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Showing papers by "Morten Willatzen published in 2008"


Journal ArticleDOI
TL;DR: This paper provides a review of the state-of-the-art electronic-structure calculations of semiconductor nanowires using empirical k.p, empirical tight-binding, semi-empirical pseudopotential, and with ab initio methods.
Abstract: This paper provides a review of the state-of-the-art electronic-structure calculations of semiconductor nanowires. Results obtained using empirical k.p, empirical tight-binding, semi-empirical pseudopotential, and with ab initio methods are compared. For conciseness, we will restrict our detailed discussions to free-standing plain and modulated nanowires. Connections to relevant experimental data, particularly band gaps and polarization anisotropy, will be made since these results depend crucially on the electronic properties. For completeness, a brief review on the synthesis of nanowires is included.

522 citations


Journal ArticleDOI
TL;DR: In this article, the governing equations of flow acoustics including nonlinearities are solved and analyzed in terms of ultrasonic flow-measurement properties for gas-flow measurement applications as gas-sound speeds are much smaller while fluid flows generally are much higher.

24 citations


Journal ArticleDOI
01 Mar 2008
TL;DR: In this article, the impact of using the fully coupled electromechanical equations including piezoelectric effect and spontaneous polarization as compared to the semi-coupled approach was studied.
Abstract: We study the impact of using the fully coupled electromechanical equations including piezoelectric effect and spontaneous polarization as compared to the semi-coupled approach, where the strain is solved first without piezoelectric coupling and then inserted into the equation for the electric potential. We show that for circular GaN/AlN quantum dots the fully coupled approach is needed for dots with a radius comparable to or larger than the height, however, when the radius is smaller than the height the semi-coupled approach is sufficient. We highlight this by studying the effect on the electronic structure using an effective mass approximation.

19 citations


Journal ArticleDOI
01 Mar 2008
TL;DR: In this article, it was shown that the governing equations for the electromechanical fields of wurtzite structures are axisymmetric, hence all electric-and mechanical-field solutions of the original three-dimensional problem can be solved as a two-dimensional mathematical model problem.
Abstract: We show that the governing equations for the electromechanical fields of wurtzite structures are axisymmetric, hence all electric- and mechanical-field solutions are axisymmetric as well and the original three-dimensional problem can be solved as a two-dimensional mathematical-model problem (1). We present results of the combined influence of lattice mismatch, piezoelectric effects, and spontaneous polarization for wurtzite (WZ) structures consisting of a GaN quantum dot embedded in a AlN matrix.

17 citations



Journal ArticleDOI
TL;DR: Differences in the strain of around 30% and in the electron energies of up to 30meV were found possible for GaN/AlN dots.

11 citations



Proceedings ArticleDOI
01 Nov 2008
TL;DR: Alguero et al. as discussed by the authors presented an adapted one dimensional transducer model originally proposed by Willatzen to calibrate Field II, which was modified to calculate the required impulse responses needed by Field II for a calibrated field pressure and external circuit current calculation.
Abstract: Field II is a program for simulating ultrasound transducer fields It is capable of calculating the emitted and pulse-echoed fields for both pulsed and continuous wave transducers To make it fully calibrated a model of the transducer's electro-mechanical impulse response must be included We examine an adapted one dimensional transducer model originally proposed by Willatzen to calibrate Field II This model is modified to calculate the required impulse responses needed by Field II for a calibrated field pressure and external circuit current calculation The testing has been performed with Pz27 piezoceramic discs from Ferroperm Piezoceramics A/S, Kvistgaard, Denmark The transmitted acoustic pressures from two sets of each five disc samples with 1008 mm diameters were measured in an automatic water bath needle hydrophone setup together with the current flow through the driving circuit Resonance frequencies at 21 MHz and 4 MHz were applied Two types of circuits were considered, one circuit with a simple resistance load of 475 Omega and one with an example of a LR tuning circuit typically found in commercial transducers The measurements were averaged 128 times and afterwards compared to the calibrated Field II program for 1, 4, and 10 cycle excitations Two parameter sets were applied for modeling, one real valued Pz27 parameter set, manufacturer supplied, and one complex valued parameter set found in literature, Alguero et al The latter implicitly accounts for attenuation Results show that the combination of the model and Field II can calculate the pressure within -15% to 5% RMS error for long excitation bursts and 7% to 23% for short excitation bursts Furthermore it is shown that current simulations can be done within 1% to maximum 33% RMS error, where best current simulations are found for 4 MHz long burst simulations and worst case is found for 21 MHz short bursts Finally it is shown that maximum pressure deviation for the real parameter set and the complex parameter simulation is 3% for pressure and 53% for current

8 citations


Journal ArticleDOI
TL;DR: In this article, Yan Voon et al. presented the effective electron barrier potential in quantum-wire superlattices subject to magnetic-field and strain effects, and showed that strong contributions from strain (lattice mismatch) may be present as well.
Abstract: A calculation of the effective electron barrier potential in quantum-wire superlattices subject to magnetic-field and strain effects is presented. It is shown that, besides the lateral-confinement contributions to the barrier potential emphasized by the authors in earlier work (Lew Yan Voon and Willatzen 2003 J. Appl. Phys. 93 9997; Lew Yan Voon et al 2004 J. Appl. Phys. 96 4660), strong contributions from strain (lattice mismatch) may be present as well. This is due to the fact that strain values can be several percent in heterostructures while electron deformation potentials are of the order of 10 eV. It is also shown that Landau and Lande magnetic-field contributions become important at magnetic fields of 10 T or higher. The driving force behind the lateral-confinement and the Landau magnetic-field contributions is the same, namely, the electron effective-mass difference in the two material constituents forming the superlattice structure; however, the dependences of the two contributions on lateral dimensions are inverse squared and squared, respectively. Similarly, the driving force behind the Lande magnetic-field contribution, being independent of lateral dimensions, is the difference in electron g factors between the two material constituents. We note that, for InAs/GaAs nanowire superlattices, it is possible to tune the effective barrier potential around 0 for cross-sectional dimensions of 5–6 nm by use of a magnetic field. Further, since the effective barrier potential is different for spin-up and spin-down polarized electrons, magnetic-field tuning can be used to separate spin-up and spin-down electrons in quantum-wire superlattices.

8 citations


Journal Article
TL;DR: In this paper, the governing two-dimensional equations of a heterogeneous material composed of a fluid (allowed to flow in the absence of acoustic excitations) and a crystalline piezoelectric cubic solid stacked one-dimensionally (along the z direction) are derived and special emphasis is given to the discussion of acoustic group velocity for the structure as a function of the wavenumber component perpendicular to the stacking direction.
Abstract: The governing two-dimensional equations of a heterogeneous material composed of a fluid (allowed to flow in the absence of acoustic excitations) and a crystalline piezoelectric cubic solid stacked one-dimensionally (along the z direction) are derived and special emphasis is given to the discussion of acoustic group velocity for the structure as a function of the wavenumber component perpendicular to the stacking direction (being the x axis). Variations in physical parameters with y are neglected assuming infinite material homogeneity along the y direction and the flow velocity is assumed to be directed along the x direction. In the first part of the paper, the governing set of differential equations are derived as well as the imposed boundary conditions. Solutions are provided using Hamilton’s equations for the wavenumber vs. frequency as a function of the number and thickness of solid layers and fluid layers in cases with and without flow (also the case of a position-dependent flow in the fluid layer is considered). In the first part of the paper, emphasis is given to the small-frequency case. Boundary conditions at the bottom and top parts of the full structure are left unspecified in the general solution but examples are provided for the case where these are subject to rigid-wall conditions (Neumann boundary conditions in the acoustic pressure). In the second part of the paper, emphasis is given to the general case of larger frequencies and wavenumber-frequency bandstructure formation. A wavenumber condition for an arbitrary set of consecutive solid and fluid layers, involving four propagating waves in each solid region, is obtained again using the monodromy matrix method. Case examples are finally discussed. Keywords—Flow, acoustics, solid-fluid structures, periodicity.

4 citations


Journal ArticleDOI
TL;DR: In this paper, a one-dimensional model accounting for electrostriction, lattice mismatch, piezoelectricity, and strain is presented with special emphasis on GaN/AlN heterostructures.


Journal Article
TL;DR: In this article, the influence of red and white Gaussian noise for electronic energies and eigen states of cylindrically shaped quantum dots was considered and analytical expressions for the eigenvalue shifts and electronic envelope functions in the k · p formalism due to stochastic variations in the confining band-edge potential.
Abstract: In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k · p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom. Keywords—cylindrical quantum dots, electronic eigenenergies, red and white Gaussian noise, ensemble averaging effects.

Journal ArticleDOI
01 Mar 2008
TL;DR: The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry as discussed by the authors.
Abstract: In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada–US–Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologia (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop.

Journal ArticleDOI
TL;DR: In this paper, the influence of size and shape on quantum-dot electronic states and intra-band oscillator strengths was investigated for conduction-band eigenstates in the framework of k ⋅ p theory using general curved coordinates.