Electrostatic electron lens in the ballistic regime

Abstract

Electrostatic focusing of ballistic electrons in a high-mobility two-dimensional electron gas is discussed and experimentally demonstrated. The focusing is achieved by a spatial modulation of the electrostatic potential along the electrons trajectories, in analogy with the modulation of the dielectric constant in conventional light-wave optics.The long electronic mean free path (mfp) in twodimensional electron-gas (2D EG) systems and improved electron-beam lithography have opened a new field of research which might be called "electron optics in solids. "A few recent examples are magnetic focusing, ' the collimation of an electron beam injected from a smooth con-

Flat-lens focusing of electrons on the surface of a topological insulator

“…[1][2][3][4] A variation in electrostatic potential is analogous to a variation in dielectric constant so that a curved gate electrode can have the refractive power of a lens-as has been demonstrated in the two-dimensional electron gas of a GaAs heterostructure. 5,6 The focal length of this electrostatic lens depends on its curvature, diverging for a flat electrode.…”

Hot Electron Ballistic Transport in Two Dimensional Structures

“…Figure 7 shows the variation of the difference between transmission coefficients to the voltage probes P 1 and Ρ2 vs. voltage applied to the lens gate (relationship between transition coefficients and measured voltage difference between Ρ1 and P2 is given in details in [6]). A clear maximum is observed at VGL ≈ -0.37 V in a good agreement with theoretical estimate (-0.38 V).…”

“…Here, we present a variety of recent experiments demonstrating realization of lateral hot electron ballistic transport [3] observation of phonon emission [4,5] and electrostatic collimation and focusing [ 6] of electronic beam in 2D electron gas.…”

“…For electrons with energy below 36 meV we demonstrate a surprisingly long inelastic mfp of the order of 2 μm. Finally, we shall discuss the angular distribution of electrons injected from a point source in 2DEG and demonstrate steering and focusing of hot and cold electrons by controlling the electrostatic profile of the emitter [5] and by putting the electrostatic lens [6] in the transport region between emitter and collector.…”

Electron focusing by multiple-quantum-point contacts

“…In solid-state devices, the electrons emerging from the quantum point contact can be directed to a small area by applying a magnetic field [2], by putting a gate behind the point contact [4,5] or by refraction of the electrons by a convex lens (i.e. a region in which the electrons have a longer wavelength) [6].…”