Excited-state relaxation in PbSe quantum dots

In solids the phonon-assisted, nonradiative decay from high-energy electronic excited states to low-energy electronic excited states is picosecond fast. It was hoped that electron and hole relaxation could be slowed down in quantum dots, due to the unavailability of phonons energy matched to the large energy-level spacings (“phonon-bottleneck”). However, excited-state relaxation was observed to be rather fast (1 ps) in InP, CdSe, and ZnO dots, and explained by an efficient Auger mechanism, whereby the excess energy of electrons is nonradiatively transferred to holes, which can then rapidly decay by phonon emission, by virtue of the densely spaced valence-band levels. The recent emergence of PbSe as a novel quantum-dot material has rekindled the hope for a slow down of excited-state relaxation because hole relaxation was deemed to be ineffective on account of the widely spaced hole levels. The assumption of sparse hole energy levels in PbSe was based on an effective-mass argument based on the light effective mass of the hole. Surprisingly, fast intraband relaxation times of 1–7 ps were observed in PbSe quantum dots and have been considered contradictory with the Auger cooling mechanism because of the assumed sparsity of the hole energy levels. Our pseudopotential calculations, however, do not support the scenario of sparse hole levels in PbSe: Because of the existence of three valence-band maxima in the bulk PbSe band structure, hole energy levels are densely spaced, in contradiction with simple effective-mass models. The remaining question is whether the Auger decay channel is sufficiently fast to account for the fast intraband relaxation. Using the atomistic pseudopotential wave functions of Pb2046Se2117 and Pb260Se249 quantum dots, we explicitly calculated the electron-hole Coulomb integrals and the PS electron Auger relaxation rate. We find that the Auger mechanism can explain the experimentally observed PS intraband decay time scale without the need to invoke any exotic relaxation mechanisms

Multi-excitons in self-assembled InAs/GaAs quantum dots: A pseudopotential, many-body approach

We use a many-body, atomistic empirical pseudopotential approach to predict the multi-exciton emission spectrum of a lens shaped InAs/GaAs self-assembled quantum dot. We discuss the effects of (i) The direct Coulomb energies, including the differences of electron and hole wavefunctions, (ii) the exchange Coulomb energies and (iii) correlation energies given by a configuration interaction calculation. Emission from the groundstate of the $N$ exciton system to the $N-1$ exciton system involving $e_0\to h_0$ and $e_1\to h_1$ recombinations are discussed. A comparison with a simpler single-band, effective mass approach is presented

Comment on "Quantum Confinement and Optical Gaps in Si Nanocrystals"

We show that the method used by Ogut, Chelikowsky and Louie (Phys. Rev. Lett. 79, 1770 (1997)) to calculate the optical gap of Si nanocrystals omits an electron-hole polarization energy. When this contribution is taken into account, the corrected optical gap is in excellent agreement with semi-empirical pseudopotential calculations.Comment: 3 pages, 1 figur

Strict inequalities of critical values in continuum percolation

We consider the supercritical finite-range random connection model where the points $x,y$ of a homogeneous planar Poisson process are connected with probability $f(|y-x|)$ for a given $f$. Performing percolation on the resulting graph, we show that the critical probabilities for site and bond percolation satisfy the strict inequality $p_c^{\rm site} > p_c^{\rm bond}$. We also show that reducing the connection function $f$ strictly increases the critical Poisson intensity. Finally, we deduce that performing a spreading transformation on $f$ (thereby allowing connections over greater distances but with lower probabilities, leaving average degrees unchanged) {\em strictly} reduces the critical Poisson intensity. This is of practical relevance, indicating that in many real networks it is in principle possible to exploit the presence of spread-out, long range connections, to achieve connectivity at a strictly lower density value.Comment: 38 pages, 8 figure

Predicion of charge separation in GaAs/AlAs cylindrical Russian Doll nanostructures

We have contrasted the quantum confinement of (i) multiple quantum wells of flat GaAs and AlAs layers, i.e. (\GaAs)_{m}/(\AlAs)_n/(\GaAs)_p/(\AlAs)_q, with (ii) ``cylindrical Russian Dolls'' -- an equivalent sequence of wells and barriers arranged as concentric wires. Using a pseudopotential plane-wave calculation, we identified theoretically a set of numbers ($m,n,p$ and $q$) such that charge separation can exist in ``cylindrical Russian Dolls'': the CBM is localized in the inner GaAs layer, while the VBM is localized in the outer GaAs layer.Comment: latex, 8 page

Temperature Dependent Empirical Pseudopotential Theory For Self-Assembled Quantum Dots

We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to the InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing of the temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single particle energy levels in the QDs show strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wave functions confined in QDs increase by about 1 - 5%, whereas the hole wave functions decrease by about 30 - 40% when the temperature increases from 0 to 300 K. The calculated recombination energies of exciton, biexciton and charged excitons show red shifts with increasing of the temperature, which are in excellent agreement with available experimental data

Synthesis of Multi-Radial Line Antenna for HIPERLAN

This paper is a postprint of a paper submitted to and accepted for publication in journal Electronics Letters and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library"[Abstract] We present a new antenna concept - the multi-radial travelling wave line antenna - that achieves a broadband conical radiation pattern suitable for use in multiple C-band wireless computer networks

On random flights with non-uniformly distributed directions

This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature which take directions according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter $\nu\geq 0$ which gives the level of drift of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of $\underline{\bf X}_d(t),t>0,$ is not an easy task, because it involves the calculation of integrals which are not always solvable. Therefore, we analyze the random flight $\underline{\bf X}_m^d(t),t>0,$ obtained as projection onto the lower spaces $\mathbb{R}^m,m<d,$ of the original random motion in $\mathbb{R}^d$. Then we get the probability distribution of $\underline{\bf X}_m^d(t),t>0.$ Although, in its general framework, the analysis of $\underline{\bf X}_d(t),t>0,$ is very complicated, for some values of $\nu$, we can provide some results on the process. Indeed, for $\nu=1$, we obtain the characteristic function of the random flight moving in $\mathbb{R}^d$. Furthermore, by inverting the characteristic function, we are able to give the analytic form (up to some constants) of the probability distribution of $\underline{\bf X}_d(t),t>0.$Comment: 28 pages, 3 figure