Phonon Dispersion Effects and the Thermal Conductivity Reduction in GaAs/AlAs Superlattices

The experimentally observed order-of-magnitude reduction in the thermal conductivity along the growth axis of (GaAs)_n/(AlAs)_n (or n x n) superlattices is investigated theoretically for (2x2), (3x3) and (6x6) structures using an accurate model of the lattice dynamics. The modification of the phonon dispersion relation due to the superlattice geometry leads to flattening of the phonon branches and hence to lower phonon velocities. This effect is shown to account for a factor-of-three reduction in the thermal conductivity with respect to bulk GaAs along the growth direction; the remainder is attributable to a reduction in the phonon lifetime. The dispersion-related reduction is relatively insensitive to temperature (100 < T < 300K) and n. The phonon lifetime reduction is largest for the (2x2) structures and consistent with greater interface scattering. The thermal conductivity reduction is shown to be appreciably more sensitive to GaAs/AlAs force constant differences than to those associated with molecular masses.Comment: 5 figure

The thermal conductivity reduction in HgTe/CdTe superlattices

The techniques used previously to calculate the three-fold thermal conductivity reduction due to phonon dispersion in GaAs/AlAs superlattices (SLs) are applied to HgTe/CdTe SLs. The reduction factor is approximately the same, indicating that this SL may be applicable both as a photodetector and a thermoelectric cooler.Comment: 5 pages, 2 figures; to be published in Journal of Applied Physic

On equations over sets of integers

Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition S+T=\makeset{m+n}{m \in S, \: n \in T} and with ultimately periodic constants is exactly the class of hyper-arithmetical sets. Equations using addition only can represent every hyper-arithmetical set under a simple encoding. All hyper-arithmetical sets can also be represented by equations over sets of natural numbers equipped with union, addition and subtraction S \dotminus T=\makeset{m-n}{m \in S, \: n \in T, \: m \geqslant n}. Testing whether a given system has a solution is $\Sigma^1_1$-complete for each model. These results, in particular, settle the expressive power of the most general types of language equations, as well as equations over subsets of free groups.Comment: 12 apges, 0 figure

A wide band gap metal-semiconductor-metal nanostructure made entirely from graphene

A blueprint for producing scalable digital graphene electronics has remained elusive. Current methods to produce semiconducting-metallic graphene networks all suffer from either stringent lithographic demands that prevent reproducibility, process-induced disorder in the graphene, or scalability issues. Using angle resolved photoemission, we have discovered a unique one dimensional metallic-semiconducting-metallic junction made entirely from graphene, and produced without chemical functionalization or finite size patterning. The junction is produced by taking advantage of the inherent, atomically ordered, substrate-graphene interaction when it is grown on SiC, in this case when graphene is forced to grow over patterned SiC steps. This scalable bottomup approach allows us to produce a semiconducting graphene strip whose width is precisely defined within a few graphene lattice constants, a level of precision entirely outside modern lithographic limits. The architecture demonstrated in this work is so robust that variations in the average electronic band structure of thousands of these patterned ribbons have little variation over length scales tens of microns long. The semiconducting graphene has a topologically defined few nanometer wide region with an energy gap greater than 0.5 eV in an otherwise continuous metallic graphene sheet. This work demonstrates how the graphene-substrate interaction can be used as a powerful tool to scalably modify graphene's electronic structure and opens a new direction in graphene electronics research.Comment: 11 pages, 7 figure

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

Ion Collisions in Very Strong Electric Fields

A Classical Trajectory Monte Carlo (CTMC) simulation has been made of processes of charge exchange and ionization between an hydrogen atom and fully stripped ions embedded in very strong static electric fields ($O(10^{10}$ V/m$)$), which are thought to exist in cosmic and laser--produced plasmas. Calculations show that the presence of the field affects absolute values of the cross sections, enhancing ionization and reducing charge exchange. Moreover, the overall effect depends upon the relative orientation between the field and the nuclear motion. Other features of a null-field situation, such as scaling laws, are revisited.Comment: Latex, 13 pages, 11 figures (available upon request), to be published in Journal of Physics

Lattice Dynamics of II-VI materials using adiabatic bond charge model

We extend the adiabatic bond charge model, originally developed for group IV semiconductors and III-V compounds, to study phonons in more ionic II-VI compounds with a zincblende structure. Phonon spectra, density of states and specific heats are calculated for six II-VI compounds and compared with both experimental data and the results of other models. We show that the 6-parameter bond charge model gives a good description of the lattice dynamics of these materials. We also discuss trends in the parameters with respect to the ionicity and metallicity of these compounds.Comment: 16 pages of RevTex with 3 figures submitted as a uuencode compressed tar fil

Disorder induced collapse of the electron phonon coupling in MgB2_{2} observed by Raman Spectroscopy

The Raman spectrum of the superconductor MgB$_{2}$ has been measured as a function of the Tc of the film. A striking correlation is observed between the $T_{c}$ onset and the frequency of the $E_{2g}$ mode. Analysis of the data with the McMillan formula provides clear experimental evidence for the collapse of the electron phonon coupling at the temperature predicted for the convergence of two superconducting gaps into one observable gap. This gives indirect evidence of the convergence of the two gaps and direct evidence of a transition to an isotropic state at 19 K. The value of the electron phonon coupling constant is found to be 1.22 for films with T$_{c}$ 39K and 0.80 for films with T$_{c}\leq$19K.Comment: 5 pages, 4 figure