research projects dr martin paul vaughan available from available from
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Research ProjectsResearch Projects
Dr Martin Paul VaughanDr Martin Paul Vaughan
available from available from http://www.physics.ucc.ie/mvaughan/pdf/Research_Projects.pdf
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Research Background
Research BackgroundTransport theoryScattering in highly mismatched alloysDensity functional calculationsFirst principles approach to alloy scattering
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Proposed projects
Proposed projectsDevelop DFT calculations of carbon in SiGeInvestigation of structural stability of graphene-like materialsDevelop code / theory for true 2D transport
Solution of the Boltzmann Transport EquationDevelopment of Monte Carlo code (possible collaboration with University of Bristol)
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Research BackgroundResearch 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 alloysGreen’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 problemObservables 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.
http://en.wikipedia.org/wiki/Density_functional_theory
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Density Functional Theory (DFT)
We use the DFT code ABINIT (others available)Examples: band structure of Si and GeThese use the local density approximation (LDA)
http://www.abinit.org/
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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 projectsProposed 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 operatorGGA calculationsGW calculations
http://www.abinit.org/
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DFT calculations of C in SiGe
Student training by supervisor:General introduction to DFT
Exchange-correlation functionsPseudopotentials
Working in a UNIX environmentBasic calculations with ABINIT (or other DFT code)Use of supercellsGuidance through existing ABINIT input files / post-processing code for C in SiGe
http://www.abinit.org/
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Investigation of novel graphene-like materials
graphene silicene germanene
BN AlN GaN
Calculated ground state densities
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Investigation of novel graphene-like materials
Investigation of structural stabilityBuckling of structureFormation energiesTensile properties (Young’s modulus, Poisson ratio)
Chemical / molecular structuresMonatomic / 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 functionsPseudopotentials
Background for graphene-like materialsWorking in a UNIX environmentBasic calculations with ABINIT (or other DFT code)Use of 2D supercellsExisting ABINIT input files
http://www.abinit.org/
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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 layersGraphene-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 modelInvestigation of quantum / semi-classical cross-overConsideration 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 theoryProgramming in C++/MatlabWorking from existing C++ code (supervisor’s) for direct solution of BTEPossible 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 transportBoltzmann 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, 075211 (2005)
[2] M.P. Vaughan and B.K. Ridley, Electron-nitrogen scattering in dilute nitrides, Phys. Rev. B 75, 195205 (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: 978-3639130867
[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, 205316 (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, 161201 (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, 165209 (2012)