An interface clusters mixture model for the structure of amorphous silicon monoxide (SiO)

Journal of Non-Crystalline Solids 320 (2003) 255–280 www.elsevier.com/locate/jnoncrysol

An interface clusters mixture model for the structure of amorphous silicon monoxide (SiO) A. Hohl a, T. Wieder a,*, P.A. van Aken b, T.E. Weirich c, G. Denninger d, M. Vidal d, S. Oswald e, C. Deneke f, J. Mayer c, H. Fuess a a

Institute for Materials Science, Darmstadt University of Technology, Petersenstraße 23, D-64287 Darmstadt, Germany Institute of Applied Geosciences, Darmstadt University of Technology, Schnittspahnstraße 9, D-64287 Darmstadt, Germany c Central facility for Electron Microscopy, Aachen University of Technology, Ahornstraße 55, D-52074 Aachen, Germany d nd 2 Institute of Physics, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany e Institute for Solid State Analysis and Structural Research, IFW Dresden, Helmholtzstraße 20, D-01171 Dresden, Germany f Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany

b

Received 11 June 2002; received in revised form 5 August 2002

Abstract The present state of research on the structure of amorphous silicon monoxide (SiO) is reviewed. The black, coal-like modification of bulk SiO is studied by a combination of diffraction, microscopy, spectroscopy, and magnetometry methods. Partial radial distribution functions of SiO are obtained by X-ray, neutron and electron diffraction. Disproportionation of SiO into Si and SiO2 is verified. High resolution TEM gives an upper limit of less than 2 nm for the typical Si cluster size. The Si K-edge electron energy-loss near-edge structure (ELNES) data of SiO are interpreted in terms of the oxidation states Si4þ and Si0 . X-ray photoelectron spectroscopy gives first details about possible stoichiometric inhomogeneities related to internal interfaces. The wipe-out effect in the 29 Si MAS NMR signal of SiO is confirmed experimentally. The new estimation of the wipe-out radius is about 1.1 nm. First-time W-band, Q-band, and X-band ESR and SQUID measurements indicate an interfacial defect structure. Frequency distributions of atomic nearest-neighbours are derived. The interface clusters mixture model (ICM model) suggested here describes the SiO structure as a disproportionation in the initial state. The model implies clusters of silicon dioxide and clusters of silicon surrounded by a sub-oxide matrix that is comparable to the well-known thin Si/SiO2 interface and significant in the volume because of small cluster sizes. Ó 2003 Published by Elsevier Science B.V. PACS: 61.43

1. Introduction

*

Corresponding author. Tel.: +49-561 301 2542; fax: +496151 16 6023. E-mail address: [email protected] (T. Wieder).

SiO is a useful material for many industrial applications [1–6]. The black, coal-like modification is used for protective layers, optical coatings, insulating layers in electronics and semiconductor

0022-3093/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V. doi:10.1016/S0022-3093(03)00031-0

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technology, heat shielding, etc. Bulk amorphous silicon monoxide can be produced by simultaneous evaporation of silicon and silicon dioxide (Si(s) + SiO2 (s) ! 2SiO(g)) in vacuum at approximately 1400 °C. (Details about thermodynamics of SiO were reported in earlier studies [7–10].) The SiO gas consists of diatomic molecules with a double bond. At least five modifications of bulk SiO exist [1,5,11,12], depending on cooling rate or condensation temperature after evaporation. Above 800 °C a yellow powder and above 1000 °C a yellow glass is formed, both are at least partly disproportionated substances, as known from earlier X-ray diffraction studies [1]. Below 800 °C a black, glassy form and for even lower temperatures a black, coal-like form of bulk SiO is obtained. Quenching by a water cooled device leads to a black, fibrous material. It may be that SiO molecules form (SiO)n chains and rings in the vapour prior to deposition [13,14]. There is no doubt that the reason for the macroscopic 1:1 stoichiometry is the condensation going along with local 1:1 stoichiometry. Up to now, the atomic structure of solid SiO could not be clarified unambiguously and is a subject of controversy. In particular the black, coal-like modification has been of interest to many researchers. This is also the commonly commercially available form. The physical properties of SiO are somewhat closer to those of SiO2 than those of Si, because there exist twice as much Si–O bonds as Si–Si bonds. Silicon atoms are expected in tetrahedral coordination with sp3 hybridisation. However, octahedral coordination of the central Si atom is found in high-pressure SiO2 phases [15]. One may then ask whether a structure of exact 1:1 stoichiometry can be set up by Si–O–Si–O chains as building units or by Si(Si2 O2 ) tetrahedra. Is the structure of SiO composed of chains and rings, i.e. (SiO)n chains with bridging Si–Si bonds or Si chains with bridging O atoms? Or is SiO totally or partially disproportionated? Do regions of the well known Si2 O3 phase [16,17] exist? Is there some disproportionation into Si2 O and Si2 O3 ? Different models for the spatial distribution of different stoichiometric regions in the bulk have been discussed in the literature. Some authors proposed that SiO is disproportionated on a microscopic

scale into Si and SiO2 [18,19]. Other authors assumed SiO to be a phase for its own [20]. Philipp suggested the random bonding model (RB model) [21,22] of a continuous random network with a binomial distribution of Si(Si4x Ox ) tetrahedra, where the fraction of pure silicon tetrahedra is 1/ 16, based on a study of SiO films. The opposite limit is the random mixture model (RM model, also called microscopic mixture model) [23,24] of disproportionation into two separated phases Si and SiO2 . The latter model is sometimes described as a mixture of phase separated regions with dia
[25]. However, meters between only 5 and 10 A this description appears inconsistent, as the size of the so-called single phase regions is not much larger than the size of the phase separating regions, i.e. the material becomes interface dominated. RB and RM model are ideal limits. More realistic models are the nanometric scaled mixture model with different cluster sizes or the mixed phase model with different bond accumulation [26] with one third pure Si. Another model for SiOx assumes Si clusters in a SiOxþy matrix [27]. Also a model with Si clusters in a SiO2 matrix seems to be possible. Such a model is not far from the shell model [28] (and the mosaic model with Si microcrystallites [29]) for SIPOS (semi-insulating polycrystalline silicon) films, as opposed to the recently presented matrix model (SiO2 clusters in a-Si matrix) [30]. The latter assumes disproportionation with a silicon fraction of 1/3. In our study a new model is suggested, called the interface clusters mixture model (ICM model), taking the interface into account. The ICM model assumes that many of the Si regions in the condensed structure are too small to be referred to as pure silicon regions. At room temperature SiO has a tendency to decompose into Si and SiO2 [31,32]. Some considerations might rule out a too close proximity to the RB model. The Si–O bond is shorter and has higher energy than the Si–Si bond, and it is wellknown to be the more stable bond causing some asymmetry during structure formation. Silicon tends to reach an oxidation state of (IV). Furthermore, the RB model has already been refuted experimentally [16,33]. In a similar way the RM model or a macroscopic mixture can be seen as too extreme under the condition of the local stoichi-

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ometry during the condensation process. During deposition, the SiO gas provides a local 1:1 stoichiometry. An overall 1:1 stoichiometry in the bulk must result after deposition. This stoichiometry cannot be changed by a disproportionation process. The formation of the SiO structure goes along with rearranging processes. Thus the structure is highly dependent on the production process. E.g. in the production of SiOx thin films, chemical vapour deposition favours a RM-like structure whereas electron beam evaporation and plasma-deposition results in a more RB-like structure [34,35]. The production of non-stoichiometric SiOx is much easier in thin films than in the bulk form with high deposition rate. Experiments on samples from different production conditions show different analytical results. The SiO X-ray diffractogram is different to that of a mixture (above a nanometric scale) of Si plus SiO2 [20,25]. Chemical reactions of SiO do not show results as expected for a simple mixture [36], i.e. neither all reactions of silicon nor all reactions of silicon dioxide can be observed with silicon monoxide. It is therefore concluded by the present authors that SiO has an unknown morphological structure, which is most probably a disproportionation on a microscopic level. In addition to possible a-Si and a-SiO2 regions, SiO may even include a new structure. The stoichiometry of the unknown structure is not necessarily 1:1, but it should be a kind of sub-oxide, i.e. the mean oxidation state of Si is neither (0) nor (IV). The ionic-covalent character of the Si–O bond [37] allows the treatment of the tetrahedral silicon coordination in terms of oxidation states. From the production conditions the question arises, whether a Si atom should always have four bonding partners, or if it sometimes might have only three. Emons et al. [12,38] describe the possibility of partial dp p double bonds between Si and O atoms. Even if the condition of tetrahedral coordination has not to be fulfilled strictly, on average every O atom must have two Si neighbours. The Si oxidation state distribution must have the mean value (II) (for the 1:1 stoichiometry). Reported results [30,39] seem to support a certain stoichiometric separation opposite to random bonding. In distinction to results concerning SiO

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films [40], Flank et al. [39] did not find significant Si2þ in the bulk and they supported disproportionation. On the basis of the known data, we developed the following idea. During the formation of the SiO structure starting from SiO molecules not only free Si bonds are saturated, but also O–Si bonds are broken, and the corresponding O atoms are linked to other Si atoms. Bridging O atoms are inserted between the original (SiO)n chains and Si atoms temporarily get free. Since this process stays incomplete, the resulting structure can be seen as a frozen non-equilibrium state. Finally, the trend for disproportionation, naturally localised in the suboxide region, causes a narrowing of that region, leading to an interface between Si and SiO2 clusters. In order to elucidate the structure of the (Ôstrange materialÕ [6]) amorphous silicon monoxide several methods were applied.

2. Experimental We examined bulk SiO samples Patinalâ from Merck KGaA (Darmstadt, Germany). They were produced in an induction vacuum sintering system by heating a Si/SiO2 mixture to 1400 °C and subsequent condensation at 600 °C. The deposition
/s) at a rate was roughly 25 mm in 40 h (2000 A residual gas pressure of 106 bar. The substance appears as brown powder in the light microscope. Its density measured by pycnometry is 2.19 g/cm3 with porosities below 2 vol.% obtained from Hg porosimetry. The 1:1 stoichiometry of the Patinalâ samples (SiOx , x  1) was checked using EDX and chemical analysis. X-ray diffraction was performed using a dif
) fractometer with Ag Ka radiation (k ¼ 0:5609 A and a scintillation detector. The experiments were carried out in air with standard conditions using Bragg–Brentano geometry. The momentum transfer k ¼ 4pðsin hÞ=k had its maximum at
1 . Neutron diffraction was carried kmax ¼ 22:26 A out at the instrument D4 of the Institut Laue– Langevin (Grenoble, France) with wavelength
, Rh k=2 filter, a Cu(2 2 0) monok ¼ 0:5026 A chromator, ambient sample environment with air pressure below 1 Pa. The resolution was roughly

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1 was obtained. Dk=k ¼ 0:03, and kmax ¼ 23:75 A Electron diffractograms were acquired at the Max Planck Institute of Metals Research (Stuttgart, Germany) by using a transmission electron mi
) with croscope operating at 120 kV (k ¼ 0:03349 A energy filter. The exposed image plates were read out, and intensity evaluation was made by applying the program ELD [41]. We achieved kmax ¼
1 . 17:37 A HRTEM and attached EDX analysis were performed with a transmission electron microscope operating at 200 kV. For element mapping by EELS, a Gatan imaging filter (GIF) attached to a transmission electron microscope working at 300 kV was used. Further HRTEM and EELS (ELNES) investigations were carried out at 120 kV. EEL spectra were collected with a parallel electron energy-loss spectrometer 1 attached to the TEM. The zero-loss peak FWHM was approximately 0.7 eV. Spectra were collected from approximately z  75 nm thick regions at an irradiated area of 1 lm in diameter yielding a probed volume of V  0:06 lm3 . Dispersion settings were 0.1 eV/channel with an acquisition time of t ¼ 30 s. During the EELS investigations, no detectable changes of the Si K ELNES due to electron beam damage were observed. For XPS, three samples were prepared in situ in UHV at a base pressure below 107 Pa: One sample was broken to get a clean fracture surface, the second was scratched with a diamond-coated file, and the third was sputter-cleaned. Measurements were performed on an XPS system 2 with Mg Ka radiation (1253.6 eV), 350 W input power, an analysed area of 400 lm diameter, pass energy 12 eV, and acceptance angle a ¼ 45° to the analyser. The X-ray source was located at 54.7° relative to the analyser axis. We applied Arþ sputtering with 3.5 keV ion energy on an area of (2 mm)2 . The 29 Si MAS NMR data were collected with a Bruker ASX-400 NMR spectrometer operating at 9.4 T and 79.49455 MHz. The spinning frequency was 5500 Hz, and a pulse width of 4 ls was used. The finally applied relaxation delay time was

1 2

Gatan DigiPEELS 766. Physical Electronics PHI 5600.

1200 s, taking into account an experimental determination of the relaxation time T1 at the beginning. ESR investigations were done with three different microwave frequencies. In the X-band (9.5 GHz) a Bruker ER 2000D-SRC (resonator Bruker ER4118X-MD-5) was used at 8 lW, in the Q-band (34 GHz) a Bruker ER 051 QG (resonator Bruker ER 5106 QT) was used at 300 lW, and in the W-band (94 GHz) a Bruker ESP 900 W (Fabry–Perot resonator) was used at 800 lW. SQUID magnetometry 3 was conducted at 3500 and 5000 G. Except for SQUID, all measurements were performed at room temperature.

3. Results 3.1. Diffraction To obtain three partial radial distribution functions, a combined evaluation of the independent X-ray, neutron, and electron diffraction experiments was performed. Here qij ðrÞ is the density of atoms of type j at the distance r from an atom of type i. The common definition for the (total) atomic pair distribution function (PDF, also called correlation function), where peak areas are directly related to the atomic coordination number, is GðrÞ ¼ 4prðqðrÞ  q0 Þ. The atomic densities were
3 [42], q ða-SiOÞ ¼ 0:060 A
3 , q0 ða-SiÞ ¼ 0:050 A 0 3
. The (total) radial and q0 ða-SiO2 Þ ¼ 0:066 A distribution function (RDF) is equal to 4pr2 qðrÞ ¼ rGðrÞ þ 4pr2 q0 [43]. We present (partial) rGij ðrÞ to give the best view on peaks at higher r. To obtain three structure factors from the measured intensities, standard data reduction was carried out including background subtraction, necessary corrections (e.g. for absorption or polarisation) [44], and application of a scaling factor for transformation into electron units or (in the case of neutrons) fm. To obtain the interference functions iðkÞ we interpolated atomic scattering amplitudes for X-rays from Hubble et al. [45], and for electrons the formula from Jiang and Li [46] was applied.

3

Quantum Design MPMS XL.

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Fig. 2. Partial radial distribution function rGOO ðrÞ for SiO. The
) between the first and the last atom of the chains distances (A are 2.64 (O–Si–O), 3.39 (O–Si–Si–O), 3.86 (O–Si–O–Si–O), 4.17 (O–Si–O–Si–O), 4.48 (O–Si–O–Si–O), 4.99 (O–Si–O–Si–O).

30 Si-O-Si-O-Si-O

Si-O

20 −1

4 πr 2 ( ρ (r) − ρ0) (Å )

For atomic scattering lengths for neutrons we used values of 4.15 fm for Si and 5.803 fm for O. The data evaluation was done according to the Faber–Ziman formalism [47], which is implemented in the Reverse Monte Carlo program MCGR [48]. Both the total and the three simultaneously evaluated partial radial distribution functions of SiO were obtained. For the latter case, all structure factors iðkÞ þ 1 were extended to
1 by adding zero for iðkÞ if neceskmax ¼ 23:75 A sary. This value of kmax corresponds to a real space
. We resolution limit of Dr  2p=kmax ¼ 0:265 A have verified good agreement of our total rGðrÞ curves with those obtained by comparable data analysis by means of traditional Fourier inversion using the modified program LAXS (also called LASIP) [49] and an own Mathematicaâ program [30]. The partial rGij ðrÞ curves are plotted in Figs. 1–3. The positivity condition and the hard-sphere cut-off of qij ðrÞ cause sharp-edged features at the bottom of the curves. The peak positions can be well associated with known values from SiO2 and pure Si as they would be expected for separated
for the Si–O phases [18,20], i.e. around 1.6 A
for the Si–Si bond. The bond and around 2.4 A O–Si and O–Si–O distances as well as the Si–Si and Si–Si–Si distances prove the tetrahedral angle at Si

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10

Si-O-Si-O

0

rG SiO(r) -10

Si-Si-O Si-Si-Si-O

-20 0

1

2

3

4

5

6

7

r (Å)

Fig. 3. Partial radial distribution function rGSiO ðrÞ for SiO. The
) between the first and the last atom of the chains distances (A are 1.64 (Si–O), 3.99 (Si–O–Si–O), 4.18 (Si–O–Si–O, Si–Si–Si– O), 5.06 (Si–O–Si–O–Si–O), 5.23 (Si–O–Si–O–Si–O), 5.82 (Si– O–Si–O–Si–O). The lack of the Si–Si–O chain indicates the disproportionation of SiO.

Fig. 1. Partial radial distribution function rGSiSi ðrÞ for SiO. The
) between the first and the last atom of the chains distances (A are 2.45 (Si–Si), 2.83 (Si–O–Si), 3.16 (Si–O–Si, Si–Si–O–Si), 3.32 (Si–Si–O–Si), 3.66 (Si–Si–O–Si), 3.90 (Si–Si–Si), 4.18 (Si– Si–Si–Si, Si–Si–O–Si), 4.72 (Si–O–Si–O–Si, Si–Si–Si–Si), 5.84 (Si–Si–Si–Si).

atoms and thus the existence of Si(Si4x Ox ) tetrahedra. A distortion of possible Si–Si–Si chains cannot be excluded. The peaks related to longer chains exhibit more broadening due to rotation angles. Our result of a non-significant Si–Si–O
is in agreement with earlier peak around 3.3 A studies on total radial distribution functions of SiO [20,24,30]. The lack of the Si–Si–O atomic chain indicates that the Si–Si bonds and the Si– O bonds tend to separate, resulting in a phase

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separation, which can be interpreted as local disproportionation of SiO into clusters of Si and SiO2 . No significant amount of double bonds from the SiO molecules is remaining. We exclude the existence of a significant amount of extended suboxide regions (e.g. Si2 O3 [17]) in the bulk. Evidently, in the bulk no significant amount of smaller than six-membered atomic rings exists. Otherwise the atomic distances and bond angles should differ significantly from the usual values for pure Si and SiO2 , as it is known for example from (SiO)n molecules [13,50,51]. 3.2. Microscopy Element mapping in the TEM does not show any structure in our samples. The resolution of the GIF is limited to about 3–4 nm. Neither the oxygen K-edge image nor the silicon K-edge image shows any structuring of the element distribution. EDX measurements are suitable for determination of local stoichiometry, but the spatial resolution is restricted by the beam diameter and by the positional stability of the specimen to a scale of several nanometres within some minutes. These analyses did not exhibit any significant deviations from the 1:1 stoichiometry. At 200 kV the HRTEM image of an amorphous region in SiO shows a homogeneous appearance of the structure at a scale of about one nanometre (Fig. 4). A Fourier transform of the imaged region and diffraction images seem to prove the completely amorphous character of the investigated sample. However, silicon and oxide regions possibly do not give significant amplitude contrast
)1 and 200 kV are when a wide aperture of (1.4 A used. The smoothness of the grain borderlines makes sure that contrast caused by sample thickness is not expected to have significant effects in the range of expected cluster sizes. An observation of stoichiometry (atomic number Z) dependent contrast (stray absorption contrast) is difficult, because of the low difference between the densities of Si and SiO2 , and because clusters of different stoichiometry are superimposed [52]. Operating at
)1 in120 kV and using a small aperture of (5 A creases the relative contribution of Z dependent contrast. With some probability stoichiometric

Fig. 4. HRTEM image of native SiO recorded at 200 kV with normal aperture. Under these conditions no contrast due to clustering can be observed.

different clusters should be better resolvable at the rim of investigated grains, if their size is larger than approximately 1.5 nm. (The observation of Si crystallites at the rim of grains from heated samples as described below confirmed that the rim was not simply oxidised.) The stray absorption contrast is distinguishable from the diffraction contrast by its independence of the tilt angle between sample and the primary beam. Another bulk SiO sample was heated for 1 h at 900 °C. This temperature was the highest without observable crystallisation. Clusters should have grown as much as they do without significant crystallisation (see Section 4.2). The sample was observed with the large and with the small aperture each with two tilt angles 0° and 10°. The images taken with large aperture show no significant diffraction by crystallites. The images with small aperture at 0° (Fig. 5) and at 10° (not shown) exhibit some spots of (Z) contrast and are similar to each other. A sample that was kept at room temperature (Fig. 6) does not show any features related to possibly existing resolvable clusters. Hence, the homogeneous appearance of the structure has to be taken for meaningful. The dependence on the annealing temperature indicates

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Fig. 5. HRTEM image of SiO (annealed for 1 h at 900 °C) recorded at 120 kV with small aperture. It exhibits some spots of contrast due to stoichiometric differences.

that the appearance of contrast in spots is not simply caused by variations of the sample thickness, but by grown clusters. After heating a SiO sample for 1 h at 1000 °C many silicon microcrystallites had formed. At 200 kV the crystallites can be identified by their lattice
), not by contrast fringes (Si(1 1 1): d ¼ 3:135 A (Fig. 7). The size of the smallest crystallites was found to be about one nanometre, which corresponds to three lattice planes (Fig. 7). This indicates the possible existence of some clusters not larger than 1 nm at room temperature. In summary, the characterisation of SiO using TEM indicates a magnitude of clustering between 1 and 2 nm for the native sample. In rare cases, some crystalline material was observed by TEM in native SiO samples (Fig. 8) [30]. The diffraction patterns could not be attributed to known phases (e.g. SiO2 modifications). We cannot exclude the existence of an unknown

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Fig. 6. HRTEM image of native SiO recorded at 120 kV with small aperture. It does not show any resolvable clusters.

Fig. 7. HRTEM image of SiO (annealed for 1 h at 1000 °C) recorded at 200 kV with normal aperture. The smallest crystallites show a size of approximately 1 nm (three lattice planes,
). Si(1 1 1): d ¼ 3:135 A

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Fig. 8. TEM diffraction pattern of native SiO showing some features of crystallinity.

phase of crystalline SiO with very low stability, which is amorphised by the TEM electron beam or because of aging. 3.3. ELNES spectroscopy The first data reduction included corrections for dark current, channel-to-channel gain variation, plural scattering, and zero-loss peak asymmetry. The experimental Si K-edge ELNES spectrum of SiO in Fig. 9 shows a pronounced maximum at 1846.8 eV, a pre-edge feature at about 5 eV prior to the main peak and a broad maximum at 1864 eV. This spectrum is in good agreement to the

Fig. 9. Experimental Si K-edge ELNES spectrum of SiO and theoretical Si K-edge XANES spectra for various tetrahedral clusters consisting of Si(O4 ), Si(SiO3 ), Si(Si2 O2 ), Si(Si3 O), and Si(Si4 ). Dotted vertical lines illustrate the similarities and peak positions of the spectra. Some of the spectra have been shifted vertically for clarity.

Si K-edge XANES spectrum published before [33]. Close to the edge threshold and for spectra recorded at small scattering angles, the core-loss edges obey the atomic dipole selection rules for the electronic transitions with a change in angular momentum Dl ¼ 1, whereas the spin remains unchanged Ds ¼ 0. Under these conditions, the ELNES is equivalent to the X-ray absorption near-edge structure (XANES). Multiple-scattering (MS) calculations provide evidence that the number, the intensity and the shape of ELNES resonances are affected by site symmetry, bond angles and number of nearestneighbours [13]. The shape of the Si K ELNES is mainly determined by the first coordination shell around the absorbing central atom [53]. No phase with a spectral shape similar to SiO exists. In order to use its profile as a coordination fingerprint, the experimental Si K ELNES spectrum was compared to ab initio self-consistent-field (SCF) real-space full-multiple-scattering (RS-FMS) calculations of the Si K-edge X-ray absorption nearedge structure using the FEFF8 code [54] for different tetrahedral (Si(O4 ), Si(SiO3 ), Si(Si2 O2 ), Si(Si3 O), and Si(Si4 )) building units. For the first
, a calculation a fixed Si–O bond length of 1.62 A
, and a tetrahefixed Si–Si bond length of 2.35 A dral O–Si–O bonding angle of 109.5° were used. The calculated spectra were aligned in energy in such a way that the peak position for the Si(O4 ) clusters agrees with the main peak of SiO (Fig. 9). Increasing the number of Si cations on the ligand sites causes a shift of peak position towards lower energy from 1846.8 eV for Si(O4 ) to 1841.7 eV for Si(Si4 ). (We found good agreement of an experimentally obtained Si K ELNES of SiO2 with the calculated Si K ELNES of the Si(O4 ) cluster [30].) For the Si(SiO3 ), Si(Si2 O2 ), and Si(Si3 O) clusters, a weak shoulder appears just above the Si K-edge threshold, which increases in intensity with increasing Si ligand count. The broad maximum at 1864 eV for SiO cannot be explained by the FMS calculations on single tetrahedral clusters. This has been pointed out by Sharp et al. [53] for SiO2 phases, since more fine structures become apparent for increasing size of clusters on the calculated spectra and concomitantly for increasing number of coordination shells.

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In a similar way to the Si K XANES [33], the observed features at the Si K ELNES of SiO, the pre-edge peak and the main maximum, can be assigned to spectral contributions of Si(O4 ) and Si(Si4 ) by comparison with the corresponding spectra of the cluster calculations (Fig. 9). The calculated Si K-edge spectra of Si(O4 ) and Si(Si4 ) are used to determine their spectral portions to the Si K ELNES of SiO by a simple linear regression procedure for normalised intensity distributions IðSiOÞ ¼ aIðSiðO4 ÞÞ þ bIðSiðSi4 ÞÞ with fitting parameters a and b. Fitting in the energy range between 1835 and 1855 eV (Fig. 10(a)) results in a ¼ 0:703  0:012 and b ¼ 0:367  0:020. We confined the fitting procedure to this energy range, because spectral features at higher energy-losses caused by

Fig. 10. Simulations (solid lines) of the Si K-edge ELNES spectrum of SiO (circles) using a linear combination of the calculated Si K-edge XANES spectra (a) for Si(O4 ) and Si(Si4 ) using the final fitting parameters and (b) for Si(O4 ), Si(SiO3 ), Si(Si2 O2 ), Si(Si3 O), and Si(Si4 ) using the fixed relative amounts from the XPS result (scratched sample) with subsequent realignment of the spectra in energy. The dashed line represents the residuals plotted on the same intensity scale. The particular goodness of fit (r2 value) is specified.

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multiple-scattering processes at higher coordination shells are not included for the FMS calculations of the Si K XANES spectra. The number of Si and O atoms in a Si(O4 ) cluster is 1 Si and (4/ 2 ¼ ) 2 O atoms and the number of Si atoms in a Si(Si4 ) cluster is (1 + 4/4 ¼ ) 2 Si atoms. Thus the elemental concentration ratio is cðSiÞ=cðOÞ ¼ ða þ 2bÞ=2a ¼ 1:03  0:04 which agrees well with the expected 1:1 ratio. This means that the overall Si oxidation state is (II), but on a simple fingerprint basis, the Si valence state in SiO seems to consist basically of Si0 and Si4þ . In agreement with the findings of Temkin [24] and Friede and Jansen [33], our SiO has a composition dominated by two different cluster types, namely Si(O4 ) and Si(Si4 ) tetrahedra, resulting from disproportionation. Fitting all Si K-edge XANES spectra of the five different clusters did not change the fitting parameters for Si(O4 ) and Si(Si4 ) and ending with zero for the other tetrahedral clusters. A calculation including a certain amount of sub-oxide is presented afterwards. The FEFF code has been successfully applied to amorphous structures, as for example Tenegal et al. [55] successfully interpreted XANES and EXAFS measurements of amorphous Si/C/N powders by using the former version FEFF6. However, our fingerprint analysis using spectra calculated by FEFF8 results in some differences to the conclusions of Flank et al. [56] concerning the peak positions. We cannot support FlankÕs identification of the peak at the lowest energy as corresponding to Siþ oxidation states. Furthermore, in comparison with our calculated Si(SiO3 ) spectrum, the peak assigned only to Si3þ in the experimental Si2 O3 spectrum [16,56] is shifted to lower energies with respect to the aligned energy values for Si4þ respectively Si(O4 ). This is caused by the special short-range order in Si2 O3 (the Si–Si bar-bells have only O back bonds) in contrast to disordered Si(SiO3 ) units in SiO. Calculated spectra for different ring type building units (e.g. a (SiO)3 ring) exhibit shapes dissimilar to the experiment, whereas spectra for different trihedral units or even a planar Si(O3 ) unit (i.e. units with only three nearest-neighbours for Si) show features similar to the experiment [30], but they cannot be accepted as prevalent building units.

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3.4. XPS X-ray photoelectron spectroscopy shows the coordination of the Si and O atoms in the surfacenear region. The binding energy dependence of the measured photoelectrons gives information on the distribution of the oxidation numbers. Five lines from Si0 to Si4þ have to be fitted to the SiO photoemission spectra in a standard procedure, that is applicable for example for SiNx [57] in the same manner as described here for SiOx . Fracturing of a SiO sample in UHV gives a new surface with minimised presence of physically adsorbed contamination, e.g. carbon [58]. Though chemical analysis of SiO samples did not show any significant amount of impurities in the volume, it might happen that a sample breaks preferentially just where impurities are located. We compared spectra of broken samples with additionally scratched samples and with additionally sputter-cleaned samples in order to make sure that varying influences of contamination are identified and removed.

A measurement of a surface of a sputtercleaned silicon wafer as standard gave a Si0 energy position of 99.8(1) eV for Si 2p at the used experimental conditions. This energy was used in the following for referencing the Si0 position in the fit procedure with an accuracy of about 0.1 eV. This is necessary, because charging shifts are occurring at these oxide samples. For our fits the Si 2p line was decomposed into Si 2p1=2 and Si 2p3=2 lines with intensity ratio 1:2 and a fixed splitting of 0.6 eV as an atomic property [59]. Furthermore, we assumed the same FWHM for both lines but increasing FWHM from Si0 to Si4þ in agreement with other authors [59,60]. In this way the best results were found (Fig. 11(a)–(c)). For the fractured sample the obtained energy positions and FWHM values for Si 2p3=2 are 99.7 and 1.0 eV for Si0 , 100.6 and 1.15 eV for Siþ , 101.6 and 1.3 eV for Si2þ , 102.7 and 1.45 eV for Si3þ , and 103.8 and 1.6 eV for Si4þ . Thus the total energy range is 4.1 eV. For the scratched sample the energy positions agree accurate to 0.1 eV, the FWHM

Fig. 11. Si 2p core level spectra of a-SiO ((a) fractured, (b) scratched, (c) sputter-cleaned sample) fitted to five peaks corresponding to different Si oxidation states respectively. Significant amounts of sub-oxide (Siþ , Si2þ , Si3þ ) are clearly resolved.

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values are 0.17 eV larger than for the fractured sample. Such small differences are most probably connected with differential charging in the analysed regions. The spectrum of the sputter-cleaned sample shows similar FWHM and peak separation as the fractured one. The energy position values are in good agreement to those for Si 2p3=2 reported by Himpsel et al. [59] and by Keister et al. [61] concerning the SiO2 / Si interface and to those for Si 2p reported by Alfonsetti et al. [62] concerning SiOx films. Our FWHM values are in good agreement to those reported by Yubero et al. [60]. They are of medium magnitude in comparison to those from Himpsel et al. and from Keister et al. (which are altogether around 0.6–0.8 eV smaller) and to those from Alfonsetti et al. (with values of approximately 2.1 eV each). Grunthaner et al. [63] reported somewhat higher energy positions, whereas Nucho and Madhukar [64] published somewhat lower values, but all authors confirmed the roughly equally spaced differences of around 1 eV. The dependence of the Si4þ energy position and thus of the total energy range on the Si–O–Si angle will be discussed in Section 4.4. For the fractured sample (Fig. 11(a)) the peak areas (intensities in arbitrary units) and the corresponding oxidation state (in brackets) are 15 (0), 7 (I), 3 (II), 8 (III), and 33 (IV). For the scratched sample (Fig. 11(b)) we have 15 (0), 9 (I), 3 (II), 12 (III), and 28 (IV). The sputtered sample (Fig. 11(c)) gave 2 (0), 9 (I), 9 (II), 20 (III), and 26 (IV). The O 1s peak position (not shown) is not significantly shifted from the value for SiO2 (533 eV). In contrast to XPS results for SiO films [40] our spectra verify disproportionation. The measured volume appears to be oxidised to a higher O content. This oxidation is probably caused by a significant amount of porosity surface. Besides Si4þ and Si0 there is a significant amount of sub-oxide, which can be quantified as 25 at.% 10 at.%. The drastic increase of sub-oxide in the sputter-cleaned sample already appeared for a small Arþ dose (3.5 keV, 1 nm removal). The O:Si intensity ratio allows the determination of the stoichiometry by applying standard sensitivity factors for the specific elements (without matrix or sputtering dependent corrections). These

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factors are 0.711 for O 1s (from aluminium oxide) and 0.339 for Si 2p (from silicon) [65]. Their ratio is equal to the intensity ratio, when there are an equal number of atoms of both elements in the measured sample volume. The sensitivity factor ratio includes the ratios of standard values of the atomic photoionisation cross sections rO =rSi and of the escape depths (connected to attenuation lengths respectively sample volume) kO =kSi . It has to be modified for SiO by applying a correction factor. The best values are average values from regions of pure Si, sub-oxide, and SiO2 . Required values at 1254 eV can be taken from literature, for example rSi ðSiO2 Þ=rSi ðSiÞ  1:1 and rO =rSi  3 [58,59,66,67]. We also get kSi ðSiO2 Þ=kSi ðSiÞ  1:1 (from Tanuma et al. [68]) or even kSi ðSiO2 Þ= kSi ðSiÞ  21=13 [59,67] and kO ðAl2 O3 Þ=kSi ðSiÞ  ðq0 ðSiÞ=q0 ðAl2 O3 ÞÞ1=2  2=3 [69]. For O 1s kO can be assumed independent from sample composition, whereas rSi kSi has to be modified from its value for Si to SiO2 respectively to SiO by applying a factor 1.12 [68] respectively an estimated factor 1.052 . The results for SiO samples were adjusted to those for a SiO2 standard sample (sputter-cleaned thermally grown oxide). The obtained O:Si ratios are 1.11 for the fractured sample, 1.19 for the scratched sample, and 1.07 for the sputter-cleaned sample. In comparison, the stoichiometry values obtained from the average Si oxidation states are 1.28, 1.22, and 1.44. These obvious discrepancies, which are considerably more pronounced for a larger modification factor [59,67], indicate some structural inhomogeneities, as discussed in Section 4.2. From angle resolved XPS measurements of the standard sample mentioned above we obtained 0.04 as a possible error in the determination of stoichiometry, if some contamination covers the surface. In order to verify the compatibility of XPS and ELNES results, the Si K ELNES of SiO has been recalculated using the XPS intensities of the scratched sample as weighting factors for all tetrahedral building units. As shown in Fig. 10 the simulation is still in satisfactory agreement to the earlier fit using only Si(O4 ) and Si(Si4 ). There would be still better agreement, if we had 1:1 stoichiometry in the XPS measurement.

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3.5. NMR In the 29 Si MAS NMR spectrum (Fig. 12) two types of atomic neighbourhood (building units) can be distinguished by their peaks from different chemical shifts. The higher peak at )110 ppm (relative to TMS standard) is related to Si(O4 ) tetrahedra in the SiO2 regions with a Si–O–Si angle distribution around 144° [70,71]. The lower peak around )69 ppm exhibits fractions from elemental silicon or sub-oxides. The intensities of spinning sidebands have to be included. Regarding the 1:1 stoichiometry, a deficiency in the signal of the elemental silicon is clearly observed. Here we have a new experimental proof of the wipe-out effect in the spectrum of SiO, which was observed by Dupree et al. [72]. Atomic nuclei located near to unpaired electrons (e.g. dangling bonds) do not contribute to the peaks in the NMR spectrum. In our special experiment all absolute NMR intensities were verified to be reproducible and adjusted to the specific intensity (per milligram Si content) from a standard sample (zeolite Si1:02 Al0:98 O4 Na0:98 H2 O with 18.1 wt% 0.3 wt% Si, error due to water content). The two peak intensities were obtained from the peak areas including sidebands with some uncertainty due to overlap. Two relaxation times T1 were evaluated by solving

Fig. 12. 29 Si MAS NMR spectrum of a-SiO with assigned areas of the peak related to Si including spinning sidebands (A) and of the peak related to SiO2 (B). 26% of the overall signal is missing in the spectrum due to the concentration of silicon dangling bonds predominantly in the silicon region and in the complete sub-oxide region.

Iðti Þ ¼ Iðt ¼ 1Þð1  expðti =T1 ÞÞ  I0 for a set for different experimental delay times ti . We obtained T1 ¼ 370 s  50 s for the Si region and T1 ¼ 440 s  50 s for the SiO2 region. These values are in a medium range in comparison to those of pure phases. Carduner et al. [73] reported a T1 value of approximately 40 min for glass wool (SiO2 ) and T1  3 min for crystalline silicon whose chemical shift is )81 ppm. For our experiment a delay time of 1200 s was estimated as appropriate. The wipe-out amount is given by the lack of measured intensity in comparison to the expected intensity calculated from the overall Si content (63.7 wt%) of the SiO sample (in mg) and from the specific intensity (in mg1 ). In conclusion 32:8= 124:6 ¼ 26:3% of the Si nuclei do not contribute to the spectrum (see Section 4.3 and Table 1). The SiO2 peak is nearly unaffected, and the other peak must be predominantly a Si peak, not a sub-oxide peak, otherwise the wipe-out rate would be exceeded with respect to the 1:1 stoichiometry. Dupree et al. assumed that the 29 Si chemical shifts follow a roughly linear trend, that is )53 ppm for Si(Si4 ), )67 ppm for Si(Si3 O), )81 ppm for Si(Si2 O2 ), )95 ppm for Si(SiO3 ), and )109 ppm for Si(O4 ). A similar linear variation of chemical shifts is known for SiOx N4x [74]. However, the above-mentioned values are questionable. The chemical shift of Si(Si4 ), i.e. )57 ppm for a-Si, which was reported by Lamotte et al. [75] and accepted by Dupree, was not clearly distinguished from that for a-Si:H. The experimental obtained chemical shift of Si2 O3 [16,17,76] at )71 ppm strongly differs from )95 ppm for Si(SiO3 ). (In fact Si2 O3 contains Si2 O6=2 building units, but contains Si3þ as well.) Williams and Cargioli [77] presented the chemical shifts of partly oxygen coordinated silicon at relative lower negative values, allowing some deviation from a strict linear variation. Especially the chemical shift for pure amorphous silicon seems to be variable in the literature [75,77,78]. Indeed, different chemical shifts of the lower peak in the SiO spectrum have been observed [33,72]. Dupree et al. [72] attributed the principal part of the left peak in the SiO spectrum as sub-oxide (mainly Siþ ) and proposed the Ching model [79] for the bulk SiO structure. Additionally, they arrived at Si cluster sizes of about 2 nm.

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The latter conclusion appears inconsistent, because the Ching model is not a model of disproportionation into 2 nm Si clusters. Etherington
for et al. [19] found cluster sizes of around 20 A their SiO samples, also contradicting the Ching model. For our samples, diffraction and XPS results rule out the Ching model, too. Considering the previously mentioned experimental results, we conclude that the peak at )69 ppm in the SiO spectrum is principally related to Si0 . However, the chemical shift position of this peak at )69 ppm proofs that the SiO is not a simple mixture of a-Si (whose position is between )40 and )60 ppm [75, 77,78]) and a-SiO2 (at )110 ppm [70,71]). Our 29 SiMAS-NMR measurement of a commercially available silicon powder (not shown) exhibits a peak of amorphous Si at )59 ppm and a peak of crystalline Si at )81 ppm as expected. 3.6. ESR and SQUID magnetometry Electron spin resonance (ESR) intensities are correlated to the number of paramagnetic centres (unpaired electrons) in the sample volume. The centres are assumed to be predominantly dangling bonds of Si atoms (indicating vacancies or voids). Holzenk€ ampfer et al. [80] presented a distribution of four trihedra (Si(Si3 ), Si(Si2 O), Si(SiO2 ), Si(O3 )), but did not include anisotropic g factors. Inokuma et al. [81] showed results for SiOx films, including anisotropic g factors for samples with different stoichiometry. In a comparable manner Ishii et al. [82] presented calculated g factors for SiNx . Measurements at different frequencies are necessary to disentangle line broadening effects from anisotropic g factor powder distributions. It was necessary to restrict the microwave power for minimising saturation effects. Such effects can be caused by long relaxation times for some of the defects. Fig. 13 shows results from X-band (narrow line), Q-band (medium line), and W-band (broad line). The apparent line widths are proportional to the magnetic field. This scaling can be explained by a g factor distribution, but not by line broadening. Thus the necessary powder averaging fit was carried out for the W-band spectrum, which has the highest g factor resolution. The g factors were determined from g ¼ hm=lB B (microwave

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Fig. 13. Comparison of the ESR spectra of a-SiO from X-band, Q-band, and W-band. The three lines have been rescaled for similar intensity and adjusted to equal magnetic field Bmiddle for the centre (zero-crossing) of the line.

frequency m, magnetic field B) with h ¼ 6:6260755  1034 J s and lB ¼ 9:2740154  1024 J/T. All four types of trihedra can exist. It is difficult to resolve their distribution, because the exact anisotropic g factors are still unknown. The best fit results were obtained for two lines with Lorentzian shape each (Fig. 14). The first line has an isotropic g factor with g ¼ 2:0055 and can be assigned to the pure silicon trihedron [83]. Here

Fig. 14. Best fit of the W-band ESR spectrum (circles) of SiO. The intensity ratio of line 1 (g ¼ 2:0055) to line 2 (g1 ¼ 2:00369, g2 ¼ 2:00346, g3 ¼ 2:00201) is 0.825/0.175.

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the line broadening dominates any g anisotropy. The absolute accuracy of the g factors was further calibrated by a small six-line (hyperfine split) ESR signal from a slight Mn2þ contamination (without significance for the whole number of unpaired spins) in the W-band spectrum. The g tensor of the second line is nearly axial with g1 ¼ 2:00369, g2 ¼ 2:00346, and g3 ¼ 2:00201. This line can probably be attributed to Si(Si2 O), for which g factors of approximately 2.0035 have been reported [81,84]. From comparison with the Q-band spectrum and from the B field accuracy of 104 the error in the g factors is estimated to be 0.0004. For the bulk material we find g factors different from those for films [81]. The intensity ratio of the lines is 0.825/0.175. The possible error in the different line intensities due to saturation effects was estimated to be smaller than 20% for all three bands. This estimation is acceptable, when there is only a small difference between experimental results for the number density of the paramagnetic defects (spin density) from ESR and from static SQUID measurements. Then the influence of a possible spin coupling in the ESR due to the high spin concentration should be small or negligible. From a comparison to a ruby calibration standard in X-band, the spin density was found to be 2.21  1019 cm3 . The experimental paramagnetic volume susceptibility in SI units is vðT Þ ¼ 1:92  104 K=T ¼ Nv g2 l2B l0 =4kB with a resulting spin density Nv ¼ 2:45  1019 cm3 (SQUID measurements). The corresponding diamagnetic volume susceptibility in SI units is v ¼ 14:6  106 ()23  106 cm3 /mol in CGS units). This compares favourably with a mean value of known values for silicon (3:9  106 cm3 /mol) [85] and for silicon dioxide ()29.6  106 cm3 /mol) [86]. A SiO sample, that was annealed for 1 h at 900 °C, gave a spin density of Nv ¼ 1:38  1019 cm3 .

4. Discussion 4.1. Indications for an abrupt interface Concerning the atomic bond lengths in the bulk SiO, the dependence on atomic coordination (i.e.

on the oxidation states of the Si atoms and thus with second neighbour influences) has to be taken into account. One cannot assign fixed atomic radii to Si atoms with respect to their oxidation states, as it is possible for ions [87]. This is caused by the covalent bonding to unequal neighbours (hybridisation). The ionic-covalent character of the Si–O bond causes some variation in the lengths of Si–Si and Si–O bonds of sub-oxide Si atoms. Hamann [88] shows this effect for the bonding between Si atoms of equal oxidation state. The effect may be even larger in some cases with unequal oxidation states. Such a variation has not been considered in earlier studies of radial distribution functions or in infrared spectroscopy [24,30,52,79]. However, the effect on the assignment of our RDF peaks should be negligible, as Si0 –Si0 and Si4þ –O2 bonds are dominant in the disproportionated SiO. In fact, the effect can play a part in causing a peak broadening, which makes the Si–Si–O peak disappearing. Finally, the variation in bond lengths in chains of four or more atoms together with the degree of freedom of the bond rotation will result in a wide distribution of chain lengths. This corresponds to the begin of the disorder region, where
from a central qðrÞ comes near to q0 at about 6 A atom (Figs. 1–3). In addition to the variation in the interatomic distances, the broadening of the Si–Si–Si peak might partially result from bond angle variations enforced by geometrical limitations due to very small Si cluster sizes. In our view, for very small Si and SiO2 clusters, the sub-oxide should form an ultrathin (abrupt) interface. This interface could even be a monolayer, and a similar effect of enforced bond angle variations as just mentioned can contribute to a further broadening or a disappearance of the Si–Si–O peak. Because the ELNES signal is broadened by multiple-scattering, ELNES measurements do not exhibit very conclusive signals from atoms, which are located in a highly disordered neighbourhood. In fact, Benfatto et al. [89] pointed out that for those atoms MS calculations are not very meaningful. In the case of disproportionated amorphous SiO, the signals of sub-oxide atoms will be affected strongly, because of the variation in the interatomic distances and bond angles, and espe-

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cially when those atoms are localised in an abrupt interface. Regardless of the local stoichiometry, XPS signals have similar conclusiveness for all Si atoms, in contrast to ELNES measurements. All Si atoms are expected to contribute to the spectrum with similar intensity. In particular, the sub-oxide content is expected to be recorded undiminished. Additionally, for a material, which is disproportionated on a nanometric scale, the charge density can undergo some averaging effect. This means that the measured disproportionation into Si0 and Si4þ in the distribution of oxidation states might be somewhat less pronounced than the actual disproportionation into Si(Si4 ) and Si(O4 ) in the distribution of tetrahedral building units. Hence, we can understand the amount of sub-oxide concluded from the XPS spectrum as an upper limit for the real fraction of sub-oxide Si atoms in the sample volume. The combined interpretation of XPS and ELNES shows that no grain-like extended sub-oxide regions are detectable. Hence, the sub-oxide is forming a thin interface, which is characteristic for the sample volume and not negligible compared to the cluster volumes. As SiO is disproportionated on a nanometric scale, its structure is determined by the interface. The latter conclusion is valid within the whole error range for the value of the sub-oxide amount. 4.2. Indications for cluster smallness In pure amorphous silicon samples crystallisation is known to start between 600 and 750 °C [78,90–93]. Amorphous Si clusters, which are completely surrounded by the oxide region, must have a minimum size (cross section dimension) of approximately d  2 nm to crystallise and to grow up to the biggest possible crystallite size by consumption of the pure Si region [52,93,94]. On the other hand, in a pure silicon region, smaller Si crystallites can form [93,94]. In this sense, the pure silicon region is assumed to be still extended to at least 0.5 nm outwards from the crystalline region after incomplete crystallisation. This means that with some probability a Si crystallite with a size of only d  2  0:5 nm can form inside a Si cluster with the size d, even for a size d which is

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smaller than 2 nm [94]. Si crystallites were not observed by HRTEM in SiO samples, which had been annealed at different temperatures up to 900 °C for 1 h. This indicates that the largest Si clusters are still not large enough for crystallisation. Thus, their sizes are limited to a maximum size of approximately 2 nm in the annealed sample and even smaller in a native sample. Considering some distribution of cluster size, the typical Si cluster size should lie in the range of 1–2 nm. The formation of an extended continuous matrix requires further rearrangement processes preceding cluster coalescence. Thus a matrix model cannot describe disproportionation in a native SiO sample. The bonding density on a crystalline Si surface is higher than that on a crystalline SiO2 surface [59]. This density mismatch between these two phases hampers an epitaxial growth of crystalline Si/SiO2 interfaces. The same is true for the interface between a-Si and a-SiO2 clusters. Two results of the sample production process can be imagined. In the first case, the condensation results in a structure with rather similar numbers of Si and SiO2 clusters. The interface region located in between must be extended to some atomic layers in order to compensate the mismatch. Due to the compensation Si clusters have preferentially convex shapes (to lower the bonding density by increasing the surface) and in reverse the bigger SiO2 clusters have preferentially concave shape (e.g. as in a SiO2 matrix). The mean volume ratio of the two cluster types is 3q0 ða-SiÞ=q0 ða-SiO2 Þ  2:3 with respect to the overall 1:1 stoichiometry. In the other case, the formation results in an ultrathin interface and a large number of small Si clusters with less SiO2 clusters. Here, some amount of the interface should be located between Si clusters. (The sub-oxidic interface similarly is assumed as ultrathin between Si and Si, Si and SiO2 , SiO2 and SiO2 .) In both cases the interface amount in the volume is significant, i.e. it cannot be neglected as in the RM model [23,24]. However, the latter case is more compatible to the RDF results, and it is possible that not all Si bonds on a Si cluster surface are saturated. In this latter case the structure could be a result of an earlier start of SiO2 cluster formation and delayed Si cluster formation during

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the sample production. This will be discussed in Sections 4.3 and 4.4. For a homogeneous sample the stoichiometry values evaluated from the O 1s to Si 2p ratio and from the averaged Si oxidation states are expected to correspond to each other. Alfosetti et al. [62] showed that for homogeneous SiOx films O:Si ratios are similar within an error of about 0.1 to stoichiometric values obtained from the Si 2p lineshape fitting method. Thus the discrepancies in our results obtained from fixed measured sample volumes indicate some inhomogeneity perpendicular to the surface on the scale of the signal depth (1–2 nm for a ¼ 45° [68]). The lateral component of the integrated intensity is not expected to cause such discrepancies. A disproportionation into clusters of sizes somewhat larger than the signal depth could result in a consistent integrated stoichiometry. In the standard evaluation of the O:Si ratio, the escape depth ratio of O and Si is included, using values assuming a homogeneous probe volume. If the probe volume has some stoichiometric gradient perpendicular to the surface, the evaluated O:Si ratio for that volume might be shifted from its real value, because it is weighted towards the element with relative higher concentration at the surface. On the other hand, from its larger escape depth compared to oxygen, the silicon signal is coming from a larger and on the whole relatively deeper located measured volume. The stoichiometry calculated from the averaged Si oxidation states is weighted more strongly by the element with relative higher concentration in regions at greater depths. As a consequence, the true value of the stoichiometry is expected in-between the experimental O:Si ratio and the result from the Si 2p fitting procedure. The deviations from this value show the opposed vertical concentration gradients of the two elements. Since our Si 2p fit results in a more oxygen-rich stoichiometry, we conclude the surface is domi
deep is domnated by Si and the region 10–20 A inated by oxide, both related to the averaged lateral stoichiometry of the measured volume. This is consistent with a hypothesis, that assumes the weaker Si–Si bonds could have been preferentially broken, when the sample was fractured, and thus more silicon regions might be located at the sur-

face. Furthermore, we conclude that Si dominated regions (i.e. Si clusters) tend to be restricted to
. We can also exclude the sizes of about 10–20 A presence of significant amounts of adsorbed O2 or H2 O, as they would only have increased the evaluated O:Si ratio. The sample is broken preferentially where porosities are located. These porosities are partly hidden in depressions and tend to be covered by an oxidic inner surface [95], which produces the oxidic deviation in the measured volume from the overall 1:1 sample stoichiometry. As a consequence, in the porosity-near part of the measured volume the only expected inhomogeneity would be that of an oxidic surface. Our result of the opposite inhomogeneity in the whole measured volume clearly shows that it is caused by the dominating volume part far from porosities, i.e. the typical bulk structure. Thus, in the bulk Si is expected to be clustered with restricted sizes as described above. The sputter-cleaned sample shows an increased structural inhomogeneity at the surface, which is probably due to grown oxide clusters with excess Si remaining at the outer surface. This structural change might be caused by the slight energy impact during sputtering, thus indicating that native SiO could be a frozen non-equilibrium system. Earlier XPS studies of Si/SiO2 interfaces [63,64] revealed some correlation between the measured Si4þ binding energy position and the average Si– O–Si bond angle. The 144° angle in bulk SiO2 corresponds to a higher Si4þ binding energy than the lower angle (i.e. around 125°) in interface-near SiO2 . On the other hand, the Si0 line exhibits some contrary behaviour: With increasing Si cluster size, its energy position slightly changes towards lower values. Rochet et al. [96] described a relation between the Si4þ –Si0 shift and the disproportionation, i.e. a smaller shift corresponds to smaller clusters. Following their results, our Si4þ –Si0 shift of 4.1 eV indicates an intermediate structure between Ôquasirandom-bondingÕ and disproportionation into 4 nm clusters [96]. As our XPS fit would have resulted in a smaller Si4þ –Si0 shift for larger FWHM values, the results of Rochet et al. verify the magnitude of our obtained sub-oxide amount (25 at.%). In contrast to the value of that difference shift, the exact values of the Si0 and Si4þ lines

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cannot be determined without some error due to the fact that the relation between Si and SiO2 cluster sizes (i.e. the question, which of the two cluster types has more proximity to bulk-like structure) is not clear yet. This question and the average Si–O–Si bond angle will be discussed using the NMR results as follows. It has not been clarified yet, whether the earlier (Section 4.1) mentioned variation in the lengths of Si–Si and Si–O bonds (of sub-oxide Si atoms in SiO) causes slightly changed chemical shifts, broadened peaks, or the appearance of spinning sidebands, because the sub-oxide amount is completely wiped out from the NMR spectrum. The stoichiometric homogeneous Si2 O3 is not expected to exhibit these variations. However, in the experiments reported by Dupree et al. [72] and by Friede and Jansen [33] no significant sidebands were detected for SiO. Our NMR spectrum (measured under comparable conditions and with even higher spinning frequency) exhibits sidebands of the peak assigned to pure silicon. Even if the sub-oxide signal was not wiped out, the sidebands cannot be attributed to a sub-oxide, otherwise they would have appeared in the earlier reported experiments. Furthermore, no sidebands for suboxide tetrahedra were reported in case of Si2 O3 at room temperature and at 120 °C [16,17,76]. Hence, the appearance of the Si0 sidebands in our spectrum is supposed to be caused by a structural difference. First of all, this difference is most probably related to different cluster sizes and shapes. The appearance of sidebands can be seen as an indication for some structural anisotropy (asymmetry) around central Si atoms in the pure Si regions. Trihedra are not candidates to cause that asymmetry, as their signal is wiped out. In a completely disordered amorphous sample this anisotropy can result from clusters, in which a considerable amount of the Si atoms has a distance from the sub-oxide Si atoms on the cluster surface not larger than the sphere of the short-range order,
. Our a-Si powder spectrum does i.e. around 6 A not exhibit any sidebands. This is then another indication for our supposed limitation of the Si cluster sizes in the disproportionated SiO. A lot of the amorphous Si clusters in the SiO are expected to be so small (near to the sphere of

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short-range order) that they cannot be seen as completely disordered. Moreover, samples of amorphous silicon can exhibit some microcrystalline character, e.g. a-Si might be seen as a mixture of a random network and a microcrystalline (lc) model substance [97]. The smaller the clusters are (i.e. the more clusters with surface dangling bonds exist), the more the lc-Si character will appear. In comparison to the reported a-Si spectrum, the Si0 chemical shift position at )69 ppm indicates that the difference between the amorphous and the crystalline character gets smaller with decreasing cluster size. The distance of the Si0 chemical shift position to the c-Si peak position corresponds to the lc-like character of our a-Si sample as well as to the Si cluster smallness in our SiO sample. 4.3. The influence of a defect structure Volume measurements of dangling bond densities (by ESR and SQUID) should not be strongly affected by porosity, as the pores are widely covered (saturated) by oxide (see Section 4.2). In fact, a local lack of unsaturated bonds can be seen as a reason for the origination of porosity during the structural formation process. Hence, regarding the evaluation of defect densities, the defects (dangling bonds) can be supposed as distributed uniformly. As the existence of extended sub-oxide regions has already been ruled out, the ESR spectra verify the significant amount of cluster interface in the whole volume, indicated by a resulting high defect density in the sub-oxide region. The variation in the interatomic distances of the sub-oxide Si atoms and the averaging of all orientations cause a broad distribution of the g factors. We assign the g ¼ 2:0055 line to the pure Si trihedra without resolving possible anisotropy from the amount located at the interface [81]. The identification of that g factor with a large amount of floating bonds instead of dangling bonds as it might be in a-Si samples [98] is not valid for excess silicon clusters and interface related defects in our SiO. However, that identification has been contradicted [99]. All the rest, i.e. our second line, is assigned to belong predominantly to the sub-oxide (interface) region. Paramagnetic centres produce a much stronger signal than the pristine NMR signal, but it is

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blurred over the whole ppm range. Nuclei within a wipe-out radius around an unpaired electron do not contribute to the NMR signal. The spectrum exhibits the wipe-out effect due to the concentration of silicon dangling bonds predominantly in the silicon region and in the complete sub-oxide region. Hence, 26% of the overall signal is missing in the NMR spectrum. The wipe-out radius can be estimated from the amount of non-contributing atoms, the number density, and the defect density of the overall pure Si region, as at least 83% of the dangling bonds are located in that region. Table 1 presents the evaluation steps for our SiO. Number densities of Si atoms and amounts of the sample volume accounting for one Si atom, which are corresponding to bulk mass densities of Si, SiO, and SiO2 , are shown for three different regions (pure Si, sub-oxide, and SiO2 ). From our experimental results we estimate the three different amounts of Si in the sample volume, i.e. 10 at.% in the sub-oxide and 45 at.% in the pure Si and SiO2 region each. This can then be converted into proportions of the three regions in the sample volume in vol.%. Amounts of defects (i.e. dangling bonds) and defect densities (all values for three different regions) are evaluated from ESR and confirmed by SQUID, assuming a uniform defect distribution (see below). Defect densities in SiO2 are expected to be some orders of magnitude smaller than in Si. Thus we have fractions of approximately 83% of

the defects in pure Si, approximately 1% in SiO2 , and thus approximately 16% of the defects in the sub-oxide. The resulting fraction of defect Si atoms in the sub-oxide region ( 1:700) is very close to that in the pure Si regions. We arrive next at Si atom numbers accounting for one defect and amounts of the sample volume accounting for one defect. From the expected overall NMR intensity without the wipe-out effect, the wipe-out amounts of the NMR intensities for the three regions are calculated assuming the highest possible sub-oxide intensity. The SiO2 peak seems unaffected, and we consider an equal intensity for undiminished pure Si and SiO2 peaks with respect to the 1:1 stoichiometry. The defect density corresponds to a mean distance of 2.4 nm between two defects in the pure Si region. The defects are expected to result from structural mismatch. Thus the probability of defect origination is expected to be lowered for atomic neighbourhoods, in which a defect already exists. Such a self-avoiding behaviour was observed for defects at the SiO2 /Si(1 1 1) interface [100]. Hence, for the calculation we assume that there is normally not more than one defect per cluster, i.e. negligible overlap of wipe-out spheres. From the values for the Si region a wipe-out number of 700  25:6=ð25:6 þ 33:1Þ  300 and a wipe-out radius of ð14 nm3  25:6=ð25:6 þ 33:1Þ  1=3 0:75=pÞ  1:1 nm result. This radius is consistent with the fact that the SiO2 intensity is little

Table 1 Evaluated parameters (with estimated errors) of the three different stoichiometric regions in amorphous SiO as explained in Section 4.3 Region

Si atomic Volume Si fracdensity per Si tion from (cm3 ) atom the ex
3 ) (A periments (at.%)

Volume fraction of the region (vol.%)

Si atoms Fraction Defect density of defects (SQUID) (cm3 ) per defect from ESR (%)

Volume per defect (nm3 )

NMR intensity (arbitrary units)

Wipe-out amount (arbitrary units)

Pure Si Suboxide SiO2

5  1022 3  1022

20 33

45  3 10  6

28  2 10  6

83  7 10  6

(7.3  0.6)  1019 (3.9  1.4)  1019

700  40 700  300

14  1 25  11

33.1  2 0.0  0

25.6  4 7.2  7

2.2  1022

45

45  3

62  4

11

(0.1  0.1)  1019

Uncertain

58.7  4

0.0  0

33

100

100

100

(2.4  0.1)  1019

1250  50

Uncertain 40  2

91.8  5

32.8  6

Overall 3  1022 sample

Atomic densities of Si atoms are corresponding to the overall bulk mass densities of Si, SiO, and SiO2 . Fractions of the three regions in Si at.% and in vol.% were estimated using the combined ELNES and XPS results. Spin densities and defect related Si atom numbers and sample volumes in the different regions were evaluated using ESR and SQUID data. The wipe-out amounts of the NMR intensities (peak areas) were calculated from the assumed unaffected overall intensity (124.6) with respect to an equal intensity for undiminished pure Si and SiO2 peaks (33:1 þ 25:6 ¼ 58:7) assuming the highest possible sub-oxide intensity (124:6  91:8  25:6 ¼ 7:2).

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affected, because the wipe-out volume amount in the SiO2 region is not more than about 10% (with a half of the 16% from sub-oxide), and the lower Si atom density in SiO2 has to be considered. The Si cluster radii are possibly smaller than our wipe-out radius, as the sub-oxide is wiped out completely. We expect the smaller Si clusters to have the higher local dangling bond densities. The wipe-out effect similarly affects closely neighbouring sub-oxide and pure Si regions, particularly regions of sub-oxide layers between Si clusters. Therefore we have no evidence that the Si clusters have to be necessarily estimated larger than the wipe-out radius, as Dupree et al. supposed. These authors assumed some undiminished sub-oxide intensity in the NMR spectrum and obtained a larger wipe-out amount and radius. Assuming a defect density of approximately 2.4  1019 cm3 , a wipe-out radius of at least 2 nm would imply that wipe-out spheres overlap at least to 1  ð1:13 =23 Þ  83%. This implies in reverse a mean value of at least 6 defects among 1000 atoms, which appears very high for a completely amorphous structure. Local accumulation of dangling bonds is expected in a pure amorphous silicon sample due to its amount of microcrystallinity [97] (see Section 4.2). For our a-Si powder sample we estimated a wipe-out amount one order of magnitude smaller than for the silicon in SiO. Finally, the wipe-out effect can explain the lack of a Si0 related peak in the NMR spectrum of annealed, disproportionated Si2 O3 [76]. The excess silicon is expected to have a very high defect concentration, as its formation is influenced by the already existing sub-oxide structure. The overall defect density (7.3  1019 cm3 ) of the Si regions in our SiO is of the order of magnitude typical for amorphous silicon [83]. For example a-Si films generated by sputtering contain 1018 –1021 cm3 unpaired spins [99]. In addition, our defect density is at least one order of magnitude higher than that observed by Inokuma et al. for SiO films of about 1018 cm3 [81], and it is higher than those densities observed by Emons and Hellmold for several SiO modifications [11]. A higher defect density in the bulk sample is in agreement with the assumption that excess Si is resulting from the structural formation process,

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which will be discussed in the following section. The high defect density provides indication for a frozen non-equilibrium structure. The defects are assumed to be dangling bonds and not floating bonds. The decrease of the number of dangling bonds in the pure Si region during annealing indicates the rearrangement of former excess silicon into more extended pure Si regions. The )110 ppm shift for Si4þ in SiO corresponds to an overall 144° Si–O–Si angle and thus bulk SiO2 structure [70,71]. The existence of bulk-like structured SiO2 clusters can be explained as a result of a structural forming process in the bulk SiO with the formation and agglomeration of Si–O bonds (i.e. the trend to increase Si4þ ) as the driving force. Here SiO2 cluster grow without being significantly influenced by the already existing suboxide structure. On the contrary we assume that the SiO2 cluster growth influences the sub-oxide (interface) structure and thereby the formation of the pure Si regions. Considering the bonding density mismatch in case of our SiO, the results provide less probability for the existence of Ôhigh densityÕ SiO2 in the interface-near region, but more probability for a ÔdilutedÕ opposite silicon region (i.e. a region with extremely limited cluster sizes and a defect structure). The influence from the SiO2 regions upon the Si regions agrees with the observed features of anisotropy (sidebands) in the NMR spectrum. As the SiO2 clusters obviously have the only bulk-like structure, the results of Rochet et al. [96] mentioned in Section 4.2 can now be interpreted as a confirmation of the limitation of Si cluster sizes. 4.4. The disproportionation process in films and bulk samples The SiO disproportionation process takes place in the sub-oxide region, as some sub-oxide is transformed into new pure Si and SiO2 regions (clusters) or contributes to further growth of already existing clusters (see the following paragraphs). The sub-oxide vanishes except for an ultrathin (abrupt) interface, as no significant sub-oxide regions can be observed at the Si/SiO2 interfaces of annealed SiOx films [101]. The interface between the clusters will have some thickness distribution.

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Nevertheless, it can be reduced in thickness nearly without serious geometric constraints, considering the variability of the Si–O–Si angle [63,64,102, 103]. (The Si–Si distance can be the same with or without bridging O.) The remaining resistance to thickness reduction is caused by the bonding density mismatch and can be lowered by forming many individual small Si clusters, connected to each other by the interface. In contrast, a Si/SiO2 interface on a flat Si(1 1 1) crystal would be extended to at least two layers and strain driven [59]. In our case, the amorphous SiO structure allows a rough interface. During the above-mentioned process Si2þ will change into Si3þ or Siþ . The latter state tends to change into Si4þ and Si0 . Barranco et al. [104] reported about the ligand exchanging process Si2þ – Si2þ ! Si3þ –Siþ , which is exothermic. The process Si3þ –Siþ ! Si4þ –Si0 is even more exothermic, but as an O inserting process it is kinetically hindered. Hinds et al. [27] showed that the decomposition is kinetically hindered below 900 °C and that the decomposition rate is nearly independent of the initial composition. The process is expected to be mostly initiated by the directly involved atoms. Ligand exchange is possible in a region of only three atomic layers. As a consequence, we suppose the disproportionation stops as soon as the interface has thinned to nearly a monolayer, because these last remnants of the sub-oxide cannot vanish without further irreversible rearrangement processes [27,104]. Those processes go along with cluster growth. In a similar way, such processes are necessary to make crystallisation possible [91]. They must be even stronger in case of SiO films with a structure tending more towards random bonding than to random mixture after production (see earlier in this paper). Annealing of SiO films as well as of films of SiOx with x  1:1 leads to rearrangement processes and Si cluster growth [105]. Hence, extensive crystallisation has started below 900 °C, in contrast to our bulk SiO (see Section 4.2). At 1000 °C the Si crystallite sizes in the films are somewhat larger (with a size of about 4.3 nm [105]) than in our bulk SiO. In comparison to bulk samples, the Si clusters in the films are only slightly constrained by the bonding density mismatch, as the nature of

the oxide in films is predominantly sub-oxidic (see below in this section). In conclusion, the growth of Si clusters in the bulk is expected to be more constricted than their growth in the films, particularly for native samples. In bulk SiO the disproportionation process is at first a disproportionation of bonding, not an agglomeration (coalescence) of clusters. Only the first process, which ends with an ultrathin sub-oxide interface, is mostly completed after sample production. We now take a closer look at the different forming and disproportionation processes in the bulk and in films. The structural forming process starts with the SiO molecules, which connect to each other forming chains and rings of type (SiO)n [13,14], building the preliminary stage for the bulk structure [106]. Fibres formed from these chains or from possible Si or SiO2 chains may still exist in the subsequently formed amorphous bulk suboxide matrix. Microfibres of SiO with diameters of around 10 nm were investigated by Songsasen and Timms [107], and a fibrous-looking structure in bulk samples was possibly already found [30]. Possibly a radical polymerisation process takes place, as it was suggested for the formation of the fibrous SiO modification [11,12]. Si atoms in different (SiO)n chains form stable bonds to a third O neighbour as well as to a first Si neighbour (i.e. to each other), thus leading to the formation of a bulk sub-oxide matrix. As a result of the production process SiO films contain mechanical stress [108,109]. As long as newly produced samples are kept in a good vacuum, they show tensile stress [52]. In comparison to films, in bulk samples with higher deposition rate even more tensile stress is expected to be produced. Films exposed to air show compressive stress, probably related to adsorption (e.g. of water vapour) and depending on porosity [52,110]. Subsequent annealing leads to the reoccurrence of tensile stress. Its reduction is concomitant with the irreversible disproportionation process [52]. Thus the reduction of tensile stress during the condensation of bulk samples causes some initial disproportionation, leading away from a RB-like structure. For the more RB-like structured films the main disproportionation process is independent of the production process. Here, the disproportionation

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probably occurs together with the production of some excess oxygen, i.e. O atoms not bonded to two Si atoms (peroxy bonding, molecular oxygen, OH groups) [111,112]. The SiO2 cluster formation is not thought to be the favoured partial process of the disproportionation. We suppose that in a film, which was deposited typically with a rate about 10
/s, the bonding density mismatch between pure A Si and sub-oxide regions provokes formation of convex shaped Si clusters and excess O possibly diffuses into the surrounding matrix. The RB-like structure facilitates Si cluster generation. Pre-existing Si clusters grow and influence the structure formation in the oxide region. Some indication of this is provided by the disappearance of Siþ peaks in XPS spectra of films [40,62]. Furthermore, the average Si–O–Si bond angle in the oxide region is smaller than in bulk SiO2 , as ascertained from IR spectroscopy [52]. All mentioned assumptions may be compared with the structural model of Hinds et al. [27,113], assuming a disproportionation of SiOx films into Si and SiOxþy regions and possible excess oxygen. Although the exact nature of the oxide region is unknown, a still somewhat RB-like character for the structure is supposed. The disproportionation process in films is believed to be diffusion controlled [114]. Crystallisation needs further rearrangement processes, which take place after generation of further tensile stress by annealing, finally ending in a structure of c-Si in a SiO2 matrix [108,109]. SiO samples which are produced without rearrangement processes (such as films produced at a low deposition rate) show a tendency to become porous. In this case, even selfshadowing effects are possible during deposition [115]. The high deposition rate of our bulk SiO
/s) is assumed to generate tensile samples ( 2000 A stress. Then enforced rearrangement processes must take part in structure formation even during the sample production. These processes exceed the effect caused by the deposition temperature, as films deposited at 500 °C contain only phase-sep
for arated regions with a maximum size of 15 A SiO2 regions [116]. When new Si–O bonds are formed, the oxide formation starts simultaneously with (or even before) the Si cluster formation, and thus cannot be influenced by the presence of pre-

275

viously formed Si clusters. This explains the relaxed, bulk-like structure of the SiO2 clusters with an average Si–O–Si bond angle of 144° (see Sections 3.5 and 4.3), which is not influenced by the sub-oxide structure or by geometrical limitations due to bonding density mismatch. The formation of bulk-like SiO2 during disproportionation independent from the production process is expected for Si2 O3 , but not for SiO films [76]. The high deposition rate and the subsequent reduction of stress favour the generation of defects (voids) in the bulk structure more than in films. Voids and microporosity can favour further disproportionation by possibly reinserting excess O. We suppose that the favoured formation of Si– O bonding and Si4þ (SiO2 clusters) is the impetus for the disproportionation. The formation of nearinterface SiO2 with relatively small Si–O–Si bond angles and smaller rings of Si(O4 ) tetrahedra is more common for SiO2 layers deposited on Si [63] and probably for annealed SiOx films, depending on x [52]. After SiO2 cluster formation in the bulk has started, excess Si will at first form the Si clusters. The driving power of the Si–O bond formation prevails, and the sub-oxide matrix diminishes during the disproportionation process as described above [104]. We conclude that the oxide region in bulk SiO consists of sub-oxidic remains (interface) of the disproportionation in between SiO2 clusters. Then the structure we call interface clusters mixture (ICM, Fig. 15) has formed. During aging or tempering processes, the disproportionation might proceed together with cluster growth going along with interface obliteration. Afterwards, the SiO2 clusters could form a matrix, as a tendency to form a matrix-like structure was reported for the Si/SiO2 interface [117]. Finally, coarsening can still occur together with vacancymediated diffusion [118]. The exact composition of formation products is obviously influenced by the production conditions and thus cannot be generalised for all SiO modifications. For the known bulk SiO modifications, the disproportionation progress depends on the deposition temperature [1,5]. When SiO is de
/s) onto an unposited at a medium rate (375 A heated substrate, the structure can be seen as still RB-like, as shown by IR spectroscopy [119].

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Fig. 15. Schematic illustration of the interface clusters mixture structure of a-SiO. The ultrathin sub-oxidic interface (gray) has a matrix-like structure (roughly 10 vol.%) between clusters of SiO2 (light gray) and more numerous smaller convex clusters of Si (black).

Starting from the coal-like SiO with supposed ICM-like structure, the probability of the formation of a SiO2 matrix increases with the production temperature. The higher the temperature the more glass-like the character of the bulk SiO will be [1]. For x near to 0 a Si matrix is probable, and for x near to 2 a SiO2 matrix. For x  1 only the suboxide region can be seen as a matrix-like structure. The ICM model describes an intermediate structure between the Si matrix model [30] and the SiO2 matrix model [117], as well as between matrix models and RB-like models. In addition, some indication against the existence of a structure like a matrix model is provided by the fact that SiO samples react neither completely like Si nor completely like SiO2 [36]. The SiO stability might be explained by the cluster smallness. When the surface Si clusters are detached, then the sample has a SiO2 surface and vice versa. Possible further support for the ICM model is provided by a photoluminescence (PL) experiment. PL was already observed for SiOx films annealed at 400–600 °C [52,105,107,120–122]. The PL was attributed to the existence of small a-Si clusters still separated from each other by the

surrounding RB-like sub-oxide region (matrix). Here, the oxygen is assumed to create an efficient potential barrier without any necessity for passivation by hydrogen [120]. The PL intensity is related to the number of Si clusters and decreases for higher annealing temperatures, when coalescence of the clusters increases. In contrast to the reported results for films, our bulk SiO annealed at 500 °C exhibited only weak PL intensity. The absence of a clear PL signal from bulk SiO, which contains a lot of small Si clusters due to disproportionation, might indicate that the Si clusters are neither surrounded by a SiO2 matrix nor by an extended sub-oxide region, but by an interface. This interface is so thin that the small Si clusters are not electrically isolated from each other. On the other hand, the weakness of the PL intensity may be caused by the large number of dangling bonds (about 1019 cm3 ) in the bulk SiO [121]. These ESR centres are non-radiative recombination centres. As their density increases, the quantum yield is reduced [123]. 4.5. The interface clusters mixture model In summary, evidence for (Si) cluster smallness in native, bulk SiO is provided by the following aspects: 1. The appearance of sidebands of the Si0 peak in the NMR spectrum indicates some anisotropy, which might be related to cluster sizes not much larger than the sphere of the short-range order (i.e. a size of below 1 nm). 2. The a-Si (i.e. Si0 ) peak in the NMR spectrum is shifted somewhat nearer to the normal position of a c-Si peak, indicating a diminished difference between the amorphous and possible crystalline character. 3. The completely homogeneous appearance of the structure of native SiO in HRTEM at 120 kV and with small aperture has some meaning, because only samples, which were annealed without crystallisation, show stoichiometry contrast due to increased cluster sizes. 4. In comparison with more RB-like structured SiO films and with a-Si, a higher temperature is necessary for crystallisation of at least the

A. Hohl et al. / Journal of Non-Crystalline Solids 320 (2003) 255–280

5.

6.

7.

8.

9.

largest Si clusters due to additional cluster growth. The stoichiometric inhomogeneity in the XPS measured sample volume on the scale of the signal depth is a more oxidic region approximately 2 nm below the surface. The sub-oxide disproportionation is halted when it reaches the thinnest possible interface, while the interface amount in the volume remains significant. The bonding density mismatch between SiO2 and Si clusters forces the excess Si clusters to take on a convex shape and to stay small. The chemical reactivity of SiO is neither like of Si nor like of SiO2 , which negates a matrix model and also a simply mixture model of Si and SiO2 . The results of Rochet et al. together with our observed Si4þ –Si0 shift and with our observed 144° (bulk SiO2 ) average Si–O–Si bond angle indicate Si cluster limitation.

Amorphous SiO has a structure of a frozen non-equilibrium state. Taking into account the above-mentioned considerations about the conditions of production, disproportionation, aging, annealing and crystallisation processes, we arrive at a structural model for the unaged, bulk, amorphous SiO. Our interface clusters mixture model (Fig. 15) includes three different stoichiometric regions, not really phase regions. The model describes the disproportionation halted in the initial stage, where small clusters of amorphous silicon dioxide and very small clusters of amorphous silicon are still surrounded and connected by a still matrix-like (widely bended) region of typically only one or two atomic layers with silicon suboxide oxidation states (more exactly oxygen coordination of Si atoms). That region is better named as an interface, as it is comparable to an abrupt (i.e. thinnest possible) Si/SiO2 interface, and it has significant amount in the volume because of small cluster sizes. This amount was estimated as about 10 at.% (Table 1). The clusters can have different sizes (cross-section dimensions) mainly between 0.5 and 2.5 nm and shapes from convex to concave. The model seems to explain, why despite its composition SiO does not react

277

chemically like a simple mixture of silicon and silicon dioxide. The interface clusters mixture model is a model of an interface-influenced clusters mixture. Therefore, it is an extension of the random mixture model. The growth of the SiO2 clusters is supposed to be the structure determining process, as the geometrical limitations of the interface bonding mainly affect the Si clusters. Clusters of silicon dioxide form right from the beginning of the disproportionation, taking a bulk-like structure, while at first silicon clusters can form only with significant defect concentration because of their smallness. A part of the a-Si clusters is supposed to have a size near to the short-range order sphere, so that they cannot be seen as completely disordered regions of pure Si. At present, there is no contradiction to a random distribution of the oxide clusters. As an approach for a complete qualitative description of the interface structure all seven theoretical possible atomic chains including one Si sub-oxide atom are presented (some are shown in Fig. 16): 1. Si4þ –O2 –Si3þ –Si0 , Si4þ –O2 –Si2þ –Si0 , and Si4þ –O2 –Siþ –Si0 ; 2. Si4þ –O2 –Si3þ –O2 –Si4þ and Si4þ –O2 –Si2þ –O2 –Si4þ ; 3. Si0 –Siþ –Si0 and Si0 –Si2þ –Si0 . There exist 18 þ 9 þ 9 ¼ 36 possible different chains with two sub-oxide atoms, as for each of the first three chains there are three possible oxidation states of the added Si atom and the possibility with and without O inclusion, and for the other two types of chains there are 6 and 3 Si inserting possibilities depending on O inclusion. A particularly high degree of disorder in the interface region is caused by the variation in the bond lengths due to the different Si oxidation states (atomic radii). In the strict sense 79 different tetrahedral building units instead of only five would have to be taken into account, assuming five possible neighbours (O, Si0 , Siþ , Si2þ , Si3þ ) of the central Si atom. These are 1 Si(O4 ) unit, 4 Si(SiO3 ) units, 10 Si(Si2 O2 ) units, 24 Si(Si3 O) units, and 40 Si(Si4 ) units, which cannot be seen as identical after rotation. In addition, the

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We have enquired the model into the set of models found in the literature. Local structural differences are confirmed to be generated by variation of the production conditions. We find a frozen nonequilibrium system of a disproportionation in the initial state, described as an extension of the random mixture model as an intermediate model between random bonding models and matrix models. With respect to its structure, bulk SiO is an exceptional amorphous substance, whose volume contains a significant amount of atoms located in interfaces. This amount of abrupt interface between amorphous clusters of silicon dioxide and of silicon is not negligible due to cluster smallness. Supplementary experiments have to be performed to obtain data from different SiO modifications. Furthermore, comparison with sub-oxides (SiOx , 0 < x < 2) is of interest, in order to determine the scope of the suggested model.

Acknowledgements

Si–O–Si bond angle, the cluster sizes and even more the cluster shapes are supposed to have a broad distribution. In contrast to bulk, amorphous SiO2 , where for example Si(O4 ) tetrahedral units can form networks of six-membered rings [124], no medium-range order is expected for bulk, amorphous SiO. To establish a quantitative model (i.e. an atomic configuration e.g. as a fit result from a Reverse Monte Carlo algorithm) much more work has to be done.

We wish to thank Dr M. Friz from Merck KGaA, Gernsheim, for providing the samples. We are grateful to Professor H. Gies and Dr I. Wolf (Institute of Geosciences, Ruhr-University Bochum) for NMR measurements. We thank Dr G. Miehe for HRTEM investigations and Dr H. Ehrenberg for SQUID measurements. We also thank Mr V. Joco for PL measurements. This work was supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, under the project number WI 942/3-1. One of us (P.v.A.) is grateful to the DFG, which financed the upgrade of the Gatan PEELS 666 to the DigiPEELS 766 system under the project number AK 26/2.

5. Conclusion

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Fig. 16. A selection illustrating the variety of the possible atomic chains in the interface containing only one Si atom with sub-oxide oxidation state.

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