Toby Young, Ph.D. 
Recent publications
1.  Young T., Numerical analysis of N electron atomic statefunctions using local basis sets, WSEAS TRANSACTIONS on MATHEMATICS, ISSN: 11092769, Vol.16, pp.412420, 2017 Abstract: This contribution presents the numerical analysis of HartreeFock’s method of computing electron atomic statefunctions using Galerkin’s finite element method. The underlying theory and computational implementation are presented in some detail for the first time and highly accurate energies are presented for free neutral atoms, ions, and for the spatially confined He atom. The method of using local basis sets is shown to be competitive with global basis sets of the Slater and modified Slater types in terms of accuracy and use. Keywords:Atomic physics, Finite element method, Numerical analysis, Quantum confinement Affiliations:
 
2.  Davydov D.^{♦}, Young T.D., Steinmann P.^{♦}, On the adaptive finite element analysis of the Kohn–Sham equations: methods, algorithms, and implementation, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.5140, Vol.106, pp.863888, 2016 Abstract: In this paper, details of an implementation of a numerical code for computing the Kohn–Sham equations are presented and discussed. A fully selfconsistent method of solving the quantum manybody problem within the context of density functional theory using a realspace method based on finite element discretisation of realspace is considered. Various numerical issues are explored such as (i) initial mesh motion aimed at coaligning ions and vertices; (ii) a priori and a posteriori optimization of the mesh based on Kelly's error estimate; (iii) the influence of the quadrature rule and variation of the polynomial degree of interpolation in the finite element discretisation on the resulting total energy. Additionally, (iv) explicit, implicit and Gaussian approaches to treat the ionic potential are compared. A quadrupole expansion is employed to provide boundary conditions for the Poisson problem. To exemplify the soundness of our method, accurate computations are performed for hydrogen, helium, lithium, carbon, oxygen, neon, the hydrogen molecule ion and the carbonmonoxide molecule. Our methods, algorithms and implementation are shown to be stable with respect to convergence of the total energy in a parallel computational environment. Affiliations:
 
3.  Teisseyre H.^{♦}, Kaminska A.^{♦}, Birner S.^{♦}, Young T.D., Suchocki A.^{♦}, Kozanecki A.^{♦}, Influence of hydrostatic pressure on the builtin electric field in ZnO/ZnMgO quantum wells, JOURNAL OF APPLIED PHYSICS, ISSN: 00218979, DOI: 10.1063/1.4953251, Vol.119, pp.21570218, 2016 Abstract: We used high hydrostatic pressure to perform photoluminescence measurements on polar ZnO/ZnMgO quantum well structures. Our structure oriented along the cdirection (polar direction) was grown by plasmaassisted molecular beam epitaxy on aplane sapphire. Due to the intrinsic electric field, which exists in polar wurtzite structure at ambient pressure, we observed a red shift of the emission related to the quantumconfined Stark effect. In the high hydrostatic pressure experiment, we observed a strong decrease of the quantum well pressure coefficients with increased thickness of the quantum wells. Generally, a narrower quantum well gave a higher pressure coefficient, closer to the bandgap pressure coefficient of bulk material 20 meV/GPa for ZnO, while for wider quantum wells it is much lower. We observed a pressure coefficient of 19.4 meV/GPa for a 1.5 nm quantum well, while for an 8 nm quantum well the pressure coefficient was equal to 8.9 meV/GPa only. This is explained by taking into account the pressureinduced increase of the strain in our structure. The strain was calculated taking in to account that inplane strain is not equal (due to fact that we used aplane sapphire as a substrate) and the potential distribution in the structure was calculated selfconsistently. The pressure induced increase of the builtin electric field is the same for all thicknesses of quantum wells, but becomes more pronounced for thicker quantum wells due to the quantum confined Stark effect lowering the pressure coefficients. Keywords:Piezoelectric fields, Quantum wells, Polarization, Zinc oxide films, High pressure Affiliations:
 
4.  Young T.D., Vargas R.^{♦}, Garza J.^{♦}, A HartreeFock study of the confined helium atom: Local and global basis set approaches, PHYSICS LETTERS A, ISSN: 03759601, DOI: 10.1016/j.physleta.2015.11.021, Vol.380, pp.712717, 2016 Abstract: Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using highorder realspace finite elements and the second is a global basis set approach using modified Slatertype orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one and twoelectron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed. Keywords:Hartree–Fock method, Confined atom model, Galerkin finite element method, Modified Slatertype orbitals Affiliations:
 
5.  Young T.D., Jurczak G., Lotsari A.^{♦}, Dimitrakopulos G.P.^{♦}, Komninou Ph.^{♦}, Dłużewski P., A study of the piezoelectric properties of semipolar 11(2)overbar2 GaN/AlN quantum dots, PHYSICA STATUS SOLIDI BBASIC SOLID STATE PHYSICS, ISSN: 03701972, DOI: 10.1002/pssb.201552156, Vol.252, No.10, pp.22962303, 2015 Abstract: GaN quantum dots grown in (inline image)’orientated AlN are studied. The inline imagenucleated quantum dots exhibit rectangular or trapezoidbased truncated pyramidal morphology. Another quantum dot type orientated on inline image is reported. Based on highresolution transmission microscopy and crystal symmetry, the geometry of inline imageorientated quantum dots is proposed. A piezoelectric model is used within a finite element method to determine and compare the strainstate and electrostatic potential associated with the quantum dot morphology and an estimation of the bandedge energy is made. We report on some novel properties of the inline imageorientated quantum dot, including mixed strainstates and strainstate bowing. Keywords:III–V semiconductors, AlN, GaN, nanostructures, piezoelectric properties, quantum dots Affiliations:
 
6.  Bangerth W.^{♦}, Heister T.^{♦}, Heltai L.^{♦}, Kanschat G.^{♦}, Kronbichler M.^{♦}, Maier M.^{♦}, Turcksin B.^{♦}, Young T.D., The deal.II Library, Version 8.2, Archive of Numerical Software, ISSN: 21978263, Vol.3, No.100, pp.18, 2015  
7.  Teisseyre H.^{♦}, Boćkowski M.^{♦}, Young T.D., Grzanka Sz.^{♦}, Zhydachevskii Y.^{♦}, Grzegory I.^{♦}, Kozanecki A.^{♦}, A monolithic whitelight LED based on GaN doped with Be, Advances in Science and Technology, ISSN: 16620356, DOI: 10.4028/www.scientific.net/AST.93.264, Vol.93, pp.264269, 2014 Abstract: In this communication, the use of gallium nitride doped with beryllium as an efficient converter for white light emitting diode is proposed. Until now beryllium in this material was mostly studied as a potential ptype dopant. Unfortunately, the realization of ptype conductivity in such a way seems impossible. However, due to a very intensive yellow emission, bulk crystals doped with beryllium can be used as light converters. In this communication, it is demonstrated that realisation of such diode is possible and realisation of a colour rendering index is close to that necessary for white light emission. Keywords:Beryllium, Gallium Nitride (GaN), Light Emitting Diode (LED), Optical Converters Affiliations:
 
8.  Young T.D., Romero E.^{♦}, Román J.E.^{♦}, Parallel finite element density functional computations exploiting grid refinement and subspace recycling, COMPUTER PHYSICS COMMUNICATIONS, ISSN: 00104655, DOI: 10.1016/j.cpc.2012.08.011, Vol.184, pp.6672, 2013 Abstract: In this communication computational methods that facilitate finite element analysis of density functional computations are developed. They are: (i) hh–adaptive grid refinement techniques that reduce the total number of degrees of freedom in the real space grid while improving on the approximate resolution of the wanted solution; and (ii) subspace recycling of the approximate solution in selfconsistent cycles with the aim of improving the performance of the generalized eigenproblem solver. These techniques are shown to give a convincing speedup in the computation process by alleviating the overhead normally associated with computing systems with many degreesoffreedom. Keywords:Density functional theory, Finite element discretization, Grid refinement, Largescale eigenvalue problem, Messagepassing parallelization Affiliations:
 
9.  Jurczak G., Young T.D., Finite element modelling of semi and nonpolar GaN/AlN quantum dots, APPLIED SURFACE SCIENCE, ISSN: 01694332, Vol.260, pp.5964, 2012 Abstract: This paper describes results of a finite element analysis of the elastic and electric field distribution in a semipolar and a nonpolar isolated quantum dot based on previously obtained measurements from transmission electron microscopy. The two quantum dot orientations are each investigated and compared in terms of the resultant piezoelectric fields and their redistribution due to growth orientation and quantum dot geometry/surface effects. Alongside that, a standard polar quantum dot is investigated as a referencestate system. It is found that the geometry of quantum dots grown in alternative orientations affect the elastic strain and, along with orientation dependent spontaneous polarisation, modify the electrostatic potential and the builtin electric fields. A theoretical verification of a reduction in the quantum confined Stark effect by determining the band edge splitting energies for electron and hole states is given. Keywords:Piezoelectricity, Continuum mechanics, Finite element method, Quantum dots Affiliations:
 
10.  Maździarz M., Young T.D., Jurczak G., A study of the effect of prerelaxation on the nanoindentation process of crystalline copper, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.63, pp.533548, 2011 Abstract: This paper examines how prerelaxation effects the development of the mechanics of a nanoindentation simulation. In particular, the forcedepth relation, indentation stressstrain curves, hardness and elastic modulus, are investigated through molecular statics simulations of a nanoindentation process, starting from initial relaxation by: (i) molecular dynamics and (ii) molecular statics. It is found that initial relaxation conditions change the quantitative response of the system, but not the qualitative response of the system. This has a significant impact on the computational time and quality of the residual mechanical behaviour of the system. Additionally, the method of determining of the elastic modulus is examined for the spherical and planar indenter; and the numerical results are compared. An overview of the relationship between the grain size and hardness of polycrystalline copper is examined and conclusions are drawn. Keywords:molecular statics, molecular dynamics, nanoindentation, copper Affiliations:
 
11.  Dimitrakopulos G.P.^{♦}, Kalesaki E.^{♦}, Kioseoglou J.^{♦}, Kehagias T.^{♦}, Lotsari A.^{♦}, Lahourcade L.^{♦}, Monroy E.^{♦}, Häusler I.^{♦}, Kirmse H.^{♦}, Neumann W.^{♦}, Jurczak G., Young T.D., Dłużewski P., Komninou Ph.^{♦}, Karakostas T.^{♦}, Morphology and strain of selfassembled semipolar GaN quantum dots in (1112) AlN, JOURNAL OF APPLIED PHYSICS, ISSN: 00218979, DOI: 10.1063/1.3506686, Vol.108, pp.10430419, 2010 Abstract: GaN quantum dots (QDs) grown in semipolar (1122) AlN by plasmaassisted molecularbeam epitaxy were studied by transmission electron microscopy (TEM) and scanning transmission electron microscopy techniques. The embedded (112)grown QDs exhibited pyramidal or truncatedpyramidal morphology consistent with the symmetry of the nucleating plane, and were delimited by nonpolar and semipolar nanofacets. It was also found that, in addition to the (1122) surface, QDs nucleated at depressions comprising {1011} facets. This was justified by ab initio density functional theory calculations showing that such GaN/AlN facets are of lower energy compared to (1122). Based on quantitative highresolution TEM strain measurements, the threedimensional QD strain state was analyzed using finiteelement simulations. The internal electrostatic field was then estimated, showing small potential drop along the growth direction, and limited localization at most QD interfaces. Keywords:Quantum dots, Transmission electron microscopy, IIIV semiconductors, High resolution transmission electron microscopy, Epitaxy Affiliations:
 
12.  Dłużewski P., Young T.D., Dimitrakopulos G.^{♦}, Komninou Ph.^{♦}, Continuum and atomistic modelling of the mixed straight dislocation, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 15431649, DOI: 10.1615/IntJMultCompEng.v8.i3.80, Vol.8, pp.331342, 2010 Abstract: A continuum and atomistic approach to the modeling of dislocations observed by highresolution transmission electron microscopy (HRTEM) is discussed in terms of the continuum theory of dislocations. The atomistic models are obtained by means of the use of a mathematical formula for discrete dislocations. A new analytical solution for a continuously distributed dislocation core is presented. This solution is employed in the finite element modeling of residual stresses induced by the net of dislocations visible on an HRTEM image of GaN structure. This paper terminates with some comments on the atomistic/finiteelement modeling of dislocation fields. Because of some confusion concerning notations used in the literature, the mathematical foundations of the continuum theory of dislocations are revisited. Keywords:dislocations, field theory, atomistic models, finite element method, highresolution transmission electron microscopy Affiliations:
 
13.  Maździarz M., Young T.D., Dłużewski P., Wejrzanowski T.^{♦}, Kurzydłowski K.J.^{♦}, Computer modelling of nanoindentation in the limits of a coupled molecularstatics and elastic scheme, JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, ISSN: 15461955, DOI: 10.1166/jctn.2010.1469, Vol.7, pp.110, 2010 Abstract: Our numerical approach to modeling elasticplastic deformation comes back to the idea of the timeindependent plasticity developed here at the molecularstatics level. We use a constitutive atomic model based on the secondmoment approximation of the tightbinding potential coupled to a linear theory of elasticity solved simultaneously within the finite element method. Our model is applied to the nanoindentation problem for copper in which the indenter is represented by the equations of a sphere. For convenience the timedependency of the nanoindentation problem is reduced to a quasistatic adiabatic scheme. A recurring theme in this paper is to determine the response of the proposed model for two differing systems: mono and polycrystalline copper. This paper discusses the forcedepth response in terms of atomic bondlengths, elasticplastic deformations, and the instantaneous stiffness of the material. We report on an increased instantaneous stiffness of polycrystalline copper compared to that of its monocrystalline counterpart. From both a distinct and a comparative analysis of both systems, based on the relaxed positions of the atoms in the structure during the simulation, we deduce that plastic deformations at grainboundaries are responsible for this change in the overall instantaneous stiffness of the material. Keywords:linear elasticity, material science, molecular statics, nanoindentation, quasicontinuum methods Affiliations:
 
14.  Young T.D., Armiento R.^{♦}, Strategies for hadaptive refinement for a finite element treatment of the harmonic oscillator Schrödinger eigenproblem, COMMUNICATIONS IN THEORETICAL PHYSICS, ISSN: 02536102, DOI: 10.1088/02536102/53/6/04, Vol.53, No.6, pp.10171023, 2010 Abstract: A Schrödinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the realspace grid on which computations are performed without modifying the standard polynomial basisset traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. Keywords:adaptive finite element analysis, Harmonic oscillator problems, Schrödinger equation Affiliations:
 
15.  Young T.D., Kioseoglou J.^{♦}, Dimitrakopulos G.P.^{♦}, Dłużewski P., Komninou Ph.^{♦}, 3D modelling of misfit networks in the interface region of heterostructures, JOURNAL OF PHYSICS DAPPLIED PHYSICS, ISSN: 00223727, DOI: 10.1088/00223727/40/13/027, Vol.40, pp.40844091, 2007 Abstract: We present a methodology for the stress–strain analysis of a film/substrate interface by combining crystallographic and continuum modelling. Starting from measurements of lattice parameters available from experimental observations, the heterostructure is recast initially in the form of a crystallographic model and finally as a continuum elastic model. The derived method is capable of handling dense arrays of misfit dislocations as well as large areas of the interface between two crystal structures. As an application we consider the misfit dislocation network in the GaN/Al2O3 interface region through determination of strain relaxation and associated residual stresses. Our calculated results are referred back to and found to be in good agreement with the experimental observations of misfit dislocation arrays obtained from high resolution transmission electron microscopy. Affiliations:

List of chapters in recent monographs
1. 3  Dłużewski P., Young T.D., Dimitakopulos G.^{♦}, Kioseoglou J.^{♦}, Komninou Ph.^{♦}, Computer Methods in Mechanics, Advanced Structured Materials, rozdział: Nonlinear finite element and atomistic modelling of dislocations in heterostructures, Springer Verlag, Kuczma M., Wilmański K. (Eds.), 1/III, pp.239253, 2010 
Conference papers
1.  Jurczak G., Young T.D., Dłużewski P., A quantum dot nucleated on the edge of a threading dislocation: elastic and electric field effects, PHYSICA STATUS SOLIDI C: CURRENT TOPICS IN SOLID STATE PHYSICS, ISSN: 16101642, DOI: 10.1002/pssc.201200551, Vol.10, pp.97100, 2013 Abstract: In this work the affect of a threading dislocation localised on the edge of GaN/AlN quantum dot is analysed. A standard piezoelectric continuum model is extended to allow the embodiment of threading dislocations that are modelled as a continuous electroelastic line defect originating in the matrix material. Two common types of dislocation are considered: an edgetype and a screwtype. quantum dot, threading dislocation, piezoelectricity, band edge structure Affiliations:
 
2.  Young T.D., A Finite Basis Grid Analysis of the HartreeFock Wavefunction Method for One and Twoelectron Atoms, AIP Conference Proceedings, ISSN: 0094243X, DOI: 10.1063/1.4825817, Vol.1558, pp.15401543, 2013 Abstract: The applicability of a gridbased method for determining the wavefunctions of atomic systems is explicitly demonstrated by calculations based on direct wavefunction theory. Integration over the real space domain is approximated by a sum over numerically determined values in Gauss quadrature points lying inside finite elements. As examples of application, calculations have been performed for the electronic configurations of hydrogen and heliumlike atoms. The results of calculations for the total energy, orbital values and functions, and some derived quantities are given. Affiliations:
 
3.  Young T.D., Marquardt O.^{♦}, Influence of strain and polarization on electronic properties of a GaN/AlN quantum dot, IWN 2008, International Workshop on Nitride Semiconductors, 20081006/1010, Montreux (CH), DOI: 10.1002/pssc.200880901, Vol.6, No.S2, pp.S557S560, 2009 Abstract: It is known that heterojunctions give rise to changes in the elastic and piezoelectric properties of a given semiconductor nanostructure. For practical applications it is decisive to understand the influence of these strain and piezoelectric fields on the electronic response of these systems, both as distinct and as coupled fields. In the present study, the confinement properties of the electron and hole wavefunctions are of interest. Therefore, a model based on a traditional envelope 8band k · p Hamiltonian is implemented and used to explore a GaN/AlN quantum dot/matrix system. Affiliations:
 
4.  Dłużewski P., Young T.D., Jurczak G., Majewski J.A.^{♦}, Nonlinear piezoelectric properties of GaN quantum dots nucleated at the edge of threading dislocations, IWN 2006, International Workshop on Nitride Semiconductors, 20061022/027, Kyoto (JP), DOI: 10.1002/pssc.200674866, Vol.4, pp.23992402, 2007 Abstract: It was observed experimentally by Rouviere et al. that GaN/AlN Quantum Dots (QDs) nucleate at the edge of threading dislocations (Appl. Phys. Lett. 75, 2632 (1999) [1]). The preferred nucleation of QDs in this way is generally assumed to be due to the influence of the stress/strain field around the dislocation core, which in turn, gives the chemical and geometric conditions for nucleation of the QDs. We solve the finite element problem for QDs situated at the edge of threading dislocations where different lattice parameters, piezoelectric and spontaneous polarisation coefficients are assumed for the QD and its matrix. By solving the elastic and electric equilibrium problems we obtain both the residual stress and electric fields. The computational scheme employed here was obtained by linking two previous finite element algorithms described inreferences (P. Dłu ̇zewski et al., Comput. Mater. Sci. 29, 379 (2004) [2]) and (G. Jurczak et al., phys. stat. sol. (c) 2, 972 (2005) and S.P. Łepkowski et al., Phys. Rev. B 73, 245201 (2005) [3, 4], respectively). This approach allows us to get a deeper physical insight into the mechanics and electrical properties of QDs and ultimately determine the efficiency of light emission from these objects. Keywords:Nanostructure, IIIV semiconductor, Piezoelectricity, Threading dislocation Affiliations:

Conference abstracts
1.  Jurczak G., Young T.D., Dłużewski P., Dimitrakopulos G.P.^{♦}, Elastic and electric properties of a semipolar (1122) GaN/AlN quantum dots, ICMM3, 3rd International Conference on Material Modelling incorporating 13th European Mechanics of Materials Conference, 20130908/0911, Warszawa (PL), pp.243244, 2013 Keywords: Semiconductor, Quantum dot, Piezoelectricity, Bandedge structure Affiliations:
 
2.  Young T.D., Teisseyre H.^{♦}, Dłużewski P., Kahouli A.^{♦}, Kriouche N.^{♦}, Brault J.^{♦}, Damilano B.^{♦}, Leroux M.^{♦}, Courville A.^{♦}, de Mierry P.^{♦}, GaN/AlGaN (1122) semipolar nanostructures: Observations by theory and experiment, 41st International School and Conference on the Physics of Semiconductors, 20120608/0615, KrynicaZdrój (PL), pp.1, 2012  
3.  Kret S.^{♦}, Bilska M.^{♦}, Ivaldi F.^{♦}, Leszczyński M.^{♦}, Czernecki R.^{♦}, Dłużewski P., Jurczak G., Young T.D., Determination of the nanoscale structural properties of the InAlN based devices by advanced TEM methods, EMRS 2012 FALL MEETING, 20120917/0921, Warszawa (PL), pp.1, 2012 Keywords: IIIV semiconductors, piezoelectricity, high resolution transmission electron microscopy, band edge structure Affiliations:
 
4.  Jurczak G., Young T.D., Dłużewski P., Elastic and Electric Field Effects of a Quantum Dot Nucleated on the Edge of a Threading Dislocation, EDS 2012, International Conference on Extended Defects in Semiconductors, 20120624/0629, Thessaloniki (GR), pp.103, 2012 Keywords: quantum dot, threading dislocation, piezoelectricity, band edge structure Affiliations:
 
5.  Young T.D., Jurczak G., Dłużewski P., Wpływ defektów struktury krystalicznej na elektromechaniczne własności nanostruktur, III National Conference of Nano and Micromechanics, 20120704/0706, Warszawa (PL), pp.125127, 2012 Keywords: Piezoelektryczność, Mechanika Ośrodków Ciągłych, Metoda Elementów Skończonych, Nanostruktura Affiliations:
 
6.  Young T.D., Teisseyre H.^{♦}, Brault J.^{♦}, Kahouli A.^{♦}, Vennegues P.^{♦}, Leroux M.^{♦}, Courville A.^{♦}, de Mierry P.^{♦}, Damilano B.^{♦}, Dłużewski P., Optoelectronic properties of a GaN quantum dot grown on a Al_{0.5}Ga_{0.5}N (1122)orientated surface, IWN 2012, International Workshop on Nitride Semiconductors, 20121014/1019, Sapporo (JP), pp.12, 2012  
7.  Young T.D., Selfconsistent meanfield approximation in a coordinate representation, Workshop deal.II, 20120806/0810, Heidelberg (DE), pp.9, 2012  
8.  Maździarz M., Young T.D., Jurczak G., PreRelaxation effect in computer modeling of nanoindentation, SolMech 2010, 37th Solid Mechanics Conference, 20100906/0910, Warszawa (PL), pp.5657, 2010 Keywords: molecular statics, molecular dynamics, nanoindentation, copper Affiliations:
