Transport and Boundary Scattering in Confined Geometries: Analytical Results

We utilize a geometric argument to determine the effects of boundary scattering on the carrier mean-free path in samples of various cross sections. Analytic expressions for samples with rectangular and circular cross sections are obtained. We also outline a method for incorporating these results into calculations of the thermal conductivity.Comment: 35 pages, Late

Scaling of Heteroepitaxial Island Sizes

Monte Carlo simulations of an atomistic solid-on-solid model are used to study the effect of lattice misfit on the distribution of two-dimensional islands sizes as a function of coverage $\Theta$ in the submonolayer aggregation regime of epitaxial growth. Misfit promotes the detachment of atoms from the perimeter of large pseudomorphic islands and thus favors their dissolution into smaller islands that relieve strain more efficiently. The number density of islands composed of $s$ atoms exhibits scaling in the form \mbox{$N_s(\Theta) \sim \Theta / \langle s \rangle^2 \, g(s/\langle s \rangle$)} where $\langle s \rangle$ is the average island size. Unlike the case of homoepitaxy, a rate equation theory based on this observation leads to qualitatively different behavior than observed in the simulations.Comment: 10 pages, LaTeX 2.09, IC-DDV-94-00

Irrational constants in positronium decays

We establish irrational constants, that contribute to the positronium lifetime at $O(\alpha)$ and $O(\alpha^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $\zeta$ values.Comment: Presented at 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, 20-25 Apr 2008. 6 pages, 3 figure

Quantum theory of intersubband polarons

We present a microscopic quantum theory of intersubband polarons, quasiparticles originated from the coupling between intersubband transitions and longitudinal optical phonons. To this aim we develop a second quantized theory taking into account both the Fr\"ohlich interaction between phonons and intersubband transitions and the Coulomb interaction between the intersubband transitions themselves. Our results show that the coupling between the phonons and the intersubband transitions is extremely intense, thanks both to the collective nature of the intersubband excitations and to the natural tight confinement of optical phonons. Not only the coupling is strong enough to spectroscopically resolve the resonant splitting between the modes (strong coupling regime), but it can become comparable to the bare frequency of the excitations (ultrastrong coupling regime). We thus predict the possibility to exploit intersubband polarons both for applied optoelectronic research, where a precise control of the phonon resonances is needed, and also to observe fundamental quantum vacuum physics, typical of the ultrastrong coupling regime

Cerenkov generation of high-frequency confined acoustic phonons in quantum wells

We analyze the Cerenkov emission of high-frequency confined acoustic phonons by drifting electrons in a quantum well. We find that the electron drift can cause strong phonon amplification (generation). A general formula for the gain coefficient, alpha, is obtained as a function of the phonon frequency and the structure parameters. The gain coefficient increases sharply in the short-wave region. For the example of a Si/SiGe/Si device it is shown that the amplification coefficients of the order of hundreds of 1/cm can be achieved in the sub-THz frequency range.Comment: 4 pages, 2 figures. Submitted to AP

Electron-Phonon Interaction in Embedded Semiconductor Nanostructures

The modification of acoustic phonons in semiconductor nanostructures embedded in a host crystal is investigated including corrections due to strain within continuum elasticity theory. Effective elastic constants are calculated employing {\em ab initio} density functional theory. For a spherical InAs quantum dot embedded in GaAs barrier material, the electron-phonon coupling is calculated. Its strength is shown to be suppressed compared to the assumption of bulk phonons