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

Radiative recombination of charged excitons and multiexcitons in CdSe quantum dots

We report semi-empirical pseudopotential calculations of emission spectra of charged excitons and biexcitons in CdSe nanocrystals. We find that the main emission peak of charged multiexcitons - originating from the recombination of an electron in an s-like state with a hole in an s-like state - is blue shifted with respect to the neutral mono exciton. In the case of the negatively charged biexciton, we observe additional emission peaks of lower intensity at higher energy, which we attribute to the recombination of an electron in a p state with a hole in a p state

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

Energy absorption in actual tractor rollovers with different tire configurations

In order to better understand the complexities of modern tractor rollover, this paper investigates the energy absorbed by a Roll-Over Protective Structure (ROPS) cab during controlled lateral rollover testing carried out on a modern narrow-track tractor with a silent-block suspended ROPS cab. To investigate how different tractor set-ups may influence ROPS and energy partitioning, tests were conducted with two different wheel configurations, wide (equivalent to normal ‘open field’ operation) and narrow (equivalent to ‘orchard/vineyard’ operation), and refer to both the width of the tires and the corresponding track. Dynamic load cells and displacement transducers located at the ROPS-ground impact points provided a direct measurement of the energy absorbed by the ROPS cab frame. A trilateration method was developed and mounted onboard to measure load cell trajectory with respect to the cab floor in real-time. The associated video record of each rollover event provided further information and opportunity to explain the acquired data. The narrow tire configuration consistently subjected the ROPS cab frame to more energy than the wide tire arrangement. To better evaluate the influence of the ROPS cab silent-blocks in lateral rollover, static and dynamic tests were performed. The results confirm that tires influence the energy partition significantly and that further understanding of silent-blocks’ dynamic performance is warranted

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