Niels Søndergaard

Photovoltaics with Piezoelectric Core—Shell Nanowires

We report on a theoretical discovery of a generic piezoelectric field in strained core-shell compound semiconductor nanowires. We show, using both an analytical model and numerical simulations based on fully electroelastically coupled continuum elasticity theory, that lattice-mismatch-induced strain in an epitaxial core-shell nanowire gives rise to an internal electric field along the axis of the nanowire. This piezoelectric field results predominantly from atomic layer displacements along the nanowire axis within both the core and shell materials and can appear in both zinc blende and wurtzite crystalline core-shell nanowires. The effect can be employed to separate photon-generated electron-hole pairs in the core-shell nanowires and thus offers a new device concept for solar energy conversion.

Strain in semiconductor core-shell nanowires

We compute strain distributions in core-shell nanowires of zinc blende structure. We use both continuum elasticity theory and an atomistic model, and consider both finite and infinite wires. The atomistic valence force-field (VFF) model has only few assumptions. But it is less computationally efficient than the finite-element (FE) continuum elasticity model. The generic properties of the strain distributions in core-shell nanowires obtained based on the two models agree well. This agreement indicates that although the calculations based on the VFF model are computationally feasible in many cases, the continuum elasticity theory suffices to describe the strain distributions in large core-shell nanowire structures. We find that the obtained strain distributions for infinite wires are excellent approximations to the strain distributions in finite wires, except in the regions close to the ends. Thus, our most computationally efficient model, the FE continuum elasticity model developed for infinite wires, is s...

Elastic and Piezoelectric Properties of Zincblende and Wurtzite Crystalline Nanowire Heterostructures.

The elastic and piezoelectric properties of zincblende and wurtzite crystalline InAs/InP nanowire heterostructures have been studied using electro-elastically coupled continuum elasticity theory. A comprehensive comparison of strains, piezoelectric potentials and piezoelectric fields in the two crystal types of nanowire heterostructures is presented. For each crystal type, three different forms of heterostructures-core-shell, axial superlattice, and quantum dot nanowire heterostructures-are considered. In the studied nanowire heterostructures, the principal strains are found to be insensitive to the change in the crystal structure. However, the shear strains in the zincblende and wurtzite nanowire heterostructures can be very different. All the studied nanowire heterostructures are found to exhibit a piezoelectric field along the nanowire axis. The piezoelectric field is in general much stronger in a wurtzite nanowire heterostructure than in its corresponding zincblende heterostructure. Our results are expected to be particularly important for analyzing and understanding the properties of epitaxially grown nanowire heterostructures and for applications in nanowire electronics, optoelectronics, and biochemical sensing.

Resolving isospectral 'drums' by counting nodal domains

Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace-Beltrami operators for pairs of flat tori in R-n with n >= 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions-where a four-parameter family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus one can count the shape of a drum (if it is designed as a flat torus in four dimensions). (Less)

Strain distributions in lattice-mismatched semiconductor core-shell nanowires

The authors study the elastic deformation field in lattice-mismatched core-shell nanowires with single and multiple shells. The authors consider infinite wires with a hexagonal cross section under the assumption of translational symmetry. The strain distributions are found by minimizing the elastic energy per unit cell using the finite element method. The authors find that the trace of the strain is discontinuous with a simple, almost piecewise variation between core and shell, whereas the individual components of the strain can exhibit complex variations.

Short wavelength approximation of a boundary integral operator for homogeneous and isotropic elastic bodies

A short wavelength approximation of a boundary integral operator for two-dimensional isotropic and homogeneous elastic bodies is derived from first principles starting from the Navier-Cauchy equation. Trace formulas for elastodynamics are deduced connecting the eigenfrequency spectrum of an elastic body to the set of periodic rays where mode conversion enters as a dynamical feature.

Wave chaos in elastodynamic cavity scattering

The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more- cylindrical cavity systems, and compared to an elastodynamic generalization of the semi-classical Gutzwiller unstable periodic orbits formulas. In contrast to quantum mechanics, complex periodic orbits associated with the surface Rayleigh waves dominate the low-frequency spectrum, and already the two-cavity system displays chaotic features.

Noise Corrections to Stochastic Trace Formulas

We review studies of an evolution operator ℒ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ℒ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ℒ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ℒn. Using an integral representation of the evolution operator ℒ, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula.

Understanding mechanical properties of nanostructures using Euler's theory

The objective of this paper is to theoretically quantify large deflections of chromium nanocantilevers using Eulers theory. We show that, remarkably, Eulers theory originally derived for elastic macroscopic rods made of homogeneous material also describes the bending of nanocantilevers. In addition, the theory yields a precise method to deduce Youngs extension modulus of the nanocantilevers. In particular, we find our nanocantilevers to be considerably softer than macroscopic chromium rods.

Families of spherical caps: spectra and ray limit

We consider a family of surfaces of revolution ranging between a disc and a hemisphere, that is spherical caps. For this family, we study the spectral density in the ray limit and arrive at a trace formula with geodesic polygons describing the spectral fluctuations. When the caps approach the hemisphere the spectrum becomes equally spaced and highly degenerate whereas the derived trace formula breaks down. We discuss its divergence and also derive a different trace formula for this hemispherical case. We next turn to perturbative corrections in the wave number where the work in the literature is done for either flat domains or curved without boundaries. In the present case, we calculate the leading correction explicitly and incorporate it into the semiclassical expression for the fluctuating part of the spectral density. To the best of our knowledge, this is the first calculation of such perturbative corrections in the case of curvature and boundary.