A series of calculations on MgB2 and related isoelectronic systems indicates that the layer of Mg 2+ ions lowers the non-bonding B π (pz) bands relative to the bonding σ (spxpy) bands compared to graphite, causing σ → π charge transfer and σ band doping of 0.13 holes/cell. Due to their two dimensionality the σ bands contribute strongly to the Fermi level density of states. Calculated deformation potentials of Γ point phonons identify the B bond stretching modes as dominating the electron-phonon coupling. Superconductivity driven by σ band holes is consistent with the report of destruction of superconductivity by doping with Al.
The efficiency of conventional solar cells is limited because the excess energy of absorbed photons converts to heat instead of producing electron-hole pairs. Recently, efficient carrier multiplication has been observed in semiconductor quantum dots. In this process, a single, high-energy photon generates multiple electron-hole pairs. Rather exotic mechanisms have been proposed to explain the efficiency of carrier multiplication in PbSe quantum dots. Using atomistic pseudopotential calculations, we show here that the more conventional impact ionization mechanism, whereby a photogenerated electron-hole pair decays into a biexciton in a process driven by Coulomb interactions between the carriers, can explain both the rate (<<1 ps) and the energy threshold ( approximately 2.2 times the band gap) of carrier multiplication, without the need to invoke alternative mechanisms.
PbSe is a pseudo-II-VI material distinguished from ordinary II-VI's (e.g., CdSe, ZnSe) by having both its valence band maximum (VBM) and its conduction band minimum (CBM) located at the fourfold-degenerate L-point in the Brillouin zone. It turns out that this feature dramatically affects the properties of the nanosystem. We have calculated the electronic and optical properties of PbSe quantum dots using an atomistic pseudopotential method, finding that the electronic structure is different from that of ordinary II-VI's and, at the same time, is more subtle than what k.p or tight-binding calculations have suggested previously for PbSe. We find the following in PbSe dots: (i) The intraband (valence-to-valence and conduction-to-conduction) as well as interband (valence-to-conduction) excitations involve the massively split L-manifold states. (ii) In contrast to previous suggestions that the spacings between valence band levels will equal those between conduction band levels (because the corresponding effective-masses me approximately mh are similar), we find a densely spaced hole manifold and much sparser electron manifold. This finding reflects the existence of a few valence band maxima in bulk PbSe within approximately 500 meV. This result reverses previous expectations of slow hole cooling in PbSe dots. (iii) The calculated optical absorption spectrum reproduces the measured absorption peak that had previously been attributed to the forbidden 1Sh --> 1Pe or 1Ph --> 1Se transitions on the basis of k.p calculations. However, we find that this transition corresponds to an allowed 1Ph --> 1Pe excitation arising mainly from bulk states near the L valleys on the Gamma-L lines of the Brillouin zone. We discuss this reinterpretation of numerous experimental results.
An exciton evolving from an m-fold degenerate hole level and an n-fold degenerate electron level has a nominal m × n degeneracy, which is often removed by electron−hole interactions. In PbSe quantum dots, the degeneracy of the lowest-energy exciton is m × n = 64 because both the valence-band maximum and the conduction-band minimum originate from the 4-fold degenerate (8-fold including spin) L valleys in the Brillouin zone of bulk PbSe. Using a many-particle configuration-interaction approach based on atomistic single-particle wave functions, we have computed the fine structure of the lowest-energy excitonic manifold of two nearly spherical PbSe quantum dots of radius R = 15.3 and 30.6 Å. We identify two main energy splittings, both of which are accessible to experimental probe: (i) The intervalley splitting δ is the energy difference between the two near-edge peaks of the absorption spectrum. We find δ = 80 meV for R = 15.3 Å and δ = 18 meV for R = 30.6 Å. (ii) The exchange splitting Δ x is the energy difference between the lowest-energy optically dark exciton state and the first optically bright exciton state. We find that Δ x ranges between 17 meV for R = 15.3 Å, and 2 meV for R = 30.6 Å. We also find that the room-temperature radiative lifetime is τR ∼ 100 ns, considerably longer than the ∼10 ns radiative lifetime of CdSe dots, in quantitative agreement with experiment.
While in solids the phonon-assisted, non-radiative decay from high-energy excited states to lowenergy 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 transferred non-radiatively to holes, which can then decay rapidly 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 to 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 calculated explicitly the electron-hole Coulomb integrals and the P→S electron Auger relaxation rate. We find that the Auger mechanism can explain the experimentally observed P→S intraband decay time scale without the need to invoke any exotic relaxation mechanisms.PACS numbers:
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