Modelling of AlAs/GaAs interfacial structures using high-angle annular dark field (HAADF) image simulations

High angle annular dark field (HAADF) image simulations were performed on a series of AlAs/GaAsinterfacial models using the frozen-phonon multislice method. Three general types of models were considered—perfect, vicinal/sawtooth and diffusion. These were chosen to demonstrate how HAADFimage measurements are influenced by different interfacialstructures in the technologically important III–V semiconductor system. For each model, interfacial sharpness was calculated as a function of depth and compared to aberration-corrected HAADF experiments of two types of AlAs/GaAs interfaces. The results show that the sharpness measured from HAADF imaging changes in a complicated manner with thickness for complex interfacialstructures. For vicinal structures, it was revealed that the type of material that the probe projects through first of all has a significant effect on the measured sharpness. An increase in the vicinal angle was also shown to generate a wider interface in the random step model. The Moison diffusion model produced an increase in the interface width with depth which closely matched the experimental results of the AlAs-on-GaAs interface. In contrast, the interface width decreased as a function of depth in the linear diffusion model. Only in the case of the perfect model was it possible to ascertain the underlying structure directly from HAADFimage analysis

Characterisation of InAs/GaAs short period superlattices using column ratio mapping in aberration-corrected scanning transmission electron microscopy

The image processing technique of columnratiomapping was applied to aberration-corrected high angle annular dark field (HAADF) images of shortperiod MBE (molecular beam epitaxy) grown InAs/GaAssuperlattices. This method allowed the Indium distribution to be mapped and a more detailed assessment of interfacial quality to be made. Frozen-phonon multislice simulations were also employed to provide a better understanding of the experimental columnratio values. It was established that ultra-thin InAs/GaAs layers can be grown sufficiently well by MBE. This is despite the fact that the Indium segregated over 3–4 monolayers. Furthermore, the effect of the growth temperature on the quality of the layers was also investigated. It was demonstrated that the higher growth temperature resulted in a better quality superlattice structure

The Lee-Yang and P\'olya-Schur Programs. I. Linear Operators Preserving Stability

In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probability theory, combinatorics, and matrix theory. We characterize all linear operators on finite or infinite-dimensional spaces of multivariate polynomials preserving the property of being non-vanishing whenever the variables are in prescribed open circular domains. In particular, this solves the higher dimensional counterpart of a long-standing classification problem originating from classical works of Hermite, Laguerre, Hurwitz and P\'olya-Schur on univariate polynomials with such properties.Comment: Final version, to appear in Inventiones Mathematicae; 27 pages, no figures, LaTeX2

Near-Simultaneous Polar and DMSP Measurements of Topside Ionosphere Field - Aligned Flows at High Latitudes

Near-simultaneous observations of topside 0' parallel flows are presented for four periods of measurement by POLAR and DMSP satellites during April 1996. The POLAR measurements are from Southern perigee measurements near 5000 km altitude, while the DMSP measurements were from 840 km altitude. These observations provide a view of wide-spread upward/downward ionospheric O(+) flows over the broad polar region along extended and multiple distinct satellite tracks. In general, the velocities are upward toward expected cleft and auroral latitudes, typically about a 2-10 km/s at 5000 km altitude, and 0-2 km/s at 840 km altitudes. At the highest, polar cap latitudes, downward velocities are more frequent at both altitudes, but especially at the lower 840 km altitude. The downward velocities were typically a few hundred d s at 840 altitude, and 0-1 km/s at 5000 km altitude. In some instances, apparently downward velocities were observed at 840 km altitudes while upward 0' flows were observed at 5000 km altitude on the same flux tube. The O+ density were characteristically 1-10 O(+)/cu cm at 5000 km altitude and 10(exp 3) - 10(exp 40 O(+)/cu cm at 840 km altitude, while the O(+) flux were characteristically 1 10(exp 5) - 10(exp 7) O(+)+/sq cm -sec at 5000 km altitudes and characteristically 10(exp 7) - 10(exp 9) O(+)/sq cm -sec at 840 km altitude. We have also examined the dual altitude parameter measurements for a polar cap field line, the POLAR and DMSP measurements approximately 30 minutes apart, and compared them with results from a transport simulation in which a flux tube was subjected to a brief pulse of soft electron precipitation and topside transverse ion heating. The simulated density and velocity altitude profiles for 5 minutes later generally matched the observations, except that the observed downward velocities (500 - 600 m/s) at 840 km altitude were much larger than those simulated