Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures

Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Å), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Å GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states

Bayesian Species Delimitation Can Be Robust to Guide-Tree Inference Errors

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Exact solution of mean geodesic distance for Vicsek fractals

The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. The obtained exact solution exhibits that the mean geodesic distance approximately increases as an exponential function of the number of nodes, with the exponent equal to the reciprocal of the fractal dimension. The closed-form solution is confirmed by extensive numerical calculations.Comment: 4 pages, 3 figure

Grain refinement of DC cast magnesium alloys with intensive melt shearing

A new direct chill (DC) casting process, melt conditioned DC (MC-DC) process, has been developed for the production of high quality billets/slabs of light alloys by application of intensive melt shearing through a rotor-stator high shear device during the DC casting process. The rotor-stator high shear device provides intensive melt shearing to disperse the naturally occurring oxide films, and other inclusions, while creating a microscopic flow pattern to homogenize the temperature and composition fields in the sump. In this paper, we report the grain refining effect of intensive melt shearing in the MC-DC casting processing. Experimental results on DC casting of Mg-alloys with and without intensive melt shearing have demonstrated that the MC-DC casting process can produce magnesium alloy billets with significantly refined microstructure. Such grain refinement in the MC-DC casting process can be attributed to enhanced heterogeneous nucleation by dispersed naturally occurring oxide particles, increased nuclei survival rate in uniform temperature and compositional fields in the sump, and potential contribution from dendrite arm fragmentation