On the interpretation of TEM images of p-n junctions a multislice approach

Abstract

Usually electron microscopy observations of weak electrostatic fields obtained by Lorentz [l, 21 or holographic [3, 41 methods are satisfactorily interpreted by means of the phase object approximation (POA). The POA basic equation describing the interaction of the electron beam with the electrostatic field V ( T ) can be obtained by considering the potential energy e V ( r ) (the electron charge being -e) as a small perturbation with respect to the energy eE of the electron beam, so that the effect of the field on the electron wavefunction can be described by a transmission function given by where 50 and yo are the coordinates of a point P in the specimen plane, and 1 is the electron wavelength. The integral is taken along an electron optical path parallel and in the same direction as the optical axis z.A question arises as to whether the use of this very simple description for the interaction between the electron beam and the electrostatic field is justified. The answer is based on the knowledge accumulated in the interpretation of strictly related case studies.For instance, the POA has been applied to the case of an electron biprism modelled as a charged wire of radius r with axis coincident with the y axis. A careful comparison between the theoretical predictions obtained by means of a simple model equivalent to the POA and the experimental data was made by Komrska et al. [5], who found them in fairly good agreement. Since then several efforts have been made by these authors in order to justify the simple model, and hence the POA, on conceptually more satisfactory grounds. The scattering of the electron by the electrostatic field of the biprism has been investigated within the framework of the scalar diffraction theory developed by Komrska [6] for the case of weak electrostatic fields. The wavefunction in the observation plane can be expressed in this case in terms of a diffraction integral; numerical calculations ') Viale B. Pichat 6/2,

Interferometric methods for mapping static electric and magnetic fields

“…Their results led them to state that the POA is hardly tenable for the interpretation of experimental data. Experience gained in the analysis of electromagnetic lenses by means of the multislice method [16], as well as continuing interest in the observation of p-n junctions by TEM methods, for which the POA is an invaluable tool, stimulated a reconsideration of the issue [17]. The analysis of results obtained by the multislice approach indicated that the maximum difference between the POA and each of the multislice calculations never exceeds 5 × 10 −4 , i.e., all of the calculations agree to four significant figures, as found by Komrska and Vlachová [12] for the case of an electron biprism.…”