Elsevier

Microelectronics Journal

Volume 36, Issue 10, October 2005, Pages 870-875
Microelectronics Journal

Quasiregular heterostructures: An overview of the current situation

https://doi.org/10.1016/j.mejo.2005.05.004Get rights and content

Abstract

Mathematical research on quasiregular sequences has provided a sound foundation for the analysis of their formal properties. However, physical research on heterostructures following these sequences appears to largely ignore this formal basis. The topology of the spectra is seldom studied in a sufficiently complete way and claims of self-similarity usually lack precision and rigour. In a critical overview of the current situation, limitations are pointed out and directions for further progress are suggested. The discussion focuses on the possible prospects, so far comparatively scarce, for device design. Theoretical research, which mostly dominates the scene, appears to have scarcely stimulated experimental work.

Section snippets

Quasiregular sequences and quasiregular heterostructures

Take a regular Cantor set and define it as a spectrum of points on the real axis. Then, such spectrum is (i) singular continuous, with fractal dimension and (ii) selfsimilar. A zoom magnification of any fraction of it reproduces the entire spectrum. Repeated magnifications with the same scale factor yield the same result and this holds equally for all fragments that we choose.

There are, on the other hand, abundant mathematical studies of different quasiregular sequences [1], [2], [3], [4], [5],

Further comments and open questions

A number of mathematical studies have been building up, which provide a basis for a formal analysis of the properties of quasiregular sequences. Yet, research on the physical properties of quasiregular heterostructures has been developed, more or less alongside, which appears to have largely ignored the former. Scaling theory, combined with a careful study of the topology of the spectra, provides an inroad into the morphological aspects. It is clear that the simple concept of selfsimilarity

Acknowledgements

This work has greatly benefitted from contacts and collaborations with R. Pérez-Álvarez, V.R. Velasco, H. Rodríguez-Coppola and C. Trallero-Giner. I also acknowledge gratefully the most efficient help of Pilar Jiménez in the preparation of this article.

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