Abstract
This paper distinguishes between two different scales of medium range order, MRO, in noncrystalline SiO_{2}: (1) the first is ~0.4 to 0.5 nm and is obtained from the position of the first sharp diffraction peak, FSDP, in the Xray diffraction structure factor, S(Q), and (2) the second is ~1 nm and is calculated from the FSDP fullwidthathalfmaximum FWHM. Manyelectron calculations yield Si–O third and O–O fourthnearestneighbor bonding distances in the same 0.4–0.5 nm MRO regime. These derive from the availability of empty Si dπ orbitals for backdonation from occupied O pπ orbitals yielding narrow symmetry determined distributions of third neighbor Si–O, and fourth neighbor O–O distances. These are segments of six member rings contributing to connected sixmember rings with ~1 nm length scale within the MRO regime. The unique properties of noncrystalline SiO_{2} are explained by the encapsulation of sixmember ring clusters by five and sevenmember rings on average in a compliant hardsoft nanoscaled inhomogeneous network. This network structure minimizes macroscopic strain, reducing intrinsic bonding defects as well as defect precursors. This inhomogeneous CRN is enabling for applications including thermally grown ~1.5 nm SiO_{2} layers for Si field effect transistor devices to optical components with centimeter dimensions. There are qualitatively similar length scales in nanocrystalline HfO_{2} and phase separated Hf silicates based on the primitive unit cell, rather than a ring structure. Hf oxide dielectrics have recently been used as replacement dielectrics for a new generation of Si and Si/Ge devices heralding a transition into nanoscale circuits and systems on a Si chip.
Introduction
There have been many models proposed for the unique properties of noncrystalline SiO_{2}. These are based on the concept of the continuous random network, CRN, structure as first proposed by Zachariasen [1, 2]. CRN models assume the short range order, SRO, of SiO_{2} is comprised of fourfold coordinated Si in tetrahedral environments through cornerconnected twofold coordinated O bridging two Si atoms in a bent geometry. The random character of the network has generally been attributed to a wide distribution of Si–O–Si bond angles, 150 ± 30° as determined by Xray diffraction [3], as well as a random distribution of dihedral angles. These combine to give a distribution of ring geometries that defines a compliant and strain free CRN structure [2].
More recently, a semiempirical bond constraint theory (SEBCT) was proposed by one of the authors (JCP) to correlate the ease of glass formation in SiO_{2} and chalcogenide glass with local bonding constraints associated with twobody bondstretching and threebody bondbending forces [4, 5]. The criterion for ease of glass formation was a meanfield relation equating the average number of stretching and bending constraints/atom with the network dimensionality of three. When applied to SiO_{2}, satisfaction of this criterion was met by assuming a broken bond bending constraint for the bridging Oatoms. This was inferred from the large bond angle distribution of the Si–O–Si bonding group, and the weak bonding force constant. The same local meanfield approach for the ease of glass formation has been applied with good success to other noncrystalline network glasses in the Ge–Se and As–Se alloy systems.
SEBCT makes no connection with medium MRO that is a priori deemed to be important with other properties. As such, SEBCT cannot identify MRO bonding that has been associated with the FSDP [6, 7]. Based on these references, the position and width of the FSDP identify two different MRO length scales. It will be demonstrated in this paper that these length scales provide a basis for explaining some of the unique nanoscale related properties of noncrystalline SiO_{2} that are enabling for device applications.
The FSDP in the structure factor, S(Q), has been determined from Xray and neutron diffraction studies of oxide, silicate, germanate, borate and chalcogenide glasses [7]. There is a consensus that the position and width of this feature derive from MRO [6–8]. This is defined as order extending beyond the nearest and nextnearest neighbor distances extracted from diffraction studies, and displayed in radial distribution function plots [2]. There has been much speculation and empirical modeling addressing the microscopic nature of bonding arrangements in the MRO regime including rings of bonded atoms [9], distances between layerlike ordering [10], and/or void clustering that are responsible for the FSDP [11]. Firstprinciple molecular dynamics calculations have been applied to the FSDP [7, 12]. One of these papers ruled out models based on layerlike nanostructures, and nanoscale voids as the MRO responsible for the FSDP [12]. References [7] and [12] did not offered alternative explanations for the FSDP based a microscopic understanding of the relationship between atomic pair correlations in the MRO regime and constraints imposed by fundamental electronic structure at the atomic and molecular levels.
Moss and Price in [7], building on the 1974 deNeufville et al. [6] observation and interpretation of the FSDP proposed that the position this feature, Q_{1}(Å^{−1}), “can be related, via an approximate reciprocal relation, to a distance R in real space by the expression R = 2π/Q”. It is important to note the MROscale bonding structures previously proposed in [9] and [10], and ruled out in [12], could not explain why a large number of oxide and chalcogenide glasses exhibit FSDP’s in a relative narrow regime of Qvalues, ~1 to 1.6 Å^{−1}. Nor could they account for the systematic differences among these Qvalues, ~1.5 for oxides, and 1.0–1.25 for chalcogenides. It has been shown in [13] that this is a result of an scaling relationship between the position of the FSDP in Qspace and the nearest neighbor bond length.
Based on [7, 8, 13, 14], the position, Q_{1}(Å^{−1}), and fullwidth at halfmaximum, FWHM, ΔQ_{1}(Å^{−1}) of the FSDP have been used to identify a second length scale within the MRO regime for a representative set of oxide and chalcogenide glasses [7, 11]. The first length scale has been designated as a correlation length, R = 2π/Q_{1}(Å^{−1}), and is determined from the Qspace position of the spectral peak as suggested in [1], and the second has been designated as a coherence length, L = 2π/ΔQ_{1}(Å^{−1}), and is determined from the FWHM [7]. This interpretation of the FSDP position and lineshape is consistent with the interpretation of diffraction peaks or local maxima in S(Q) for noncrystalline and crystalline solids [2]. These are interpreted as interatomic distances or equivalently atomic pair correlations that are repeated throughout a significant volume of the sample within the Xray beam, but not in a periodic manner characteristic of long range crystalline order. Like other diffraction features, e.g., the width of the Si–Si pair correlation length in SiO_{2} as determined in [3], is also associated with a characteristic real space distance, e.g., of a MROscale cluster of atoms.
In referring to the FSDP, Moss and Prince in [7] noted that “such a diffraction feature thus represents the build up of correlation whose basic period is well beyond the first few neighbor distances”; this basic period is within the MRO domain. It was also pointed out by them that “In fact, the width of this feature can be used to estimate a correlation range over which the period in question survives”, or persists.
Returning to paper published in 1974 by deNeufville, Moss and Ovshinsky; this article addressed photodarkening in As_{2}(S, Se)_{3} in a way that anticipated the quantitative definitions for R and L in subsequent publications [7]. This is of historical interest since FSDPs were observed for the first time in each compound and/or alloy studied, and these were associated with a real space distance of ~5.5 A in the MRO regime. It was also noted that the width of this feature in reciprocal (Q) space identified a larger scale of order over which these MROregime correlations persisted; this has subsequently been defined as the coherence length, L.
Experimental Results for SiO_{2}
The position and width of the FSDP in glassy SiO_{2} have received considerable attention, and are wellcharacterized [7, 8, 14]. Based on these references and others as well, Q_{1}(Å^{−1}) is equal to 1.52 ± 0.03 Å^{−1}, and ΔQ_{1}(Å^{−1}) to 0.66 ± 0.03 Å^{−1}. The calculated values of the correlation length, R = 2π/Q_{1}(Å^{−1}), and the coherence length, L = 2π/ΔQ_{1}(Å^{−1}), are, respectively, R = 4.13 ± 0.08 Å, and L = 9.95 ± 0.05 Å. R gives rise to features in the RDF in a regime associated with rings of bonded atoms; these are a universal aspect of the CRN description of noncrystalline oxides and chalcogenides which include twofold coordinate atoms [2].
In a continuous random network, CRN, such as SiO_{2}, the primitive ring size is defined by the number of Si atoms connected through bridging O atoms to form the smallest high symmetry ring structure. This primitive ring is the noncrystalline analog of the primitive unit cell (PUC) in crystalline solids and this provides an important connection between the properties of noncrystalline and nanocrystalline thin films.
It has been first demonstrated in the Bell and Dean model [15, 16], and later by computer generated modeling [17–19], and molecular dynamic simulations as well [8], that the ring size distribution for SiO_{2} is dominated by sixmember rings with six silicon and six oxygen atoms.
The contributions to the partial structure factor, S_{ ij }^{N} (Q) associated with Si–O, O–O and Si–Si pair correlation distances have been determined using classical molecular dynamics simulations as addressed in [8]. Combined with RDFs from the Bell and Dean model [16], and computer modeling [17, 18, 20], these studies identify interatomic pair correlations in the regime of 4–5 Å that contribute to the position of FSDP. Figure 3 of [16], is a pair distribution histogram that indicates a (1) a Si–O pair correlation, or third nearest neighbor distance of 4.1 ± 0.5 Å, and (2) an O–O pair correlation, or fourth nearest neighbor distance of 4.5 ± 0.3 Å. These features are evident in the computed and experimental radial distribution function plots for Xray diffraction in Fig. 4, and neutron diffraction in Fig. 5, also of [16]. As indicated in Fig. 1 of this paper, the 4.1 Å feature is assigned with Si–O third nearestneighbor distances, and the 4.5 Å feature is assigned to fourth nearestneighbor O–O distances. Figure 1 is a schematic representation of local cluster that has been used to determine the Si–O–Si bond angle using manyelectron ab initio quantum chemistry calculations in [18].
The importance of Si atom dstate symmetries in calculations of the electronic structure of noncrystalline SiO_{2} was recognized in [18], published in 2002. These symmetries, coupled with the O 2pπ states play a significant role in narrowing the two pair distribution distances identified above. The cluster displayed in Fig. 1 is large enough to include the correlation length, R in the MRO regime. The calculations of [18] demonstrated that Si dstate basis Gaussian functions when included into a manyelectron, ab initio calculation play a determinant role in generating a stable minimum for a Si–O–Si bond angle, Θ, that is smaller than the ionic bonding value 180°. In addition these values of Θ, and the bond angle distribution, ΔΘ (1) were different from what had been determined by the Xray diffraction studies of Mozzi and Warren in [3], but (2) were in excellent agreement with more recent studies that employed a larger range of k or Q[19]. The values obtained by Mozzi and Warren [3] are Θ ~ 144°, and ΔΘ]FWHM ~ 30°, whereas the studies in [19] obtained values of Q ~ 148° and ΔΘ]FWHM ~ 13–15° that were essentially the same as those calculated in [16]. The Bell and Dean model of [15] in Fig. 2 gave a Si–O–Si bond angle of 152°, and also wide bond angle distribution with a FWHM ~ 15°. Of particular significance is the significantly narrower Si–O–Si bond angle distribution of the calculations in [18], and the Xray diffraction studies of [19]. The bond angles and bond distributions of [16, 18, 19] have important implications for the existence of high symmetry six member Si–O rings their importance as the primitive ring structure in both αquartz and βquartz, as well as noncrystalline SiO_{2}.
The identification of the specific MRO regime features obtained from S(Q) rely heavily on the pair correlation functions derived from the Bell and Dean model [16], as well as from computer modeling of the Gaskell group [21] and Tadros et al. [17, 20]. Combined with [16], The Si dπO 2pπSi dπ symmetry determined overlap and charge transfer from occupied O πstates into otherwise empty Si dπ states, plays the determinant role in forcing the narrowness of this MRO length scale feature. Stated differently, pairs of Si atoms connected through an intervening O atom as in Fig. 1, are strongly correlated by the local symmetries forced on these Si dπstates. This correlation reflects the even symmetry of the respective Si dstates, and the odd symmetry of the O pstates. In contrast, the coherence length, L, as determined from the FWHM of the FSDP cannot be assigned to a specific interatomic repeat distance identified in any of the models addressed above, but instead is an average cluster dimension, in the spirit of the definitions in [6] and [7].
The coherence length, L in SiO_{2}, as computed from the FWHM of the FSDP, is 9.5 ± 0.5 Å, and this identifies the cluster associated with this length scale. Based on a simple extension of the schematic diagram in Fig. 1, this cluster includes a coupling of at least two, and no more than three symmetric sixmember primitive rings. If this cluster is extended well beyond two to three rings in all directions, it would eventually generate the crystal structure of αquartz. This helical aspect of this structure gives rise to a right or lefthanded optical rotary property of αquartz [22]. The helical structure of αquartz has its parentage in trigonal Se, which is comprised of right or lefthanded helical chains with three Se atoms per turn of the helix. The twoatom helix analog is the cinnabar phase of HgS with six atoms/turn, three Hg and three S. αquartz is the threeatom analog with nine atoms/turn, three Si and six O [22]. Returning to noncrystalline SiO_{2}, the coupling of two to threesixmember rings is consist with the relative fraction of six member rings, ~50% in the Bell and Dean [16] construction as well as other estimates of the ring fraction.
Moreover, this two to three ring clustered structure is an example of the MRO structures addressed in [7]. With respect the FSDP, Moss and Price noted that “such a diffraction feature thus represents the build up of correlation whose basic period is well beyond the first few neighbor distances”; it therefore in the MRO regime. They also pointed out that: “In fact, the width of this feature (the, FSDP) can be used to estimate a correlation range over which the period in question survives”. This incoherent coupling associated with less symmetric five and sevenmember rings than determines the correlation, or coherence range over which this period survives.
Revisiting the CRN in Context of Correlation and Coherence Length Determinations
The pair correlation assignments made for R and L are consistent with the global concept of a CRN, but the length scales for correlation, R, and coherence. L, are quantitatively different that what was proposed originally in [1], and discussed at length [3]. Each of these envisioned the CRN randomness to be associated with the relative widths of bond lengths and bond angles, as in Fig. 2 in the Bell and Dean [16]. Based on this model the Si–O pair correlation has a width <0.05 Å, and the Si–O–Si bond angle displays a 30° width, corresponding to a Si–Si pair correlation width at least twotothree larger. In these conventional descriptions of the CRN, any dihedral angle correlations, or fouratom correlations, are removed by bondangle widths.
The identification of the MRO length scales, R and L, also has important implications for the use of semiempirical bond constraint theory (SEBCT) for identifying and/or describing ideal glass formers. This theory is a meanfield theory based on average properties that are determined by constraints restricted to SRO bonding arrangements [4, 5, 23]. The identification and interpretation of the two MRO length scales discussed above indicates that this emphasis on SRO is not sufficient for identifying the important nanoscale properties of SiO_{2}. Indeed MRO is deemed crucial for establishing the unique and technologically important character of noncrystalline SiO_{2} over a dimensional scale from 1 to 2 nm thick gate dielectrics to centimeter dimensions for highquality optically homogeneous components, e.g., lenses.
The FSDP has been observed, and studied in other noncrystalline oxide glasses, e.g., B_{2}O_{3}, GeO_{2}, as well chalcogenide glasses including sulfides, GeS_{2} and As_{2}S_{3}, and selenides, GeSe_{2}, As_{2}Se_{3} and SiSe_{2}[6, 7]. The values of R and L have been calculated, and display anion, O, S and Se and cation coordination specific behaviors. For example, the values of the correlation length R, and the coherence length L, have been obtained from the position, and FWHM of the S(Q) FSDP peak for (a) SiO_{2}: R = 4.1 ± 0.2 Å, and L = 9.5 ± 0.5 Å; (b) B_{2}O_{3}: R = 4.0 ± 0.2 Å, and L = 11 ± 1 Å; and (c) GeSe_{2}: R = 6.3 ± 0.3 Å, and L = 24 ± 4 Å.
It has been noted previously elsewhere [7, 13], that quantitative differences between the position of the FSDPs in SiO_{2} and GeSe_{2} can be correlated directly with differences between the respective (1) Si–O and Ge–Se bondlengths, 1.65 and 2.39 Å, and (2) Si–Si and Ge–Ge next neighbor features as determined by the respective Si–O–Si and Ge–Se–Ge bond angles, ~148° and ~105°. This was addressed in [1] and [24], where it was shown that the products of nearest neighbor bond length (in Å) and positions of the FSDP (Q(Å^{−1}) are approximately the same, ~2.5 ± 0.4 for the oxide and chalcogenide glasses [1, 24]. Based on this scaling, the value R for GeSe_{2} (x = 0.33), is estimated to be 6.2 ± 0.2 Å, compared with the averaged experimental value of R = 6.30 ± 0.07 Å.
This values of Q_{1}(Å^{−1}) show interesting correlations with the nature of the CRNs. For the three oxide glasses in Table 1Q_{1}(Å^{−1}) ~ 1.55 ± 0.03, and is independent of the network coordination, i.e., 3–2 for B_{2}O_{3} and 4–2 SiO_{2} and GeO_{2}. In contrast, the value of Q_{1}(Å^{−1}) decreases to ~1.05 for 4–2 selenides, and then increases to ~1.25 for the 3–2 chalcogenides. This indicates a longer correlation length in the 3–2 alloys that is presumed to be associated with repulsions between lone pairs on As, and either the Se or S atoms of the particular alloy for the 3–2 chalcogenides.
It is significant to note that the scaling relationship based on SRO, breaks down for the coherence length L for GeSe_{2}. The scaled ratio for L is estimated to be 15 Å compared with the higher average experimental value of L = 24 ± 4 Å [11, 25]. The comparisons based on scaling are consistent with R being determined by the extension of a local pair correlation determined by the ring structures in the SiO_{2} and GeSe_{2} CRNs. The microscopic basis for L in SiO_{2}, and B_{2}O_{3} as well, is determined by characteristic interring bonding arrangements with a cluster size that related to coupling of two, two or three rings, respectively. These determine the period of the cluster repetition, and the encapsulation of these more symmetric rings by less symmetric rings of bonded atoms; i.e., five and sevenmember rings in SiO_{2}. The interring coupling in SiO_{2} is direct result of the softness of the Si–O–Si bonding force constant in SiO_{2}[4, 5]. For the case of the GeSe_{2} CRN because of the smaller Ge–Se–Ge bond angle and repulsive effects between the Se lone pair electrons and the bonding electrons localized in the more covalent Ge–Se bonds, the coherence length is not attributed to rings of bonded atoms, but rather to a hard soft cluster mixture. The hard soft structure in GeSe alloys is determined by compositionally dependent constraints imposed by local bonding, e.g., locally rigid groups with Ge atoms separated by one bridging Se atom, Ge–Se–Se, and locally compliant groups associated with two bridging Se atoms, Ge–Se–Se–Ge [23]. Similar considerations apply to the period of the hardcomponent of a hardsoft structure that have been proposed as the driving force for glass formation, and the associated low densities of defect and defect precursors which are associated with either broken and strainedbonds, respectively. The criterion is SiO_{2} and B_{2}O_{3} is determined by a nanostructures that includes a multiplicity of different ring sizes, whereas the criterion is a volume percolation threshold that applies in chalcogenides glasses, and is consistent with locally rigid, and locally compliant groups been phaseseparated into hardsoft mixtures [26]. The same considerations apply in Aschalcogenides, and for the compound As_{2}Se_{3} and GeSe_{2} compositions that include local small discrete molecules that add compliance to the otherwise locally rigid CNRs that includes As–Se–As and Ge–Se–Ge bonding, respectively [23].
The conclusion is that SEBCT, even with local modifications for symmetryassociated broken bending constraints, and additional constraints due to lone pair and terminal atom repulsions [23], has limited value in accounting the elimination of macroscopic strain reduction for technology applications. This property depends on MRO, as embodied in hardsoft mixtures, and/or percolation of shortrange order ground that exceeds a volume percolation threshold [23, 27].
Nanocrystalline and Nanocrystalline/Noncrystalline Alloys
Extension of the MRO concepts of the previous sections from CRNS to nanocrystalline and nanocrystalline/noncrystalline composites of technological importance is addressed in this section. One way to formulate this issue is to determine conditions that promote hardsoft mixtures in materials that are (1) chemically homogeneous, but inhomogeneous on a nanometer length scale, or (2) both chemically inhomogeneous and phaseseparated. The first of these is addressed in homogeneous HfO_{2} thin films, and the second for phase separated Hf silicates, as well as other phase separated materials in which SiO_{2} in a chemical constituent [28].
Nanograin HfO_{2} Films
The nanograin morphology of deposited and subsequently high temperature, >700°C, annealed HfO_{2} thin films is typically a mixture of monoclinic (m) and tetragonal (t) grains differentiated by Hf 5d features in combination with O 2p π states that comprise local symmetry adapted linear combinations (SALCs) of atomic states into molecular orbitals (MO) [28, 29]. These MOs are essentially oneelectron states, in contrast to occupied Hf states that must by treated in a manyelectron theory [30]. Of particular importance are the πbonded MOs that contribute to the lowest conduction band features in O K edge XAS spectra [28, 29]. Figure 2 indicates differences in these band edge features for nanograin tHfO_{2} and mHfO_{2} thin films in which the grainmorphology has been controlled by interfacial bonding. The tHfO_{2} films display a single asymmetric band edge feature, whereas mHfO_{2} films display two band edge features. Figure 3 is for films that have with a mixed t/m nanograin morphology, and a thickness that is increased from 2 to 3 nm, and then to 4 nm. Based of features in these spectra, and 2nd derivative spectra as well, the 2 nm film displays neither a t, nor a mnanograin morphology, while the thicker films display a doublet structure indicative of a mixed nanograin morphology.
The band edge 5d E_{g} splittings in Figs. 2 and 3 indicate a cooperative Jahn–Teller (J–T) distortion [28]. The theoretical model in [31] indicates that an electronic unit cell comprised of seven PUCs, each ~0.5 to 0.55 nm is necessary for a cooperative J–T effect, and this requires a nanograin dimensions of ~3 to 3.5 nm. This indicates a dimensional constraint in the 2 nm thick film. This film is simply too thin to support a high concentration of randomly oriented nanograins with an electronic unit cell large enough to support a J–T distortion. These 2 nm films are generally characterized as Xray amorphous. Asdeposited 3 and 4 nm thick films also display no J–T, but when subjected to the same 900°C anneal as the 2 nm thick film, the dimensional constraint is relaxed and J–T distortions are stabilized and are observed in O K edge XAS.
These differences in nanoscale morphology identify several scales of MRO for HfO_{2}, as well as other TM d^{0} oxides, TiO_{2} and ZrO_{2}. The first is the PUC ~ 0.5 to 0.55 nm, and the second and third are for coupling of unit cells. The first coupling is manifest in 1.5–2.0 nm grains that are analogues of the SiO_{2} clusters comprised of 2–3 symmetric sixmember rings. The second length scale is 3–3.5 nm and is sufficient to promote J–T distortion which persist in thicker annealed film and bulk crystals as well. The PUC of HfO_{2} then plays the same role as the symmetric or regular sixmember ring of noncrystalline SiO_{2} and in crystalline aquartz.
Differences in nanograin order have a profound effect on intrinsic bonding defects in HfO_{2}. In films thicker than 3 nm they contribute to high densities of vacancy defects (~10^{12} cm^{−2}, or equivalently 10^{18} cm^{−3}), clustered on internal grain boundaries of nanograins large enough to display J–T term splittings [28]. These are indicated in Fig. 4.
Nanograin HfO_{2} in the MRO size regime of 1.5–2 nm can also formed in phaseseparated Hf silicates (HfO_{2})_{ x }(SiO_{2})_{1−x}, alloys in two narrow compositional regimes: 0.15 <x < 0.3, and 0.75 <x < 0.85. For the lower xregime, the phase separation of an asdeposited homogeneous silicate yields a compliant hardsoft structure. This is comprised of Xray amorphous nanograins with <3 nm dimensions that are encapsulated by noncrystalline SiO_{2}. For the higher xregime. The phase separated silicates include Xray amorphous nanograins <3 nm in size, whose growth is frustrated by a random incorporation of 2 nm clusters of compliant noncrystalline SiO_{2}. The concentration of these 2 nm clusters exceeds a volume percolation threshold accounting for the frustration of larger nanograin growth [27].
Each of these phaseseparated silicate regimes exhibits low densities of defects and defect precursors. However, these diphasic silicates have not studied with respect to radiation stressing, so it would be illadvised and inappropriate to call then SiO_{2}lookalikes, a label that has been attached to the homogeneous Hf Si oxynitride alloys in the next subsection based on radiation stressing [32].
Homogeneous Hf Si Oxynitride Alloys
There is a unique composition (HfO_{2})_{0.3}(SiO_{2})_{0.3}(Si_{3}N_{4})_{0.4}(concentrations ± 0.025) hereafter HfSiON_{334}, which is stable to annealing temperatures >1,000°C, and whose electrical response after Xray and γray stressing is essentially the same as SiO_{2}[32].This similarity is with respect to (1) the linear dependence on dosing, (2) the sign of the fixed charge, always positive, and (3) the magnitude of the defect generation. The unique properties are attributed to a fourfold coordinated Hf substitute onto 16.7% of the possible fourfold coordinated Si bonding sites. This concentration is at the percolation threshold for connectivity of compliant local bonding arrangements [27]. Larger concentrations of (Si_{3}N_{4}) for the same or different combinations of HfO_{2} and SiO_{2} bonding leads to chemical phase separation with loss of bonded N, and therefore qualitatively different thin films.
Other Diphasic Materials with 20% SiO_{2}
There are at least two other diphasic materials with a dimensionally stabilized symmetric nanocrystalline phase, and a 20% compliant noncrystalline phase, 2 nm clusters of SiO_{2}. This includes a 20% mixture of noncrystalline SiO_{2} with (1) nanocrystalline zincblendestructured ZnS grains, or (2) a fine nanograin ceramic as in Corning cookware [33]. In each of these thin materials, TEM imaging indicates that the 20% SiO_{2} is distributed uniformly in compliant clusters with an average size of ~2–3 nm. These encapsulated nanoclusters reduce macroscopic strain, but equally important suppress the formation of more asymmetric crystal structures, e.g., wurtzite ZnS, which would lead to anisotropic optical properties, and make these films in unusable for use as protective layers in optical memory stacks for digital video disks (DVD) for information storage and retrieval. In the second application, the SiO_{2} makes these ceramics macroscopically strain free, and capable on being moved from the “oven to the refrigerator” without cracking [33].
(Si_{3}N_{4})_{ x }(SiO_{2})_{1−x}Gate Dielectrics
Si oxynitride pseudobinary alloys (Si_{3}N_{4})_{ x }(SiO_{2})_{1−x}, have emerged in the late 1990s as replacement dielectrics [34]. These alloys have been used with small and high concentrations of Si_{3}N_{4} with different objectives. At low concentration levels <5% Si_{3}N_{4}, for blocking Boron transported from Bdoped polySi gate dielectrics [24], and at significantly higher concentrations, ~50 to 60% Si_{3}N_{4}, as required for a significant increase in the dielectric constant from ~3.9 to ~5.4 to 5.8 [35].
The midgap interface state density, D_{it}, and the flatband voltage V_{fb} were obtained from a conventional C–V analysis of metal–oxide–semiconductor capacitors on ptype Si substrates with ~10^{17} cm^{−3} doping, pMOSCAPs, with Al gate metal layers deposited after a post metal anneal in forming gas. Both D_{it} and and V_{fb} display qualitatively similar behavior as function of x for both asdeposited and Sidielectric layers annealed at 900°C in Ar for 1 min [34]. The annealed dielectrics are processed at temperatures that validate comparisons with pMOSCAPs with thermally grown SiO_{2} and similarly processed Al gates. D_{it} decreases from ~10^{11} cm^{−2} eV^{−1} for Si_{3}N_{4} (x = 1), to ~10^{10} cm^{−2} eV^{−1} for x ~ 0.7 to a value comparable to state of the art SiO_{2} MOSCAPs. The value of D_{it} is relatively constant, 1.1 ± 0.2 × 10^{−10} cm^{−2} eV^{−1}, for values of x from 0.65 to 0.0 (SiO_{2}). In a complementary manner, V_{fb} increases from −1.3 eV for Si_{3}N_{4} (x = 1), to −0.9 eV at x ~ 0.7, and then remains relatively constant, −0.8 ± 0.1 eV for values of x from 0.65 to 0.0 (SiO_{2}). The values of D_{it} and V_{fb} are comparable to those for thermally grown SiO_{2}, and therefore have been the basis for use of these Si oxynitrides in commercial devices [34].
The electrical measurements are consistent with significant decreases in macroscopic strain for Si oxnitride alloys with SiO_{2} concentrations exceeding about 35% or x = 0.65. This suggests a hardsoft mechanism in this regime similar to that in Hf silicates. At concentrations <0.35, i.e., SiO_{2} = 65%, the roles of the hard and soft components are assumed to be reversed. However, strain reduction over such an extensive composition regime suggests a more complicated nanoscale structure that has a mixed hardsoft character over a significant composition region, The proposed mixed phase is comprised of equal concentrations of Si_{3}N_{4} encapsulating SiO_{2} at high Si_{3}N_{4} concentrations, and an inverted hardsoft character with SiO_{2} encapsulating Si_{3}N_{4} at lower Si_{3}N_{4} concentrations. If this is indeed the case, it represents a rather interesting example of a double percolation process [26, 36].
Summary and Conclusions
This will be displayed in a bulleted format.

1.
The spectral position of the FSDP for glasses, and its FWHM are associated with real space distances as obtained from the structure factor S(Q) derived from Xray or neutron diffraction\are in the MRO regime. The first length scale has been designated as a correlation length, R = 2π/Q_{1}(Å^{−1}), and the second length scale has been designated as a coherence length, L = 2π/ΔQ_{1}(Å^{−1}) where Q_{1}(Å^{−1}) and ΔQ_{1}(Å^{−1}) are, respectively, the position and FWHM of S(Q).

2.
The values of the correlation length R, and the coherence length L, obtained in this way are for: (a) SiO_{2}:R = 4.1 ± 0.2 Å, and L = 9.5 ± 0.5 Å; (b) B_{2}O_{3}:R = 4.0 ± 0.2 Å, and L = 11 ± 1 Å; and (c) GeSe_{2}: R = 6.3 ± 0.3 Å, and L = 24 ± 4 Å.

3.
Based on molecular dynamics calculations and modeling, the values of R correspond to third neighbor Si–O, and associated with segments of sixmember rings in SiO_{2}. The larger value of R in GeSe_{2} is consistent with scaling based on Ge–Se bond lengths and therefore has a similar origin.

4.
Based on molecular dynamics calculations and modeling, the coherence length features are not a direct result of interatomic pair correlations. This is supported by the analysis of Xray diffraction data as well, where the coherence length is determined by the width of the FSDP rather than by an additional peak in S(Q).

5.
The ring clusters contributing to the coherence lengths for SiO_{2} are comprised of two, or at most three symmetric sixmember rings, that are stabilized by back donation of electrons from occupied 2p π states on O atoms to empty π orbitals on the Si atoms. These rings are encapsulated by more compliant structures with lower symmetry irregular five and sevenmember rings to form a compliant hardsoft system.

6.
The coherence length in Ge_{ x }Se_{1−x} alloys is different in Serich and Gerich composition regimes, and is significantly larger in each of these regimes than at the compound composition, GeSe_{2} which they bracket. It is determined in each alloy regime, and at the compound composition by minimization of macroscopic strain by a chemical bonding selforganization as in which site percolation dominates. There is a compliant alloy regime which extends from x = 0.2 to 0.26 in which locally compliant bonding arrangements, Ge–Se–Se–Ge, completely encapsulate a more rigid cluster comprised of locally rigid Ge–Se–Ge bonding. For compositions greater than x = 0.26 and extending to x = 0.4, macroscopic compliance results form a diphasic mixture which includes small molecules with Ge–Se, and Ge–Ge bonding.

7.
The hardsoft mix in noncrystalline SiO_{2} with a length scale of at most 1 nm establishes the unique properties of gate dielectrics >1–1.5 nm thick, and for cm glasses with cmdimensions as well.

8.
There is an analog between the properties of nanocrystalline HfO_{2}, and phase separated HfO_{2}SiO_{2} silicate alloys, ZnSSiO_{2} alloys and ceramicSiO_{2} alloys that establishes their unique properties in device applications as diverse as gate dielectrics for aggressively scaled dielectrics, protective layers for stacks in with rewritable optical information storage, and for temperature compliance in ceramic cookware.

9.
pMOSCAPs with Si oxynitride pseudobinary alloys (Si_{3}N_{4})_{ x }(SiO_{2})_{1−x}, gate dielectrics display an defect densities for interface trapping, D_{it}, and fixed positive charge that determines the flatband voltage, V_{fb}, comparable to those of thermally grown SiO_{2} dielectrics for a range of concentrations extending for ~70%, x = 0.7, Si_{3}N_{4} to SiO_{2}. The electrical measurements are consistent with significant decreases in macroscopic strain, suggesting a hardsoft mechanism in this regime similar to that in Hf silicates. However, strain reduction over such an extensive composition regime suggests a more complicated nanoscale structure that has a mixed hardsoft character over a significant composition region, The proposed mixed phase is comprised of equal concentrations of Si_{3}N_{4} encapsulating SiO_{2} at high Si_{3}N_{4} concentrations, and an inverted hardsoft character with SiO_{2} encapsulating Si_{3}N_{4} at lower Si_{3}N_{4} concentrations. If this is indeed the case, it represents a rather interesting example of a double percolation process.

10.
The properties of the films and bulk materials identified above are underpinned by the realspace correlation and coherence lengths, R and L, obtained from analysis of the SiO_{2} structure factor derived from Xray or neutron diffraction. The real space interpretation relies of the application of manyelectron theory to the structural, optical and defect properties on noncrystalline SiO_{2}.
References
Zachariasen WH: J. Am. Chem. Soc.. 1932, 54: 3841. COI number [1:CAS:528:DyaA38Xls1OnsQ%3D%3D] COI number [1:CAS:528:DyaA38Xls1OnsQ%3D%3D] 10.1021/ja01349a006
Zallen R: The physics of amorphous solids. WileyInterscience, New York; 1983. 10.1002/3527602798
Mozzi L, Warren BE: J. Appl. Crystallogr.. 1969, 2: 164. COI number [1:CAS:528:DyaE3cXmvFar] COI number [1:CAS:528:DyaE3cXmvFar] 10.1107/S0021889869006868
Phillips JC: J. NonCryst. Solids. 1979, 34: 153. COI number [1:CAS:528:DyaL3cXotVKgug%3D%3D]; Bibcode number [1979JNCS...34..153P] COI number [1:CAS:528:DyaL3cXotVKgug%3D%3D]; Bibcode number [1979JNCS...34..153P] 10.1016/00223093(79)900334
Phillips JC: J. NonCryst. Solids. 1981, 43: 37. COI number [1:CAS:528:DyaL3MXhs1Gkt7Y%3D]; Bibcode number [1981JNCS...43...37P] COI number [1:CAS:528:DyaL3MXhs1Gkt7Y%3D]; Bibcode number [1981JNCS...43...37P] 10.1016/00223093(81)901721
DeNeufville J, et al.: J. NonCryst. Solids. 1974, 13: 191. COI number [1:CAS:528:DyaE2cXlt12isbs%3D]; Bibcode number [1974JNCS...13..191D] COI number [1:CAS:528:DyaE2cXlt12isbs%3D]; Bibcode number [1974JNCS...13..191D] 10.1016/00223093(74)90091X
Moss SC, Price DL: Physics of disordered materials. Edited by: Adler D, Fritzsche H, Ovshinsky SR. Plenum, New York; 1985:77.
Du J, Corrales LR: Phys. Rev. B. 2005, 72: 092201. and references therein and references therein
Uchino T, et al.: Phys. Rev. B. 2005, 71: 014202. Bibcode number [2005PhRvB..71a4202U] Bibcode number [2005PhRvB..71a4202U] 10.1103/PhysRevB.71.014202
Elliott SR: Phys. Rev. Lett.. 1991, 67: 711. COI number [1:CAS:528:DyaK3MXlsVaqtrk%3D]; Bibcode number [1991PhRvL..67..711E] COI number [1:CAS:528:DyaK3MXlsVaqtrk%3D]; Bibcode number [1991PhRvL..67..711E] 10.1103/PhysRevLett.67.711
Rao NR, et al.: J. NonCryst. Solids. 1998, 240: 221. Bibcode number [1998JNCS..240..221R] Bibcode number [1998JNCS..240..221R] 10.1016/S00223093(98)007054
Massobrio C, Pasquarello A: J. Chem. Phys.. 2001, 114: 7976. COI number [1:CAS:528:DC%2BD3MXjtVGgt74%3D]; Bibcode number [2001JChPh.114.7976M] COI number [1:CAS:528:DC%2BD3MXjtVGgt74%3D]; Bibcode number [2001JChPh.114.7976M] 10.1063/1.1365108
Price DL, et al.: J. Phys. Condens. Matter. 1989, 1: 1005. COI number [1:CAS:528:DyaL1MXitlOnsL8%3D]; Bibcode number [1989JPCM....1.1005P] COI number [1:CAS:528:DyaL1MXitlOnsL8%3D]; Bibcode number [1989JPCM....1.1005P] 10.1088/09538984/1/5/017
Sussman S, et al.: Phys. Rev. B. 1991, 43: 1194. Bibcode number [1991PhRvB..43.1194S] Bibcode number [1991PhRvB..43.1194S] 10.1103/PhysRevB.43.1194
Bell RJ, Dean P: Nature. 1966, 212: 1354. COI number [1:CAS:528:DyaF2sXlvVGgtA%3D%3D]; Bibcode number [1966Natur.212.1354B] COI number [1:CAS:528:DyaF2sXlvVGgtA%3D%3D]; Bibcode number [1966Natur.212.1354B] 10.1038/2121354a0
Bell RJ, Dean P: Philos. Mag.. 1972, 15: 1381. Bibcode number [1972PMag...25.1381B] Bibcode number [1972PMag...25.1381B] 10.1080/14786437208223861
Tadros A, Klenin MA, Lucovsky G: J. NonCryst. Solids. 1985, 75: 407. COI number [1:CAS:528:DyaL28XisVGmsQ%3D%3D]; Bibcode number [1985JNCS...75..407T] COI number [1:CAS:528:DyaL28XisVGmsQ%3D%3D]; Bibcode number [1985JNCS...75..407T] 10.1016/00223093(85)902492
Whitten JL, et al.: J. Vac. Sci. Technol. B. 2002, 20: 1710. COI number [1:CAS:528:DC%2BD38XmtVClu7c%3D] COI number [1:CAS:528:DC%2BD38XmtVClu7c%3D] 10.1116/1.1490382
Neufeind J, Liss KD: Bur. Bunsen. Phys. Chem.. 1996, 100: 1341.
Tadros A, Klenin MA, Lucovsky G: J. NonCryst. Solids. 1984, 64: 215. COI number [1:CAS:528:DyaL2cXktFamsLw%3D]; Bibcode number [1984JNCS...64..215T] COI number [1:CAS:528:DyaL2cXktFamsLw%3D]; Bibcode number [1984JNCS...64..215T] 10.1016/00223093(84)902187
Evans KM, Gaskell PH, Nex CMM: The structure of noncrystalline materials 1982. Edited by: Gaskell PH, Parker JM, Davis EA. Talyor and Francis, London; 1983:426.
Zallen R, et al.: Phys. Rev. B. 1970, 1: 4058. Bibcode number [1970PhRvB...1.4058Z] Bibcode number [1970PhRvB...1.4058Z] 10.1103/PhysRevB.1.4058
Lucovsky G, Phillips JC: J. Phys. Condens. Mater.. 2007, 19: 455218. Bibcode number [2007JPCM...19S5218L] Bibcode number [2007JPCM...19S5218L] 10.1088/09538984/19/45/455218
Wu Y, et al.: J. Vac. Technol. B. 1999, 17: 3017.
Shatnawi MTM, et al.: Phys. Rev. B. 2008, 77: 094134. Bibcode number [2008PhRvB..77i4134S] Bibcode number [2008PhRvB..77i4134S] 10.1103/PhysRevB.77.094134
Phillips JC: J. Phys. Condens. Mater.. 2007, 19: 455213. Bibcode number [2007JPCM...19S5213P] Bibcode number [2007JPCM...19S5213P] 10.1088/09538984/19/45/455213
Scher H, Zallen R: J. Chem. Phys.. 1970, 53: 3759. COI number [1:CAS:528:DyaE3cXlt1Cnt7o%3D]; Bibcode number [1970JChPh..53.3759S] COI number [1:CAS:528:DyaE3cXlt1Cnt7o%3D]; Bibcode number [1970JChPh..53.3759S] 10.1063/1.1674565
Lucovsky G, Jpn J, et al.: Appl. Phys. 46. 2007, 1899. and references therein and references therein
Cotton FA: Chemical applications of group theory. WileyInterscience, New York; 1953.
de Grott F, Kotani A: Core level spectroscopy of solids. CRC, Boca Ratan; 2008. Chapters 2, 3 and 4 Chapters 2, 3 and 4
Bersuker IB: J. Comput. Chem.. 1997, 18: 260. COI number [1:CAS:528:DyaK2sXisl2lsQ%3D%3D] COI number [1:CAS:528:DyaK2sXisl2lsQ%3D%3D] 10.1002/(SICI)1096987X(19970130)18:2<260::AIDJCC10>3.0.CO;2M
Chen DK, et al.: IEEE Trans. Nucl. Sci. 2007, 54: 1931. and references therein and references therein
Lucovsky G: Phys. Status Solid A. 2009, 206: 915. COI number [1:CAS:528:DC%2BD1MXntVSntr8%3D]; Bibcode number [2009PSSAR.206..915L] COI number [1:CAS:528:DC%2BD1MXntVSntr8%3D]; Bibcode number [2009PSSAR.206..915L] 10.1002/pssa.200881312
Hattangady SV, et al.: J. Vac. Technol. A. 1996, 14: 3017. COI number [1:CAS:528:DyaK28Xntlalt7c%3D]; Bibcode number [1996JVST...14.3017H] COI number [1:CAS:528:DyaK28Xntlalt7c%3D]; Bibcode number [1996JVST...14.3017H] 10.1116/1.580165
Wu Y, et al.: IEEE Trans. Electron. Devices. 2000, 47: 1361. COI number [1:CAS:528:DC%2BD3cXltl2ls78%3D]; Bibcode number [2000ITED...47.1361W] COI number [1:CAS:528:DC%2BD3cXltl2ls78%3D]; Bibcode number [2000ITED...47.1361W] 10.1109/16.848278
Lucovsky G, Phillips JC: J. Phys. Condens. Mater.. 2007, 19: 455218. Bibcode number [2007JPCM...19S5218L] Bibcode number [2007JPCM...19S5218L] 10.1088/09538984/19/45/455218
Acknowledgments
One of the authors (G. L.) acknowledges support from the AFOSR, SRC, DTRA and NSF.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Lucovsky, G., Phillips, J.C. Nanoregime Length Scales Extracted from the First Sharp Diffraction Peak in Noncrystalline SiO_{2} and Related Materials: Device Applications. Nanoscale Res Lett 5, 550 (2010). https://doi.org/10.1007/s1167100995206
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s1167100995206
Keywords
 Noncrystalline materials
 Nanocrystalline thin films
 Nanocrystalline/noncrystalline composites
 Chemical bonding selforganizations
 Percolation theory