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Calculation of profile of charge carrier concentration in modulation doped structure with a wide potential well
Author(s) -
Shchurova L.Yu.
Publication year - 2009
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200910399
Subject(s) - electron , physics , quantum well , doping , electron density , charge density , quantum , condensed matter physics , modulation (music) , charge carrier , quantum mechanics , atomic physics , laser , acoustics
We investigate the equilibrium state of interacting electron system with Fermi statistics in modulation doped structure with a wide quantum well. The model is formulated for the carrier system with a sufficiently high density, such that the de Broglie wavelength of electrons is smaller than the width of the quantum well. Due to a significant interaction of electrons with electric field of the doped layer, a state with strongly‐inhomogeneous density of electrons is formed. Within the hydrodynamic approach, we set up formalism for calculating the electron density across the width of the potential well. We have obtained the exact solution of the equations, which is expressed in terms of hypergeometric functions. Based on the deduced formulas, we performed numerical computations for the profile of carriers' concentrations in a potential well in the modulation doped Si/SiGe/Si structures.