Optimising uniformity of InAs/(InGaAs)/GaAs quantum dots grown by metal organic vapor phase epitaxy

A route towards optimisation of uniformity and density of InAs/(InGaAs)/GaAs quantum dots grown by metal organic vapor phase epitaxy (MOVPE) through successive variations of the growth parameters is reported. It is demonstrated that a key parameter in obtaining a high density of quantum dots is the V/III ratio, a fact which was shown to be valid when either AsH₃ (arsine) or tertiary-butyl-arsine (TBA) were used as group V precursors. Once the optimum V/III ratio was found, the size distribution was further improved by adjusting the nominal thickness of deposited InAs material, resulting in an optimum thickness of 1.8 monolayers of InAs in our case. The number of coalesced dots was minimised by adjusting the growth interruption time to approximately 30 s. Further, the uniformity was improved by increasing the growth temperature from 485 °C to 520 °C. By combining these optimised parameters, i.e. a growth temperature of 520 °C, 1.8 monolayers InAs thickness, 30 s growth stop time and TBA as group V precursor, a full-width-half-maximum (FWHM) of the low temperature luminescence band of 40 meV was achieved, indicating a narrow dot size distribution.     

Experimental and theoretical investigations of optical properties of GaN/AlGaN MQW nanostructures. Impact of built-in polarization fields

We report the results from detailed optical spectroscopy from MOCVD grown GaN/AlGaN multiple quantum wells (MQWs), as opposed to most previous studies where MBE was employed by means of photoluminescence (PL) technique. In this paper we will present theoretical and experimental results demonstrating how polarization induced electric fields and bound interface charges in GaN/AlGaN MQWs affect the emission peak energy, PL line shape, as well as the emission line width. Theoretically estimated fields in this work are consistent with experimental data. Transition energy of the heavy hole and electron ground state Ee-hh in GaN/AlGaN MQWs were calculated and it is found that it stays in good agreement with the experimental data.     

Selective optical doping to predict the performance and reveal the origin of photocurrent peaks in quantum dots-in-a-well infrared photodetectors

Resonant optical pumping across the band gap was used as artificial doping in InAs/In_0.15Ga_0.85As/GaAs quantum dots-in-a-well infrared photodetectors. Through efficient filling of the quantum dot energy levels by simultaneous optical pumping into the ground states and the excited states of the quantum dots, the response was increased by a factor of 10. Low temperature photocurrent peaks observed at 120 and 148 meV were identified as intersubband transitions emanating from the quantum dot ground state and the quantum dot excited state, respectively by a selective increase of the electron population in the different quantum dot energy levels.     

-matrices satisfy Newton's inequalities

Newton's inequalities are shown to hold for the normalized coefficients of the characteristic polynomial of any - or inverse -matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.

     

Approximate cores of replica games and economies: Part II: Set-up costs and firm formation in coalition production economies

A model of a coalition production economy allowing set-up costs, indivisibilities,and nonconvexities is developed. It is shown that for all sufficiently large replications, approximate cores of the economy are nonempty.     

Symmetries and the polarized optical spectra of exciton complexes in quantum dots

A systematic and simple theoretical approach is proposed to analyze true degeneracies and polarized decay patterns of exciton complexes in semiconductor quantum dots. The results provide reliable spectral signatures for efficient symmetry characterization, and predict original features for low C(2v) and high C(3v) symmetries. Excellent agreement with single quantum dot spectroscopy of real pyramidal InGaAs/AlGaAs quantum dots grown along [111] is demonstrated. The high sensitivity of biexciton quantum states to exact high symmetry can be turned into an efficient uninvasive postgrowth selection procedure for quantum entanglement applications.     

A general asset-liability management model for the efficient simulation of portfolios of life insurance policies

New regulations and a stronger competition have increased the importance of stochastic asset-liability management (ALM) models for insurance companies in recent years. In this paper, we propose a discrete time ALM model for the simulation of simplified balance sheets of life insurance products. The model incorporates the most important life insurance product characteristics, the surrender of contracts, a reserve-dependent bonus declaration, a dynamic asset allocation and a two-factor stochastic capital market. All terms arising in the model can be calculated recursively which allows an easy implementation and efficient simulation. Furthermore, the model is designed to have a modular organization which permits straightforward modifications and extensions to handle specific requirements. In a sensitivity analysis for sample portfolios and parameters, we investigate the impact of the most important product and management parameters on the risk exposure of the insurance company and show that the model captures the main behaviour patterns of the balance sheet development of life insurance products.     

Fast linear algebra is stable

In Demmel et al. (Numer. Math. 106(2), 199–224, 2007) we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of n-by-n matrices can be done by any algorithm in O(n ^ω+η ) operations for any η >  0, then it can be done stably in O(n ^ω+η ) operations for any η >  0. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in O(n ^ω+η ) operations. J. Demmel acknowledges support of NSF under grants CCF-0444486, ACI-00090127, CNS-0325873 and of DOE under grant DE-FC02-01ER25478.     

New Coins from Old, Smoothly

Given a (known) function f:[0,1]→(0,1), we consider the problem of simulating a coin with probability of heads f(p) by tossing a coin with unknown heads probability p, as well as a fair coin, N times each, where N may be random. The work of Keane and O’Brien (ACM Trans. Model. Comput. Simul. 4(2):213–219, 1994) implies that such a simulation scheme with the probability ℙ _p (N<∞) equal to 1 exists if and only if f is continuous. Nacu and Peres (Ann. Appl. Probab. 15(1A):93–115, 2005) proved that f is real analytic in an open set S⊂(0,1) if and only if such a simulation scheme exists with the probability ℙ _p (N>n) decaying exponentially in n for every p∈S. We prove that for α>0 noninteger, f is in the space C ^α [0,1] if and only if a simulation scheme as above exists with ℙ _p (N>n)≤C(Δ _n (p)) ^α , where \varDelta _n(x):=max{?{x(1-x)/n},1/n}\varDelta _{n}(x):=\max\{\sqrt{x(1-x)/n},1/n\}. The key to the proof is a new result in approximation theory: Let B⁺_n\mathcal{B}^{+}_{n} be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree n. We show that a function f:[0,1]→(0,1) is in C ^α [0,1] if and only if f has a series representation ?_n=1^￥F_n\sum_{n=1}^{\infty}F_{n} with F_n ? B⁺_nF_{n}\in \mathcal{B}^{+}_{n} and ∑ _k>n F _k (x)≤C(Δ _n (x)) ^α for all x∈[0,1] and n≥1. We also provide a counterexample to a theorem stated without proof by Lorentz (Math. Ann. 151:239–251, 1963), who claimed that if some j_n ? B⁺_n\varphi_{n}\in\mathcal{B}^{+}_{n} satisfy |f(x)−φ _n (x)|≤C(Δ _n (x)) ^α for all x∈[0,1] and n≥1, then f∈C ^α [0,1].