Hot-electron transport through thin dielectric films: Boltzmann theory and electron spectroscopy

J. Bernasconi, E. Cartier, and P. Pfluger
Phys. Rev. B 38, 12567 – Published 15 December 1988
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Abstract

The transport problem of hot quasifree electrons through thin planar dielectric films of thickness d is considered by solving the steady-state Boltzmann equation for the electron current density J(E,μ,x), 0≤x≤d, within the film. The current density of injected electrons at x=0, J(i)(E,μ), evolves to J(E,μ,d), the current density of electrons escaping the layer at x=d, which is calculated.

In our approach, electron transport is assumed to be controlled simultaneously by energy-dependent elastic and inelastic scattering with scattering rates γel(E) and γinel(E), respectively. For inelastic scattering, one single inelastic scattering process with energy loss ΔE is assumed. With this assumption, the Boltzmann equation transforms into a set of coupled integro-differential equations which describe the cascading down of hot electrons in discrete energy steps ΔE during solid-state transport. The resulting cascade problem is then solved analytically in the two-flux approximation. The transport of zero-energy-loss electrons in the topmost energy interval ΔE at the maximum energy E0 is considered separately. In this interval, no in-scattering from higher energies occurs and the Boltzmann equation for J(E0,μ,x) becomes energy decoupled. An exact formal solution of the zero-energy-loss transport problem is presented and exact and approximate results for the two limiting cases of pure elastic and pure inelastic scattering are compared. Our theoretical results are then applied to typical electron transmission experiments such as internal photoemission for transport analysis (IPTA), low-energy electron transmission (LEET), and x-ray photoelectron spectroscopy (XPS) in the substrate-overlayer configuration.

It is shown that energy-dependent elastic and inelastic scattering rates in wide-band-gap insulators can be extracted from IPTA and LEET experiments with our theoretical analysis. Using these results, the experimentally determined J(E,μ,d) can be reconstructed. Our analysis also allows for a rigorous definition of XPS escape lengths in terms of scattering rates.

  • Received 22 August 1988

DOI:https://doi.org/10.1103/PhysRevB.38.12567

©1988 American Physical Society

Authors & Affiliations

J. Bernasconi, E. Cartier, and P. Pfluger

  • Asea Brown Boveri Corporate Research, CH-5405 Baden-Dättwil, Switzerland

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Issue

Vol. 38, Iss. 17 — 15 December 1988

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