On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

Properties of cubic GaN grown by MBE

We review our investigation of cubic GaN films on (001) GaAs, focusing on the structural, optical, and electrical properties of these films. Cubic GaN films grown epitaxially on GaAs suffer from the large lattice mismatch between these two materials in that they contain extremely high densities of structural defects. Surprisingly, the optical quality of these films does not seem much affected by the presence of defects, as intense photoluminescence is detected a? room temperature and above. Finally, the rather high background electron concentrations in our films is shown to be a consequence of contamination with O and not to be an intrinsic property of cubic phase GaN. (C) 1997 Elsevier Science S.A.

ON THE RATE-EQUATIONS OF SEMICONDUCTOR-LASERS FOR MEASURING SPONTANEOUS EMISSION FACTOR

The rate equations used for measuring spontaneous emission factor beta is examined through the comparison of numerical results, The results show that beta obtained by using total spontaneous emission rate R(sp) = N/tau sp is about double of that using R(sp) = BN2, The magnitude difference between the measured beta and that predicted by classical theory [8] will disappear by using more reasonable R(sp) = BN2. The results also show that the magnitude of beta may be underestimated by ignoring the nonradiative recombination rates.

Growth of Cubic GaN by MOCVD at High Temperature

High quality cubic GaN (c-GaN) is grown by metalorganic vapor deposition (MOCVD) at an increased growth temperature of 900 ℃, with the growth rate of 1.6 μm/h. The full width at half maximum (FWHM) of room temperature photoluminescence (PL) for the high temperature grown GaN film is 48meV. It is smaller than that of the sample grown at 830 ℃. In X-ray diffraction (XRD) measurement, the high temperature grown GaN shows a (002) peak at 20° with a FWHM of 21'. It can be concluded that, although c-GaN is of metastable phase, high growth temperature is still beneficial to the improvement in its crystal quality. The relationship between the growth rate and growth temperature is also discussed.

Strain Analysis of Cubic AlGaN/GaNGrownon GaAs（100） Substrate by MOVPE

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Choice of calibration equations of the TSM method

For the reciprocal-test fixtures, there are six independent S-parameters to. be determined, and the thru-short-match (TSM) calibration can provide eight calibration equations. In this paper, the relation of calibration equations is investigated. It has been shown that the four equations obtained from the measurement with a transmission standard can be used simultaneously in the calibration. Experimental results show that the different choice of equations will lead to quite different solution, and the calibration accuracy can be improved by taking advantages of the established relation among the calibration equations and properly choosing calibration equations.

MOCVD growth of cubic GaN: Materials and devices

Many impressive progresses have been made recently on the growth of cubic-phase GaN by MBE and MOCVD. In this paper, some of our recent progress will be reviewed, including the growth of high quality cubic InGaN films, InGaN/GaN heterostructure blue and green LEDs. Cubic-phase GaN films were grown on GaAs (100) substrates by MOCVD. Growth conditions were optimized to obtain pure cubic phase GaN films up to a thickness of 4 mum. An anomalous compressive strain was found in the as-grown GaN films in spite of a smaller lattice constant for GaN compared with that of GaAs substrates. The photoluminescence FWHM of high quality InGaN epilayers was less than 100 meV The InGaN/GaN heterostructure blue LED has intense electroluminescence with a FWHM of 20 nm.

Design of high brightness cubic-GaN LEDs grown on GaAs substrate

The Principle of optical thin film was used to calculate the feasibility of improving the light extraction efficiency of GaN/GaAs optical devices by wafer-bonding technique. The calculated results show that the light extraction efficiency of bonded samples can be improved by 2.66 times than the as-grown GaN/GaAs samples when a thin Ni layer was used as adhesive layer and Ag layer as reflective layer. Full reflectance spectrum comparison shows that reflectivity for the incident light of 459.2 nm of the bonded samples was improved by 2.4 times than the as-grown samples, which is consistent with the calculated results.

Defect states in cubic GaN epilayer grown on GaAs by metalorganic vapor phase epitaxy

Defect states in cubic GaN epilayers grown on GaAs were investigated with the photoluminescence technique. One shallow donor and two acceptors were identified to be involved in relevant optical transitions. The binding energies of the free excitons, the bound excitons. the donor and the acceptors were determined. These values are in good agreement with recent theoretical results.

Orientation relationship between hexagonal inclusions and cubic GaN grown on GaAs(001) substrates

Cubic GaN/GaAs(0 0 1) epilayers and hexagonal inclusions are characterized by X-ray diffraction (XRD), Photoluminescence (PL), Raman spectroscopy, and transmission electron microscopy (TEM). The X-ray {0 0 0 2} and (1 0 (1) over bar 0) pole figures show that the orientation relationships between cubic GaN and hexagonal inclusions are (1 1 1)//(0 0 0 1), <1 1 2 >//<1 0 (1) over bar 0 >. The distribution of hexagonal inclusions mainly results from the interfacial bonding disorder in the grain boundaries parallel to hexagonal <0 0 0 1 > directions and the lattice mismatch in <0 0 0 1 > directions on {1 0 (1) over bar 0} planes. In order to reduce the energy increase in cubic epilayers, hexagonal lamellas with smaller sizes in <0 0 0 1 > directions often nucleate inside the buffer layer or near the interface between the buffer layer and the epitaxial layer, and penetrate through the whole epitaxial layer with this orientation relationship. (C) 2001 Elsevier Science B.V. All rights reserved.