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.
Highlights
The 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)
Expected should be the possible inventions of some novel electronic and optoelectronic devices. 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
Both the classical and the nano- heterostructures of semiconductors have developed dramatically based on the well-recognized theories, especially the theory on the density of states (DOS) of electrons in a semiconductor material and the relevant electron-states-architecture (ESA) dimensionality [1]
Summary
Both the classical and the nano- heterostructures of semiconductors have developed dramatically based on the well-recognized theories, especially the theory on the density of states (DOS) of electrons in a semiconductor (or generally crystalline) material and the relevant electron-states-architecture (ESA) dimensionality [1]. Some problems exist in the previous theory and it had been suspected that some fundamental theoretical changes would be needed for the improvement. Both unusual assumptions of the energy-level dispersion (ELD) [2,3] and the spatial extension shrinkage (SES) have been proposed and it is shown that they have acted quite well for the improvement. In proceeding with this investigation, the quantum mechanical picture and the relevant fundamental theories have really been changed
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