A theory of vacuum tunneling microscopy
Abstract
A theory of scanning electron microscope, recently developed by Binning et al., is presented. The theory follows Tersoff and Hamann in applying the transfer hamiltonian formalism to vacuum tunneling between a sample consisting of an infinitely extended single crystal plane and a field emission tip. A general expression for the tunneling current for any two electrodes of arbitrary shape is derived and discussed. Reasoning by analogy with field ion microscopy it is argued that the operation of the device depends on the strong enhancement of local electric fields due to microscopic imperfections of the topmost atomic layers of the central facet, such as small atomic clusters and kink sites. These local fields and the equally important multiple image potential lead to a strong dependence of the tunneling barrier on the polar angle. Accounting for this effect, which was not considered by Tersoff and Hamann, complicates the analysis significantly. The tunneling current is expressed as a convolution type integral involving the spectral densities of the samples and of the tip. It is argued that this integral can be interpreted in terms of an instrument function depending only on the tip or probe parameters, which is convoluted with a function depending only on characteristics of the sample. Simple limiting cases of the theory are considered. A discussion of the resolution predicted by the theory is presented.
- Publication:
-
Physics Letters A
- Pub Date:
- November 1983
- DOI:
- 10.1016/0375-9601(83)90969-6
- Bibcode:
- 1983PhLA...99..167F
- Keywords:
-
- Crystal Surfaces;
- Electrical Resistance;
- Electrodes;
- Electron Microscopy;
- Electron Tunneling;
- Atomic Structure;
- Carrier Density (Solid State);
- Convolution Integrals;
- Crystal Defects;
- Current Density;
- Hamiltonian Functions;
- Scanning Tunneling Microscopy;
- Solid-State Physics