Transition between direct and indirect band gap in silicon nanocrystals (original) (raw)
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Microelectronic Engineering, 2013
We present a comparative study of the energy-gap dependence on diameter d of ''small'' (d < 20 Å) hydrogen-terminated Si quantum dots, using density functional theory (DFT) with the hybrid functional of Becke, Lee, Parr and Yang (B3LYP). These accurate real space ab initio calculations [see , Garoufalis et al., Phys. Rev. Lett. 87 (2001) 276402] are used to compare the size dependence of the band gap according to quantum confinement theory in relation to the empirical bond-order-length-strength (BOLS) correlation mechanism, usually applied to larger nanocrystals. Our results for the gap variation, in the range of diameters considered here, are in very good agreement with quantum confinement theory and they reproduce by extrapolation the experimental band gap of bulk silicon with high accuracy (error smaller than 1%). On the contrary, extrapolation of fitted band gaps by BOLS scheme, grossly overestimates the band gap of bulk (by almost 80%); whereas, forcing the agreement of bulk band gap results in largely underestimated dot band gaps, in the range of diameters considered here.
Theoretical analysis of electronic band structure of 2- to 3-nm Si nanocrystals
Physical Review B, 2013
We introduce a general method which allows reconstruction of electronic band structure of nanocrystals from ordinary real-space electronic structure calculations. A comprehensive study of band structure of a realistic nanocrystal is given including full geometric and electronic relaxation with the surface passivating groups. In particular, we combine this method with large scale density functional theory calculations to obtain insight into the luminescence properties of silicon nanocrystals of up to 3 nm in size depending on the surface passivation and geometric distortion. We conclude that the band structure concept is applicable to silicon nanocrystals with diameter larger than ≈ 2 nm with certain limitations. We also show how perturbations due to polarized surface groups or geometric distortion can lead to considerable moderation of momentum space selection rules.
We present a comprehensive, ground-state density functional theory study of the size dependence of the optical and electronic properties and the stability of spherical silicon nanocrystals (NCs) with different impurities on the surface. We vary the size of the NCs from 1.0 to 3.5 nm, considering single-bonded (CH 3 , F, Cl, OH) and double-bonded (O, S) impurities and bridged oxygen. We show that the density of states (DOS) and absorption indices of the NCs with single-bonded impurities are very similar to each other and the fully hydrogenated NCs, except for the 1.0-nm NCs, where a slight difference is present. In the case of the NCs with double-bonded impurities, the DOS and absorption indices exhibit a significant difference, compared to the fully hydrogenated NCs, for sizes up to 2.5 nm. We argue that this difference arises from the difference in the contribution from the impurity to the states around the gap, which can considerably change the character of the states. We demonstrate that the double-bonded impurities contribute significantly to the states around the gap, compared to the single-bonded impurities, causing changes in the symmetry of these states. This observation was further supported by analyzing the changes of the Fourier transform of the charge densities of the highest occupied and lowest unoccupied eigenstate. We also show that the formation energies of NCs with bridged oxygen and fluorine are the lowest, regardless of the size. Furthermore, we show that high hydrogen concentration can be used to suppress the addition of oxygen and fluorine on the surface of the Si NCs.
Joint Density of Electronic States in Silicon Nanocrystals
physica status solidi (a), 2000
We deduce the values of the absorption cross-section of silicon nanocrystals and the spectral behaviour of the joint density of their electronic states in a wide range of energies. The very large variation of their values versus energy of the absorbed light is attributed to the enhanced optical transition oscillator strength but reduced density of electronic states towards higher confinement energies.
Physica Status Solidi (c), 2005
In this paper we report on a first-principle calculation of the electronic and structural properties of hydrogenated silicon nanocrystals both in the ground- and in an excited-state configuration. The presence of an electron-hole pair created under excitation is taken into account and its effects on both the electronic spectrum and the cluster geometry are pointed out. The interpretation of the results is done within a four-level model, which also allows the explanation of the experimentally observed Stokes shift. Size-related aspects are also analysed and discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Journal of Physics: …, 2005
In order to adjust the optimum region of diameters of Si based nanocrystals, which can emit in the visible region of the spectrum, we have partially substituted in Si nanocrystals layers of Si atoms by similar layers of Ge atoms and calculated the optical and HOMO-LUMO gaps as a function of Ge concentration and of the size of the nanocrystals, up to about 20Ǻ in diameter. For the calculation of the optical gap of Si x Ge y :H z nanocrystals as a function of x , y, and z, we have used the framework of Time Dependent Density Functional Theory (TDDFT) with the hybrid nonlocal exchange-correlation functional of Becke, Lee and Yang (B3LYP). Our results show that by proper adjustment of x y and z we can optimize either the range of diameters for a desired gap, or the value of the optical gap for a given diameter.
Real space optical gap calculations in oxygenated Si nanocrystals
Journal of Physics: Conference Series, 2005
We have calculated the optical gap of small oxygenated Si nanocrystals with diameters in the range between 2 and 10 Å using the Density Functional Theory (DFT) with the hybrid nonlocal exchange correlation functional of Becke an Lee, Yang and Parr (b3LYP), which includes partially exact Hartre-Fock exchange. The optical gap is obtained from the B3LYP HOMO-LUMO gap by a well established correlation relation. Our results are in very good agreement with experimental measurements in oxygen containing samples, and confirm out earlier conclusions [Phys. Rev Lett. 87 276402 (2001)] for the role of oxygen in the optical gap of Si nanocrystals.
Journal of Mathematical Chemistry, 2009
Tight-binding transferable parameters are created to reproduce ab initio energies of hydrogen-terminated Si-nanocrystals in order to extend the study of electronic and 0th order optical properties, through the HOMO-LUMO energy gap, to other larger or less symmetric silicon nanocrystals. For practical reasons the study is restricted to clusters where each Si atom has either three or no H neighbors. Results obtained so far are promising for future improvements and extensions to other systems.
Journal of Chemical Theory and Computation, 2017
We present a time-dependent DFT study of optical gap of light-emitting nanomaterials, the pristine and heavily B and P co-doped silicon crystalline nanoparticles. Twenty DFT exchange-correlation functionals sampled from the best currently available inventory such as hybrids and range-separated hybrids are benchmarked against ultra-accurate quantum Monte Carlo results on small model Si nanocrystals. Overall, the range-separated hybrids are found to perform best. The quality of DFT gaps is correlated with deviation from the Koopmans' theorem as a possible quality guide. In addition to providing a generic test of the TDDFT ability to describe optical properties of silicon crystalline nanoparticles, the results also open up a route to benchmark-quality DFT studies of nanoparticles sizes approaching those studied experimentally. 1