Morten Willatzen

The k.p Method: Electronic Properties of Semiconductors

I Homogeneous Crystals.- One-Band Model.- Perturbation Theory#x2014 Valence Band.- Perturbation Theory #x2013 Kane Models.- Method of Invariants.- Spin Splitting.- Strain.- II Nonperiodic Problem.- Shallow Impurity States.- Magnetic Effects.- Electric Field.- Excitons.- Heterostructures: Basic Formalism.- Heterostructures: Further Topics.- Conclusion.

Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles

We demonstrate that a pair of perpendicular electrical dipolar scatterers resonating at different frequencies can be used as a metamaterial unit cell to construct a nanometer-thin retarder in reflection, designing nanocross and nanobrick plasmonic configurations to function as reflecting quarter-wave plates at ~1520 and 770 nm, respectively. The design is corroborated experimentally with a monolayer of gold nanobricks, transforming linearly polarized incident radiation into circularly polarized radiation at ~780 nm.

Detuned Electrical Dipoles for Plasmonic Sensing

We demonstrate that a pair of electrical dipolar scatterers resonating at different frequencies, i.e., detuned electrical dipoles, can be advantageously employed for plasmonic sensing of the environment, both as an individual subwavelength-sized sensor and as a unit cell of a periodic array. It is shown that the usage of the ratio between the powers of light scattered into opposite directions (or into different diffraction orders), which peaks at the intermediate frequency, allows one to reach a sensitivity of ≈ 400 nm/RIU with record high levels of figure of merit exceeding 200. Qualitative considerations are supported with detailed simulations and proof-of-principle experiments using lithographically fabricated gold nanorods with resonances at 800 nm.

Electromechanical phenomena in semiconductor nanostructures

Electromechanical phenomena in semiconductors are still poorly studied from a fundamental and an applied science perspective, even though significant strides have been made in the last decade or so. Indeed, most current electromechanical devices are based on ferroelectric oxides. Yet, the importance of the effect in certain semiconductors is being increasingly recognized. For instance, the magnitude of the electric field in an AlN/GaN nanostructure can reach 1–10 MV/cm. In fact, the basic functioning of an (0001) AlGaN/GaN high electron mobility transistor is due to the two-dimensional electron gas formed at the material interface by the polarization fields. The goal of this review is to inform the reader of some of the recent developments in the field for nanostructures and to point out still open questions. Examples of recent work that involves the piezoelectric and pyroelectric effects in semiconductors include: the study of the optoelectronic properties of III-nitrides quantum wells and dots, the current controversy regarding the importance of the nonlinear piezoelectric effect, energy harvesting using ZnO nanowires as a piezoelectric nanogenerator, the use of piezoelectric materials in surface acoustic wave devices, and the appropriateness of various models for analyzing electromechanical effects. Piezoelectric materials such as GaN and ZnO are gaining more and more importance for energy-related applications; examples include high-brightness light-emitting diodes for white lighting, high-electron mobility transistors, and nanogenerators. Indeed, it remains to be demonstrated whether these materials could be the ideal multifunctional materials. The solutions to these and other related problems will not only lead to a better understanding of the basic physics of these materials, but will validate new characterization tools, and advance the development of new and better devices. We will restrict ourselves to nanostructures in the current article even though the measurements and calculations of the bulk electromechanical coefficients remain challenging. Much of the literature has focused on InGaN/GaN, AlGaN/GaN, ZnMgO/ZnO, and ZnCdO/ZnO quantum wells, and InAs/GaAs and AlGaN/AlN quantum dots for their optoelectronic properties; and work on the bending of nanowires have been mostly for GaN and ZnO nanowires. We hope the present review article will stimulate further research into the field of electromechanical phenomena and help in the development of applications.

Dynamic Electromechanical Modeling of Dielectric Elastomer Actuators With Metallic Electrodes

In this paper, a nonlinear electromechanical model for a PolyPower dielectric elastomer actuator is proposed based on an electric circuit model coupled with a viscoelastic mechanical model. The parameters of the model are found by fitting to an electrical step impulse for the mechanical part and by standard methods for the electric circuit. The resulting model is compared with experiments for a range of sinusoidal stimuli. The comparison shows good agreement between experiments and model results.

Optical transparency by detuned electrical dipoles

We demonstrate that optical transparency can be realized with plasmonic metamaterials using unit cells consisting of detuned electrical dipoles (DED), thereby mimicking the dressed-state picture of the electromagnetically induced transparency (EIT) in atomic physics. Theoretically analyzing the DED cells with two and three different silver ellipsoids, we show the possibility of reaching a ?10 times decrease in group velocity and a propagation loss of ?1?dB per cell within the optical wavelength range of 625?640?nm. Similar configurations are realized with lithographically fabricated gold nanorods placed on a glass substrate and subsequently covered with a ~15-?m-thick polymer layer, featuring EIT-like transmission spectra with transparency windows at wavelengths of ~850?nm.

Extraordinary absorption of sound in porous lamella-crystals

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

Ultrasound transducer modeling-general theory and applications to ultrasound reciprocal systems

A tutorial presentation on the theory of reciprocal ultrasound systems is given, and a complete set of modeling equations for one-dimensional multi-layer ultrasound transducers is derived from first principles. The model includes dielectric losses and mechanical losses in the transducer material layers as well as sound absorption in the transmission medium. First, the so-called constitutive relations of a piezoelectric body are derived based on general thermodynamic considerations, assuming that transducer operation takes place under almost isentropic conditions. Second, full attention is given to transducers oscillating in the thickness mode, discarding all other vibration modes. Dynamic transducer equations are determined using Newtons Second Law, Poissons equation, and the definition of strain applied to a piezoelectric transducer with one or more non-piezoelectric layers on the front surface (multilayer transducer). Boundary conditions include continuity of normal velocity and stress across material interfaces as well as a subsidiary electrical condition over the piezoceramic electrodes. Sound transmission is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter. This allows, e.g., a detailed treatment of receiver signal variations as the receiver moves from the near-field zone to the far-field zone of the transmitter. In the remaining part of the paper, receiver voltage and current signals are obtained by solving the full set of dynamic equations numerically. Special attention is given to transducers consisting of a) a pure piezoceramic layer only, b) a piezoceramic layer and a quarter-wavelength matching layer of polyphenylensulphide (PPS), c) a piezoceramic layer and a half-wavelength matching layer of stainless steel, and d) a piezoceramic layer and a half-wavelength matching layer of stainless steel tuned to resonance by a parallel inductance. Results are also given for receiver incoming pressure and receiver voltage signals when sound reception takes place in the near-field and far-field zones of the transmitter.

Dynamic coupling of piezoelectric effects, spontaneous polarization, and strain in lattice-mismatched semiconductor quantum-well heterostructures

A static and dynamic analysis of the combined and self-consistent influence of spontaneous polarization, piezoelectric effects, lattice mismatch, and strain effects is presented for a three-layer one-dimensional AlN∕GaN wurtzite quantum-well structure (with GaN as the central quantum-well layer). It is shown that, contrary to the assumption of Fonoberov and Balandin [J. Appl. Phys. 94, 7178 (2003); J. Vac. Sci. Technol. B 22, 2190 (2004)], even in cases with no current transport through the structure, the strain distributions are not well captured by minimization of the strain energy only and not, as is in principle required, the total free energy including electric and piezoelectric coupling and spontaneous polarization contributions. Furthermore, we have found that, when an ac signal is imposed through the structure, resonance frequencies exist where strain distributions are even more strongly affected by piezoelectric-coupling contributions depending on the amount of mechanical and electrical losses in...

Schrödinger problems for surfaces of revolution—the finite cylinder as a test example

A set of ordinary differential equations is derived employing the method of differentiable forms so as to describe the quantum mechanics of a particle constrained to move on a general two-dimensional surface of revolution. Eigenvalues and eigenstates are calculated quasianalytically in the case of a finite cylinder (finite along the axis) and compared with the eigenvalues and eigenstates of a full three-dimensional Schrodinger problem corresponding to a hollow cylinder in the limit where the inner and outer radii approach each other. Good agreement between the two models is obtained for a relative difference less than 20% in inner and outer radii.