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The Calculation of the Switching of Molecular Quantum Dot Cellular Automata for Mixed Valence Molecules


Project Description

The field of Nanoelectronics is concerned with the materials, devices, circuits and systems relevant to contemporary integrated circuits (ICs). Modern ICs which are the ‘electronic brain’ and memory, inside mobile phones, laptop and desktop PCs are comprised of billions of Field Effect Transistors (FETs). The gate length of such an FET ~ 10 nm, constituting an in service nano-device. The gate is the terminal that controls the current flow through the channel from the source to the drain, thus the FET acts as a switch. At this length scale, where a FET consists of few hundred atoms, quantum mechanics must be applied to decipher the operating principles and the engineer must draw upon the expertise from Condensed Matter Physics. In this project, the revolutionary Quantum Dot Cellular Automata (QDCA) devices and circuits, a brand new paradigm for computer architecture, are examined via computer simulation. QDCA are transistorless and the charge configuration of quantum dots encodes binary information.

The Quantum Dot Cellular Automata (QDCA) paradigm for nano-computing, put forward by the Notre Dame [https://www3.nd.edu/~lent] group, manages to achieve the minimal heat dissipation and the ultimate in coding one bit, in the charge configuration state of a mixed valence molecule. The elementary device for a QDCA system is a molecular six dot cell {Enrique P. Blair et al. 2010, 2016}. There are four ‘active’ dots forming a square in the ‘upper’ plane and two ‘null’ dots located in the ‘lower’ plane. Two mobile electrons occupy these dots and due to the Coulombic electrostatics repulsion they will tend to sit in the antipodal sites. These two states of the cell with electrons occupying the sites at diagonal opposite corners encode ‘0’ and ‘1’ binary states {Enrique P. Blair et al. 2010, 2016}. For a single cell in the absence of neighbouring molecules, these two states are degenerate. The electrons can transfer between dots located in a molecule via quantum mechanical tunnelling. The basic interaction for QDCA circuits is the cell – cell coupling via the Coulombic force.

As molecules are too small to be contacted directly, the QDCA nano-computing is controlled by using clocking wires buried inside the substrate with the molecules placed at the surface {Enrique P. Blair et al. 2010, 2016}. In the null state the clock potential beneath the molecule pulls the electrons into the lower plane. In the active state, the clock potential beneath the molecule pushes the electrons out of the lower plane. The computational state is then determined by the geometry of the cellular array. A multiphase clock signal applied to the wires can then sweep bit packets through the system.

The present project is to calculate the switching response for a pair of cells composed of a mixed valence Diferrocenylacetylene (DFA) molecules. The physical system consists of the external driver molecular and the test molecule (electronic system) being driven {Enrique P. Blair et al. 2016}. However, the test molecule can vibrate (vibronic modes) so this aspect must be included. The vibration system can exchange energy with the thermal environment. The density matrix for this system, whose time evolution is given by a Lindblad equation, employing the Markovian approximation, will be solved, giving a treatment of the molecular switching including dissipation {Enrique P. Blair et al. 2016}. The MATLAB Quantum Optics Toolbox will be used to solve for the density matrix as it has advanced features (representation of tensor operators and superoperators) designed for this purpose {Sze M Tan 1999}. The extensions to the density matrix formalism for the non-Markovian case will also be tackled for the molecular switching problem {H. P. Breuer and F. Petruccione (2010)}.

Qualifications:

The successful candidate should have (or expect to achieve) a minimum of a UK Upper Second Class Honours Undergraduate Degree in BSc Physics or BEng Electrical & Electronic Engineering or BSc Applied Mathematics with a strong interest in applied quantum mechanics, theory and computer simulation.

Application Procedure:

Initially interested candidates are encouraged to make an informal enquiry to the Principal Supervisor Dr Gerard Edwards () including a copy of a curriculum vitae and a covering letter, indicating your interest in this project.

Contact Details:

Dr Gerard Edwards
Tel. +44 1244 512314
Email -

Supervisory Team

Principal Supervisor (Director of Studies): Dr G. Edwards, Department of Electronic & Electrical Engineering
Second Supervisor: Dr G. Spink, Department of Chemical Engineering


Funding Notes

There is no funding attached to this project. It is for self - funding students only.

References

Enrique P. Blair, Steven A. Corcelli, and Craig S. Lent, ‘Electric field driven electron transfer in mixed valence molecules’, J. of Chemical Physics 145, (2016), 014307
Enrique P. Blair, Eric Yost, and Craig S. Lent, ‘Power dissipation in clocking wires for clocked molecular quantum-dot cellular automata’, J. Computational Electronics 9, (2010), 49
Sze M Tan, ‘A computational toolbox for quantum and atomic optics’, J. Opt. B: Quantum Semiclass. Opt. 1, (1999), 424
H. P. Breuer and F. Petruccione, ‘The Theory of Open Quantum Systems’, Oxford Uuniversity Press, 2010



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