Evaluation of optical and electronic properties of silicon nano-agglomerates embedded in SRO: applying density functional theory
© Espinosa-Torres et al.; licensee Springer. 2014
Received: 19 May 2014
Accepted: 12 August 2014
Published: 17 September 2014
In systems in atomic scale and nanoscale such as clusters or agglomerates constituted by particles from a few to less than 100 atoms, quantum confinement effects are very important. Their optical and electronic properties are often dependent on the size of the systems and the way in which the atoms in these clusters are bonded. Generally, these nanostructures display optical and electronic properties significantly different to those found in corresponding bulk materials. Silicon agglomerates embedded in silicon rich oxide (SRO) films have optical properties, which have been reported to be directly dependent on silicon nanocrystal size. Furthermore, the room temperature photoluminescence (PL) of SRO has repeatedly generated a huge interest due to its possible applications in optoelectronic devices. However, a plausible emission mechanism has not been widely accepted in the scientific community. In this work, we present a short review about the experimental results on silicon nanoclusters in SRO considering different techniques of growth. We focus mainly on their size, Raman spectra, and photoluminescence spectra. With this as background, we employed the density functional theory with a functional B3LYP and a basis set 6-31G* to calculate the optical and electronic properties of clusters of silicon (constituted by 15 to 20 silicon atoms). With the theoretical calculation of the structural and optical properties of silicon clusters, it is possible to evaluate the contribution of silicon agglomerates in the luminescent emission mechanism, experimentally found in thin SRO films.
Small silicon clusters can be obtained, for instance, when using photochemical etching treatment and pulsed laser evaporation method which in turn show also photoluminescence (PL). Nevertheless, such small silicon clusters are short-lived intermediate species, and it is very difficult to control the number of atoms in the Si clusters formed. On the other hand, some silicon clusters have been prepared by organic synthesis methods, and a similarity of the PL and absorption spectra to those measured in porous Si (p-Si) has been pointed out. With respect to the latter material, it is currently agreed that the quantum confinement effects and the hydrogen saturation (surface effects) of Si nanocrystallites play key roles in the origin and mechanism of PL in p-Si where strong visible PL is observed when it is fabricated by electrochemical anodization . Besides, their optical and electronic properties have caught much attention from the perspective of solid-state physics and its application to optical devices [2, 3].
Kanemitsu and co-workers [4, 5] and Furukawa et al.  synthesized several kinds of Si clusters, Si backbone polymers, network polymers, and planar siloxane structures and studied their optical properties to understand the dimensional effects of Si-based nanostructures such as p-Si. In the chain clusters and polymers, sharp PL bands were observed with very small Stokes shifts. On the other hand, following the line of nanostructures with Si clusters, we find that such structures which have generated great interest is the silicon rich oxide (SRO) thin film; this material exhibits optical properties in the same manner to p-Si, but it is significantly less chemically reactive than p-Si.
Si-nanocrystals (Si-nCs) embedded in dielectric matrices such as silicon dioxide exhibit unique optical and electrical properties which are determined by quantum size and Coulomb blockade effects . Si-nCs can emit and absorb light at energies which can be controlled by their sizes, i.e., their gaps can be tuned. This latter fundamental property of Si-nCs is very useful in third-generation solar cells .
Commonly, SRO is considered as a multi-phase material constituted by a mixture of silica (SiO2), off-stoichiometric oxides (SiO x , x < 2), and elemental silicon. After thermal treatment at temperatures above 1,000°C, the off-stoichiometric oxides, SiO x (x < 2), react to produce silicon nanoclusters, structures with different oxidation states with or without defects, and silica . Silicon nanocrystals and silicon agglomerates have been characterized in SRO films employing transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), energy-filtered transmission electron microscopy (EFTEM), X-ray diffraction (XRD), and atomic force microscopy (AFM)  as characterization techniques. The formation, shape, and size of Si-nCs depend on the excess silicon and annealing parameters (time and temperature) and also on the type of carried gas used to grow nanostructures.
According to Raghavachari and Rohlfing , the behavior of small-sized silicon clusters is frequently correlated with the trend of binding energy per atom as a function of cluster size. In this type of systems, the electronic configuration corresponding to both a single atom and a complex of atoms in the cluster is a determining factor in the cluster stability .
Over the past 20 years, medium-sized silicon clusters Si n (n > 10) have attracted much attention both experimentally  and theoretically . Considerable effort has been devoted to determine the ground-state geometric structures, namely the global minima as a function of the cluster size n. For n ≤ 7, the global minima are firmly established by both ab initio calculations and Raman/infrared spectroscopy measurements, whereas for n ≤ 12 the global minima based only on ab initio calculations [14–16] are well accepted.
For 13 ≤ n ≤ 20, an unbiased search for the global minima has been undertaken based on either the genetic algorithm coupled with semi-empirical tight-binding (TB) technique  or the single-parent evolution algorithm coupled with density functional (DF), TB, and density functional theory (DFT) methods [18, 19]. Establishing successfully the geometry corresponding to the global minimum energy is a critical step for a further reliable evaluation of the optical and structural properties, and thereby it contributes properly to the understanding of the underlying mechanisms of luminescence.
It is well-known that crystalline silicon (c-Si) has an indirect band gap, which means that every optical transition must be accompanied by the creation or annihilation of a phonon. Besides, this material presents an optical disadvantage attributed to low band gap value Eg,c-Si = 1.12 eV at room temperature (RT), corresponding to a wavelength λg,c-Si = 1,107 nm. This fact leads to the radiation emitted by, for example, a light-emitting diode (LED) made of c-Si which corresponds to the infrared emission and then it is non-visible by the human eye.
However, by using nanoscaled silicon structures, the optical disadvantage can be overcome, because of the presence of radiative optical transitions brought about in quantum confined states of Si nanostructures which generate visible radiation, but the disadvantage of the indirect band gap still remains. Average PL decay times τPL for Si-nCs with diameters d ~ 3.4 nm are reported to be in the order of 100 to 500 μs at RT .
Broadly, the SRO can be obtained by different techniques; however, the low-pressure chemical vapor deposition (LPCVD) technique is frequently used because it results a simple method that easily allows the controlled fluctuations of silicon excess. In this technique, the partial pressure ratio caused by the flow of reactive gases, defined as Ro = P(N2O)/P(SiH4), is used to determine the silicon excess. For example, for Ro = 3, we have a silicon excess of 17 at.%, and Ro = 100 is used to obtain stoichiometric silicon dioxide. When SRO films are obtained by LPCVD technique, the most intense light emission observed corresponds to films with approximately 5 at.% silicon excess as reported, although silicon nanocrystals were not observed in such films .
It is possible that small-sized silicon agglomerates (Si n , n < 20) were present in these particular films (for the case of Ro = 30) which would hardly be detected due to atomic instead of nanoscale dimensions. Size regimes in the evolution of semiconductor spectroscopic properties were introduced by Efros and Efros . For many years, different methods have been used for the preparation of silicon nanocrystals, e.g., chemical vapor deposition , Si ion implantation , colloidal synthesis , magnetron sputtering , and electron beam evaporation . A high-temperature thermal treatment above 1,000°C is generally required in order to produce crystallites. All these techniques allow one to form Si-nCs with sizes mainly ranging from 2 to 6 nm, and it is possible to obtain Si-nCs with sizes less than 2 nm in SRO films as deposited with Ro = 30 prepared using the LPCVD technique. Their electronic and optical properties depend on the preparation conditions and methods of fabrication. However, there are some common typical properties for Si-nCs which are independent of the manufacturing technique used. In particular, the nanocrystals' surroundings, which can be either vacuum or some host material like SRO, represent a high potential barrier for carriers (electrons or holes). Such a barrier is often referred to as a confining quantum potential that mainly defines the energy spectrum of the Si-nCs.
There is a large uncertainty in the calculated values of the optical gaps as a function of Si-nC diameter. We can mention two factors influencing the accuracy of the optical gap measurements as follows: First, the nanocrystals which are studied by different research groups have been prepared using different techniques. This fact leads to nanocrystals having different surroundings, surface bonds, and shapes, all of which could lead to scatter in the experimental data. Second, it is difficult to determine exactly the dot sizes and the size distribution in luminescent agglomerate of nanocrystals. Theoretically, the problem persists mainly due to the difficulty to define an appropriate parameter for determining the diameter. For simplicity, a spherical geometry is used in most of the models suggested, since the actual shape of the agglomerates formed and considered as a molecule is totally irregular.
The motivation of this work is to present a theoretical study of the optical and electronics properties of Si-nCs which are embedded in SRO structures regardless of the technique used to fabricate such structures. For this, we review firstly some important experimental results about the measurements of the structural and optical properties carried out on SRO samples grown by different techniques. The aim of this review is twofold; on the one hand, we show relevant information in relationship to actual quantification of Si-nCs about their size, electromagnetic range of emission, molecular structure, and important parameters which are responsible for making variations of these properties. On the other hand, we take this experimental information as background in order to focus correctly our theoretical research predicted by using the DFT method corresponding to atomic composition of different silicon isomers suggested simulating the Si-nC embedded in SRO films.
This paper is outlined as follows: the ‘Methods’ section includes the elemental analytical expressions of energy in nanocrystals. In the ‘Results and discussion’ section, we present two parts: in the first one, we show and discuss the experimental identification and quantification of silicon nanocrystals in SRO films, and then we present and discuss the theoretical results about the structural and optical properties of silicon clusters using DFT method. Finally, the last section presents the conclusions.
Elemental analytical expressions of energy in nanocrystals
Different proposals of elemental models to get analytical expressions of energy of Si-nC are found in the literature, which pretend to explain correctly the energy spectrum of this type of nanostructures. However, this task is not easy because of the complexity associated to these nanoclusters which do not have a well-defined geometry and their composition is nonhomogeneous. Among the several geometries suggested for studying the optical properties of Si-nCs, we find that the spherical geometry is predominantly accepted as a first approximation to understand, to a certain degree, the emission mechanisms in the nanocrystals. In order to obtain the electronic states in a nanocrystal, with a spherical shape, its Hamiltonian, , must be solved. Gaponenko  used spherical coordinates r, θ, and φ to solve this Hamiltonian, where the total potential energy U(r) of the electron inside the spherical region has radial symmetry. By standard methods, the eigenfunctions of this Hamiltonian are found to be where n is the principal quantum number, l is the orbital number, and m is the magnetic number. Here, Yl,m(θ, φ) are the spherical functions. With these solutions Ψn,l,m(r, θ, φ) when introduced in the Hamiltonian, we arrive to the equation . The energy values of the electronic states in a spherical nanocrystal are obtained as a solution to this equation, when the potential U(r) is considered as infinitely high. The energy spectrum is given by , where a = 0.543 nm is the lattice constant of Si and χ nl are the roots of the spherical Bessel functions.
On the other hand, inside the Si-nCs, the electrons and holes are interacting through Coulomb attraction; this fact leads to the formation of excitons. An exciton is known as a bound pair formed by an electron and a hole interacting by Coulomb force forming a hydrogen-like system. When the Bohr radius of the exciton is larger than the size of the nanocrystal, it takes place a quantum confinement. Considering that silicon dioxide surrounds the silicon nanocrystals, and due to it forms a high potential barrier (approximately 9 eV), the excitons are confined within the volume of the nanocrystal. This causes drastic changes in both the electronic band structure and the emission spectrum.
where EG is the bulk band gap and R is the size of the Si-nC. The first term proportional to R−1 is the Coulomb term, and the second one proportional to R−2 is the shift as a result of quantum localization of electrons and holes (quantum confinement). Equation 1 is possible to establish because the correlation between electron and hole positions, induced by the Coulomb interaction, is not enough strong. Independently of confinement energies for electrons and holes, the major effect is additive.
ϵ0 is the permittivity of vacuum and ϵr is the relative permittivity of Si-nC. Four years later, in 1988 Kayanuma  accounted for the electron-hole spatial correlation effect and modified the Brus equation, including a negative term proportional to Rydberg energy.
where ΔE = E − E G . Apart from this model, many others have been developed with several refinements. The EMA is a rough approximation which assumes the cluster (or nano-agglomerated) to be in a well of infinite potential energy where the Coulomb terms are excluded from the analysis. Brus  improved the original model including the Coulomb terms taking into account the effect of the dielectric constant of the matrix on the exciton binding energy and using finite potential wells for calculating energy states. Other EMA models were developed by Kayanuma  and Kayanuma and Momiji  using quantum confinement finite potentials for modeling clusters with cylindrical and spherical geometries.
where ER is the Rydberg energy for the semiconductor in bulk and is given by . In Equation 4, the term e2 is the Coulombic term and 0.248 ER gives the spatial correlation energy which is a minor correction. This method is characterized by the overestimate energy values E(R), particularly for smaller nano-sized agglomerates with dimensions less than 20 Å. More accurate models using finite barriers give the ratio of the energy gap reduced to the size of the cluster as R α 1/γ where γ is an empirical derivative value in the range from 1.3 to 1.8.
At first glance, it may be redundant to present the above theory related with analytical expressions of energy of Si-nCs, but we must keep in mind that these formulae have frequently used to estimate emission radiation in Si-nC. Nevertheless, their predictions are limited since the theoretical models ignore a lot details that in practice the Si-nCs present themselves. It opens the opportunity to establish a new formalism capable of explaining in depth the underlying physical mechanisms involved in the radiative emission of Si-nCs.
Results and discussion
Experimental identification and quantification of silicon nanocrystals in SRO films
Identification of vibrational modes in Si-nCs by Raman spectroscopy
Fascinatingly, the sample with Ro = 10 displays a strong Raman peak for Si nanocrystals at 509.1 cm−1 (Figure 1a, the lower curve), indicating that for films with a high Si excess during the 30 min of pre-annealing Si nanocrystals were already formed. After 30 min of annealing at 1,100°C (Figure 1b), a small Raman peak around 521.1 cm−1 for Ro = 20 is observed (the middle curve and see inset on Figure 1b), while for Ro = 30 (the lower curve), no peaks were found. Further heating treatment for another 150 min proceeds with this trend; for Ro = 20, an increase of the intensity is observed, whereas for Ro = 30, no characteristic peaks for Si phases were found.
Structural characterization of Si-nCs by X-ray diffraction
Detection of Si-nC by energy-filtered transmission electron microscopy
By using EFTEM, spatial resolution down to 1 nm can be succeeded. However, EFTEM has no limitations related to the crystallinity of the Si-nCs and can detect both amorphous and crystalline nanoclusters. Moreover, high energy resolution of EFTEM can make it possible to distinguish Si and SiO2 plasmon energies.
The raw images obtained from EFTEM measurements were slightly contrasted, and the subtraction of the contribution from SiO2 background by yielding a well-defined Si nanocluster was applied. EFTEM is advantageous when analyzing a number of specimens in a short time. Thus, EFTEM is more appropriate for statistical analysis.
Dimensional estimation of Si-nCs by high-resolution transmission electron microscopy
After Voyles  first discerned the distribution of dopant atoms using scanning transmission electron microscopy, active studies are being carried out to examine the single atom or point defects in the crystal lattices. Not many studies, however, were done to investigate point defects in normal HRTEM. It is well known that groups of point defects, either lined up along specific crystallographic orientation or clusters can give rise to contrast in conventional TEM.
Figure 4 displays HRTEM images of SiO x deposited at 1,150°C by HFCVD technique . On the left side, we obtained agglomerates with a size of 4.0 nm on the average; likewise, on right side, the size was 6.5 nm.
Chemical bonds in Si-nCs detected by Fourier transform infrared spectroscopy
FTIR is a powerful tool for recognizing types of chemical bonds in a molecule by generating an infrared absorption spectrum that is like a molecular ‘pattern.’
A deposition temperature of 350°C and a He dilution of 50% gave a film composition close to SiO1.9. Figure 6 (right) displays the FTIR spectra for a SRO sample obtained by HWCVD using a hydrogen flow of 125 sccm varying the distance from source to substrate from 3 to 7 mm. This sample was annealed at 1,100°C during 1 h . The vibrational frequencies corresponding to the five peaks are as follows: 467.2, 471.3, 475.5, 478.3, and 481.2 cm−1.
Radiative emission in Si-nCs measured by photoluminescence technique
As can be seen in Figure 7 (right), photoluminescence is only observed in annealed samples  (curves labeled with T180 mean, 180 min of annealing time at 1,100°C). As a matter of fact, only samples annealed at 1,100°C produce high emission, and the highest photoemission is obtained for SRO30 (Ro = 30) films. The PL is only obtained from the visible (VIS) to the near-infrared (NIR) range, and its intensity reduces with Ro decreasing. Comparatively, SRO10 produces negligible emission as that of SRO30. Also, we can appreciate a wavelength shift to blue emission when Ro is increased (higher levels of energy)
Theoretical results about the structural and optical properties of silicon clusters using DFT method
In 1980, Pulay published a method  known as the direct inversion of the iterative subspace (DIIS). Like the Davidson method , DIIS applies direct methods to a small linear algebra problem (now a system of linear equations instead of an eigenvalue problem) in a subspace formed by taking a set of trial vectors from the full-dimensional space. Pulay found that DIIS could be useful for accelerating the convergence of self-consistent field (SCF) procedures and, to a lesser extent, geometry optimizations. In a previous paper , we employed a SCF model with a restricted hybrid (Hartree-Fock/density functional theory) HF-DFT-SCF calculation using Pulay mixing + geometric direct minimization level of theory, compiled in the SPARTAN 08/10 software package  for evaluating small silicon clusters.
Møller-Plesset (MP) perturbation theory is one of the several quantum chemistry post-Hartree-Fock ab initio methods in the field of computational chemistry. It improves on the Hartree-Fock method by adding electron correlation effects by means of the Rayleigh-Schrödinger perturbation theory (RS-PT), usually to the second (MP2), third (MP3), or fourth (MP4) order. Their main idea was published as early as 1934 by Møller and Plesset . The MP2/6-31G (d) level of theory is selected for geometry relaxation to approximately account for the correlation effect of all electrons to the geometric structures. In order to identify the most stable isomers among nearly degenerated isomers, Zhu and Zeng  performed calculations for single point of the coupled cluster single or double substitution from the Hartree-Fock determinant CCSD (T)/6-31G (d), where (T) refers to include triple excitations non-iteratively .
The CCSD (T) method is often called the ‘gold standard’ of computational chemistry , because it is one of the most accurate methods applicable to reasonably large molecules. It is particularly useful for the description of non-covalent interactions where the inclusion of triple excitations is necessary for achieving a satisfactory accuracy. While it is widely used as a benchmark, the accuracy of CCSD (T) interaction energies has not been reliably quantified yet against more accurate calculations.
Moreover, for the isomer with the lowest CCSD (T)/6-31G (d) energy, its stability was further examined by calculating its vibrational frequencies at the HF/6-31G (d) level of theory (a hybrid density functional model using a medium-sized basis set) . Structures of the low-lying isomers of Si15-Si20 have been reported in the literature [17, 24], and some of them are likely true global minima.
Structural and optical properties calculated for isomers Si15
Since 1998, Ho et al.  employed the unbiased tight-binding model (TBM) search and disclosed the low-lying clusters 15A-15D which contain the capped trigonal prism unit form. The isomer having the global minimum at the CCSD (T)/6-31G (d) level is the 15A (C3v) one whose geometry is a tri-capped trigonal prism fused with a tri-capped trigonal anti-prism. The vibrational frequency analysis at the MP2/6-31G (d) level shows that the 15A isomer has two imaginary frequencies. Thus, isomer 15A (C3v) may not be a stable structure but a transition-state structure at the MP2/6-31G (d) level of theory. A structural perturbation to 15A (C3v) followed by geometry relaxation gives rise to isomer 15A with Cs symmetry (possesses only a mirror plane σh). Isomer 15A (Cs) shows no imaginary frequencies. Ours results confirm that isomer 15A has no symmetry (C1) and is the global minimum.
On the other hand, isomers 15A and 15D have a variety of defined peaks. The most intense peak for isomer with the global minimum (15A) corresponds to a frequency of 493.086 cm−1, and the local minimum with the highest difference in energy (15D) displays the most intense peak at 409.9 cm−1.
Results obtained for isomers 15B and 15C predict emission in most of the visible region and extends until the IR region. For isomer 15B, the most intense peak lies in IR and has a wavelength of 871.74 nm, whereas for isomer 15C, the most intense peak lies at 750.42 nm (red emission).
Structural and optical properties calculated for isomers varying from Si 15 to Si 20
Band gap (eV)
UV-VIS lambda max
The band gap calculated for the most stable isomer is 3.051 eV. Also, a great value for dipole moment was obtained (3.097 Debye). The nano-agglomerate size of the global minimum has resulted to be the lowest of this set of isomers (0.72508 nm). Finally, the highest zero-point energy (ZPE) and ovality values correspond to the global minimum.
Structural and optical properties calculated for isomers Si16
For Si16 cluster, Zhu and Zeng  found that isomer 16A with C2h symmetry gives the lowest energy at the CCSD (T)/6-31G (d) level, similar to the prediction of Ho et al. ; nevertheless, we have found that isomer 16B is the one with the global minima with a difference of only 0.18 eV with respect to isomer 16A.
The isomer 16A can be described as two fused pentagonal prisms. Its structure is unique in the sense that it is neither based on the tri-capped trigonal prism motif (as 16B) nor based on a stacking sequence of fourfold and fivefold rings with capping atoms (as 16C).
Numerical data for isomers 16A to 16C are listed in Table 1. The isomer 16B exhibits not only the lowest energy and the highest band gap (2.45 eV), ovality, and ZPE but also the lowest parameter D, polarizability/atom, and the lowest wavelength for the most intense peak, for this set of isomers.
For isomer 16B, the highest intensity of emission corresponds to 583.65 nm, and the second peak observed is at a wavelength of 576 nm (both in yellow color). We observe a redshift for the other two isomers. Isomer 16B displays a wideband of emission (from green to red color), with the most intense peak at 750.89 nm (red color), while isomer 16C has the most intense calculated emission at 630.16 nm.
Structural and optical properties calculated for isomers Si17
Ho et al.  have reported for Si17 isomers, 17A, with C3v symmetry as ‘possibly the lowest energy structure,’ and it does contain a tri-capped trigonal prism (TTP) unit and a hexagonal chair unit. The six-atom hexagonal chair unit can be viewed as a fragment in bulk diamond silicon [61, 62]. The calculated emission in this work confirms this assertion (emission in the near infrared, see Table 1).
It is interesting to note that the more spherical-like Si17 isomer, 17C, is very competitive in stability compared to the prolate-shaped isomer 17A . Using a level theory of HF/6-31G*, Zhu and Zeng  report isomer 17C as the structure with the global minimum in energy for Si17 isomers, and isomer 17A using other levels of theory (MP2/6-31G*, MP3/6-31G*, MP4(SDQ)/6-316*, CCSD/6-31G*, CCSD(T)/6-31G*). Isomer 17B exhibits an unusual energy difference of 8.659 eV with respect to the global minimum (as can be seen in Table 1). During our calculations, it had instability and troubles to get convergence. Probably, this was the reason for which Zhu did not report the evaluation of isomer 17B using other levels of theory.
The Raman shift due to the quantum confinement can be described by a phenomenological approach founded on the negative dispersion of optical phonons with finite momentum and the averaging and folding of phonon frequencies in small particles. An analytic expression of this approach to describe the Raman frequency shift as also employed by Paillard et al.  is in which 0.543 nm is the lattice constant of silicon, L is the crystallite size, the parameter A = 52.3, and the exponent γ = 1.586 which are used to explain the vibrational confinement due to the finite size in a nanocrystal, and these values depend on each specific system. We have evaluated all Raman spectra corresponding to Si17 isomers A to C, using DFT. Figure 12b shows, as an example, the spectrum which corresponds to isomer Si17A.
Calculated emission for isomer 17A results in a narrowband with emission only in the near infrared. The predicted emission for isomer 17B is in the tail infrared but results with a very low intensity.
Structural and optical properties calculated for isomers Si18
FTIR spectra for isomer 18A shows the most intense calculated response at the vibrational frequency of 409 cm−1; nevertheless, frequencies of 450 and 458 cm−1 were calculated too.
The shift of the phonon peak towards lower wavenumbers and broadening of the peak width, in the Raman spectra, are attributed to the confinement of optical phonons in nano-dimensional Si crystals . The shift of the phonon peak could be used to calculate the crystallite size of Si. Using DFT, we have evaluated the Raman spectra for isomers Si18 A to C. In Figure 14b, we display the Raman spectrum for Si18 A. In this case, the phonon peak appears at a frequency of 485.7 cm−1.
The frequencies that have been observed in experimental reports are a little higher than the calculated ones for this isomer (see Figure 6, left). Isomer 18B displays the most intense peak at 260 cm−1. Each isomer Si18 has 48 vibrational modes. Isomer 18C presents the two most intense peaks at the vibrational frequencies 179 and 262 cm−1; and two of the calculated wavenumber were imaginary.
Structural and optical properties calculated for isomers Si19
Ho et al.  found for Si19 cluster a spherical-like isomer 19A. The isomer 19B which contains a tetra-capped trigonal prism unit and a magic number cluster Si6 unit is very competitive in stability compared with 19A. Isomer 19B was found based on a novel single-parent evolution algorithm coupled with DFTB/DFT methods. Isomer 19C is composed of a TTP unit and a Si10 (bi-capped tetrahedral anti-prism) unit . Its energy is slightly higher than both 19A and 19B.
Figure 16a displays the FTIR spectra for isomers Si19 A, B, C. We can appreciate manifold vibrational frequencies varying from 200 to 500 cm−1. The strongest vibrations, for the most stable isomer, include the most intense peak at 325 cm−1, with an adjacent shoulder around 351 cm−1. The highest vibration is due to silicon atom located in the highest part or trigonal prism. The third most important vibration of isomer 19B occurs at 472 and 479 cm−1 and is associated to the bending mode Si-Si vibration of atoms in the base of the trigonal prism.
The atomic structure of isomer 19C seems like two small agglomerates joined, along the central part, for a simple silicon-silicon bond. The isomer 19C is the isomer Si19 which has the smallest size and dipole moment of all but presents the highest ovality (see numerical data in Table 1).
Raman spectroscopy provides useful information about the structure of silicon nano-agglomerates. The position and intensity of peaks in the spectrum reflect the molecular structure and can be used to determine the chemical identity of the sample. No two structures give exactly the same Raman spectrum, and the intensity of the scattered light is proportional to the amount of material present. Raman spectroscopy has shown to be useful for investigating the physical properties such as crystallinity, phase transitions, and isomers or polymorphs. We evaluate the Raman spectra for Si19 agglomerates. Figure 16b displays the Raman spectrum for Si19A.
In this work, we calculated theoretically the IR, UV-VIS, and Raman spectra, the orbital energy levels including the frontier orbitals (HOMO and LUMO) and a selected set of geometric properties of medium-sized silicon agglomerates from Si15 to Si20 including all stable isomers. These Si-nCs present a size which is less than 1 nm. Their gap energies oscillate between 1.053 and 3.051 eV. The equilibrium energy calculated for several proposed Si clusters at ground state and at the first six excitation states calculated results very useful to evaluate the possible impact to the PL from different silicon structures present in SRO films. From the theoretical PL spectra obtained in this work, we can conclude that this family of silicon agglomerates emits in the visible region, extending in some cases to the near infrared.
NDET is currently a Ph.D. candidate at the Researching Center for Semiconductors Devices (IC-CIDS) in the Science Institute of Autonomous University of Puebla, Mexico. He has been working on the origin of luminescence in silicon and silicon rich oxide thin films. His research interests include modeling using molecular mechanics, semi-empirical and Hartree-Fock methods, and density functional theory, and material science including methods for deposition and characterization techniques of semiconductors and superconductors. He also has explored other topics including phtalocyanines, graphene, and carbon nanotubes. DHL is currently a researcher and professor in the Science Institute - Center of Investigation for Semiconductors Devices (IC-CIDS) of Autonomous University of Puebla, Mexico. He has been working on the optical properties of semiconductors in the framework of local and nonlocal theory, Casimir forces with dispersive spatial effects, and luminescent effects in compound semiconductor. Recently, his research interest is focused on spintronics in semiconductor materials and luminescence in graphene and nanotubes of carbon. JFJFG is currently a researcher and professor in the Science Institute - Center of Investigation for Semiconductors Devices (IC-CIDS) of Autonomous University of Puebla, Mexico. He has been working on silicon rich oxide, specifically in luminescence. Also, he has been working with porous materials (porous silicon and porous aluminum), their structure and electrical and optical properties. His research interests are the conduction process and the modeling of these processes. JALL is currently a researcher and professor in the Science Institute - Center of Investigation for Semiconductors Devices (IC-CIDS) of Autonomous University of Puebla, Mexico. He has been working on the structural, electrical, and optical characterization of materials and MOS structures. His research interest is the physics and technology of nanostructured materials and silicon devices. Additionally, his research interests are, too, the nanotechnology, material characterization, and optoelectronic devices such as sensor, LEDs, and solar cells. JMJ is currently a researcher and professor in the Science Institute - Center of Investigation for Semiconductors Devices (IC-CIDS) of Autonomous University of Puebla, Mexico. He has been working on compound semiconductor families III-V (GaAs, GaSb, GaAlAs, GaAlSb, GaAlSbAs, InGaSbAs), II-VI (ZnO, ZnS, CdO, CdS, CdSe, CdSSe), and IV-VI (PbS, WO3, Cu2O), epitaxial growth by LPE, synthesis by spray pyrolysis and chemical bath, semiconductor devices (LD and APDs), and structural and photoluminescence characterization of materials and devices. DEVV is currently a Ph.D. student in the Science Institute - Center of Investigation for Semiconductors Devices (IC-CIDS) of Autonomous University of Puebla, Mexico. She started to work on the growth and characterization of nonstoichiometric silicon oxide obtained by HFCVD. Her research interests include experiments and structural, optical, and electrical characterization of SiO x films and MOS structures.
This work has been partially supported by CONACyT-154725, PIFI-2013, and VIEP-BUAP-2013. N.D. Espinosa-Torres acknowledges the financial support of CONACYT by the scholarship given to carry out Ph.D. studies. We thank also the M.Sc. student Angel Pedro Rodríguez Victoria for his collaboration in PL measures in porous silicon.
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