Microprobe photoluminescence measurement on heteroepitaxial GaAs on Si grown by metalorganic chemical vapor deposition

Microprobe photoluminescence (PL) measurements at 77 K were used to study the effect of the GaAs layer thickness on optical quality and variations in strain in GaAs/Si containing microcracks. PL peak intensities increase with the increase in thickness of GaAs layers and the peak intensity for the 5.5 m GaAs layer was a factor of 20 higher than those for the 1–2 m GaAs layers. Spatial nonuniformities in strain in the vicinity of two microcracks reveal that stress was almost released at the intersection of two microcracks and is maximum half way between two microcracks.On leave from Semiconductor Materials Lab., Korea Institute of Science and Technology (KIST)     

On laplace continued fraction for the normal integral

The Laplace continued fraction is derived through a power series. It provides both upper bounds and lower bounds of the normal tail probability % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x), it is simple, it converges for x>0, and it is by far the best approximation for x3. The Laplace continued fraction is rederived as an extreme case of admissible bounds of the Mills' ratio, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x)/(x), in the family of ratios of two polynomials subject to a monotone decreasing absolute error. However, it is not optimal at any finite x. Convergence at the origin and local optimality of a subclass of admissible bounds are investigated. A modified continued fraction is proposed. It is the sharpest tail bound of the Mills' ratio, it has a satisfactory convergence rate for x1 and it is recommended for the entire range of x if a maximum absolute error of 10^-4 is required.The efforts of the author were supported by the NSERC of Canada.     

Superstable theories with few countable models

Summary We prove here: Theorem. LetT be a countable complete superstable non -stable theory with fewer than continuum many countable models. Then there is a definable groupG with locally modular regular generics, such thatG is not connected-by-finite and any type inG ^eq orthogonal to the generics has Morley rank. Corollary. LetT be a countable complete superstable theory in which no infinite group is definable. ThenT has either at most countably many, or exactly continuum many countable models, up to isomorphism.Supported by NSF grant DMS 90-06628     

Enumeration of Almost-Convex Polygons on the Square Lattice

We classify self-avoiding polygons on the square lattice according to a concavity measure, m, where 2m is the difference between the number of steps in the polygon and the perimeter of the minimal rectangle bounding the polygon. We generate series expansions for the perimeter generating functions S_m(x) for polygons of concavity m. We analyze the series S_m(x) for m = 0 to 3. If N_m,n denotes the number of polygons of perimeter 2n and concavity m, with m = o(n^1/2), we prove that N_m,n ? 2^2n?m?7n^m+1/m!, and that the radius of convergence of the series counting all polygons with m = o(n) is equal to 1/4. Our numerical data leads us to conjecture that in fact for m = o(n^1/2), a result confirmed for m = 0 and 1.