research projects - physics department ucc · research projects dr martin paul vaughan research...

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Research Projects

Dr Martin Paul Vaughan

Research Background

Research Background

Transport theory

Scattering in highly mismatched alloys

Density functional calculations

First principles approach to alloy scattering

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Proposed projects

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)

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]

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]

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.

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 Ge

These 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.

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Proposed projects

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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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



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

graphene silicene germanene

BN AlN GaN

Calculated ground state densities


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 π-bonds etc.

Epitaxial substrates etc.

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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


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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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.


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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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)

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, 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)

research projects - physics department ucc · research projects dr martin paul vaughan research...

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