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Research Projects Dr Martin Paul Vaughan available from available from

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Research Background Transport theory Scattering in highly mismatched alloys Density functional calculations First principles approach to alloy scattering

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Proposed projects Develop DFT calculations of carbon in SiGe Investigation of structural stability of graphene- like materials Develop code / theory for true 2D transport Solution of the Boltzmann Transport Equation Development of Monte Carlo code (possible collaboration with University of Bristol)

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Research Background

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Transport theory Solutions of the Boltzmann Transport Equation Development of the ‘ladder’ method for polar optical phonon scattering (non-parabolic 3D & 2D) [1-4]

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Transport theory High field effects Hot phonon effects in semiconductors [5] Hot electron transport [6]

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Highly mismatched alloys Green’s function approach to understanding band structure and scattering in dilute nitrides Scattering [1-4] Density of states [2-4, 7-9]

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Density Functional Theory (DFT) Overview: First Principles method for dealing with intractable many-body problem Observables of the lowest energy state – the ground state are obtained via functionals For example: an integral is a functional of the integrand that yields a scalar value In DFT, we deal with functionals of the ground state density.

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Density Functional Theory (DFT) We use the DFT code ABINIT (others available) Examples: band structure of Si and Ge These use the local density approximation (LDA)

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First Principles approach to alloy scattering n-type scattering due to C in Si [10] n-type mobility Si(1-x)C(x) [10] Currently working on p-type mobility for C in SiGe alloys.

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Proposed projects

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DFT calculations of C in SiGe C in Ge: possible hybridization of conduction and valence bands. Possible localised state forming in valence band.

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DFT calculations of C in SiGe Is hybridisation real? Is a localised state forming? Problems with convergence for C in Ge? Investigations (beyond LDA): Relaxed ground state calculations already performed. Based on these, we can investigate Scissor operator GGA calculations GW calculations

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DFT calculations of C in SiGe Student training by supervisor: General introduction to DFT Exchange-correlation functions Pseudopotentials Working in a UNIX environment Basic calculations with ABINIT (or other DFT code) Use of supercells Guidance through existing ABINIT input files / post-processing code for C in SiGe

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Investigation of novel graphene-like materials graphenesilicenegermanene BNAlNGaN Calculated ground state densities

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Investigation of novel graphene-like materials Investigation of structural stability Buckling of structure Formation energies Tensile properties (Young’s modulus, Poisson ratio) Chemical / molecular structures Monatomic / bi-atomic layers etc. Hydrogen on -bonds etc. Epitaxial substrates etc.

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Investigation of novel graphene-like materials Student training by supervisor: General introduction to DFT Exchange-correlation functions Pseudopotentials Background for graphene-like materials Working in a UNIX environment Basic calculations with ABINIT (or other DFT code) Use of 2D supercells Existing ABINIT input files

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Transport in true 2D Pseudo-2D structures: e.g. the quantum well Quantised energy levels due to confinement Step-like density of states Often approached using Quantum Transport for low carrier densities and Semi-classical Transport for high densities.

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Transport in true 2D Semi-classical model for phonon scattering developed for 2D [3-4] Still needs to be generalised for a magnetic field Quantum wells and lines etc. are pseudo-2D in that they still have thicknesses of many atomic layers Graphene-like materials may be considered as being true 2D – no quantized levels due to confinement.

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Transport in true 2D Development of code for true and pseudo 2D transport Incorporation of magnetic field into semi-classical pseudo 2D model Investigation of quantum / semi-classical cross- over Consideration of methodology for semi-classical approach (heavily assisted): Direct solution of Boltzmann’s Transport Equation (BTE) Monte Carlo simulation

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Transport in true 2D Student training by supervisor: General introduction to transport theory Programming in C++/Matlab Working from existing C++ code (supervisor’s) for direct solution of BTE Possible collaboration with Bristol University working on existing MatLab code for Monte Carlo simulation (may involve visit to meet author of code)

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Projects Summary DFT calculations of carbon in SiGe * Investigation of graphene-like materials * True 2D transport Boltzmann Transport Equation (BTE) Monte Carlo (MC) code † * Tyndall; † Possible collaboration with Uni. Bristol;

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References [1] M.P. Vaughan and B. K. Ridley, Solution of the Boltzmann equation for calculating the Hall mobility in bulk GaNxAs1-x, Phys. Rev. B 72, (2005) [2] M.P. Vaughan and B.K. Ridley, Electron-nitrogen scattering in dilute nitrides, Phys. Rev. B 75, (2007) [3] M.P. Vaughan and B. K. Ridley, The Hall Mobility in Dilute Nitrides, Dilute III-V Nitride Semiconductors and Material Systems, Physics and Technology, Ed. A. Erol, Springer Berlin Heidelberg (2008) [4] M.P Vaughan, Alloy and Phonon Scattering: Development of Theoretical Models for Dilute Nitrides, VDM Verlag Dr. Müller (2009) ISBN: [5] Y. Sun, M.P. Vaughan et al., Inhibition of negative differential resistance in modulation doped n-type Ga(x)In(1-x)N(y)As(1- y)/GaAs quantum wells, Phys Rev B 75, (2007) [6] M.P. Vaughan, Hot Electron Transport, Semiconductor Modeling Techniques, Springer Series in Materials Science 159, Springer Berlin Heidelberg (2012) [7] M.P. Vaughan and B. K. Ridley, Effect of non-parabolicity on the density of states for high-field mobility calculations in dilute nitrides, Phys. Stat. Sol. (c) 4, 686 (2007) [8] L Ivanova, H Eisele, MP Vaughan, P Ebert, A Lenz, R Timm, O Schumann, et al, Direct measurement and analysis of the conduction band density of states in diluted GaAs(1- x)N(x) alloys, Phys Rev B 82, (2010) [9] MP Vaughan, S Fahy, EP O'Reilly, L Ivanova, H Eisele and M Dähne, Modelling and direct measurement of the density of states in GaAsN, Phys. Stat. Sol. (b) 248, 1167 (2011) [10] M.P. Vaughan, F. Murphy-Armando and S. Fahy, First-principles investigation of the alloy scattering potential in dilute Si(1-x)C(x), Phys. Rev. B 85, (2012)

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