Infinite Horizon Problems in the Calculus of Variations

Set-Valued and Variational Analysis - In this paper we consider a class of infinite horizon variational problems resulting from a transformation of singular variational problems. Herein we assume...     

Donor-like defects in ZnO substrate materials and ZnO thin films

We have investigated donor-like defects in ZnO substrate material grown by three different methods, and in epitaxial ZnO thin films grown on sapphire by pulsed laser deposition. Temperature dependent Hall effect measurements yield information about dominant donors. The thermal activation energies lie in a wide range from about 20 meV to about 370 meV. Deep level transient spectroscopy is used to obtain parameters of deep donor-like defects. For that, a high-speed diode contact configuration was laid out for the epitaxial thin films in order to determine the defect parameters with high precision. The identified levels are E1, E3 and E4, though the level E4 is observed only in single crystals grown by seeded chemical vapor transport. PACS 72.10.Fk; 72.80.Ey; 73.50.-h     

MOVPE of InP Using Trimethylindium – Trimethylamine Adduct

Growth of InP layers by MOVPE using trimethylindium-trimethylamine (TMIn–TMN) is described. Low temperature photoluminescence results reveal the high crystal quality indicated by the well resolved excitonic spectra and high internal quantum efficiency. A strong near-gap luminescence degradation with decreasing substrate temperature during the growth corresponds with the increasing deep level concentration estimated by the DLTS-investigations. In the specimens prepared at higher temperatures carbon and zinc are believed to be the main residual acceptors. From C–V data free carrier concentrations of 10¹⁵ cm⁻³ were obtained.     

A correlation between concentration of deep levels and growth conditions for VPE?GaP

A minimum in deep level concentration in VPE-GaP is found which corresponds to exceptional growth conditions near a relative maximum of the growth rate r in dependence on the GaCl input pressure pG̊aCL. The minimum occurs at the cross-over between mass flow controlled growth (at low pG̊aCL.) and surface reaction controlled growth (at high pG̊aCL.).     

Pontryagin Principle for State-Constrained Control Problems Governed by a First-Order PDE System

This paper considers multidimensional control problems governed by a first-order PDE system and state constraints. After performing the standard Young measure relaxation, we are able to prove the Pontryagin principle by means of an -maximum principle. Generalizing the common setting of one-dimensional control theory, we model piecewise-continuous weak derivatives as functions of the first Baire class and obtain regular measures as corresponding multipliers. In a number of corollaries, we derive necessary optimality conditions for local minimizers of the state-constrained problem as well as for global and local minimizers of the unconstrained problem.     

Second-order sufficient conditions for control problems with mixed control-state constraints

References 1–4 develop second-order sufficient conditions for local minima of optimal control problems with state and control constraints. These second-order conditions tighten the gap between necessary and sufficient conditions by evaluating a positive-definiteness criterion on the tangent space of the active constraints. The purpose of this paper is twofold. First, we extend the methods in Refs. 3, 4 and include general boundary conditions. Then, we relate the approach to the two-norm approach developed in Ref. 5. A direct sufficiency criterion is based on a quadratic function that satisfies a Hamilton-Jacobi inequality. A specific form of such a function is obtained by applying the second-order sufficient conditions to a parametric optimization problem. The resulting second-order positive-definiteness conditions can be verified by solving Riccati equations.The authors wish to thank K. Malanowski for helpful discussions.     

Anionic and cationic substitution in ZnO

In this contribution we review the impact of anionic and cationic substitutions on the electronic properties of bulk ZnO crystals, thin films and ZnO powders. p-type doping is discussed with focus on the anionic substitution of oxygen by nitrogen or phosphorous. n-type doping is exemplarily reviewed for substitution of Zn by group III elements. The impact of isoelectronic substitution of zinc (with Cd or Mg) or of oxygen (with S, Se, Te) on the band gap are also discussed for the respective ternary alloy. The substitution of Zn by the transition metal Mn introduces several electronic levels in the band gap which significantly alter the absorption and emission properties. Further, devices based on substitutional effects in ZnO are reviewed: Schottky diodes (unipolar device) and pn-diodes (bipolar device).     

Investigation of acceptor states in ZnO by junction DLTS

We have realized a p-type ZnO surface layer by N⁺ ion implantation of a high quality ZnO wafer and subsequent annealing. The conduction type of this surface layer was revealed by scanning capacitance microscopy. Rectifying current–voltage characteristics for processed devices were coherent with the existence of an internal pn junction. Deep donor- and acceptor-like defects were investigated by junction deep level transient spectroscopy. The donor-like levels correspond to those commonly observed for E1 and E3 defects. The acceptor states resolved have thermal activation energies of about 150 meV and 280 meV, respectively.     

Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics

In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear–quadratic regulator problem.