Physica Scripta. Vol. 42, 124-128, 1990. zyxwvut Wave Aspects of Electron and Ion Emission from Point Sources J. Summhammer and J. Schmiedmayer Atominstitut der Osterreichischen Universitaten, SchiittelstraDe 115, A-1020 Wien, Austria zyxwvut Received August 28, 1989; accepted November zyxwvutsrqp 30, 1989 Abstract Electrons emitted from single-atom tips are analysed in a model with the tip as a round tubelike constriction. The source creates two-dimensional mini- mum wavepackets whose temporal evolution agrees well with observed beam divergences. With few-atom tips interference effects may arise due to the electron's non localized emission from several atoms. The phase space den- sity of emitted electrons is around k3, and electron-electron correla- tion experiments become feasible. In ion field emission mode observed beam divergences are dominated by thermal broadening and other effects rather than quantum mechanical principles. Applications include electron inter- ferometers of lower energy and wider beam separation than hitherto in use, as well as proton and possibly other ion interferometers. Highly focused low energy beams could also be produced. 1. Introduction Recently Fink zyxwvutsrqp [ 1, 21 has achieved the production of tungsten (1 1 1)-tips ending in only a few atoms, and sometimes even in a single atom. Similar results have also been reported by Morin [3]. And Binh [4] has described so called teton tips where a fine tungsten needle of a few atomic distances in diameter is grown in the (1 1 1)-direction on top of a much wider tip. In all cases the effective radii at the foremost tip region are around lOA. Therefore the application of only moderate voltages suffices to generate fields strong enough to either have electrons tunnel into the vacuum or gas atoms be field ionized. The electron beams emitted from these sources are as high as 10 pA and hence very intense, while ion beams reach some lOpA at a gas pressure of lOP4Torr. Their apertures were reported to be as low as 2' for electrons and some zyxwvutsrqpo 0.5" for He ions [2]. These properties make these sources ideal for use as local probes as well as for basic quantum experiments. Especially the fact that the size of the emitting region is of the order of the initial wavelength of the emitted particles suggests that some of the features of the beam are of wave mechanical nature. The purpose of this note is to gain an understanding of just these features. 2. Single-atom tips 2.1. Theoretical picture We will focus special attention on electron emission from single-atom tips. Here, the final atom represents a con- striction [5] in which the transverse momentum states of the electron are quantized in two dimensions. The constriction terminates in a barrier formed by the Coulomb attraction of the last atom and the external electric field. If the barrier is not too wide with respect to the electron's wavelength at the Fermi-level, there is a fair chance that the electron will tunnel through it. Once outside, the electric field accelerates it to the positive electrode, which usually is a detection screen (Fig. 1). Now even in the vicinity of the tip the z-component of this Physica Scripta 42 field is several times the radial component and it becomes even more dominant with increasing distance. Therefore the electron experiences predominantly a forward acceleration. And hence the Schrodinger equation between screen and tip can be put as where V(z) represents the potential along the z-axis. There is no radial zyxwv (=x, y) dependence of the potential so that the wavefunction evolves freely in these directions. Hence one can try a separation ansatz in which the radial components are represented by a sum of plane waves and the axial com- ponent is given by a function O(z, t) yet to be determined: II/(x, t, z, t> = +(x, y, t)@, t> (2) Inserting into (1) leads to a Schrodinger equation for O(z, t). But independently of the knowledge of this function one can now calculate the radial part +(x, y, t). This is of particular interest, since it determines the size of the spot observed at the screen and the angular divergence of the beam. To obtain it explicitly one must match this wavefunction at t = 0 (time of emission of the electron from the tip) with the transverse component of the wavefunction in the tip at the outside of the tip U screen Fig. zyxwvuts 1. Sketch of the experimental scheme. 2A = original l/e-width of the z x-y wavepacket.