Research Projects

1. Research Projects Dr Martin Paul Vaughan available from http://www.physics.ucc.ie/mvaughan/pdf/Research_Projects.pdf

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

3. 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)

4. Research Background

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

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

7. 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]

8. 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

9. 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/

10. 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]

11. Proposed projects

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

13. 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/

14. 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/

15. Investigation of novel graphene-like materials Calculated ground state densities graphene silicene germanene BN AlN GaN

16. 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.

17. 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/

18. 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

19. 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.

20. 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

21. 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)

22. 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;

23. 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)