Si Nanostructures Embedded in SiO2: Electronic and Optical Properties
a
Stefano Ossicini a, Elena Degoli a, Marcello Luppi* b, Rita Magri b INFM-S and Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia; b INFM-S3 and Dipartimento di Fisica, Università di Modena e Reggio Emilia 3
ABSTRACT We present ab initio results for the structural, electronic and optical properties of silicon nanostructures confined by silicon dioxide. We investigate the role of the dimension, symmetry and bonding situations at the interfaces. In particular we consider Si/SiO2 superlattices and Si nanocrystals embedded in SiO2 matrix. In the case of Si/SiO2 superlattices the presence of oxygen defects at the interface and the dimensionality are the key points in order to explain the experimental outcomes concerning photoluminescence. For Si nanocrystals embedded in SiO2 we show, in agreement with experimental results, the close interplay between chemical and structural effects on the electronic and optical properties. Keywords: Si nanostructures, low dimensional systems, electronic and optical properties, density functional theory
1. INTRODUCTION Nowadays modern microelectronics tends to reduce to the nanometer size the elements of the integrated circuits [1]. The progress in this field depends both on the development of the nanometer size technology and on the knowledge about the processes taking place at such a quantum scale level. A lot of efforts have been undertaken to study the lowdimensional structures, both from fundamental and applied points of view. A number of materials have been announced to be prospective candidates for different quantum scale applications [2]. The main goal is to have the possibility of integrating low-dimensional structures showing appropriate optoelectronic properties with the well established and highly advanced silicon microelectronic present technology [3,4]. Therefore, after the initial impulse given by the pioneering work of Canham on porous silicon [5], nanostructured silicon has received extensive attention both from experimental and theoretical point of view during the last ten years (for review see Refs. [6,7,8,9,10,11,12]). This activity is mainly centered on the possibility of getting relevant optoelectronic properties from nanocrystalline Si, which in the bulk crystalline form is an indirect band gap semiconductor, with a very inefficient light emission in the infrared. Although some controversial interpretations of the visible light emission from low-dimensional Si structures still exist, it is generally accepted that the quantum confinement, caused by the restricted size, and the surface passivation are essential for this phenomenon [12]. Due to the intrinsic reactivity of porous silicon with the ambient most of its properties were unstable. So the research moved towards more stable systems, such as those formed by silicon quantum wells confined by SiO2 layers [13,14,15,16,17] and by silicon nanocrystals dispersed in an oxide matrix [18,19,20]. In this paper we will review our activity in the field of the theoretical determination of the structural, electronic and optical properties of Si nanostructures embedded in SiO2. We’ll firstly give a brief introduction of the ab initio methods (section 2) used in our calculations. Then we’ll present our results on the optical properties of Si quantum films in Si/SiO2 superlattices, where the importance of the dimensionality and of the interface bonds is underlined (section 3). Section 4 will be devoted to the development of a model for the calculation of the optoelectronic properties of Si *
[email protected]; phone +39 059 205 5323; fax +39 059 205 5235; http://www.ldsn.unimo.it; Dipartimento di Fisica, Università di Modena e Reggio Emilia, Via Campi 213/A, I-41100 Modena, Italy
Optical Properties of Nanocrystals, Zeno Gaburro, Editor, Proceedings of SPIE Vol. 4808 (2002) © 2002 SPIE · 0277-786X/02/$15.00
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nancrystallites embedded in a SiO2 matrix, an argument of particular relevance owing to the recent observation of optical gain from Si nanocrystals formed by ion implantation in SiO2 [20]. In both sections a detailed comparison with the experimental results will be presented. Finally Section 5 will be dedicated to the conclusions.
2. METHODS OF CALCULATION In our calculations we have employed several ab initio methods based on density functional theory (DFT) [21]. In the following we will present the used methods with respect to the different considered systems. Concerning the self-consistent electronic structures of the Si-based superlattices (SL’s), that will be presented in section 3, they have been calculated by means of the Linear Muffin-Tin Orbital method in the Atomic-Sphere Approximation (LMTO-ASA) [22]. Exchange and correlation effects have been included within the local density approximation (LDA). Due to the LDA we underestimate the energy gaps: 0.56 eV and 6.36 eV instead of the experimental values of 1.1 eV and 9.0 eV for Si and SiO2 bulk materials, respectively. The shortcoming of LDA has been resolved using the so-called scissor operator adding a self-energy correction [23]. In order to overcome the lack of periodicity perpendicular to the interface, we use, for SL's calculations, supercells formed by a variable number of Si elementary cells, separated by SiO2 layers. Once the self-consistent electronic properties have been calculated, the optical properties of the SL's have been computed by evaluating the imaginary part of the dielectric function ε2 in the optical limit. The computation of the optical matrix elements have been realized in the gradient representation with a large basis set that includes angular momentum up to l=3, assuring the accuracy of the calculation [24,25]. The summation over k is performed using the tetrahedron method and all the calculation are made for photon energies up to 20 eV. Our total energy calculations on Si nanocystals (NC) in SiO2 matrix and on Si-H NC (section 4) have been based on the CASTEP code [26]. The theoretical basis is the DFT in the gradient-corrected LDA version (GGA) [27]. Our choice for exchange and correlation terms has been the GGA-PBE approach [28]. The electron-ion interaction is described using a pseudopotential concept. Ultrasoft pseudopotential [29] in a separable Kleinman-Bylander form have been used [30]. In particular for O we have chosen a soft potential with a large core radius, suitable for fast solid state calculations. In order to speed up the run the pseudopotential representation is in real space and the kinetic energy cut-off is set to 265 eV for Si NC in SiO2 and 260 eV for Si-H NC. The calculation has been performed with one special k-point for the BZ sampling. To correct the results obtained at relatively low cutoff energy and k-point sampling we used Finite Basis Set Correction [26]. The Density Mixing method [31] with the DIIS Pulay Mixing Scheme [32] in conjunction with the Conjugate Gradient technique [33] has been used to minimize the electronic configuration. The geometry optimization (GO) with the cell optimization has been performed using the BFGS scheme [34]. In the case of Si NC in SiO2, for the band structure calculations at relaxed geometry, we have used the same acknowledgements as for the GO run but with a “band by band” electronic minimization method and 29 special k-points. We have decided to consider 44 unoccupied states for the estimation of the conduction band (CB) behavior. The optical properties have been obtained with a LDA approach, increasing the number of the k-points to 20 and including 44 empty states. Only direct (same k-point) interband (VB-CB) transitions have been taken into account.
3. ELECTRONIC AND OPTICAL PROPERTIES OF SI/SIO2 SUPERLATTICES : THE ROLE OF INTERFACE DEFECTS In this section we will discuss the electronic and optical outcomes obtained for our Si/SiO2 (001) wells as a function of the Si layer thickness and of the surface passivation [35,36]. For these structures the elementary Si cell is constituted of 5 Si layers for a thickness of 5.43 Å, while the SiO2 thickness of 7.68 Å is the same for all the considered SL's and is large enough to make the central SiO2 layer exhibits bulk-like properties. We used a ß-cristobalite (BC) structure for the silicon dioxide layer that has the diamond like symmetry as Si and leads to a simple model for the interface. The lattice parameter for the BC is approximately √2 74
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times that for Si, thus we obtain a perfect match using a lattice constant of √2 times 5.43 Å =7.68 Å for SiO2, as Batra et al. [37] and Tit at el. [38] did, and growing the BC structure along the diagonal of the (001)-surface unit cell of the Si layer. Using this interface model we have formed between Si and SiO2 as many bonds as possible but a Si atom at the interface remains unsaturated. For this reason we have introduced a double-bonded extra oxygen atom positioned at a distance of 1.446 Å from the Si surface in accordance with the passivating mechanism suggested by Kageshima et al. [39]. Experiments show that the interface is rather abrupt and with very few interface states (this implies a density bulge which has also been observed [40]) and it's also known that the Si/SiO2 interface contains all the suboxide-charge states Si+1, Si+2 and Si+3. The model that we use produces a density bulge at the interface and contains also the suboxide charge states Si+1 and Si+2 but not the Si+3 as in the case of the energy optimized model due to Pasquarello et al. [41] and Kageshima and Shiraishi [39]. To analize the role played by the dimensionality we have considered three different Si[n]-SiO2 wells with n (the number of elementary Si cells) equal to 1,2 and 3: the thickness of the wells, taken as the distance between the Si atoms at the two interfaces along the growth direction, is 5.43 Å, 10.86 Å and 16.29 Å, respectively.
Fig. 1: The Si/SiO2 (001) superlattice elementary cell with one unit of Si: Si atoms are pale grey and O atoms are dark grey. The βcristobalite is matched to the Si by rotating the former about the [001] axis by π/4. An extra oxygen atom (black) is added to saturate the interface bonds.
To understand the role played by oxygen related defects at the interface of the well we have considered two systems, the first fully passivated through a double-bonded extra oxygen atom (the black atoms in Fig. 1) added to saturate the Si dangling bonds, and the second with an oxygen vacancy at the interface produced removing the same extra oxygen atom. The electronic and optical calculations have been performed in both cases for each one of the three structures. Concerning the role of dimensionality we observe, in the three fully passivated cases, that the material is a semiconductor, as the band structure of the Si[1]-SiO2 SL in Fig. 2(a) shows, and that there is an opening of the gap when the thickness of the Si layer decreases. The band structure shows a gap which is slightly indirect for the presence of a state at the top of the valence band (mostly related to the Si atoms in the inner Si layer) that is partially due to the interaction between the interface Si and its double-bonded O atom. If we remove this extra oxygen, leaving the two dangling bonds of the interface Si unsaturated, we find that the material is still a semiconductor with a new state, a
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dangling bond interface state, at the top of the valence band that reduces the band gap by 0.12 eV (Fig. 2(b)). Looking at the band structure for the Si[2]-SiO2 and Si[3]-SiO2 SL's with the oxygen vacancy at the interface, we find that, as for the fully saturated lattices, the material is an indirect semiconductor with a progressive gap opening observed when the thickness of the Si layer is reduced. The interface state, found for the partially passivated Si[1]-SiO2 SL, is now inside the valence band: the interesting fact is that the energy separation between this interface state and the bottom of the conduction band is almost unaffected by the Si layer thickness. In the last years, a lot of experimental works have been done on the optical properties of Si/SiO2 quantum wells and SL's, nevertheless the situation is still not clear [13,14,15,16,17]. Our task in this work is to clarify the experimental panorama for the Si/SiO2 quantum wells and SL's through the comparison between theory and experiments.
Fig. 2: Band structure of the (a) fully saturated and (b) partially saturated Si[1]-SiO2(001) superlattice projected along two symmetry directions of the two-dimensional BZ of the (001) surface. K and M represents, respectively, the k-points in the corner and in the middle of the side of the two-dimensional BZ. A self-energy correction of 0.8 eV has been added to the conduction states. Energies (in eV) are referred to the valence band maximum.
Unfortunately, the experimentalists measure the PL spectra of this SL's but, from a theoretical point of view, a quantitative description of this process that includes phenomena such as relaxation, excitonic interactions etc., is too complex and in this case is beyond the realm of the present investigation. So we have evaluated the imaginary part of the dielectric function that is directly related to the dipole matrix elements; these elements give information directly on absorption and indirectly on the relevant radiative PL processes if we consider the simplest radiative recombination mechanism in which an electron excited from the valence to the conduction band through the absorption of an energy E can directly recombine through the emission of the same energy.
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The results obtained for the optical properties reflect directly the electronic ones. Actually, if we look at the imaginary part of the dielectric function for the fully saturated Si[1]-SiO2 SL we find new interesting optical features in the visible range completely absent in bulk Si. If then we introduce the interface defect (the O vacancy) in the superlattice, comparing the ε2 for the fully saturated and partially saturated lattice we observe a new intense asymmetric peak at the low energy edge. The same asymmetric peak can be observed for the ε2 of the Si[2]-SiO2 and Si[3]-SiO2 SL's with the oxygen vacancy at the interface. This peak can be fitted by two gaussian bands: the first band, more intense, located at ∼1.7 eV, is related to the interface state and the second one, weaker and located at ∼1.9 eV, is due to the Si bulk-like states. Increasing the Si layer thickness these two gaussian bands remain recognizable in the ε2 behaviour but their position changes. Repeating the fitting of these peaks with the gaussian bands for each lattice and plotting them together we are able to see if and how these states are affected by dimensionality. In these case the ε2 are shifted higher in energy of 0.8 eV (an appropriate value for our Si confined systems as previous studies [42] have shown) in order to overcome the LDA underestimation of the gap having in this way a better comparison with the experimental data.
FIG. 3: ε2 first asymmetric peak (dashed line) and its gaussian fit (solid line) for the (a) Si[3]-SiO2, (b) Si[2]-SiO2 and (c) Si[1]-SiO2 superlattices. The letter I indicates the interface gaussian band while the letter Q indicates the bulklike gaussian band.
In Fig. 5 the gaussian bands are shown labelled with a I for the interface band and with a Q for the bulk-like band for the lattices with 3 (Fig. 3(a)), 2 (Fig. 3(b)) and 1 (Fig. 3(c)) Si cells. A shift to higher energies (from ∼1.4 eV to ∼1.9 eV) is evident for peak Q when the thickness of the Si layer decreases: this is tipically a quantum confinement effect. The energy peak positions related to the quantum confinement states are also confirmed by the corresponding results for the fully saturated systems. The peak I, instead, is almost unaffected by the dimensionality of the Si slab and remain Proc. of SPIE Vol. 4808
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positioned at around 1.7 eV. Quite interesting is the experimental work presented by Kanemitsu and co-workers [17]: they have studied the luminescence properties of crystalline-Si/SiO2 single quantum wells, formed on SIMOX wafers, by selective excitation spectroscopy that provide detailed informations on the luminescence mechanism. In very thin well samples (≤2 nm) they observed efficient PL in the visible spectral region. In this asymmetric PL spectra they were able to fit two gaussian bands: a weak band that shifts to higher energy (from ∼1.5 eV to ∼1.9 eV) with decreasing Si layer thickness (from 1.7 nm to 0.6 nm), and a strong band, at ≈ 1.65 eV, almost independent on the well thickness. Kanemitsu et al. [17] have attributed the weak band to quantum confinement effects and the strong one to radiative recombination in the interface region; moreover, from the presence of TO-phonon related structures, both in the resonant PL spectrum and in the PL polarization spectrum of the quantum confined related band, they speculate about an indirect nature of the optical-transition for the size quantized states of the 2D Si wells. On the light of the Kanemitsu model that seems to be the most accurate and promising, we are now able to show the role played by quantum confinement and by oxygen-related defects at the interface between Si and SiO2. The good agreement between our outcomes in Fig. 3 and Kanemitsu [17] results in Fig. 4 fully confirm his interpretation on the nature of the PL in these materials. Not only the energy positions of the quantum confined and interface related peaks are in good agreement, but also the relative intensity of the two bands, one respect to the other, agrees; however since the concentration of interface defects is not well known in the experimental results this last agreement must be further investigated. Moreover, as in the experiments, the polarization degree of our ε2 is stronger for the quantum confined related peak than for the size insensitive interface related peak.
FIG. 4: Photoluminescence spectra of c-Si/SiO2 single quantum wells under 488 nm laser excitation at 2 K: (a) 1.7, (b) 1.3 and (c) 0.6 nm thickness. The asymmetric PL spectra can be fitted by two gaussian bands, the weak Q band and the strong I band [17].
From the energy band, optical results and the comparison with the experiments we can conclude that both quantum confined and interface states play an essential role in the optical spectra of Si/SiO2 SL’s.
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4. STRUCTURAL, ELECTRONIC AND OPTICAL PROPERTIES OF SI NANOCRYSTALS EMBEDDED IN A SIO2 MATRIX In this section we present a simple model to study the properties of Si NC embedded in SiO2 matrix from a theoretical point of view [43]. We have requested for our system two main qualities: a silicon skeleton with a crystalline behavior, for simulating the NC and the simplest Si-SiO2 interface, with the minimum number of dangling bonds or defects. To reach these goals we have built up a cubic supercell (l=14.32 Å) of SiO2 BC repeating two times along each cartesian axe the unit cell of SiO2 BC, whose diamond-like geometry allows the drawing of simple Si-SiO2 interfaces [39]. Then we have cut out from the SiO2 structure some oxygen atoms and linked together the silicon atoms left with dangling bonds. In this way we have modeled an initial supercell, suitable for calculation, made of 64 Si and 116 O atoms with 10 Si bonded together to form a small NC (0.7 nm, the mean diameter) with Td interstitial symmetry (Fig. 5a) and highly strained bond length if compared to the Si-bulk case (+33%). All bonds have been fully saturated and the O atoms at Si NC surface have been single bonded with Si. On this structure we have performed total energy minimization runs, leaving free to relax all the atoms positions and the cell parameters. At the same time we have built up two other comparison systems. The first (Si10H16-I) is a Si NC with the same characteristics of the previous one but covered with H atoms and included in a vacuum supercell (l=14.32 Å) (Fig. 5b) on which we have performed total energy calculation with the same prescription used before. The second (Si10H16-II) is obtained in the same way as the Si10H16-I, but starting from the relaxed positions of the Si atoms obtained for the Si10 NC in SiO2 BC and performing only electronic energy minimization. In these ways we had the possibility of “isolating” the properties linked only to the Si structure of the NC, both in the relaxed and in the in-BC-like geometry, in order to evaluate the role of the Si-O interface in Si NC embedded in SiO2. Unlike refs. [44,45], we are interested not only on the role of different passivants and bonds at the interface but also, since our Si NC is not in vacuum, to the role of the Si NC-host interface and of the whole embedding relaxed SiO2 matrix. Very recently a similar calculation, but without geometry optimization, appeared for Si NC and Ge NC in SiC [46].
Fig.5: a) Stick and ball picture of the final optimized structure of Si10 NC in SiO2 BC. The dark gray spheres represent O atoms, light gray Si and white the Si atoms of the nanocrystal. b) Stick and ball picture of the final optimized structure of Si10H16-I. Light gray spheres stand for Si atoms while white ones for H atoms. Proc. of SPIE Vol. 4808
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Looking at the final structure after the geometry optimization runs, for the Si10 NC in SiO2 BC we find that the skeleton is still crystalline-like (diamond) with a Si-Si bond length of 2.67 Å, that means a strain of 14% respect to the bulk case. The NC relaxation causes a complex deformation of the SiO2 matrix around it, both in bond lengths and angles. It seems as if the lack of oxygen atoms and the compression of the NC volume determine an empty region that the SiO2 structure tends to fill up stressing bonds and angles in various ways. Nevertheless the deformation doesn’t affect all the SiO2 matrix. It is actually possible to find still a good BC crystalline structure, in terms of angles and bond-length, at a distance from the dot’s atoms of 0.8-0.9 nm. The NC is therefore surrounded by a cap-shell of stressed SiO2 BC with a thickness of about 1 nm which progressively goes towards a pure crystalline BC. The crystalline behaviour is maintained also in the optimised geometry of Si10H16-I, where even the distances between the Si atoms are practically the same as in bulk case. This shows how the SiO2 matrix in the previous case has conditioned the relaxing process of the NC from its initial configuration, forcing the Si-Si distances to settle in a mean value between the Si distances in SiO2 BC and bulk Si bond length. For what reward the hydrogen-cover, H atoms remain positioned following the tetrahedral symmetry of the NC, with a final Si-H distance of 1.472 Å.
Fig. 6: a) Band structure along high symmetry points of the BZ for the Si10 NC in SiO2 BC at relaxed geometry. b) Absorption spectrum of the Si10 NC in SiO2 BC. The vertical line indicates the calculated Eg for SiO2 BC (bulk).
On these relaxed structures and on Si10H16-II, we have then performed band structure and optical properties calculations. Fig. 6a shows the result for the band structure of Si10 NC in SiO2 BC relaxed. The system is still a semiconductor with an energy gap (Eg) of 2.07 eV that must be compared with the value of 5.84 eV for the Eg of BC 80
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SiO2 (bulk) (calculated with the same technique) and with 4.68 eV for Si10H16-I and 4.03 eV for Si10H16-II. With respect to the SiO2 BC case, the strong reduction is originated by the presence, at the valence and conduction band edges, of confined, flat, states that are due only to the presence of the Si NC, whereas deep inside the valence and conduction bands the more k-dispersed states related to the SiO2 matrix are still present. The Eg reduction is very marked also in comparison with the two isolated NC’s covered with H. This is in agreement with what we have observed studying SiH-O isolated clusters varying the type and the amount of Si-O bonds [43,47]. The triple degeneracy of both the top of the VB and the bottom of the CB which characterizes the energy levels of the two isolated NC is no more present. This suggest that the Si-O interface between the NC and the SiO2 play a key role in determining the organization of the Si NC related states at the band edges, with strong effects on the Eg value. Therefore, the electronic behavior of SiO2 matrix is radically changed with the introduction of the Si10 NC and at the same time the properties of the isolated Si NC are modified by the Si-O interface, i.e. by the SiO2 coverage. The system has to be considered as a whole. The orbitals analysis and in particular of the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) helps to have a clearer view of this whole. In Fig. 7 the HOMO and LUMO isosurfaces at fixed value for the Si10 NC in SiO2 BC are reported; we clearly see that the distribution is mainly confined on the Si NC region (more evident choosing bigger values) but some weight on the interface O atoms is surely present The first behavior supports the view of Si NC related states at the band edges suggested by the band structure analysis; the second point out the role of oxygen. The behavior of the orbitals relative to the more k-dispersed states well inside the VB confirms the localization of these states on the SiO2 BC crystalline region of the supercell. The NC related states at the band edges originate strong absorption features in the optical region as witnessed from Fig. 6b). These features are entirely new and can be (taking into account the different Si NC dimensions in theory and experiment) at the origin of the PL observed in the red optical region for Si NC immersed in a SiO2 matrix [19]. Moreover our results concerning the role of the interface Si-O region with respect to the absorption process help in clarify X-ray absorption fine structure measurements made on Si NC produced by ion implantation in SiO2 [19]. Light emitting silicon nanocrystals embedded in SiO2 have been investigated by X-ray absorption measurements both in total electron (TEY) and photoluminescence yields (PLY). The difference between TEY and PLY indicates the presence of a strained interface region between the Si NC and the SiO2 matrix that participates to the optical process in agreement with our theoretical outcomes [19].
Fig. 7: Isosurfaces at fixed value (25% of max. amplitude) of the square modulus of highest occupied (HOMO) and lowest unoccupied (LUMO) Kohn-Sham orbitals for the Si NC in the SiO2 matrix.
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5. CONCLUSIONS In this paper we have presented the results of ab initio calculations related to some of the interesting properties that arises when silicon is reduced to nanometric dimensions. We have shown that for Si nanostructures embedded in SiO2 it is important to clarify the role of the dimensions, of the symmetry and of the bonding situations at the interfaces. In particular in the case of Si quantum wells confined by SiO2 layers we have demonstrated how oxygen defects at the interface influences the optical results. For Si NC embedded in SiO2 matrix our results pointed out the close interplay between chemical and structural effects on the electronic and optical properties. These results are important with respect to the comprehension of the mechanisms that make Si nanostructures so attractive.
ACKNOWLEDGEMENTS INFM-PRA RAMSES and CNR-MADESSII
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