On the Concepts of Resistance and Capacitance in Semiconductor Nanostructures
Macucci, Massimo
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https://hdl.handle.net/2142/72016
Description
Title
On the Concepts of Resistance and Capacitance in Semiconductor Nanostructures
Author(s)
Macucci, Massimo
Issue Date
1993
Doctoral Committee Chair(s)
Ravaioli, Umberto
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Physics, Electricity and Magnetism
Physics, Condensed Matter
Abstract
In this thesis, the significance and the range of applicability of the classical concepts of capacitance and resistance to semiconductor nanostructures are investigated. In particular, the combination law for the conductances of two parallel mesoscopic constrictions is discussed, reaching the conclusion that, as long as the bifurcation into parallel constrictions takes place at interfaces not allowing significant interconstriction coupling, conductances add, in the same way as do for macroscopic resistors connected in parallel. Criteria for the design of systems of parallel constrictions for which the addition law breaks down have been found, with the observation that the insertion of a scatterer outside the region with parallel constrictions causes communication between them. The parallel constriction system is investigated from the point of view of shot noise, finding, once again, a behavior analogous to the one of macroscopic devices connected in parallel.
A modified recursive Green's function method for the computation of conductance among the various terminals of a quantum waveguide coupler has been developed, which allows a fast, quasi-3-D simulation of such structures. The device under investigation, containing two quantum wires between which tunneling is possible for a certain length, has been subdivided into transverse slices and a self-consistent solution of the Schrodinger and Poisson equations has been obtained for each slice. The transmission coefficients and, therefore, the conductance, have been computed by connecting the solutions for the various slices by means of the new recursive Green's function procedure. The results show a behavior similar to the one of optical waveguide couplers.
Finally, the validity of the classical concept of differential capacitance has been investigated for quantum dots. A model two-dimensional quantum dot with electron confinement obtained with a quasi-parabolic potential has been studied, solving the Schrodinger equation self-consistently. Large dots (with a size greater than 160 nm) are characterized by a substantially constant capacitance, while smaller ones exhibit a largely fluctuating capacitance as a consequence of quantum effects, which, for shrinking size, become prevalent with respect to the electrostatic interaction.
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