Research Projects
Dr Martin Paul Vaughan
available from http://www.physics.ucc.ie/mvaughan/pdf/Research_Projects.pdf
Research Background
Research Background
Transport theory
Scattering in highly mismatched alloys
Density functional calculations
First principles approach to alloy scattering
Proposed projects
Proposed projects
Develop DFT calculations of carbon in SiGe
Investigation of structural stability of graphenelike 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
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 alloys
Green’s function approach to understanding
band structure and scattering in dilute nitrides
Density of states [2-4, 7-9]
Scattering [1-4]
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
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]
Currently working on p-type
mobility for C in SiGe alloys.
n-type mobility Si(1-x)C(x) [10]
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.
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
http://www.abinit.org/
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
http://www.abinit.org/
Investigation of novel graphene-like materials
Calculated ground state densities
graphene
silicene
germanene
BN
AlN
GaN
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 p-bonds etc.
Epitaxial substrates etc.
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
http://www.abinit.org/
Transport in true 2D
Pseudo-2D structures: e.g. the
quantum well
Quantised energy levels due to
confinement
Often approached using Quantum
Transport for low carrier densities
and Semi-classical Transport for
high densities.
Step-like density of states
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.
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 crossover
Consideration 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 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;
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(1y)/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)