Grzegorz Jurczak, Ph.D., Eng. 

Doctoral thesis
20060629  Anizotropia sprężysta kryształów. Analiza i modelowanie numeryczne metodą elementów skończonych.
 595 
Recent publications
1.  Jurczak G., Variation of secondorder piezoelectric coefficients with respect to a finite strain measure, Acta Crystallographica Section A FOUNDATIONS AND ADVANCES, ISSN: 20532733, DOI: 10.1107/S2053273318008628, Vol.A74, pp.518523, 2018 Abstract: In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that secondorder piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higherorder piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for secondorder piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely 43m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of secondorder piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements. Keywords:piezoelectricity, nonlinear piezoelectricity, elastostriction, finite strain measure Affiliations:
 
2.  Jurczak G., Dłużewski P., Finite element modelling of threading dislocation effect on polar GaN/AlN quantum dot, PHYSICA ELOWDIMENSIONAL SYSTEMS & NANOSTRUCTURES, ISSN: 13869477, DOI: 10.1016/j.physe.2017.08.018, Vol.95, pp.1115, 2018 Abstract: In this paper the effect of adjacent threading dislocation at the edge of the GaN/AlN quantum dot is analysed by use of the finite element analysis. Elastic as well electric effects related to dislocation core are taken into account. Two types of threading dislocations: edge and screwtype, common for IIInitride epitaxial layers, are considered. Also, three different QD geometries are considered to estimate the impact of the threading dislocation on the quantum heterostructure. It is demonstrated that the local elastic and electric fields around dislocation affect local piezoelectric fields builtin the quantum dot. Local lattice deformation near the dislocation core reduce residual strains in the quantum dot. It is prominent in the case of edgetype dislocation. The presence of an electric charge along dislocation line provides significant shift of the total potential towards the negative values. However, estimated difference in bandtoband transition energy for edge and screwtype dislocations are rather small, what suggest low sensitivity to the charge density along dislocation line. Unexpectedly, local strain field around the edgetype dislocation, slightly compensate the negative affect of the electrostatic potential. Keywords:Quantum dot, Threading dislocation, Piezoelectricity, Finite element modelling Affiliations:
 
3.  Jurczak G., Dłużewski P., Finite element modelling of nonlinear piezoelectricity in wurtzite GaN/AlN quantum dots, COMPUTATIONAL MATERIALS SCIENCE, ISSN: 09270256, DOI: 10.1016/j.commatsci.2015.09.024, Vol.111, pp.197202, 2016 Abstract: In this paper we evaluate the effect of higher order elastic and piezoelectric coefficients on elastic and electric fields in IIInitride wurtzite crystals. To this end, finite element calculations of GaN/AlN QDs of different types are presented and compared. We show that the nonlinear elastic and piezoelectric effects modify the elastic strain field, electrostatic potential, and the buildin electric field in the QDs. These higher order effects lead to corrections of the peak values of the strain field and the electrostatic potential over 8% above the linear model. An even more significant effect, exceeding 13%, is observed for the magnitude of the electric field. Our calculations clearly show that the impact of the nonlinear correction strongly depends on the application, i.e. on the morphology and crystallographic orientation of the quantum dot. It turns out that nonlinear effects play an important role in the semipolar (View the MathML source112¯2) and nonpolar (View the MathML source112¯0) QDs. Because of the theoretical nature of physical parameters describing nonlinear material (obtained by DFT calculations) further studies and experimental verification of the nonlinear effects in nitride structures are necessary. Keywords:Piezoelectricity, Heterostructure, Nonlinearity, Quantum dot Affiliations:
 
4.  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:
 
5.  Cholewiński J., Maździarz M., Jurczak G., Dłużewski P., Dislocation core reconstruction based on finite deformation approach and its application to 4HSiC crystal, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 15431649, DOI: 10.1615/IntJMultCompEng.2014010679, Vol.12, No.5, pp.411421, 2014 Abstract: A proper reconstruction of discrete crystal structure with defects is an important problem in dislocation theory. Currently, procedures for dislocation core reconstruction presented in the literature usually neglect configuration changes. The present paper discusses a new approach, which uses an iterative algorithm to determine an atomistic configuration of the dislocation core. The mathematical background is based on finite deformation theory, in which an iterative algorithm searches for the new atomic configuration corresponding to the actual atomic configuration of the deformed crystal. Its application to the reconstruction of 4HSiC crystal affected by the system of four threading dislocations is presented as an example. Molecular statics calculations suggest a lower potential energy, as well as dislocation core energy, peratom energy, and peratom stresses for the structure reconstructed by use of the iterative algorithm against the classical solution based on the Love's equations. Keywords:dislocation, dislocation core energy, finite deformation, molecular statics Affiliations:
 
6.  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:
 
7.  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:
 
8.  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:
 
9.  Alfonso C.^{♦}, Alexandre L.^{♦}, Leroux Ch.^{♦}, Jurczak G., Saikaly W.^{♦}, Charai A.^{♦}, ThibaultPenisson J.^{♦}, HOLZ lines splitting on SiGe/Si relaxed samples: Analytical solutions for the kinematical equation, ULTRAMICROSCOPY, ISSN: 03043991, Vol.110, No.4, pp.285296, 2010 Abstract: Sample thinning for TEM observation introduces large changes with respect to the initial strain state of the bulk sample and particularly relaxation via the free surfaces which leads to HOLZ lines splitting in the CBED pattern. This phenomenon has been simulated owing to extensive calculations either in the kinematical or the dynamical framework of electron diffraction mainly using displacement fields resulting from finite element modelling of the sample relaxation. HOLZ line splitting is well reproduced and numerical fits can be used to compare experimental and calculated curves. This paper proposes new analytical solutions for the kinematical equation of electron diffraction. Simple mathematical functions are used to approximate the deformation profiles. We showed that, under certain conditions, the rocking curve profile can be analytically calculated, thus providing some clue to separate different contributions to the rocking curves against deformation profile. These simplified analytical expressions are used to extract the maximum amplitude displacement within the sample with about 10% accuracy. This accuracy can even be improved to 1% with a short adjustement routine. The influence of the shape of the displacement profile on the rocking curves is demonstrated. Keywords:Convergent beam electron diffraction, Kinematical theory of electron diffraction, Analytical expressions, Strain measurement Affiliations:
 
10.  Dłużewski P., Maździarz M., Traczykowski P.^{♦}, Jurczak G., Niihara K.^{♦}, Nowak R.^{♦}, Kurzydłowski K.^{♦}, A hybrid atomisticcontinuum finite element modelling of nanoindentation and experimental verification for copper crystal, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 22993649, Vol.15, pp.3744, 2008 Abstract: Problem of locally disordered atomic structure is solved by using a hybrid formulation in which nonlinear elastic finite elements are linked with discrete atomic interaction elements. The continuum approach uses nonlinear hyperelasticity based upon the generalized strain while the atomistic approach employs the TightBinding SecondMoment Approximation potential to create new type of elements. The molecular interactions yielding from constitutive models of TBSMA were turned into interactions between nodes to solve a boundary value problem by means of finite element solver. Nanostructure, Nanoindentation, Molecular statics, Finite element modelling Affiliations:
 
11.  Teisseyre H.^{♦}, Suski T.^{♦}, Łepkowski S.P.^{♦}, Perlin P.^{♦}, Jurczak G., Dłużewski P., Daudin B.^{♦}, Grandjean N.^{♦}, Strong electric field and nonuniformity effects in GaN/AlN quantum dots revealed by high pressure studies, APPLIED PHYSICS LETTERS, ISSN: 00036951, DOI: 10.1063/1.2219381, Vol.89, No.5, pp.5190213, 2006 Abstract: The photoluminescence (PL) from GaN quantum dots (QDs) embedded in AlN has been investigated under hydrostatic pressure. The measured pressure coefficient of emitted light energy [dE / dP] shows a negative value, in contrast with the positive pressure coefficient of the GaN band gap. We also observed that increasing pressure leads to a significant decrease of the light emission intensity and an asymmetric broadening of the PL band. All these effects are related to the pressureinduced increase of the builtin electric field. A comparison is made between experimental results and the proposed theoretical model which describes the pressure behavior of nitride QDs. Keywords:IIIV semiconductor, Quantum dot, Piezoelectricity, Photoluminescence Affiliations:
 
12.  Łepkowski S.P.^{♦}, Majewski J.A.^{♦}, Jurczak G., Nonlinear elasticity in IIIN compounds: abinitio calculations, PHYSICAL REVIEW B, ISSN: 10980121, Vol.72, pp.2452010, 2005 Abstract: We have studied the nonlinear elasticity effects in zincblende and wurtzite crystallographic phases of IIIN compounds. Particularly, we have determined the pressure dependences of elastic constants in InN, GaN, and AlN by performing ab initio calculations in the framework of planewave pseudopotential implementation of the densityfunctional theory. The calculations have been performed employing two exchangecorrelation functionals, one within the local density approximation and the other within the generalized gradient approximation. We have found that C11 , C12 in zincblende nitrides and C11 , C12 , C13 , C33 in wurtzite nitrides depend significantly on hydrostatic pressure. Much weaker dependence on pressure has been observed for C44 elastic constant in both zincblende and wurtzite phases. Further, we have examined the influence of pressure dependence of elastic constants on the pressure coefficient of light emission, dE / dP, in wurtzite InGaN / GaN and GaN / AlGaN quantum wells. We have shown that the pressure dependence of elastic constants leads to a significant reduction of dE / dP in nitride quantum wells. Finally, we have considered the influence of nonlinear elasticity of IIIN compounds on the properties of hexagonal nitride quantum dots (QDs). For typical wurtzite GaN / AlN QDs, we have shown that taking into account pressure dependence of elastic constants results in the decrease of volumetric strain in the QD region by about 7%. Simultaneously, the average z component of the piezoelectric polarization in the QDs increases by 0.1 MV/ cm compared to the case when linear elastic theory is used. Both effects, i.e., decrease of volumetric strain as well as increase of piezoelectric field, decrease the bandtoband transition energies in the QDs. Keywords:IIIV semiconductor, abinitio calculation, nonlinear elasticity, third order elastic coefficient Affiliations:
 
13.  Łepkowski S.P.^{♦}, Majewski J.A.^{♦}, Jurczak G., Nonlinear elasticity in wurtzite GaN/AlN planar superlattices and quantum dots, ACTA PHYSICA POLONICA A, ISSN: 05874246, Vol.108, No.5, pp.749754, 2005 Abstract: The elastic stiffness tensors for wurtzite GaN and AlN show a significant hydrostatic pressure dependence, which is the evidence of nonlinear elasticity of these compounds. We have examined how pressure dependence of elastic constants for wurtzite nitrides influences elastic and piezoelectric properties of GaN/AlN planar superlattices and quantum dots. Particularly, we show that builtin hydrostatic pressure, present in both quantum wells of the GaN/AlN superlattices and GaN/AlN quantum dots, increases significantly by 0.3–0.7 GPa when nonlinear elasticity is used. Consequently, the compressive volumetric strain in quantum wells and quantum dots decreases in comparison to the case of the linear elastic theory. However, the zcomponent of the builtin electric field in the quantum wells and quantum dots increases considerably when nonlinear elasticity is taken into account. Both effects, i.e., a decrease in the compressive volumetric strain as well as an increase in the builtin electric field, decrease the bandtoband transition energies in the quantum wells and quantum dots. Keywords:IIIV semiconductor, nonlinear elasticity, third order elasic coefficient Affiliations:
 
14.  Jurczak G., Maciejewski G., Kret S.^{♦}, Dłużewski P., Ruterana P.^{♦}, Modelling of indium rich clusters in MOCVD InxGa1−xN/GaN multilayers, JOURNAL OF ALLOYS AND COMPOUNDS, ISSN: 09258388, DOI: 10.1016/j.jallcom.2004.05.038, Vol.382, No.12, pp.1016, 2004 Abstract: Chemical composition in a ternary alloy is examined using a quantitative high resolution transmission electron microscopy, finite element modelling of the thin foil relaxation phenomena and microscopy image simulation. The measurement of local lattice distortion on transmission electron microscopy images is a powerful tool for chemical composition determination. However, for the correct interpretation of the results, one needs to take into account the inhomogeneous relaxation of the sample and the strain averaging across the sample. The 3D finite element modelling of such phenomena have been performed as a function of chemical composition and geometry of an indium rich cluster in a MOCVD InxGa1−xN/GaN quantum well. Lattice distortion field measured on: experimental transmission electron microscopy image and simulated one, obtained on the basis of finite element simulation, are compared. This procedure allows an accurate determination of chemical composition in such heterostructures. Keywords:Indium clusters, Vapour deposition, Transmissionelectron microscopy, Elasticity, Finite element method, Lattice distortion, Image simulation Affiliations:
 
15.  Dłużewski P., Maciejewski G., Jurczak G., Kret S.^{♦}, Laval J.Y.^{♦}, Nonlinear FE analysis of residual stresses induced by dislocations in heterostructures, COMPUTATIONAL MATERIALS SCIENCE, ISSN: 09270256, DOI: 10.1016/j.commatsci.2003.10.012, Vol.29, No.3, pp.379395, 2004 Abstract: In this paper the field theory of dislocations is used in the finite element analysis of residual stresses in epitaxial layers. By digital processing of the HRTEM image of a GaAs/ZnTe/CdTe system the tensor maps of dislocation distribution are extracted. Such obtained maps are used as the input data to the finite element code. The mathematical foundations of this code are based on the compatibility equations for lattice distortions. The surface tension induced by misfit dislocations is considered here in terms of a 3D boundaryvalue problem for stress equilibrium in the interfacial zone. The numerical results show how strongly the surface tension depends on the nonlinear elastic behaviour of the crystal structure. Keywords:Microscopy and microanalysis techniques, Nonlinear elasticity, Dislocation structure, Finite element analysis, Residual stresses, Layered structures Affiliations:
 
16.  Ruterana P.^{♦}, Singh P.^{♦}, Kret S.^{♦}, Jurczak G., Maciejewski G., Dłużewski P., Cho H.K.^{♦}, Choi R.J.^{♦}, Lee H.J.^{♦}, Suh E.K.^{♦}, Quantitative evolution of the atomic structure of defects and composition fluctuations at the nanometer scale inside InGaN/GaN heterostructures, PHYSICA STATUS SOLIDI BBASIC SOLID STATE PHYSICS, ISSN: 03701972, Vol.241, No.12, pp.26432648, 2004 Abstract: The cover picture of this issue depicts indium composition fluctuations in InGaN/GaN multi quantum wells. The coded color strain distribution (left) was derived from finite element method calculations of the strain relaxation process and high‐resolution transmission electron microscopy (HRTEM) image simulations, superimposed on the HRTEM image of the quantum wells. The possible corresponding shape and εxx strain profiles in the indium rich clusters (right) hint at a concentration close to pure InN in their core. The paper by Pierre Ruterana et al. [1] was presented at the 5th International Symposium on Blue Laser and Light Emitting Diodes (ISBLLED‐2004), held in Gyeongju, Korea, 15–19 March 2004. Keywords:HRTEM, quantum well, composition fluctuation, strain distribution Affiliations:
 
17.  Dłużewski P., Jurczak G., Antúnez H.J., Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials, Computer Assisted Mechanics and Engineering Sciences, ISSN: 1232308X, Vol.10, No.1, pp.6979, 2003 Abstract: A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative instead of additive  decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models. Keywords:Anisotropic material, Constitutive behaviour, Elastic material, Finite element method, Logarithmic strain measure Affiliations:
 
18.  Dłużewski P., Jurczak G., Maciejewski G., Kret S.^{♦}, Ruterana P.^{♦}, Nouet G.^{♦}, Finite Element Simulation of Residual Stresses in Epitaxial Layers, Materials Science Forum (MSF), ISSN: 16629752, DOI: 10.4028/www.scientific.net/MSF.404407.141, Vol.404407, pp.141146, 2002 Abstract: A nonlinear finite element approach presented here is based on the constitutive equations for anisotropic hyperelatic materials. By digital image processing the elastic incompatibilities (lattice mismatch) are extracted from the HRTEM image of GaN epilayer. Such obtained tensorial field of dislocation distribution is used next as the input data to the FE code. This approach is developed to study the stress distribution associated with lattice defects in highly mismatched heterostructures applied as buffer layers for the optically active structures. Keywords:Dislocations, Anisotropic Hyperelasticity, Residual Stresses Affiliations:

List of chapters in recent monographs
1. 399  Jurczak G., Maździarz M., Dłużewski P., Nanomechanics: Selected problems, rozdział: Atomisticcontinuum modelling of coupled fields and defects in semiconductor crystals, Wydawnictwo Politechniki Krakowskiej, Muc A., Chwał M., Garstecki A., Szefer G. (Eds.), pp.7798, 2015 
Conference papers
1.  Jurczak G., Maździarz M., Dłużewski P., Dimitrakopulos G.P.^{♦}, Komninou Ph.^{♦}, Karakostas T.^{♦}, On the applicability of elastic model to very thin crystalline layers, JOURNAL OF PHYSICS: CONFERENCE SERIES, ISSN: 17426588, DOI: 10.1088/17426596/1190/1/012017, No.1190, pp.15, 2019 Abstract: Elastic model of continuum material is often used to simulate the relaxation of crystalline heterostructures. There are many reports on the successful application of the theory of elasticity to nanosized crystalline heterostructures, even if the continuum condition for them is hardly fulfilled. On the other hand, progress in epitaxial growth allows for the preparation of stable ultrathin layers with thickness of few monolayers. For such ultrathin layers, results provided by continuum model and molecular statics/dynamics calculations become diverging. The key problem seems to be located at the modelling of the interface between layers, which is problematic in the continuum approach. By applying a stepwise substitutive compositional interfacial function, it is possible to obtain good agreement with molecular dynamics calculations, even for a single monolayer heterostructure. We propose another approach that uses composition as an extra parameter during finite element calculations, along with classical nodal displacements. Such an approach creates a chemoelastic coupling that allows to interpolate the composition much like in the case of atomistic calculations. Keywords:ultrathin layers, elastic relaxation, molecular statics, finite elemenet modelling Affiliations:
 
2.  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:
 
3.  Alexandre L.^{♦}, Jurczak G., Alfonso C.^{♦}, Saikly W.^{♦}, Grosjean C.^{♦}, Charai A.^{♦}, Thibault J.^{♦}, Microscopy of semiconducting materials CBED and FE study of thin foil relaxation in crosssection samples of Si/SiGe and Si/SiGe/Si heterostructures, Proceedings in Physics, ISSN: 09308989, DOI: 10.1007/9781402086151_90, Vol.120, pp.415418, 2008 Keywords: Convergentbeam electron diffraction, elastic strain relaxation, finite element modelling 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:
 
5.  Łepkowski S.P.^{♦}, Jurczak G., Quantum confined Stark effect in vertically correlated GaN/AlN quantum dots, ICNS6, 6th International Conference on Nitride Semiconductors, 20050828/0902, Bremen (GE), DOI: 10.1002/pssc.200565229, Vol.3, No.6, pp.20522055, 2006 Abstract: We investigate Quantum Confined Stark Effect (QCSE) in vertically correlated wurtzite GaN/AlN QDs, having hexagonal pyramidshape. We show that the QCSE in these structures depends not only on the vertical dimensions, i.e., the height of the QDs and the thickness of the barriers, but also on their base diameter. We show that for typical wurtzite GaN/AlN QDs, having the base diameter of 19.5nm, drop of the electrostatic potential in the QD region slightly increases with increasing the width of barriers. Consequently, the bandtoband transition energies in the QDs decrease. Qualitatively similar but a factor of two stronger dependences is obtained for superlattices of QWs having the same vertical dimensions. The increase of the base diameter of the dots results in stronger dependences of both the electrostatic potential and the bandtoband transition energy on the thickness on barriers. Keywords:IIIV semiconductor, Quantum dot, Piezoelectricity, Quantum confined Stark effect Affiliations:
 
6.  Jurczak G., Łepkowski S.P.^{♦}, Dłużewski P., Suski T.^{♦}, Modeling of elastic, piezoelectric and optical properties of vertically correlated GaN/AlN quantum dots, EMRS 2004, Symposium on Science and Technology of Nitrides and Related Materials/Wide Band Gap IIVI Semiconductors, EMRS 2004 FALL MEETING SYMPOSIA C AND F, 20040806/0810, Warszawa (PL), DOI: 10.1002/pssc.200460604, Vol.2, No.3, pp.972975, 2005 Abstract: We theoretically investigate elastic, piezoelectric and optical properties of wurtzite GaN/AlN quantum dots, having hexagonal pyramidshape, stacked in a multilayer. We show that the strain existing in quantum dots and barriers depends significantly on the distance between the dots i.e. on the width of AlN barriers. Drop of the electrostatic potential in the quantum dot region slightly increases with increasing of the barrier width. This increase is however much smaller for QDs than for superlattice of quantum wells. Consequently, bandtoband transition energies in the vertically correlated quantum dots show rather weak dependence on the width of AlN barriers. Keywords:IIIV semiconductor, quantum dot, piezoelectricity, elastic strain, electrostatic potential Affiliations:
 
7.  Ruterana P.^{♦}, Singh P.^{♦}, Kret S.^{♦}, Cho H.K.^{♦}, Lee H.J.^{♦}, Suh E.K.^{♦}, Jurczak G., Maciejewski G., Dłużewski P., Size and shape of In rich clusters and InGaN QWs at the nanometer scale, IWN 2004, International Workshop on Nitrides Semiconductors, 20040619/0623, Pittsburgh (US), DOI: 10.1002/pssc.200461463, Vol.2, No.7, pp.23812384, 2005 Abstract: Following the need to accurately understand the In composition fluctuations and their role on the optical properties of the GaN based heterostructures, an investigation of MOCVD InGaN/GaN quantum wells is carried out. To this end, quantitative High Resolution Transmission Electron Microscopy (HRTEM) is coupled with image simulation and Finite Element Method (FEM) for the thin foil relaxation modelling. The results show that the indium content can reach x = 1 in the clusters inside the core. In these MOCVD QWs, we attempt to connect the Quantum dot density, composition, and shape to the growth conditions, in order to help the engineering process of highly efficient devices. Affiliations:

Conference abstracts
1.  Jurczak G., Dłużewski P., The effect of finite strain measure change on secondorder piezoelectricity, EUROMAT 2019, European Congress and Exhibition on Advanced Materials and Processes 2019, 20190901/0905, Stockholm (SE), pp.1, 2019 Abstract: Very rapid technological development in the electronic branch of the industry observed during last decades, together with the progressive miniaturisation of electronic devices induce increasing interest in the subject of piezoelectric semiconducting heterostructures. In some cases, the linearity of the piezoelectric effect under extreme strain and electric field conditions is challenged for these heterostructures. There are many experimental reports in the literature dealing with nonlinear piezoelectricity as well as theoretical calculations which predict the nonlinear behaviour of such crystalline heterostructures. piezoelectricity; second order piezoelectric coefficients; Affiliations:
 
2.  Jurczak G., Maździarz M., Dłużewski P., Dimitrakopulos G.^{♦}, Komninou Ph.^{♦}, Karakostas T.^{♦}, On the Applicability of the Theory of Elasticity to Very Thin Layers, EDS2018, 19th International Conference on Extended Defects in Semiconductors, 20180624/0629, Thessaloniki (GR), pp.1, 2018 Abstract: Theory of elasticity, a continuum model of a macroscopic material is commonly used to model a relaxation of a crystalline heterostructures. There are many reports on the successful application of theory of elasticity to nanometer crystalline heterostructures, even if the continuum condition for these structures is hardly fulfilled. On the other hand progress in epitaxial growth techniques allows to prepare the stable ultra thin layers with the thickness about a single monolayer. For such extremely thin layers the theory of elasticity seems to fail in describing the relaxation process. The results provided by theory of elasticity and experimental measurements or molecular statics/dynamics become diverging. The key problem in that case seems to be located at the interface between layers and related to composition change, which is problematic in classic, elastic approach. By applying a “substitutive” composition of the interface layers which is just an interpolation, it is possible to obtain a good agreement with molecular statics, even for 1 monolayer heterostructure. Instead of classic approach to the composition within the theory of elasticity, we propose another approach which takes into account the composition as an extra degree of freedom along with classical displacement. Such approach creates a chemoelastic coupling with composition interpolated by use of the Vegard’s law. This allows to take into account a composition changes at the interface and avoid mesh refining necessary at the classic approach. Keywords:theory of elasticity, semiconductor, monolayer, relaxation Affiliations:
 
3.  Jurczak G., Maździarz M., Dłużewski P., Finite element modelling of threading dislocation effect on GaN/AlN quantum dot, ICMM5, 5th International Conference on Material Modeling, 20170614/0616, Rome (IT), pp.1, 2017 Keywords: Quantum dot, Threading dislocation, Piezoelectricity, Finite element modelling Affiliations:
 
4.  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:
 
5.  Jurczak G., Maździarz M., Dłużewski P., Effect of threading dislocation on elastic and electric properties of semipolar GaN/AlN quantum dot, ICMM3, 3rd International Conference on Material Modelling incorporating 13th European Mechanics of Materials Conference, 20130908/0911, Warszawa (PL), pp.186187, 2013 Keywords: Semiconductor, Piezoelectricity, Dislocation Affiliations:
 
6.  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:
 
7.  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:
 
8.  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:
 
9.  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:
