Physics of Atomic-Scale Wires: Technical Description |
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Introduction The aim of this project is to develop the ability, using first principles electronic structure techniques, to model conduction processes in atomic-scale and molecular wires on semiconductor surfaces, and to understand the formation and conduction properties of these systems. To this end, the ability to model open systems (i.e. systems with a current flowing through them) will be developed within first principles and semi-empirical electronic structure techniques, working primarily with the existing, powerful code CONQUEST. The development of microelectronics has been characterised by a continuing drive towards increased miniaturisation (as exemplified by the biannual Semiconductor Industry Association Technology Roadmap). However, clear, physics-based limits to the size of microelectronic components (especially transistors) are rapidly approaching, including: gate oxide thickness, which is shrinking to the point where variations on the atomic scale will be disastrous; lithography costs, which for the feature sizes required is becoming prohibitively expensive; and even the roughness in etch masks due to polymer size, which will have damaging effects. Nanotechnology, and in particular nanoelectronics (using atomic-scale and molecular wires and devices), is being rapidly pursued as an alternative to further miniaturisation of conventional devices. Recently, the ability to model accurately the electronic structure of many tens of thousands of atoms has been developed in linear scaling techniques (in particular, the CONQUEST density functional theory (DFT) code written by the applicant in collaboration with Professor M.Gillan at UCL (Bowler, Bush and Gillan 2000) has performed calculations on over 16,000 atoms - well beyond anything achieved before(Bowler, Miyazaki and Gillan 2001)). This opens the possibility of using accurate theoretical methods (both first principles, such as DFT, and semi-empirical, such as tight binding) to understand the structure, growth and electronic properties of nanoelectronic devices. However, since these devices will in general be connected to each other and the outside world, the ability to treat open boundary conditions (in the presence of electric currents) is required. Among the large class of systems which are emerging as interesting for nanotechnology applications are atomic-scale and molecular wires. The interest in these systems is two-fold: first, they have exciting possibilities for applications in nanoelectronics, for instance as interconnects (though they may well be more suitable for carrying a signal rather than a current) and even for certain implementations of quantum computers; second, they offer the opportunity to study quantised conduction and the effects of confinement in two dimensions on electrons. In recent years, rapid developments in experimental techniques (particularly the advent of reliable atomic-level manipulation with the scanning tunneling microscope (STM)) have made the controlled fabrication and manipulation of such structures possible. A detailed theoretical understanding of these wires is immensely important. Theoretical Developments (Methodology) The theoretical developments will be based on the existing CONQUEST code; this is an efficiently parallelised linear scaling DFT code. Linear scaling methods (where the computer effort scales linearly with the number of atoms in the system, rather than with the cube of the number of atoms, as is true for standard methods) typically solve for the density matrix of a system, enforcing a spatial cutoff; CONQUEST represents the density matrix in terms of localised, atomic-like orbitals, whose form is varied to achieve the ground state with accuracy comparable to traditional methods. This also enables it to be used as an ab initio tight binding code as well as a full ab initio code (by fixing the form of the localised orbitals). This basis, coupled with its efficiency and power, make it an ideal starting point for the work in this proposal. A necessary first step towards being able to model open systems is to develop CONQUEST as an embedding code. At present, it would be simple to embed a region of full DFT into a matrix of ab initio tight binding; the first part of the work will further develop this capability so that a specific region of interest can be embedded into an infinite system. This will, among other benefits, remove the need for periodic boundary conditions when studying isolated, non-periodic features. This development will take place over the first year of the project, starting first with a semi-empirical tight binding code which parallels the tight binding part of CONQUEST. The main part of the methodological development will focus on open systems. Typically, a system of interest is placed between two electrodes held at different Fermi energies, leading to a current density. Left and right propagating wavefunctions or Green's functions are then found, with the different Fermi energies giving different populations of the different states. The initial work will take place using CONQUEST as an ab initio tight binding code for simplicity. Using the embedding formalism described above, the ideas of Todorov et al.(2000) will be implemented. Solving for the density matrix of the system will be perfectly possible, either directly or via the Green's function; it will need, however, to become a complex quantity (due to the open boundaries); this will yield a current density. A good check on the low bias solutions will be to perform a scattering calculation on the zero-bias, self-consistent potential; the density matrix for the zero-bias problem will also yield an excellent initial value for the low-bias problem. These developments will take place over the second (ab initio tight binding) and third (full DFT) years of the project. It will also be necessary to develop the ability to represent the localised orbitals by atomic-like orbitals as well as the present representation (which is a flexible basis set of B-splines). This will make modelling of first-row elements and first-row transition elements significantly easier. A further development which may be necessary is the implementation of ultrasoft pseudopotentials; both of these are well understood, and should not present a significant problem. While this is a challenging and far-reaching series of developments, it is clear how to implement and test them in a gradual manner. The benefits of being able to model conduction processes in nanostructures with open boundaries are also extremely exciting. Atomic-scale and Molecular Wires Various systems have been identified as being interesting for study, and being under intensive investigation by the applicant's collaborators. Naturally, should new systems of interest be discovered (either experimentally or theoretically), the focus of the investigation will shift towards these. The two types of wire to be studied (atomic-scale and molecular) are different both in terms of formation and properties: atomic-scale wires are inorganic, and are created using atomic scale manipulation (with and STM) or via self-assembly during semiconductor growth; molecular wires are organic, and are synthesised using standard methods and deposited or arranged either at random, or via atomic scale manipulation. For both of these types of wire, I will study structure at zero bias, and the response to the injection of charge carriers at zero bias, as well as the likely coupling between these carriers and the lattice (electron-phonon coupling). As the open boundary conditions become implemented, I will move to studying conduction processes at non-zero biases, initially with ab initio tight binding, and later with full DFT. The systems identified for study as atomic-scale wires include the ``dangling bond'' wire (where I have already studied the effect of injecting charge(Bowler and Fisher 2001)) on Si(001), and bismuth nanolines on Si(001) (where I have studied the structure(Bowler 2000)). Work on these systems will start in the first year, and, using different theoretical developments, extend over the first four years. The systems for study as molecular wires will require several of the theoretical developments (such as the new localised orbital representation) before work can begin. After an initial study on alkyl and benzyl thiols (which is intended partly as a validation exercise), the properties of cyclo-dextrin inclusion complexes (a polymer inside a molecular tube formed circumferentially from between six and eight glucose molecules) will begin in the fourth year. Conducting polymers such as polyaniline will be of most interest. The final (and in many ways most ambitious) part will be a study of conduction mechanisms in protein molecules, with care being paid to electron-phonon coupling and possible solitons, with the aim of discovering how a protein can sustain a large current density. References
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