A. Modinos

Field emission from surface states in semiconductors

Abstract The consequences of tunneling from surface states on the total energy distribution of field emitted electrons from a clean germanium surface are investigated in some detail. A model for the surface states due to Handler is employed and tunneling from the surface states is treated semiclassically. The results of the calculation are compared with available experimental data.

Resonance transfer of electrons in the reflection of atoms from metal surfaces

A theory is presented of resonance electron transfer in the reflection of atoms from metal surfaces. It is based on a time-dependent one-electron Hamiltonian with the atom moving on a classical trajectory. The matrix elements that couple the atomic to the metallic electron states are expressed in terms of quantities which depend explicitly on the surface density of states and it is shown how these can be calculated to a good approximation for a give surface. The theory is applied to the reflection of sodium atoms in the 30–400 eV range from a tungsten (110) surface at temperatures in the range 270–2000 K. It is shown that the motion of the reflected atom parallel to the surface may lead, because of the asymmetry of the electronic structure, to significantly different results for different directions of the parallel velocity. It is also shown that the form of the variation of the upward shift of the atomic level determines to a considerable degree the functional dependence of the non-adiabatic charge transfer on the velocity of the reflected atom. The temperature variation of the neutral fraction of the reflected Na atoms from the W(110) surface is calculated and compared with the experimental results of Overbosch et al. [Surface Sci. 92 (1980) 310]. The calculated ratio of the high temperature value to the low temperature value of the neutral fraction is considerably larger than the experimental value of this quantity.

Field emission spectroscopy of transition metals

Abstract The first chapter of this review paper is devoted to the essentials of the theory of fieldemission spectroscopy of transition metals. In this chapter we derive the formulae that are necessary for a physical interpretation of field-emission energy distribution (FEED) data, and we sketch the different methods of calculating the FEED distribution. In the second chapter of the paper we present a summary of the results of the different calculations of FEED distributions that have been made so far, and we discuss the physical significance of these results in some detail. Part of the analysis and conclusions in section 2 is based on data not previously published and is presented here for the first time. Recent studies of the effect of ordered overlayers on the FEED distribution are reviewed. Finally, we discuss briefly field-emission from ferromagnetic crystals on the basis of the energy-band theory of ferromagnetism.

On the theory of the oscillatory survival probability in noble gas ion-surface scattering

Abstract We present a simple analytic model of neutralisation of ions colliding with solid surfaces. The model is applied to 0.3–2.0 keV He+ scattered from Pb and Ga. We obtain, for appropriate values of the parameters, good agreement with the experimental data.

The polarization of physisorbed inert atoms due to the short range interaction with the metal substrate

Abstract We present a study of the polarization of physisorbed inert atoms (Ne, Ar, and Kr) due to the short range interaction with the metal substrate, using the method described in ref. [8]. The potential inside the metal is replaced by a constant and the metal-vacuum interface is represented by a step barrier. The adsorbed atom is represented by a spherical potential of the muffin-tin type superimposed on the constant potential on the vacuum side of the metal-vacuum interface. The potential within the adatom sphere is replaced by that of the free inert atom as calculated by Schwarz [9]. We calculate the Local Density of States of the metal-adatom system, the induced dipole moment, and the binding energy of the adatom. The effect on the induced polarization of the geometry of the surface and of the crystal potential is treated on a semi-empirical basis. Our numerical results are in reasonably good agreement with the available experimental data.

Virtual surface states

Abstract Under conditions appropriate to a field emission experiment true surface states cannot exist. This paper demonstrates that virtual surface states do exist and have properties which for most practical purposes are identical to those of true surface states.

On the interpretation of ion neutralisation spectra at metal surfaces

We present a theoretical analysis of the energy distribution of the Auger electrons emitted from a Ni(111) surface during the neutralisation of He+ ions incident on the surface with very low energy, i.e. ∼0.05 eV. We calculate the energy distribution of the emitted electrons in two limiting cases. In case A, it is assumed that the matrix element of the Auger transition is determined by the tails of the electronic wavefunctions on the vacuum side of the metal-vacuum interface. In case B, it is assumed that the ejected electron originates within the metal, in which case the energy distribution of the emitted electrons is, to a first approximation, proportional to an integral fold of the density of states in the bulk of the metal and the density of states at the position of the ion on the vacuum side of the interface ( ∼2.5–3.5 A from the last plane of atoms). The calculations take into account the broadening of the energy distribution due to the position-dependence of the valence level of the ion. The results obtained from case B, unlike those of case A, are in reasonable agreement with the experimental spectrum. A discrepancy between theory and experiment remains at the lower energy part of the spectrum, but this is, probably, to a large extent, due to inaccurate subtraction of secondary electron emission from the experimental data.

Effect of atomic cores on electron tunneling through layers of neutral adsorbates

Abstract A systematic theory to account for the effect of the atomic cores on an electron, tunneling through layers of neutral adsorbates is developed for the one dimensional case. The theory utilizes in particular the final stage interaction formalism of the T scattering matrix. The theory will be particularly useful when the atomic core effect can be treated as a perturbation. The theory gives explicit formulas for the transmission coefficient when the atomic Pseudopotentials are replaced by δ-functions. An approximate calculation, in relation to field emission from tungsten covered with a few layers of inert gas atoms, suggests that in the limit of a weak attractive Pseudopotential the effect of atomic core scattering is equivalent to a reduction in the effective work function by an amount which is of the order of magnitude observed experimentally.

Theory of thermionic emission

Abstract A comprehensive theory of thermionic emission from clean metal surfaces is presented. The theory takes into account the energy band structure of the metal, inelastic scattering due to electron-electron collisions and the thermal vibration of the atoms. We applied the theory to thermionic emission from Cu(100). We calculated the thermally emitted current from this plane as a function of applied field. We find an almost periodic deviation from the Schottky line, similar in nature with that which is observed in emission from polycrystalline emitters [1]. We believe that accurate measurements of the amplitude and phase of these deviations from the Schottky line can, when analysed in the manner described here, provide valuable information on the surface optical potential. We have also calculated the total energy distribution of the emitted electrons for a typical value of the applied field. The dependence of the above measurable quantities on the parameters which enter the theory is analysed and demonstrated by explicit numerical calculations.

Theoretical analysis of the structure in the current versus reciprocal field curves in photofield emission

Abstract We present a semiquantitative analysis of the structure observed in the logarithm of the current versus reciprocal field curves in photofield emission. It is assumed that only a set of selected, through k-conservation, final states contribute to the photocurrent. As the top of the barrier decreases, with increasing field, electron transmission into vacuum from a final state changes from tunnelling to free transmission as the top of the barrier passes the energy of the final state. The observed knees are manifestations of such transitions. The knee in the log i versus 1 F curve occurs in the vicinity of that value of the field for which the barrier maximum equals the final state energy, but the two are not exactly equal.