Evolution of Real-Number Dimensional Electron-States Architectures in Semiconductor Heterostructures: Theoretical Model Modification

• 1、State Key Laboratory of Information Photonics and Optical Communications at Beijing University of Posts and Telecommunications, Beijing 100876
• 2、Zh. I. Alferov Russian-Chinese Joint Laboratory of Information Optoelectronics and Nanoheterostructures, Beijing 100876
• 3、BUPT-HTGD Joint Laboratory of Quantum Optoelectronics and Bivergentum Theory, Beijing 100876

Abstract：This work has been dedicated to the modification of the theoretical model of real-number dimensional electron-states architectures (ESA) previously proposed on the basis of the concept of energy level divergence. The similarity functions in description of the ESA evolution in a well-type heterostructure are re-defined in terms of a newly conceived higher-dimensional-side adjoint function of the essentially-true density-of-states function. According to this definition, the two similarity functions denoting the evolutions towards the 2- and 3-dimensionality extremities, respectively, for the well-type GaAs-system heterostructures at the temperature of 2K are simulated and the expected elegant curves have been presented. And, consequentially, the value of the width of energy level divergence has been determined. Finally, corresponding to arbitrary values of the well-thickness of the above-mentioned structure, the ESA dimensionality values continuously variable within the real-number domain of [2,3] are well specified and thus the completeness of the fundamental mathematical framework of the theoretical model is achieved.

Keywords： energy level divergence theory of real-number dimensional electron-states-architectures higher-dimensional-side adjoint function similarity function in description of electron-states architecture evolution width of energy level divergence