Title: "Model for Electric Potential for Gate Electrodes in a Quantum Bus"

Authors:

family-names: Koprucki

given-names: Thomas
orcid: https://orcid.org/0000-0001-6235-9412

family-names: Shehu

given-names: Aurela
orcid: https://orcid.org/0000-0002-1994-0612

Date-Released: 2024-04-05
Version: 1.0.0

Mathematical Model MM1: Electron Shuttling Model

Description: The gate electrodes form an electric potential landscape that generates an array of QDs in the QW. Suitable pulsing allows to propagate the QDs along the channel and thus enables conveyor-mode shuttling. As the device is operated at deep cryogenic temperature (50 mK), there exist no thermally activated electrons in the conduction band and space charge regions can be safely neglected. In this case, the electric potential $Φ (r, t)$ obeys the homogeneous Poisson equation.

Properties: Is Deterministic, Is Space-Continous, Is Time-Continous, Is Linear

Computational Task CT1: Calculation of the electric potential

Description:
For a given set of gate voltages entering the boundary condition F3, solve the Poisson equation F1 with the material law F2 together with the boundary conditions F3 and F4. The device structure enters the material law F2 by the spatial profile of the relative permittivity $ε (r)$ .
Formulations: F1, F2, F3, F4
Input: $U_{k}^{t o t}$ , k = 1:6, F2
Output: $Φ$

Relations between Mathematical Formulations and Computational Tasks:
F2 Contained As Assumption In CT1.
F3 Contained As Boundary Condition In CT1.
F4 Contained As Boundary Condition In CT1.

Publication

P1: WIAS-Preprint 3082

DOI: 10.20347/WIAS.PREPRINT.3082

Relations between Mathematical Model and Publication:

MM1 Used In P1

Relations between Computational Task and Publication:

CT1 Documented In P1

Research Field

RF1: Semiconductor Physics

WikiData: Q4483523

Research Problem

RP1: Electrostatics in a Si/SiGe quantum bus

Description: Simulation of the electrostatics in a Si/SiGe quantum bus

Mathematical Model Collection Template

Contents