Fabrication of photonic band-gap crystals

We describe the fabrication of three-dimensional photonic crystals using a reproducible and reliable procedure consisting of electron beam lithography followed by a sequence of dry etching steps. Careful fabrication has enabled us to define photonic crystals with 280 nm holes defined with 350 nm center to center spacings in GaAsP and GaAs epilayers. We construct these photonic crystals by transferring a submicron pattern of holes from 70-nm-thick polymethylmethacrylate resist layers into 300-nm-thick silicon dioxide ion etch masks, and then anisotropically angle etching the III-V semiconductor material using this mask. Here, we show the procedure used to generate photonic crystals with up to four lattice periods depth

Dynamic response and stability of a gas-lubricated Rayleigh-step pad

The quasi-static, pressure characteristics of a gas-lubricated thrust bearing with shrouded, Rayleigh-step pads are determined for a time-varying film thickness. The axial response of the thrust bearing to an axial forcing function or an axial rotor disturbance is investigated by treating the gas film as a spring having nonlinear restoring and damping forces. These forces are related to the film thickness by a power relation. The nonlinear equation of motion in the axial mode is solved by the Ritz-Galerkin method as well as the direct, numerical integration. Results of the nonlinear response by both methods are compared with the response based on the linearized equation. Further, the gas-film instability of an infinitely wide Rayleigh step thrust pad is determined by solving the transient Reynolds equation coupled with the equation of the motion of the pad. Results show that the Rayleigh-step geometry is very stable for bearing number A up to 50. The stability threshold is shown to exist only for ultrahigh values of Lambda equal to or greater than 100, where the stability can be achieved by making the mass heavier than the critical mass

Ballistic electron emission microscopy spectroscopy study of AlSb and InAs/AlSb superlattice barriers

Due to its large band gap, AlSb is often used as a barrier in antimonide heterostructure devices. However, its transport characteristics are not totally clear. We have employed ballistic electron emission microscopy (BEEM) to directly probe AlSb barriers as well as more complicated structures such as selectively doped n-type InAs/AlSb superlattices. The aforementioned structures were grown by molecular beam epitaxy on GaSb substrates. A 100 Å InAs or 50 Å GaSb capping layer was used to prevent surface oxidation from ex situ processing. Different substrate and capping layer combinations were explored to suppress background current and maximize transport of BEEM current. The samples were finished with a sputter deposited 100 Å metal layer so that the final BEEM structure was of the form of a metal/capping layer/semiconductor. Of note is that we have found that hole current contributed significantly to BEEM noise due to type II band alignment in the antimonide system. BEEM data revealed that the electron barrier height of Al/AlSb centered around 1.17 eV, which was attributed to transport through the conduction band minimum near the AlSb X point. Variation in the BEEM threshold indicated unevenness at the Al/AlSb interface. The metal on semiconductor barrier height was too low for the superlattice to allow consistent probing by BEEM spectroscopy. However, the superlattice BEEM signal was elevated above the background noise after repeated stressing of the metal surface. A BEEM threshold of 0.8 eV was observed for the Au/24 Å period superlattice system after the stress treatment

Copying equations to assess mathematical competence: An evaluation of pause measures using graphical protocol analysis

Can mathematical competence be measured by analyzing the patterns of pauses between written elements in the freehand copying of mathematical equations? Twenty participants of varying levels of mathematical competence copied sets of equations and sequences of numbers on a graphics tablet. The third quartile of pauses is an effective measure, because it re- flects the greater number of chunks and the longer time spent per chunk by novices as they processed the equations. To compensate for individual differences in speeds of elementary operations and skill in writing basic mathematical symbols, variants on the measure were devised and tested

Non-Divergence of Unipotent Flows on Quotients of Rank One Semisimple Groups

Let $G$ be a semisimple Lie group of rank $1$ and $\Gamma$ be a torsion free discrete subgroup of $G$. We show that in $G/\Gamma$, given $\epsilon>0$, any trajectory of a unipotent flow remains in the set of points with injectivity radius larger than $\delta$ for $1-\epsilon$ proportion of the time for some $\delta>0$. The result also holds for any finitely generated discrete subgroup $\Gamma$ and this generalizes Dani's quantitative nondivergence theorem \cite{D} for lattices of rank one semisimple groups. Furthermore, for a fixed $\epsilon>0$ there exists an injectivity radius $\delta$ such that for any unipotent trajectory $\{u_tx\}_{t\in [0,T]}$, either it spends at least $1-\epsilon$ proportion of the time in the set with injectivity radius larger than $\delta$ for all large $T>0$ or there exists a $\{u_t\}_{t\in\mathbb{R}}$-normalized abelian subgroup $L$ of $G$ which intersects $g\Gamma g^{-1}$ in a small covolume lattice. We also extend these results when $G$ is the product of rank-$1$ semisimple groups and $\Gamma$ a discrete subgroup of $G$ whose projection onto each nontrivial factor is torsion free.Comment: 23 page