Research ProjectsResearch Projects

Dr Martin Paul VaughanDr Martin Paul Vaughan

available from available from http://www.physics.ucc.ie/mvaughan/pdf/Research_Projects.pdf

Research Background

Research BackgroundTransport theoryScattering in highly mismatched alloysDensity functional calculationsFirst principles approach to alloy scattering

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)

Research BackgroundResearch Background

Transport theory

Solutions of the Boltzmann Transport Equation

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

Transport theory

High field effects

Hot phonon effects in semiconductors [5]

Hot electron transport [6]

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]

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

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/

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.

Proposed projectsProposed projects

DFT calculations of C in SiGe

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

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/

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/

Investigation of novel graphene-like materials

graphene silicene germanene

BN AlN GaN

Calculated ground state densities

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.

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/

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.

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.

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

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)

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;

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)