TITLE:
Novel Understanding of Electron States Architecture and Its Dimensionality in Semiconductors
AUTHORS:
Xiaomin Ren
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
JOURNAL NAME:
Optics and Photonics Journal,
Vol.3 No.2B,
July
23,
2013
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.