Novel Understanding of Electron States Architecture and Its Dimensionality in Semiconductors

Xiaomin Ren

State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), and Zh. I. Alferov Russian-Chinese Joint Laboratory of Information Optoelectronics and Nanoheterostructures, Beijing, China.

DOI: 10.4236/opj.2013.32B075                

Abstract

Some important insights into the electron-states-architecture (ESA) and its dimensionality (from 3 to 0) in a semiconductor (or generally crystalline) material are obtained. The self-consistency of the set of density of states (DOS) expressions with different dimensionalities is remediated through the clarification and rearrangement of the wave-function boundary conditions for working out the eigenvalues in the wave vector space. The actually too roughly observed and theoretically unpredicted critical points for the dimensionality transitions referring to the integer ones are revealed upon an unusual assumption of the intrinsic energy-level dispersion (ELD). The ELD based quantitative physical model had been established on an immediate instinct at the very beginning and has been properly modified afterwards. The uncertainty regarding the relationship between the de Broglie wavelength of electrons and the dimensionality transitions, seeming somewhat mysterious before, is consequentially eliminated. The effect of the material dimensions on the ELD width is also predicted and has been included in the model. The continuous evolution of the ESA dimensionality is convincingly and comprehensively interpreted and thus the area of the fractional ESA dimensionalities is opened. Another new assumption of the spatial extension shrinkage (SES) closely related to the ELD has also been made and thus the understanding of the behavior of an electron or, in a general sense, a particle has become more comprehensive. This work would manifest itself a new basis for further development of nanoheterostructures (or low dimensional heterostructures including the quantum wells, quantum wires, quantum dots and especially the hetero-dimensional structures). Expected should also be the possible inventions of some novel electronic and optoelectronic devices. More basically, it leads to a new quantum mechanical picture, the essential modifications of Schrödinger equation and Newtonian equation that give rise to a full cosmic-scope picture, and a super-low-speed relativity assumption.

Keywords

Energy-level Dispersion; Spatial Extension Shrinkage; Electron-states-architecture; Density of States; Di-mensionality; Quantum Wells, Wires and Dots; Schrödinger Equation; Newtonian Equation; Relativity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Zh. I. Alferov, “The Double Heterostructure: Concept and Its Applications in Physics, Electronics and Technology”, Nobel Lecture, December 8, 2000.
[2]	X. M. Ren, "Theoretical Investigation on the Continuous Evolution of the Electron-Gas Dimensionality: From Bulk Materials to Quantum Dots" (postdeadline paper), 2012 Asia Communication and Photonics Conference, November 7-11, 2012.
[3]	X. M. Ren, "Modification of the Theory on the Energy-Level Dispersion and the Continuity of the Electron-Gas Dimensionality" (invited talk / plenary session; to be delivered), 21st International Symposium on Nanostructures: Physics and Technology, June 24-28, 2013