Trit framework [1–3]. The parameter k connects to the effective source temperature through the emission physics: higher source temperature → larger emission area → larger θ_eff → larger k → fewer visible fringes. We test the formula against five independent experiments across five orders of magnitude in particle energy and three particle types. For thermionic and Schottky electron sources the formula outperforms standard QM by a factor of 2–6× in R². For cold FEG sources and C60 molecules the formula correctly reduces to QM (k → 0). The C60 result leads to a clean new distinction: V_Trit(KE) applies to elementary particles, where the energy space geometry directly governs wave-particle balance; for composite particles V_Trit = 1 and interference is from the centre-of-mass de Broglie wave. This difference is falsifiable: varying electron energy should reveal a visibility peak at KE = 211.66 keV; varying C60 velocity should show no such peak.
This article describes elucidations of conditions for electron interference observation, device designs, and numerical simulations for the solid-state biprism. The solid-state biprism is solid-state version of the already realized vacuum biprism, and is also proposed as a test ground for electron interference observation and a new conceptual device. Towards the realization of this device, the designed semiconductor device structures show that interference pattern with a pitch of 86 nm and a visibility of 0.6 can be realized with an electron energy of 20 meV, a transverse energy spread of 0.3 meV, and an operation temperature of 4 K.
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements, and chip-based applications rely on intensive, tunable, coherent sources for free low-energy electron-matter waves. In most cases, the electrons get field emitted from a metal nanotip, where its radius and geometry toward a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter-wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 6.4 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy, and sensor technology.
We report a double-slit experiment of hot electrons in a semiconductor under a magnetic field. The pitch of the double slit buried in the semiconductor is 40 nm and the electron energy is of the order of 100 meV. By applying a magnetic field, the change in current that passes through the slits is observed at the segmented collector. The measured current shows a clear minimum around B=0 T, with this behavior agreeing with a theoretical calculation based on double-slit interference. Quantitative estimation is consistent with this order of current variation. We think that these results show evidence of the observation of hot electron interference by a double slit in a semiconductor.