Search

The electronic properties of hydrogenated, spherical, Si/Ge and Ge/Si core-shell nanocrystals with a diameter ranging from 1.8 to 4.0 nm are studied within Density Functional Theory. Effects induced by quantum confinement and strain on the near-band-edge states localization, as well as the band-offset properties between Si and Ge regions, are investigated in detail. On the one hand, we prove that Si(core)/Ge(shell) nanocrystals always show a type II band-offset alignment, with the HOMO mainly localized on the Ge shell region and the LUMO mainly localized on the Si core region. On the other hand, our results point out that a type II offset cannot be observed in small (diameter less than 3 nm) Ge(core)/Si(shell) nanocrystals. In these systems, quantum confinement and strain drive the near-band-edge states to be mainly localized on Ge atoms inducing a type I alignment. In larger Ge(core)/Si(shell) nanocrystals, instead, the formation of a type II offset can be engineered by playing with both core and shell thickness. The conditions that favor the transition from a type I to a type II alignment for Ge(core)/Si(shell) nanocrystals are discussed in detail., Comment: 12 pages, 7 figures

First-principles calculations of work function tuning induced by different chemical terminations on Si(100) surface are presented and discussed. We find that the presence of halogen atoms (I, Br, Cl, and F) leads to an increase of the work function if compared to the fully hydrogenated surface. This is a quite general effect and is directly linked to the chemisorbed atoms electronegativity as well as to the charge redistribution at the interface. All these results are examined with respect to previous theoretical works and experimental data obtained for the (100) as well as other Si surface orientations. Based on this analysis, we argue that the changes in the electronic properties caused by variations of the interfacial chemistry strongly depend on the chemisorbed species and much less on the surface crystal orientation.

Carrier multiplication is a non-radiative recombination mechanism that leads to the generation of two or more electron-hole pairs after absorption of a single photon. By reducing the occurrence of dissipative effects, this process can be exploited to increase solar cell performance. In this work we introduce two different theoretical fully ab-initio tools that can be adopted to study carrier multiplication in nanocrystals. The tools are described in detail and compared. Subsequently we calculate carrier multiplication lifetimes in H- and OH- terminated silicon nanocrystals, pointed out the role played by the passivation on the carrier multiplication processes.

Carrier Multiplication (CM) is a Coulomb-driven non-radiative recombination mechanism which leads to the generation of multiple electron-hole pairs after absorption of a single high-energy photon. Recently a new CM process, termed space separated quantum cutting, was introduced to explain a set of new experiments conducted in dense arrays of silicon nanocrystals. The occurrence of this effect was hypothesized to generate the formation of Auger unaffected multiexciton configurations constituted by single electron-hole pairs distributed on different interacting naocrystals. In this work we discuss ab-initio results obtained by our group in the study of CM effects in systems of strongly interacting silicon nanocrystals. By solving a set of rate equations, we simulate the time evolution of the number of electron-hole pairs generated in dense arrays of silicon nanocrystals after absorption of high energy photons, by describing the circumstances under which CM dynamics can lead to the generation of Auger unaffected multiexciton configurations.

Si nanocrystals have been extensively studied because of their novel properties and their potential applications in electronic, optoelectronic, photovoltaic, thermoelectric and biological devices. These new properties are achieved through the combination of the quantum confinement of carriers and the strong influence of surface chemistry. As in the case of bulk Si the tuning of the electronic, optical and transport properties is related to the possibility of doping, in a controlled way, the nanocrystals. This is a big challenge since several studies have revealed that doping in Si nanocrystals differs from the one of the bulk. Theory and experiments have underlined that doping and codoping are influenced by a large number of parameters such as size, shape, passivation and chemical environment of the silicon nanocrystals. However, the connection between these parameters and dopant localization as well as the occurrence of self-purification effects are still not clear. In this review we summarize the latest progress in this fascinating research field considering free-standing and matrix-embedded Si nanocrystals both from the theoretical and experimental point of view, with special attention given to the results obtained by ab-initio calculations and to size-, surface- and interface-induced effects.

This work contains two papers: the first published in 2022 and entitled "On the nature of some Euler's double equations equivalent to Fermat's last theorem" provides a marvellous proof through the so-called discordant forms of appropriate Euler's double equations, which could have entered in a not very narrow margin and the second instead published in 2024 and entitled "Some Diophantus-Fermat double equations equivalent to Frey's elliptic curve" provides the possible proof, which Fermat has not published in detail, but which uses the characteristic of all right-angled triangles with sides equal to whole numbers, or the famous Pythagorean identity. Some explanations in session(III) are provided: the first makes evident the nature of the "proof a' la Fermat" and the subsequent sessions clarify the direct and interesting connection of the two elementary proofs and it is necessary if you want to understand how two different elementary proofs of Fermat's Last Theorem are possible. It must be observed that those proofs must in no way be interpreted as a sort of absurd revenge of elementary number theory over more modern analytic and algebraic treatments.The author himself has added a section in which he connects his concepts with some of those used by Wiles in his complex demonstration.This implies that, to a certain extent, Wiles' demonstration inspired the author of those works. Ultimately in this paper we will illustrate how only thanks to some of Euler's discoveries was it possible to shed light on the so-called too narrow margin never written by Fermat. For this reason we will also provide some details on an article that was the real inspiration for achieving these results (see Last Conclusions)., Comment: 39 pages cum laude, 4 figure- This extraordinary gold version is definitive !!! arXiv admin note: text overlap with arXiv:1604.03753

It is shown that an appropriate use of so-called double equations by Diophantus provides the origin of the Frey elliptic curve and from it we can deduce an elementary proof of Fermat's Last Theorem., Comment: The paper is incomplete and the statement of the Fundamental Theorem is inadequate. Therefore, the paper is obsolete

In the present theoretical work we have considered impurities, either boron or phosphorous, located at different substitutional sites in silicon quantum dots (Si-QDs) with diameters around 1.5\,nm, embedded in a SiO2 matrix. Formation energy calculations reveal that the most energetically-favored doping sites are inside the QD and at the Si/SiO2 interface for P and B impurities, respectively. Furthermore, electron and hole transport calculations show in all the cases a strong reduction of the minimum voltage threshold, and a corresponding increase of the total current in the low-voltage regime. At higher voltage, our findings indicate a significant increase of transport only for P-doped Si-QDs, while the electrical response of B-doped ones does not stray from the undoped case. These findings are of support for the employment of doped Si-QDs in a wide range of applications, such as Si-based photonics or photovoltaic solar cells.

In this work we aim at understanding the effect of n-type and p-type substitutional doping in the case of matrix-embedded and freestanding Si nanocrystals. By means of ab-initio calculations we identify the preferential positioning of the dopants and its effect on the structural properties with respect to the undoped case. Subsequently, we consider the case of phosphorus and boron co-doped nanocrystals showing that, against the single-doping situation, the energetics strongly favors the binding of the impurities at the NC surface. Indeed we demonstrate that the polar B-P bond forms a stable permanent electric dipole that radially points inwards the nanocrystal. Such noteworthy characteristic and its physical consequences are discussed alongside new potential applications.

The possibility of controlling the optical transition probability between neighbouring silicon nanoclusters (Si-NCs) constitutes nowadays an attractive prospect in nanophotonics and photovoltaics. In this work, by means of theoretical ab-initio calculations we investigate the effect of strain on the opto-electronic properties of Si-NCs pairs. We consider two sources of strain: the strain induced by an embedding SiO2 matrix, and the strain generated by mutual NC-NC forces occurring at small distances. Independently on its source, we observe a fundamental impact of the strain on the orbitals localization and, as a consequence, on the transition probability between energy states, belonging or not to the same NC. The resulting picture allots to the structural strain a fundamental role in the NC-NC interaction mechanisms, suggesting the possibility of enabling a strain-controlled response in Si-NC ensambles.

We report on the possibility of describing the absorption and emission characteristics of an ensemble of silicon nanocrystals (NCs) with realistic distributions in the NC size, by the sum of the reponses of the single NCs. The individual NC responses are evaluated by means of ab-initio theoretical calculations and the summation is performed by taking into account the trend of the optical properties as a function of NC size and oxidation degree. The comparison with experimental results shows a nice matching of the spectra, also without any tuning of the parameters. Finally, the possibility of adapting the model in order to reproduce the experimental data is explored and discussed.

Being a source of clean and renewable energy, the possibility to convert solar radiation in electric current with high efficiency is one of the most important topics of modern scientific research. Currently the exploitation of interaction between nanocrystals seems to be a promising route to foster the establishment of third generation photovoltaics. Here we adopt a fully ab-initio scheme to estimate the role of nanoparticle interplay on the carrier multiplication dynamics of interacting silicon nanocrystals. Energy and charge transfer-based carrier multiplication events are studied as a function of nanocrystal separation showing benefits induced by the wavefunction sharing regime. We prove the relevance of these recombinative mechanisms for photovoltaic applications in the case of silicon nanocrystals arranged in dense arrays, quantifying at an atomistic scale which conditions maximize the outcome., Comment: Supplementary materials are freely available online

This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for {\zeta}(s). We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper "Remarques sur un beau rapport entre les s\'eries des puissances tant direct que r\'eciproches". This more general functional equation gives origin to a special function, here named {\cyr \E}(s), which we prove that it can be continued analytically to an entire function over the whole complex plane using techniques similar to those of the second proof of Riemann. Moreover we are able to obtain a connection between Jacobi's imaginary transformation and an infinite series identity of Ramanujan. Finally, after studying the analytical properties of the function {\cyr \E}(s), we complete and extend the proof of a Fundamental Theorem, both on the zeros of Riemann Zeta function and on the zeros of Dirichlet Beta function, using also the Euler-Boole summation formula., Comment: 26 pages, 2 figures

By means of ab-initio calculations we investigate the optical properties of pure a-SiN$_x$ samples, with $x \in [0.4, 1.8]$, and samples embedding silicon nanoclusters (NCs) of diameter $0.5 \leq d \leq 1.0$ nm. In the pure samples the optical absorption gap and the radiative recombination rate vary according to the concentration of Si-N bonds. In the presence of NCs the radiative rate of the samples is barely affected, indicating that the intense photoluminescence of experimental samples is mostly due to the matrix itself rather than to the NCs. Besides, we evidence an important role of Si-N-Si bonds at the NC/matrix interface in the observed photoluminescence trend.

The effect of the local fields on the absorption spectra of silicon nanoclusters (NCs), freestanding or embedded in SiO2, is investigated in the DFT-RPA framework for different size and amorphization of the samples. We show that local field effects have a great influence on the optical absorption of the NCs. Their effect can be described by two separate contributions, both arising from polarization effects at the NC interface. First, local fields produce a reduction of the absorption that is stronger in the low energy limit. This contribution is a direct consequence of the screening induced by polarization effects on the incoming field. Secondly, local fields cause a blue shift on the main absorption peak that has been explained in terms of perturbation of the absorption resonance conditions. Both contributions do not depend either on the NC diameter nor on its amorphization degree, while showing a high sensitivity to the environment enclosing the NCs.

The case study of a 32-atoms Si nanocrystallite (NC) embedded in a SiO2 matrix, both crystalline and amorphous, or free-standing with different conditions of passivation and strain is analyzed through ab-initio approaches. The Si32/SiO2 heterojunction shows a type I band offset highlighting a separation between the NC plus the interface and the matrix around. The consequence of this separation is the possibility to correctly reproduce the low energy electronic and optical properties of the composed system simply studying the suspended NC plus interface oxygens with the appropriate strain. Moreover, through the definition of an optical absorption threshold we found that, beside the quantum confinement trend, the amorphization introduces an additional redshift that increases with increasing NC size: i.e. the gap tends faster to the bulk limit. Finally, the important changes in the calculated DFT-RPA optical spectra upon inclusion of local fields point towards the need of a proper treatment of the optical response of the interface region.

We compare, through first-principles pseudopotential calculations, the structural, electronic and optical properties of different size silicon nanoclusters embedded in a SiO2 crystalline or amorphous matrix, with that of free-standing, hydrogenated and hydroxided silicon nanoclusters of corresponding size and shape. We find that the largest effect on the opto-electronic behavior is due to the amorphization of the embedded nanocluster. In that, the amorphization reduces the fundamental gap while increasing the absorption strength in the visible range. Increasing the nanocluster size does not change substantially this picture but only leads to the reduction of the absorption threshold, following the quantum confinement rule. Finally, through the calculation of the optical absorption spectra both in a indipendent-particle and many-body approach, we show that the effect of local fields is crucial for describing properly the optical behavior of the crystalline case while it is of minor importance for amorphous systems.

The structural, electronic and optical properties of Si nanocrystals of different size and shape, passivated with hydrogens, OH groups, or embedded in a SiO2 matrix are studied. The comparison between the embedded and free, suspended nanocrystals shows that the silica matrix produces a strain on the embedded NCs, that contributes to determine the band gap value. By including the strain on the hydroxided nanocrystals we are able to reproduce the electronic and optical properties of the full Si/SiO2 systems. Moreover we found that, while the quantum confinement dominates in the hydrogenated nanocrystals of all sizes, the behaviour of hydroxided and embedded nanocrystals strongly depends on the interface oxidation degree, in particular for diameters below 2 nm. Here, the proportion of NC atoms at the Si/SiO2 interface becomes relevant, producing surface-related states that may affect the quantum confinement appearing as inner band gap states and then drastically changing the optical response of the system.

In recent years many experiments have demonstrated the possibility to achieve efficient photoluminescence from Si/SiO2 nanocrystals. While it is widely known that only a minor portions of the nanocrystals in the samples contribute to the observed photoluminescence, the high complexity of the Si/SiO2 interface and the dramatic sensitivity to the fabrication conditions make the identification of the most active structures at the experimental level not a trivial task. Focusing on this aspect we have addressed the problem theoretically, by calculating the radiative recombination rates for different classes of Si-nanocrystals in the diameter range of 0.2-1.5 nm, in order to identify the best conditions for optical emission. We show that the recombination rates of hydrogenated nanocrystals follow the quantum confinement feature in which the nanocrystal diameter is the principal quantity in determining the system response. Interestingly, a completely different behavior emerges from the OH-terminated or SiO2-embedded nanocrystals, where the number of oxygens at the interface seems intimately connected to the recombination rates, resulting the most important quantity for the characterization of the optical yield in such systems. Besides, additional conditions for the achievement of high rates are constituted by a high crystallinity of the nanocrystals and by high confinement energies (small diameters).

We present a unified ab-initio study of electronic and optical properties of TiO2 rutile and anatase phases, with a combination of Density Functional Theory and Many Body Perturbation Theory techniques. The consistent treatment of exchange-correlation, with the inclusion of many body one-particle and two-particles effects in self-energy and electron-hole interaction, produces a high quality description of electronic and optical properties, giving, for some quantities, the first available estimation for this compound. In particular, we give a quantitative, direct evaluation of the electronic and direct optical gaps, clarifying their role with respect to previous values obtained by various experimental techniques. We obtain a description for both electronic gap and optical spectra that is consistent with experiments, analysing the role of different contributions to the experimental optical gap and relating them to the level of theory used in our calculations. We also show the spatial nature of excitons in the two crystalline phases, highlighting the localization character of different optical transitions. This paper aims at understanding and firmly establishing electro-optical bulk properties, so far not yet clarified, of this material of fundamental and technological interest for green energy applications., Comment: 33 pages, 7 figures

A first-principles calculation of the impurity screening in Si and Ge nanocrystals is presented. We show that isocoric screening gives results in agreement with both the linear response and the point-charge approximations. Based on the present ab initio results, and by comparison with previous calculations, we propose a physical real-space interpretation of the several contributions to the screening. Combining the Thomas-Fermi theory and simple electrostatics, we show that it is possible to construct a model screening function that has the merit of being of simple physical interpretation. The main point upon which the model is based is that, up to distances of the order of a bond length from the perturbation, the charge response does not depend on the nanocrystal size. We show in a very clear way that the link between the screening at the nanoscale and in the bulk is given by the surface polarization. A detailed discussion is devoted to the importance of local field effects in the screening. Our first-principles calculations and the Thomas-Fermi theory clearly show that in Si and Ge nanocrystals, local field effects are dominated by surface polarization, which causes a reduction of the screening in going from the bulk down to the nanoscale. Finally, the model screening function is compared with recent state-of-the-art ab initio calculations and tested with impurity activation energies.

In this paper we present a simple method for deriving an alternative form of the functional equation for Riemann's Zeta function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work "Remarques sur un beau rapport entre les series des puissances tant directes que reciproques" in Memoires de l'Academie des Sciences de Berlin 17, (1768), permit to define a special function, named A(s), which is fully symmetric and is similar to Riemann's "XI" function. To be complete we find several integral representations of the A(s) function and as a direct consequence of the second integral representation we obtain also an analytic continuation of the same function using an identity of Ramanujan., Comment: 18 pages, 1 figure

We show that the optical and electronic properties of nanocrystalline silicon can be efficiently tuned using impurity doping. In particular, we give evidence, by means of ab-initio calculations, that by properly controlling the doping with either one or two atomic species, a significant modification of both the absorption and the emission of light can be achieved. We have considered impurities, either boron or phosphorous (doping) or both (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 nm to 1.8 nm in diameter. We have found that the codoped nanocrystals have the lowest impurity formation energies when the two impurities occupy nearest neighbor sites near the surface. In addition, such systems present band-edge states localized on the impurities giving rise to a red-shift of the absorption thresholds with respect to that of undoped nanocrystals. Our detailed theoretical analysis shows that the creation of an electron-hole pair due to light absorption determines a geometry distortion that in turn results in a Stokes shift between adsorption and emission spectra. In order to give a deeper insight in this effect, in one case we have calculated the absorption and emission spectra going beyond the single-particle approach showing the important role played by many-body effects. The entire set of results we have collected in this work give a strong indication that with the doping it is possible to tune the optical properties of silicon nanocrystals., Comment: 14 pages 19 figures

The absorption and emission spectra of silicon nanocrystals up to 1 nm diameter including geometry optimization and the many-body effects induced by the creation of an electron-hole pair have been calculated within a first-principles framework. Starting from hydrogenated silicon clusters of different size, different Si/O bonding at the cluster surface have been considered. We found that the presence of a Si-O-Si bridge bond originates significative excitonic luminescence features in the visible range that are in fair agreement with the experimental outcomes., Comment: 12 pages 4 figures

The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter "SHIN" {The letter SHIN is the thirteenth letter of the Arabian alphabet}. It includes three other papers, published in the International journal "Kragujevac Journal of Mathematics". The methods, the techniques and the style of the demonstration inside such a work, are all related to Leonhard Euler, the very great Swiss mathematician., Comment: 46 pages, 15 figures

This Paper (one first and draft version) contains some small imperfections, one its correct and definitive version has been already submitted to one prestigious review of mathematics. More precisely "the Special Function SHIN, II" will be published in the "Kragujevac Journal of Mathematics, 29 (2006) "., Comment: This paper has been withdrawn