Defining the Role of Silicon Substrate Orientation on the

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The Role of Silicon Substrate Orientation on The Microstructure, Texture and Stresses in Poly-crystalline Diamond Film Lokendra Jain, K.V. Mani Krishnan, Aditya Prasad, Hitesh Mehtani, Devi Shanker Misra, Abha Misra, and Indradev Samajdar Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b00853 • Publication Date (Web): 22 Aug 2017 Downloaded from http://pubs.acs.org on August 26, 2017

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Crystal Growth & Design

Defining the Role of Silicon Substrate Orientation on the Poly-crystalline Diamond Film: A Novel Approach for Characterizing Faceted Microstructures L. Jain1, K.V. Mani Krishna2, Aditya Prasad3, H. K. Mehtani5, D. S. Misra1, Abha Misra4 and I. Samajdar5 1

Department of Physics, Indian Institute of Technology Bombay, Mumbai-400 076, India Materials Science Division, Bhabha Atomic Research Center, Trombay, Mumbai, India 3 Department of Metallurgical & Materials Engineering, IIT Kanpur, India 4 Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, Karnataka, India 5 Department of Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, India. 2

Abstract Poly-crystalline diamond films (~10 micron thick) were grown on five different silicon (Si) substrate orientations by microwave plasma chemical vapor deposition (MPCVD). The selected Si substrates had a range of f(θ): 0.18 to 0.65. It is to be noted that f(θ) scales inversely with the packing density of the interface. As f(θ) decreased, three changes in the polycrystalline diamond microstructures were observed. (i) At the film surface -fiber texture increased but fiber dropped. (ii) A novel reconstruction technique was proposed and tested for faceted microstructures. The reconstructed microstructures revealed that the observed texture changes, with decrease in f(θ), was accompanied by elimination of very fine facets. (iii) Noticeable differences in Raman estimated stress gradients were also observed: lowest stress gradients for more closed packed substrates. Keywords: Polycrystalline Diamond Film, Chemical Vapor Deposition, Crystallographic Texture, Residual Stress, Faceted Microstructure.

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Introduction: In a year 2000 review on “diamond thin films: a 21st century material” [1], May highlighted the applications, present as well as potential, of this novel artificial material. This was also the year when cost of CVD (chemical vapor deposited) diamond fell below 1 dollar: opening up further possibilities for a variety of interesting applications. The applications of artificial diamonds depend on the microstructure [2-9]. For example, Telling and Field [9] showed clear orientation and grain size dependence of fracture/erosion in the polycrystalline diamond film. Ascheulov et al [4], on the other hand, used polycrystalline diamond coating on the Zircaloy-2 clads to retard oxidation and hydrogen ingress. All such exciting technological applications, however, depend on controlling the microstructure evolution of the diamond film. Naturally, there are extensive scientific studies [4,6-13] on the microstructure control of polycrystalline diamond. Microstructure control can be achieved by controlling the nature of the substrate and/or the process. Combinations of cost, availability and favorable properties have made single-crystal silicon (Si) wafers the favored substrate for CVD deposition of polycrystalline diamond films [14-18]. However, depositions have also been successfully attempted on other substrates: namely, Mo [2,3], Cu [19-21], Pt [22-25], Ni [26,27], and steel [28-31]. It is to be noted that the substrate needs to be capable of forming an intermediate layer for achieving a good bonding [1,15,16]. With Si substrate, the intermediate layer is reported to be carbide [16]. Copper and platinum substrates [19,20], on the other hand, were shown to form an intermediate layer of graphite and even a small amount of amorphous carbon [19,20]. It appears that diamond seed, provided on the substrate, transforms to the intermediate layer and later this promotes nucleation of diamond grains [1,15,16,21]. Wild et al [7] made a classical observation on the through


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thickness texture gradients. It was reported that random grains nucleated first, while growth selection (and texturing) [7,8,10-13] took place later. It is important to note, as pointed out by Jiang et al [19], the diamond grains (on a Pt substrate) have an OR (orientation relationship) with graphite: (0002)graphite//(111)diamond. It is hence expected, and also reported by various researchers, that control of substrate roughness [14,18] or orientation [15-17,23] may affect the crystallographic texture and microstructure of the diamond film. For example, roughening of Si substrate was shown to enhance nucleation sites [14]; while Lee et al [15] stipulated that the conditions of carburization and substrate orientations were critical for the microstructural evolution. More definitive evidence on the effects of substrate orientation, the so-called ‘epitaxial tilting’, on the texture/microstructure/stresses has been shown by Plitzko et al [16]. Chen et al [17], on the other hand, had reported clear difference in the surface morphology of the diamond film based on the orientation of the Si substrate ((111) versus (100)). Further, the intermediate carbide layer not only promotes growth of diamond but also provides partial stress relief at the interface [32]. The state of stress in polycrystalline diamond thin films is an important aspect. There are stresses from thermal mismatch between the substrate-film and the growth or intrinsic stresses [33-36]. It has been shown [37], through finite element simulations, that intense concentration of normal and shear stress may lead to failure. Experimental data also showed clear evidences of film rupture with the change in intrinsic stresses (from compressive to tensile) [37,38] and/or with clear developments in growth induced anisotropic residual shear stresses [8]. Though there are phenomenological evidences relating the nature of the substrate (substrate orientation, roughness and curvature) with adhesion or stability of polycrystalline diamond film, the available data is not really comprehensive.



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There is a large body of literature on the nature of the substrate and the quality of the microstructure: crystallographic texture, morphology of diamond grains and residual stress. However, these are not systematic. For example, there has never been an attempt to systematically and significantly alter the substrate orientation and relate the same with different aspects of microstructure in the as-deposited (under identical conditions) polycrystalline diamond films. Similarly, no information is available on the possible changes in terms of preferred nucleation and/or growth of the diamond grains. This has been the motivation behind the present study. In this study, polycrystalline diamond films were deposited on different Si substrates. The selected substrates had large differences in the closed-packed nature of the surface on which coating was performed. The depositions were undertaken under identical parameters, and films of similar thickness were produced on different silicon substrate orientations. A systematic study on the microstructure, texture and through-thickness intrinsic stresses (measured from Raman peak shift) was then performed. In addition, a novel reconstruction technique was proposed, and tested, for faceted poly-crystalline diamond microstructure. The technique was then used to establish, phenomenologically, the role of substrate orientation on the microstructural evolution: especially on the facet size distribution. Experimental Details: Polycrystalline diamond films were grown in a 2 kW and 2.45 GHz microwave plasma chemical vapor deposition (MPCVD) reactor. MPCVD based diamond growth is a well-established technique and has been used extensively [8,11,35,36] for both single and polycrystalline diamond film deposition. For this study, five different Silicon (Si) substrates, for details refer


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table 1, were used. Prior to the deposition, the substrate surfaces were scratched thoroughly with 0.2 µm diamond powder. The substrates did not have any differences in surface chemistry, as they were cleaned with hydrofluoric acid and de-ionized water before putting them into the deposition chamber. They also had similar (see table 1) surface roughness values and identical size (~720 µm thickness). Pressure and, temperature for all 5 depositions, were kept at 110 torr and 840°C, respectively. The flow rates of the methane/hydrogen mix were also kept the same between all five depositions. The final products were hence five different diamond films, grown under identical deposition parameters, in five different Si substrates. It is unknown if the growth rate differed with silicon substrate orientations. All the substrates were deposited together, and an approximate film thickness of ~10 µm was achieved independent of the substrate orientation. However, a future study to explore the growth kinetics, with different substrate orientations and deposition parameters, seems warranted. Scratching the silicon substrate with fine diamond powder is a prerequisite for typical heteroepitaxial deposition of polycrystalline diamond films [1]. And this was used in the present study. Of course, an alternate technique of biased enhanced nucleation [1] exists which can be used to grow polycrystalline diamond films without the need for diamond seeds. However, the authors do not have expertise on this technique and it was not used. The polycrystalline diamond films were subjected to detailed characterizations with EBSD (electron backscattered diffraction), X-ray bulk texture measurements, optical profilometry and intrinsic stresses (from Raman peak shifts). The EBSD measurements were made on a FeiTM Quanta-3D FEG (field emission gun) SEM (scanning electron microscope) with TSL-EDAXTM EBSD system. The SEM was operated at a low vacuum mode, and hence conducting coating was not necessary. Though sample roughness (or Ra values) varied from 218-235 nm, use of large



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working distance plus dynamic focus were effective in enabling EBSD scans of the polycrystalline as-deposited diamond without any sample preparation. It is to be noted that the same regions were also scanned with EBSD and surface profilometer (Zeta-20 optical profiler, of ZetaTM instruments). A novel technique for accurate estimation of facet sizes from the profilometric data of the surface (to be discussed later in the results and discussion) was proposed and tested. Crystallographic textures were measured by X-ray diffraction at the top-surface of the diamond films. These were performed in a Panalytical MRDTM system. The ODFs (orientation distribution function) were calculated by inversion of four incomplete pole figures. The series expansion method [39] and the computer programs MTM-FHM [40] were used for analyses. The inverse pole figures were estimated from respective ODFs. The volume fraction of different orientations was estimated by convoluting the X-ray ODFs (Orientation Distribution Function) using suitable model functions of 11° Gaussian spread [40]. Texture indices (TI) were estimated from

∫ [ f ( g )]

2

dg , where f(g) is the ODF intensity [41]. TI can be used as an index of relative

texturing/anisotropy. The Raman estimated stresses were calculated using a LabRam HR 800TM JobinYvon spectrometer with a 516 nm Ar+ ion laser, spectra were obtained in the range 1250-1360 cm-1. Along with the measured stress on the surface of the film, a depth profile was done with the step of 1 µm to calculate the Raman estimated stress from the entire volume of the deposited films.


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Results and Discussion: Selection of Silicon Substrates The motivation of this study was to explore the role, if any, of silicon (Si) substrate orientations on the evolution of crystallographic texture, microstructure and intrinsic stresses in MPCVD deposited (identical deposition condition) poly-crystalline diamond film. Naturally, the selection of the substrate orientations was critical. The substrates were obtained from poly-crystalline and single-crystalline Si. The former, as shown in figure 1a and collated in table 1, were in the form of very large Si grains (at least several millimeters in size) with different crystallographic orientations. The nature of these orientation, or their interfacial energy [42-44], is expected to scale with f(θ)1.

f(θ) =

---------------------------------(1)

where a is the lattice parameter and θ is the angle between closed-packed and non-closed packed planes. Other than the large grains from polycrystalline Si (figure 1a), single-crystal (001) Si wafer (figure 1b) was also used. As pointed out earlier, the substrates had identical dimensions, similar surface roughness (table 1). However, the GOS (grain orientation spread) differed significantly between the substrates. GOS is a measure of long-range misorientation. First the average orientation (quaternion average) of a grain or region (~1mm2) was estimated. Then deviations of all measurement points (in that region) were calculated with respect to the quaternion average. The average deviation represented the GOS value.

1

f(θ) is inverse proportional to the interface packing density.



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As shown in table 1, the GOS decreased with f(θ): from ~0.9 to ~0.4 °/mm2 as f(θ) changed from 0.65 to 0.18. In the next sections, data on texture/microstructure/stresses are presented on the polycrystalline diamond films grown on substrates with different f(θ) and GOS. Texture and Microstructure Figure 2a shows the crystallographic textures2, as respective IPFs (inverse pole figures), on the top-surface of the polycrystalline diamond film. Drop in f(θ), or increase in the closed packed nature of the Si substrate, clearly affected the texture: as there was a visible strengthening of the -fiber texture. The overall texture developments, as in figure 2b, can be generalized as increase in -fiber and drop in -fiber textures as f(θ) decreased. It is also important to note that these changes in the fiber volume fractions also affected texturing or anisotropy. The later has been often represented [41] as maximum ODF intensity (f(g)Max). As shown in figure 2c, f(g)Max increased from 2.3 to 3.9. This is not an insubstantial increase. However, f(g)Max can be strongly biased by texture symmetry [42], and texture index (TI) is a better representation of the overall anisotropy [41]. With decrease in f(θ), TI increased consistently but marginally: 1.3 to 1.6. In other words, significant differences in substrate f(θ) brought noticeable developments in constituent fiber textures (figures 2a and 2b), but relatively minor changes in texturing or anisotropy (figure 2c). Surface profilometer provided images of the top (~10 micron from the Si substrate) surfaces of the polycrystalline diamond films, see figure 3. Qualitatively the faceted microstructures did not appear to be significantly altered by significant changes (table 1) in the Si substrates. Any facet size measurements are, however, strongly biased by the facet-inclination. In this manuscript a 2

For further description on crystallographic texture, fiber texture, etc.; the reader may use the following reference [42].


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novel technique for characterization of faceted microstructures is proposed and tested. This is discussed in the next section. Later in this manuscript, this new technique was effectively utilized to deliberate on the microstructure evolution with respect to substrate orientation. A Novel Technique for Characterization of Faceted Structures In the context of the faceted microstructure relevant to this study, determination of the accurate size distribution of the facets is crucial. For this purpose, profilometric data were used. The idea was to compute the facet sizes by grouping all the connected points with similar plane normals (thus belonging to the same facet) within a user defined tolerance. This is somewhat similar to the popular technique of identification of grains based on the orientation at each pixel in the EBSD technique. However, the former requires accurate determination of the local plane normal at each of the measured profilometric data points. The determination of the local normal is very sensitive to the noise in profilometric data and may lead to significant errors in facet size estimation. Hence, a new scheme for the determination of accurate plane normal from a relatively noisy profilometric data of faceted microstructures was developed. The scheme is based on identifying the `critical data points' that minimize the `reconstruction error' to reproduce the features and microtextures of the faceted structures. The appendix describes this algorithm in details. This algorithm was then used on simulated as well as real data, and finally on the faceted diamond microstructures (next section). Figure 4 shows a simulated data of a pyramid, where a deliberate random noise was created. Naturally, the plane normal of the noisy/raw data had a very large scatter. After processing the noisy/raw data with the proposed algorithm, the data changed substantially. As shown in figure 4, the isometric view and the facet normal became extremely close (deviation of less than 1°) to



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the facet normal of a pyramid. The proposed algorithm was thus tested successfully against simulated raw/noisy data of a pyramid. It was then decided to test the algorithm against an actual object of a known geometry: a Knoop indenter (see figure 5). The measurements were performed with an optical profilometer at a step size of 0.093 µm and the machine Z resolution (∆Z) of 18 nm. The raw data was a scan consisting of 1024 × 768 measurement points, and as shown in figure 4, although the surface topology is captured well for visualization, the local plane normal as evaluated from the data can be seen to be very noisy. The same image could be faithfully reconstructed using a total of 9 ‘critical data points’ and the mean reconstruction error (̅) was less than 50 nm. Further, the computed facet normals were within 1° of deviation from the expected values. More specifically to this manuscript, the proposed algorithm not only generated accurate facet normal data, it also provided distribution of the facet area fraction versus size. This, as deliberated in the next section, was crucial for a discussion on the growth of faceted microstructures. Evolution of the Faceted Structure The algorithm was finally tested on actual diamond microstructures. As shown in figure 6, the reconstruction was very effective. The reconstruction, see figure 6a, brought about ‘sharpening’ of the profilometer image. It also showed that some of the finer facets (visible in the raw profilometer data) were actually artifacts. Naturally, and as shown in figure 6b, the reconstruction significantly changed the facet size distribution. For example, the raw data of diamond films on Si (100) substrate gave an average facet size of less than 1µm. The same data after reconstruction provided a facet size of ~ 2.4 µm. Qualitatively (figure 6c) and even quantitatively (figure 6d), there was a difference in facet size distribution with the Si substrate


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orientation. Si substrates with higher f(θ), or less closed-packed nature of the interface, had finer facets. As the f(θ) reduced, from 0.65 to 0.18 (see table 1), the average facet size reduced nominally (from ~2.4 to 2.1 µm) but many fine facets were eliminated. More specifically, with (18 13 21) Si substrate (f(θ) of 0.65) number fraction of facets below 0.5 µm size was 0.21. This reduced to only 0.12 with the substrate orientation changed to most closed packed nature, Si (100) with f(θ) of 0.18. In other words, the newly proposed and tested, reconstruction algorithm could establish a clear role of substrate orientation on the faceted microstructure of polycrystalline diamond film: increased closed-packed nature of the Si substrate led to the elimination of the finer facets of the poly-crystalline diamond microstructure. Intrinsic Stresses and Stress Gradients The nature of the Si substrate also affected the intrinsic stresses. As described elsewhere [8], intrinsic stresses in polycrystalline diamond films can be estimated from the shift of characteristic Raman peak (which comes at 1332 cm-1). As shown in figure 7a, the intrinsic stresses at the surfaces of the respective diamond films were always compressive. However, the magnitude of this compressive stress increased by ~3-times, as the f(θ) reduced. Raman focusing [22,24] also enabled through thickness stress measurements of the diamond films, see figure 7b. As expected [8,37,38], the compressive stress at the film surface transformed to tensile stresses towards the film-substrate interface. Such a conversion of intrinsic stresses has been reported in the past [8,33,38], and has been shown to originate from growth-induced stresses [8,33,38]. A strong stress gradient, or an anisotropic shear enforced by changes in growth directions [8], may enable film rupture plus severe plastic deformation of the silicon substrate. Such a failure will happen beyond a critical film thickness [8,34], which was much higher [8] than the film



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thickness used in this work. Figure 7c shows a strong dependence of the aforementioned stress gradient with silicon substrate orientation: reduced f(θ) provided a significant reduction in stress gradient. Summarizing the Influence of the Substrate Orientation This manuscript was initiated with an objective of systematic exploration of the role of silicon substrate orientation on the crystallographic texture, microstructure and stresses in polycrystalline diamond film. Such a relationship has been stipulated, even experimentally observed [14-18,45], in the past literature. This study wanted to explore the same comprehensively. The selected silicon substrate orientations (see figure 1 and table 1) had differences in their closed packed nature (packing density: as generalized by f(θ)) of the surface plane and also in the GOS. The f(θ) is expected [42] to scale (inversely) with solid-vapor interface energy (and packing density) of the Si. Otherwise, the nature of the substrates and the deposition parameters were kept identical. Decrease in f(θ), or increase in the closed packed nature of the Si substrate’s surface had three effects. (i) At the surface (10 micron from Si-diamond interface) -fiber texture increased, while -fiber dropped. (ii) Many of the fine facets, as validated through a novel reconstruction technique, disappeared. (iii) Through thickness gradients in intrinsic stresses diminished. An immediate question arises: are (i)-(iii) interrelated? Wild et al [7] made some interesting observations on facets and growth selection in polycrystalline diamond. They demonstrated that growth selection generates -fiber texture


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near film surface, while the nucleation near substrate-film interface was randomized. A rationalization on the growth selection appeared from the ‘suspected’ growth advantage for certain facets. Wild et al [7] showed that surface of the diamond film consisted of {111} facets. It is to be noted that these were stipulated as crystallographic faces, and did not involve any reconstruction. As deliberated earlier, the raw data, without reconstruction, may involve significant noise even on the facet normals. Calculating crystallographic facets is more difficult, as the solutions may have certain ambiguity, in the absence of the data of orientation of underlying crystal. The facet growth advantage was also explored through simulations by Smerka et al [46]. They showed {001} facets3 to grow faster than {100} facets. This manuscript, and with effective use of the reconstruction, the growth selection appeared to be enforced by elimination of the finer facets. It is important to appreciate the origin of the facets. There are two possibilities. They are, as Wild et al [7] had shown quite elegantly, individual diamond grain with geometrically necessary faces. The other possibility is that they are growth ledges. Observations on growth ledges or steps are common [47-51] in homoepitaxially grown shown single crystalline diamond. The frequencies of such ledges were affected by the doping and processing parameters [48,49,51,52]. The existing literature also showed that the presence of growth ledges enhanced growth kinetics and increased the internal stresses. The facets reported in this manuscript are often part of the same diamond grain or orientation. Hence they appear similar in nature as the growth ledges in single crystal diamond. Analytical models [53,54] had shown that ledges could reduce (~50%) the interfacial energy of {111}-diamond interface. Presence of dopants, and its stipulated influence on interfacial energy, 3

and this was in terms of the facet normal: same conventions as used in the present manuscript.



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may affect, significantly, the relative presence of the ledges [53,54]. As the ledge edge/corner acts as a source sink for vacancies, presence of ledges also affect the internal stresses and defect concentration [55]. It appears that the substrate f(θ) had also affected the presence of ledges: more ledges for the non-closed packed Si substrates. Absence of finer ledges, established through the novel reconstruction, naturally reduced the intrinsic stresses and provided a growth selection for the -fiber texture. Such model appears plausible. However, an explanation for substrate f(θ) being proportional to the frequency of the ledges in the diamond grains remains pending. Any such model needs to be strongly deliberated and tested (both experimentally and theoretically); though the present results remain reproducible, consistent and novel. Conclusion: This study involved five different silicon (Si) substrates and deposition of polycrystalline diamond films, of nearly the same (~10 µm) thickness, on these substrates under identical deposition conditions. The selected substrates had a range of f(θ) values (0.65 to 0.18), which is expected to be inversely proportional to the closed packed nature and energy of the respective interfaces. As the f(θ) decreased, or Si substrate became more closed packed, At the film surface -fiber texture increased and -fiber dropped. A novel reconstruction technique, proposed and tested in this manuscript, showed clear elimination of finer facets. These facets, part of the same grain or orientation, appeared similar to the growth ledges (commonly reported in single crystal diamond). Raman estimated through thickness intrinsic stress gradients reduced.


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It has been hypothized that all three experimental observations are related. Non-closed packed Si substrates surfaces encouraged more frequent ledges on individual diamond grains. The relative absence of growth ledges appeared to lead into growth selection (of -fiber texture) and lower gradients of intrinsic stresses. Though the proposed hypothesis needs to be further tested, the experimental results remain novel and reproducible.

Acknowledgement: Support from the National Facility of Texture & OIM (a DST-IRPHA facility at IIT Bombay) is acknowledged. Financial support from Department of Science and Technology (DST, India) is gratefully acknowledged. Authors also acknowledge the SAIF (Sophisticated Analytical Instruments Facility), IIT Bombay for the Raman measurements. Part financial support from DST is also acknowledged.

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Appendix Let us assume that a pyramidal feature (figure A1: typical in a faceted structure) has been scanned using a surface profilometer. The raw data will include height or elevation (Zm (x, y)) at every scan point ((x, y)). Let us also assume that the measured raw data contains a random noise proportional to the machine’s Z resolution (∆Z). Let Zt(x, y) represent the corresponding correct (true) height of the feature (figure A1). The measured height (Zm) can be expressed as, Zm = (∆Z)(r)(Zt)---------------------------------(i) where r is a random number such that − 1 ≤ r ≤ 1. As shown in figure A1, for a given ∆Z the error can be reduced by increasing the scan step size. However, coarse step size may result in missing the features altogether. In this manuscript, we proposed the following scheme for reconstructing the surface from a relatively noisy raw data. The idea behind this scheme is: for a given noise level in the height data, normals of the facets can be estimated with more accuracy by considering those points of the facet which are farther apart. The farthest spaced data points, however, need to be adequate to reconstruct the feature by interpolating the other ignored points. In other words, these are the most ‘critical data points’ (CDP) of any feature, which describe the shape of the real feature to closest approximation. This is shown in figure A1 as points Zm1, Zm5, Zm9. Accurate identification of the CDP involved



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estimation of ‘error’ committed in ignoring the ‘other’ measurement points. Appropriate CDP, from the existing profilometric raw data, can then be used to faithfully reconstruct the feature. In general, the profilometric data obtained from optical profilometer does contain noise. Two kinds of noise were observed. (1) Visually obvious erroneous points such as abrupt and extremely localized perturbations in height or elevation profile. (2) Random noise proportional to machine resolution limit (in height). Median filter is effective in removing the type (1) noise without introducing significant loss of information. The proposed algorithm effectively handles the second component of error or random noise. The proposed algorithm is illustrated in figure A2. First step was to initialize the reconstructed r

surface Z = Z

m (x, y)*

by considering only the bounding points ((x, y) *) or vertices (figure A1) of

the mesh represented by (x, y) of the profilometric data. The rest of the data points were then interpolated using a bilinear interpolation on to scan grid (x, y). Delauncy triangulation [56] m

using point set Z

(x, y)*

was used for the effective bilinear interpolation. Reconstruction error (ε

(x, y)), see figure A2, at each of the scan point (x, y) was estimated by comparing the r

m

interpolated points of the Z (x, y) with the actual measured points Z

(x, y).

The `critical data points'

(CDP) were the bounding points with maximum ε(x, y). The parameter δtol used for judging the stopping criterion was set proportional to expected noise level (∆Z). Since the CDPs were obtained by comparing the constructed surface with real measurement data points, they themselves had similar error. The CDPs also corresponded to inflections (or sudden change in slopes) in the real surface. The error from raw profilometric data was even more pronounced at these locations. By the nature of the present algorithm, plane normals estimation shall suffer less due to these errors in case of the facets whose dimensions are large. However, in


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case of the smaller features, these errors cannot be ignored. In order to further fine-tune the estimation of the facet normals, we employed a least square fitting procedure for finding out the m

plane normal of each of the facet. For this, we identified the measured data points (Z

(x, y))

belonging to each of the facet and then found the facet plane normal using least square fitting. The computed plane normals thus had contribution from each of the point lying in the facet and had less dependency on the measurement error of the `critical data points'. This algorithm was tested successfully against a simulated pyramid (figure 4) with artificially imposed noise, and also against a Knoop indenter (figure 5). Finally, the algorithm was applied on actually polycrystalline diamond microstructure (figure 6) with clear improvements of the features and facets plane normal measurements. The observed changes in diamond crystallographic texture (figure 2) was shown to relate with changes in facet frequency.



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(a)

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(b)

Figure 1: EBSD (electron backscattered diffraction) IPF (inverse pole figure) maps of (a) polycrystalline and (b) single-crystal silicon (Si) substrates used in this study. In (a), (18 13 21), (9 5 22), (6 5 9) and (5 4 11) Si grains (designated by respective plane normals) were present, while (b) represents (100) single-crystal Si. The IPF and unit cells of the Si substrate orientations are shown. These substrates were selected based on their f(θ) values, also refer table 1.


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(a)

(b)

(c)



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Figure 2: (a) IPF (inverse pole figure) plots of the crystallographic texture at the top-surface of the polycrystalline diamond films. From the X-ray ODFs (orientation distribution function), (b) volume fractions of -fiber and -fiber textures and (c) maximum ODF intensity and texture index (TI) values are estimated. These are plotted as a function of Si substrate orientations and f(θ) values.

(a)

(b)

(c)

(d)


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(e) Figure 3: Diamond film microstructures (from the top-surface: as obtained by surface profilometry) for different Si substrate orientations (see table 1) of: (a) Si (18 13 21), (b) Si (9 5 22), (c) Si (6 5 9), (d) Si (5 4 11), and (e) Si (1 0 0).

Figure 4: Demonstration of the algorithm in case of a simulated pyramid. The figure includes side (with respect to Z) and top (with respect to facet plane normal) views of both noisy and reconstructed data. Also included the respective facet normals (in pole figure representation) of the data sets.



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Figure 5: Demonstration of the algorithm in case of a Knoop indenter. Included are raw and reconstructed data for grey scale image and facet normal.


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(a)



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(b)

(c)


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(d)

Figure 6: (a) Raw and reconstructed data of diamond films grown on silicon (100) substrate. These include surface profilometer images, and combined profilometer plus EBSD data on facet plane normal. Reconstruction clearly improved clarity of the features/facets (as shown with the insets) and (b) refined the facet size distribution. This is shown as area fraction versus facet size for raw and reconstructed data. (c) Reconstructed profilometer plus EBSD images and (d) area fraction versus facet size for diamond films grown on (100) and (18 13 21) silicon substrates.

(a)



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(b)

(c)

Figure 7: (a) Raman estimated internal stress at the surface of the diamond film grown with different Si substrate. Two extreme Raman peaks are included for reference. (b) Raman stresses are also shown at different depths (from surface). (c) Estimated (from (b)) stress gradients for different Si substrate. Reconstructed surface

Z5t

Original Surface Surface based on raw data

Z5m

Normal of Reconstructed surface Normal of Original surface

(r)∆Ζ

x1 Z1m

x2

x3

x4 (Z r)

Reconstructed data Ideal data (Z t) Raw data(Z m)

Normal of surface from raw data

x5

x6

x7

∆x

x8

x9 Z9m

Figure A1: Schematic illustrating the effect of noise in the profilometric data on the computed m m normals. Considering the noise present in the measured data, it is clear that points Z 1, Z 5,

Zm9 faithfully describe the actual surface and thus can be considered as ‘critical data points’. More importantly, the local normals determined using the surface reconstructed (red arrows) from these ‘critical data points’ lie very close to the actual normals (green arrows), in contrast to local normals computed from the raw data (black arrows).


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Figure A2: Flow chart explaining the algorithm for surface reconstruction. Here, (x,y)*p denotes the set of 'critical data points' for the current iteration, which will be added to existing set of the `critical data points' ((x,y)* ) if the stopping criteria (achieving mean reconstruction error (є ) less tol than user specified tolerance ( δ ).

Substrate orientation

Unit cell representation

f(θ)

Grain Orientation Spread (GOS: in °/mm2)

Surface Roughness Ra(nm)

Tabl e 1: Diffe rent silico n (Si) subst rate orien tations, used for the growth of poly-crystalline diamond films, are listed. The table includes plane normal of the Si substrates, schematic of the unit cell and f(θ). f(θ) =

[42], where a

is the lattice parameter and θ is the angle between closed-packed and non-closed packed planes. f(θ) is a measure of the closed-packed nature (or packing density) of the interface and is expected [42-44] to scale with the interfacial energy. Also included are the grain orientation spread (GOS) and surface roughness of the respective Si substrates.


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Si (18 13 21 )

0.65

0.92

225

Si (9 5 22)

0.62

0.84

218

Si (6 5 9)

0.50

0.72

230

Si (5 4 11)

0.43

0.45

220

Si (1 0 0)

0.18

0.41

235

"For Table of Contents Use Only,"

Manuscript title: Defining the Role of Silicon Substrate Orientation on the Poly-crystalline Diamond Film: A Novel Approach for Characterizing Faceted Microstructures Authors List: L. Jain1, K.V. Mani Krishna2, Aditya Prasad3, H. K. Mehtani5, D. S. Misra1, Abha Misra4 and I. Samajdar5 1

Department of Physics, Indian Institute of Technology Bombay, Mumbai-400 076, India Materials Science Division, Bhabha Atomic Research Center, Trombay, Mumbai, India

2



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3

Department of Metallurgical & Materials Engineering, IIT Kanpur, India Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, Karnataka, India 5 Department of Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, India. 4

TOC Graphic:

Raw and reconstructed data of diamond films grown on silicon (100) substrate. These include surface profilometer images, and combined profilometer plus EBSD data on facet plane normal. Reconstruction clearly improved clarity of the features/facets (as shown with the insets)

Synopsis: This study involved five different silicon (Si) substrates and deposition of polycrystalline diamond films, of nearly the same (~10 µm) thickness, on these substrates under identical deposition conditions. The selected substrates had a range of f(θ) values (0.65 to 0.18), which is expected to be inversely proportional to the closed packed nature and energy of the respective interfaces. As the f(θ) decreased, or Si substrate became more closed packed,


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At the film surface -fiber texture increased and -fiber dropped. A novel reconstruction technique, proposed and tested in this manuscript, showed clear elimination of finer facets. These facets, part of the same grain or orientation, appeared similar to the growth ledges (commonly reported in single crystal diamond). Raman estimated through thickness intrinsic stress gradients reduced. It has been hypothized that all three experimental observations are related. Non-closed packed Si substrates surfaces encouraged more frequent ledges on individual diamond grains. The relative absence of growth ledges appeared to lead into growth selection (of -fiber texture) and lower gradients of intrinsic stresses. Though the proposed hypothesis needs to be further tested, the experimental results remain novel and reproducible.


Defining the Role of Silicon Substrate Orientation on the

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