Interpretation of Holographic Contour Maps of Reverse Biased p-n Junctions

Abstract

. 2014 Reverse-biased p-n junctions have been observed by means of electron holography using a transmission electron microscope equipped with an electron biprism and a field emission gun. Aim of this work is to present and discuss an analytical model for the electric field associated to a periodic array of alternating p and n stripes lying in a half-plane which simulates the experimental setup and allows the interpretation of the main features of the observed holograms and the quantitative evaluation of the effect of the fringing field on the holograms and on the reconstructed images. Microsc. Microanal. Microstruct. 6 (1995) Classification Physics Abstracts

A bridge between two important problems in optics and electrostatics

“…It has been shown how a simple initial guess can lead, through a series of elementary but clever calculations, to the solution of two important problems in optics and electrostatics. As the electrostatic problem was raised in the attempt to interpret holographic and phase contrast images obtained in a transmission electron microscope [2,5], the arguments developed in this paper can find their collocation as an advanced topic in lectures on electron optics (where the students can also profitably be exposed to the exact solution of the diffraction problem, in addition to the standard Kirchhoff-Fresnel theory [1]) and on light optics and holography, if the teacher wants to show how the basic ideas are developed in the companion field of electron optics [8].…”

“…finding the electrostatic potential V (x, y, z) produced by a parallel array of stripes having width b (and pitch in the y direction b/cos α el ) which lie in the half-plane z = 0; x 0, tilted at an angle α el with respect to the edge normal (−π/2 < α el < π/2) [5]. For α el = 0 we re-obtain the case of junctions perpendicular to the edge [2].…”

“…This state of affairs happens for the following two problems, the first being the diffraction of a plane wave at a perfectly conducting thin half-plane [1] and the second the electrostatic field around a periodic array of reverse biased p-n junctions, still lying in a thin half-plane [2].…”

“…It should be noted that the solution given by Sommerfeld of the diffraction problem, although a milestone in theoretical physics and still one of the few exact solutions in this field, is not very simple, as it requires the mastering of complex integration methods and the clever use of multivalued functions [1]. Likewise, the solution of the electrostatic problem, for the case of junctions perpendicular to the edge of the half-plane, can also be found by some not very intuitive mathematics [2]. Nonetheless, both problems can be solved in a very simple and didactically interesting way, relying on an approach found by Gori [3,4] who constructed the complete solution of the Sommerfeld problem starting from a simple particular solution used as a building block.…”

Interpretation of Holographic and Lorentz Images of an Array of Reverse Biased P-N Junctions in a Semi-Infinite Specimen

“…In this work we consider, in particular, the theoretical and interpretative aspects, as we have improved a model for the electric field associated to a periodic array of alternating p and n stripes lying in a half plane 4 (physically corresponding to an array of zero-width step junctions) by taking into account that the junctions are tilted with respect to the specimen edge. This model satisfactorily represents the finiteness of a real specimen.…”