Local monotonicity of Riemannian and Finsler volume with respect to boundary distances

We show that the volume of a simple Riemannian metric on $D^n$ is locally monotone with respect to its boundary distance function. Namely if $g$ is a simple metric on $D^n$ and $g'$ is sufficiently close to $g$ and induces boundary distances greater or equal to those of $g$, then $vol(D^n,g')\ge vol(D^n,g)$. Furthermore, the same holds for Finsler metrics and the Holmes--Thompson definition of volume. As an application, we give a new proof of the injectivity of the geodesic ray transform for a simple Finsler metric.Comment: 13 pages, v3: minor corrections and clarifications, to appear in Geometriae Dedicat

Observation of a (2X8) surface reconstruction on Si_(1-x)Ge_x alloys grown on (100) Si by molecular beam epitaxy

We present evidence supporting the formation of a new, (2×8) surface reconstruction on Si_(1−x)Ge_x alloys grown on (100) Si substrates by molecular‐beam epitaxy. Surfaces of Si_(1−x)Ge_x alloys were studied using reflection high‐energy electron diffraction (RHEED) and low‐energy electron diffraction (LEED) techniques. RHEED patterns from samples with Ge concentrations, x, falling within the range 0.10–0.30 and grown at temperatures between 350 and 550 °C, exhibit n/8 fractional‐order diffraction streaks in addition to the normal (2×1) pattern seen on (100) Si. The presence of fractional‐order diffracted beams is indicative of an eight‐fold‐periodic modulation in electron scattering factor across the alloy surface. LEED patterns from surfaces of samples grown under similar conditions are entirely consistent with these results. In addition, the LEED patterns support the conclusion that the modulation is occurring in the direction of the dimer chains of a (2×1) reconstruction. We have examined the thermal stability of the (2×8) reconstruction and have found that it reverts to (2×1) after annealing to 700 °C and reappears after the sample temperature is allowed to cool below 600 °C. Such behavior suggests that the reconstruction is a stable, ordered phase for which the pair‐correlation function of surface Ge atoms exhibits an eightfold periodicity in the "1" direction of a Si‐like (2×1) reconstruction. We also present a simulation in the kinematic approximation, confirming the validity of our interpretation of these finding

Characterization of Si/Si_(1-y)C_y superlattices grown by surfactant assisted molecular beam epitaxy

Si/Si_(0.97)C_(0.03) superlattices grown on Si(001) substrates by Sb surfactant assisted molecular beam epitaxy are characterized by in situ reflection high energy electron diffraction (RHEED), atomic force microscopy, transmission electron microscopy (TEM), and high resolution x‐ray diffraction. The RHEED shows that, in the absence of Sb, the growth front roughens during Si_(0.97)C_(0.03) growth and smooths during subsequent Si growth. In contrast, when Sb is present, the growth front remains smooth throughout the growth. This observation is confirmed by cross‐sectional TEM, which reveals that for samples grown without the use of Sb, the Si/Si_(0.97)C_(0.03) interfaces (Si_(0.97)C_(0.03) on Si) are much more abrupt than the Si_(0.97)C_(0.03)/Si interfaces. In the case of Sb assisted growth, there is no observable difference in abruptness between the two types of interfaces. Atomic force microscopy micrographs of the Si_(0.97)C_(0.03) surface reveal features that could be the source of the roughness observed by RHEED and TEM

Sb-surfactant-mediated growth of Si/Si1–yCy superlattices by molecular-beam epitaxy

Si/Si0.97C0.03 superlattices were grown on Si(001) substrates by molecular beam epitaxy (MBE) to study the use of Sb as a surfactant during Si1–yCy growth. In situ reflection high energy electron diffraction (RHEED) shows that while carbon easily disrupts the two-dimensional growth of homoepitaxial Si, such disruption is suppressed for layers grown on Sb-terminated Si(001) surfaces. Cross-sectional transmission electron microscopy (TEM) reveals that for samples grown without the use of Sb, the Si/Si0.97C0.03 interfaces (Si0.97C0.03 on Si) were much more abrupt than Si0.97C0.03/Si interfaces. In the case of Sb-mediated growth, differences in abruptness between the two types of interfaces were not readily observable

Epitaxial silicon grown on CeO2/Si(111) structure by molecular beam epitaxy

Using electron beam evaporation, a Si/CeO2/Si(111) structure has been grown in a molecular beam epitaxy machine. In situ low energy electron diffraction, cross sectional transmission electron microscopy, selected area diffraction, and atomic force microscopy have been used to structurally characterize the overlying silicon layer and show it to be single crystalline and epitaxially oriented. Rutherford backscattering and energy dispersive x-ray analysis have been used to confirm the presence of a continuous 23 Å CeO2 layer at the interface. Rutherford backscattering and x-ray photoemission spectroscopy show an additional presence of cerium both at the exposed silicon surface and incorporated in low levels (~ 1%) within the silicon film, suggesting a growth mechanism with cerium riding atop the silicon growth front leaving behind small amounts of cerium incorporated in the growing silicon crystal

Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin

Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Electronic properties of Si/Si1–x–yGexCy heterojunctions

We have used admittance spectroscopy and deep-level transient spectroscopy to characterize electronic properties of Si/Si1–x–yGexCy heterostructures. Band offsets measured by admittance spectroscopy for compressively strained Si/Si1–x–yGexCy heterojunctions indicate that incorporation of C into Si1–x–yGexCy lowers both the valence- and conduction-band edges compared to those in Si1–xGex by an average of 107 ± 6 meV/% C and 75 ± 6 meV/% C, respectively. Combining these measurements indicates that the band alignment is type I for the compositions we have studied, and that these results are consistent with previously reported results on the energy band gap of Si1–x–yGexCy and with measurements of conduction band offsets in Si/Si1–yCy heterojunctions. Several electron traps were observed using deep-level transient spectroscopy on two n-type heterostructures. Despite the presence of a significant amount of nonsubstitutional C (0.29–1.6 at. %), none of the peaks appear attributable to previously reported interstitial C levels. Possible sources for these levels are discussed

Difficulty of distinguishing product states locally

Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is not enough for optimal decoding. For simple examples of pure product states, the gap in performance is known to be rather small when arbitrary local strategies are allowed. Here we restrict to local strategies readily achievable with current technology; those requiring neither a quantum memory nor joint operations. We show that, even for measurements on pure product states there can be a large gap between such strategies and theoretically optimal performance. Thus even in the absence of entanglement physically realizable local strategies can be far from optimal for extracting quantum information.Comment: 5 pages, 1 figur