Rupture of Polycrystalline Diamond Film: Defining Role

Article pubs.acs.org/crystal

Delamination/Rupture of Polycrystalline Diamond Film: Defining Role of Shear Anisotropy L. Jain,† Reeti Bajpai,† Ritwik Basu,‡ Devi Shanker Misra,† and Indradev Samajdar*,‡ †

Department of Physics and ‡Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400 076, India S Supporting Information *

ABSTRACT: Polycrystalline diamond films were synthesized by microwave plasma chemical vapor deposition. Films were mechanically stable until 30 μm thickness, while further deposition led to catastrophic film delamination and rupture. This coincided with fracture of the single-crystal silicon substrate, creating polycrystalline silicon with clear shear markings. Films grown to 12, 18, 21, and 30 μm were subjected to detailed investigations. Larger film thickness modified intrinsic stresses (estimated from Raman shift) from mildly compressive to strongly tensile. However, normal in-plane residual stresses and dislocation densities, as estimated from X-ray diffraction, dropped. Film growth enhanced anisotropies in crystallographic texture brought changes to grain morphology and significantly increased out-of-plane residual shear stress. Though different models of film delamination/rupture were deliberated, they fail to assimilate all aspects of experimental observations. Shear anisotropy-induced lateral stresses, on the other hand, can explain film rupture and relate the same with substrate/film microstructural developments. stress measurements remains nontrivial.16 The reason, though obvious, is rarely highlighted in literature. The mechanical measurements estimate total stress: elastic stresses and its possible relaxation through ‘minor’ plasticity.25 Diffraction measurements typically estimate changes in interplanar spacing and hence are purely elastic in nature.12,15,20,22 Raman peak shifts, and often referred6,11,12 intrinsic stresses, are an indirect estimation of both elastic stresses and elasto-plastic effects of crystallographic flaws present.19 Another neglected aspect of stress, in thin-film research, is the tensorial nature. A standard22 biaxial X-ray stress measurement can estimate in-plane normal stresses and out-of-plane shear stresses. In the analysis of film instabilities, however, the approach of biaxial stress measurements is rarely used. The ‘conventional’ thinking is to consider the role of total stresses6,11,12 or stress gradients.7 Though arguments are also extended26 to the role of ‘lateral’ stresses, the possible effects of out-of-plane shear remain neglected. This was the motivation behind the present study: quantification of through thickness residual stress components and their implications on film instability.

1. INTRODUCTION The quality of thin films,1−3 in particular diamond films,4−10 is often attributed to the state of residual stress. For example, insufficient mechanical stability of films has been related to total and/or thermal stresses1,6,8,11 and also to developments of hoop stress.7 Stresses in films are viewed either as compressivetensile or intrinsic-thermal.1,3,5,6,8,10−17 The former refers to the vectorial nature of the in-plane stresses. Thermal stresses represent a mismatch between coefficient of thermal expansions of substrate and film and can be evaluated numerically.6,8 It is important to appreciate the meaning of intrinsic stresses. There are two possible definitions: (i) nonthermal stresses existing without application of a load18 and (ii) stresses arising through accumulation of crystallographic flaws.19 All of these stresses develop through processing and often exhibit strong correlation(s) with microstructure.3,5,7,9,14,20 Almost any thin-film research, including the present study, considers through thickness stress developments as of critical importance. It is thus important to evaluate experimental capabilities/limitations of stress measurements.21−23 Stresses can be estimated by mechanical response, from diffraction, and through property changes. Thin-film research has some excellent examples of all three. Examples of the mechanical response include measurements through indentations1,24 and bend tests,2,9 strain gauge interferometry,3 and curvature measurements.6,12 X-ray and neutron diffractions can offer12,15,20,22 the entire residual stress tensor, while Raman peak shifts estimate stresses through intrinsic changes in the state of atomic vibrations.10,12 A quantitative comparison between different © 2017 American Chemical Society

2. EXPERIMENTAL METHODS Polycrystalline diamond films were grown in a 2 kW and 2.45 GHz microwave plasma chemical vapor deposition (MPCVD) reactor. This study used a single-crystal (100) silicon wafer: 720 μm thick and Received: September 8, 2016 Revised: February 8, 2017 Published: March 6, 2017 1514

DOI: 10.1021/acs.cgd.6b01328 Cryst. Growth Des. 2017, 17, 1514−1523

Crystal Growth & Design

Article

Figure 1. (a) Angular conventions (with respect to specimen, X-ray source, and detector) used for the XRD measurements (texture, stress, and line profiles). The same conventions are also represented, schematically, in terms of rotations between laboratory (L) and specimen (S) coordinate systems. (b) Schematic of the tensorial components of the film residual stress: includes both normal (σ11, σ22, and σ33) and shear (τ12, τ13, and τ23) components of the stress tensor. 203 mm in diameter. The single wafer was cleaved into smaller pieces of approximately 150 mm2 area. The mirror polished cleaved pieces were scratched with 0.1 μm diamond powder. This process provides diamond powder seeds: an essential step11,12 in generating nucleation centers for the subsequent heteroepitaxial diamond film growth. Two points need to be noted. First, all of the substrates had similar surface roughness. The substrates are not expected (nor observed) to have differences in surface chemistry (before MPCVD, the substrates were cleaned with hydrofluoric acid and deionized water). Second, a similar process has been used earlier11,12,16,17 for MPCVD-based diamond growth. Temperature and pressure, for the MPCVD process, were kept at 850 °C and 110 Torr, respectively, while different deposition time periods were used. Table 1S (Supporting Information) provides a summary of deposition time periods and corresponding values of the film thicknesses. The samples, with different film thicknesses (12, 18, 21, and 30 μm), were then subjected to detailed X-ray diffraction (XRD) measurements. XRD measurements were performed on a Panalytical MRD system with an Eulerian cradle (four-circle goniometer) using Cu Kα radiation. Suitable X-ray optics allowed accurate and reproducible measurements. An X-ray lens (Polycap) was used on the incident beam (point focus: 2 mm × 2 mm) side, while a curved crystal monochromator plus multichannel solid-state area detector (Pixel) were deployed on the diffracted beam side. XRD data were used for residual stress,16,21,27,28 crystallographic texture,25,29,30 and peak profile25,31,32 estimations. For texture, four XRD pole figures [(110), (111), (100), and (311)] were measured in standard25,29,30 reflection mode. Both background and powder corrections were employed. For the latter standard, a 0.1 μm diamond powder was used. The orientation distribution functions (ODFs) were calculated by inversion of the pole figures. The series expansion method29 and the computer programs MTM-FHM,30 where FHM represents the fast harmonic method, were used. ODF data were further analyzed to plot inverse pole figures (IPFs), relative texturing, and volume fractions of ideal (110) (100), (111), (311) orientations (or corresponding ND// ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨311⟩ fibers).

Volume fractions were estimated by convoluting the respective ODFs with suitable model functions, with an integrated ODF value of 1 and which used a 11° Gaussian spread. Both maximum ODF intensities and more accurate texture index (TI)33−35 values were used to describe relative texturing of the films. TI =

∫ [f (g )]2 dg

(1)

where f(g) is the ODF intensity. In this study, two procedures for residual stress measurements were employed: the standard single-pole d-sin2ψ21,22,27,28 and multiple poles grazing incident X-ray diffraction (GIXRD).15,22,27 For further discussion on residual stress measurements/analysis, it is important to highlight the angular and stress conventions (see Figure 1). The measurement direction (direction of the diffraction vector) is defined22 by the rotation angle ϕ (around the specimen surface normal) and the tilt angle ψ (angle of inclination of the specimen surface normal with respect to the diffraction vector). On the other hand, ω is the incident angle between the incident beam and specimen surface. These angles are shown in Figure 1a. The stresses are shown, see Figure 1b, as tensorial components: σii for normal stress and τij for the shear counterparts. To determine residual stresses, appropriate interplanar spacings (dhkl θψ ) need to be measured. dhkl(ψ , φ) = d0[1 + S1(σ11 + σ12) + 1/2S2σφ sin 2 ψ ]

(2)

where S1 and S2 are elasticity parameters, which can be related to the Poisson’s ration υ and Young’s modulus E:

S1 = − υ/E

(3)

and

S2 = (1 + υ)/E

(4)

Normal and shear stresses are taken as

σφ = σ11 cos2 φ + σ12 sin(2φ) + σ22 sin 2 φ 1515

(5)



Article

Figure 2. Polycrystalline diamond films grown to (a) 30 (30 h), (b) 32 (32 h), and (c) 34 (34 h) μm film thicknesses. (b) A ruptured film exposing the silicon substrate, while a ruptured silicon substrate is visible in (c). Also included are the electron micrographs of the diamond films corresponding to (a) and (b).

τφ = τ13 cos φ + τ23 sin φ

affected by grain size, only if such grain sizes are in the nm range.25 As the present diamond film had grain sizes in μm (as shown in the latter), eq 9 can be taken as representing the defect/dislocation densities of the film. Electron backscattered diffraction (EBSD) sample preparation and measurements were done in a Fei Quanta-3dFeg dual beam field emission gun (FEG) scanning electron microscope (SEM). For the cross-sectional sample preparation, the focused ion beam (FIB) source of Ga+ ions at 30 keV and 0.1 nA was used. EBSD measurements were taken, under low (60 Pascal) vacuum, in a TSL-EDX OIM EBSD system. The Raman spectra were obtained in the range of 1250−1360 cm−1 using a LabRam HR 800 JobinYvon spectrometer with a 516 nm Ar+ ion laser.

(6)

For d-sin2ψ measurements, ±40° ψ was used. The slopes and ψ-splitting of the d-sin2ψ plots determined21,22,27,28 respective values of σii and τij. GIXRD, on the other hand, was performed over a fixed ω,15,22,27 and ω is expected to determine the depth of penetration (κ) as,

κ = (sin 2 θ − sin 2 ψ )/(2μ sin θ cos ψ )

(7)

where μ is the mass absorption coefficient, and ω decides ψ from pure geometry:

ψ=ω−θ

(8)

Thus, from the different poles, different d-spacing and ψ values can be estimated. GIXRD is also capable of measuring σii and τij for all poles and at different κ values. It needs to be noted that GIXRD estimates effective or overall d-shift and hence offers orientation-independent mean stresses. Both d-sin2ψ and multiple {hkl} GIXRD used biaxial stress analysis,22 involving measurements at ϕ = 0, 45, and 90°. The analysis also involved Reuss21,25 as the continuum elasticity model, E = 1080 GPa, and υ = 0.1. All stress analysis was performed using a commercial software: X’Pert Stress Plus. Dislocation densities were measured from the X-ray line profiles by using the momentum method.25,31,32 The fourth-order restricted moments of the X-ray line profiles has the form:31

M4(q) q2

=

Λ⟨p⟩ 3Λ2⟨p⟩2 2⎛ q ⎞ 1 q ln ⎜⎜ ⎟⎟ + + 3π 2εF 4π 2 4π 2q2 ⎝ q1 ⎠

3. RESULTS As shown in Figure 2, beyond 30 μm film thickness, clear delamination/rupture of the diamond films (Figure 2b) was noted. This was observed in the deposition chamber, during or immediately after the deposition. The rupture of the films also led to fracture of the silicon substrate (Figure 2c). However, the film microstructures (SEM micrographs taken at the top surface of the film, see Figure 2) did not appear to change with deposition time. Figure 3 collates a few of the GIXRD measurements in the specimen with 30 μm film thickness. GIXRD has an advantage over the conventional sin2Ψ method, as one can measure the stresses at different depths of the specimen by changing the incident angle ω, see eq 7. Figure 3 shows the intensity-2θ plots obtained at different ω values. The figure also shows Si peak(s) at an estimated [eq 7] X-ray penetration (κ) of ∼30 μm, while no such peak was noted for κ of 28 μm. This validates eq 7 for the given material and angular conventions. More importantly, Figure 3 and Table 1 also establish changes in stress patterns: • Stress (σ11) transformation from compressive to tensile, as depth of penetration reduced from 30 to top 10 μm.

(9)

4π

where, q = λ (sin θ − sin θ0), εF is the average column length or the area weighted particle size measured in the direction of the diffraction vector g, K is the Scherrer constant, L is the taper parameter, ⟨p⟩ is the average of the square of the dislocation density, q0 and q1 are the fitting parameters not interpreted physically, Λ is a geometrical constant describing the strength of the dislocation contrast, and θ0 is the exact Bragg angle. The dislocation density is calculated by fitting eq 9 to the M (q) linear part of 42 .31 It may be noted that the formulation can be q

1516



Article

drop in estimated dislocation densities with increasing film thickness. This coincided, as in Figure 4b, with both a narrowing and shift (from standard Raman peak of 1332 cm−1) in Raman peaks. The intrinsic stresses were estimated10 as intrinsic stresses = − 1.08(υm − υo)(Gpa)

(10)

−1

where υo = 1332 cm , and υm is the measured peak position. Laser Raman analysis established that mildly compressive stresses (−0.28 GPa) were present in the lowest film thickness of 12 μm, see Table 2. This changed to strong tensile stresses Table 2. Thermal, Raman, and Total Stresses Estimated for Different Film Thicknesses

Figure 3. GIXRD normal (σϕ) and shear (τϕ) stress estimations at different ω and correspondingly different κ (depth of penetration). The measurements, made on 30 μm diamond film, show the presence of a Si (311) peak only at the estimated κ of 30 μm, thereby confirming effectiveness of [eq 7]. (For interpretation of color, reader may consult the web version.)

10 308 1318

15 235 988

20 72 785

25 −107 378

12 μm

18 μm

21 μm

30 μm

thermal stress (Appendix) Raman estimated intrinsic stress total stress

−1.32 −0.28 −1.6

−1.32 0.32 −1

−1.32 1.77 0.45

−1.32 2.89 1.57

(+2.89 GPa) when the film thickness was at 30 μm. Depth profiling through GIXRD, Table 1, also revealed a qualitatively similar pattern. It is clear that both σ11 (GIXRD) and intrinsic (Raman) stresses changed from compressive to tensile with an increase in film thickness. This is in agreement with published literature.10,16 However, Raman analysis estimated significantly higher stress values than the GIXRD. This point needs to be deliberated. Raman spectroscopy had a typical depth of penetration of 1 μm, and measurements were taken from the top surface of the respective films. GIXRD, on the other hand, offered cumulative stresses over a relatively large (see Table 1) depth of penetration κ. Second, GIXRD measured only σ11, while Raman analysis is expected to estimate overall intrinsic stresses. These two factors appear to rationalize the higher stresses estimated in Raman analysis. Before presenting results on X-ray texture and d-sin2ψ stress measurements, it is important to point out the low mass absorption coefficient (μ) of diamond assures, in the absence of glancing incidence mode, penetration over the entire film thicknesses (12−30 μm). Hence texture/d-sin2ψ stress measurements on the respective samples represent “average” data for the corresponding films (12−30 μm thickness).

Table 1. GIXRD Estimated σ11 and τ13a depth (κ in μm) σ11 (MPa) τ13 (MPa)

thickness

30 −471 144

These measurements were obtained from 30 μm film (as in Figure 3). Depth of X-ray penetration (κ) was obtained from eq 7. As indicated in Figure 3, validity of eq 7 was established from the appearance of a Si peak at κ ≥ 30 μm.

a

• A large increase in the τ13: 0.14 GPa for the entire 30 μm film versus 1.32 GPa for the top 10 μm. This appears to be first report on a significant increase in out of plane residual shear stress τ13. Results obtained for GIXRD were further confirmed when samples grown to different film thicknesses (12−30 μm) were subjected to X-ray line profile (Figure 4a) and Raman peak shift (Figure 4b) analysis, see Figure 4. Figure 4a describes a clear

Figure 4. (a) Estimated dislocation densities and (b) Raman spectra for films grown to different thicknesses (12−30 μm). The dislocation densities were estimated from X-ray line profiles [eq 9]. As exact magnitude for dislocation density requires additional “calibration”, the lowest dislocation density was taken as “1”, and other values were normalized. In (b), intrinsic stresses were estimated [eq 10] from the Raman spectra. 1517



Article

Figure 5. (a) IPFs, estimated from X-ray ODFs (orientation distribution functions), for films grown to different thicknesses. Contour levels are drawn at 1, 1.5, 2, 3, 4, 6, 7, 15, 22, and 32 times random. From the respective ODFs, (b) volume fractions of the major fibers (ND// ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨311⟩), (c) texture index (eq 1), and maximum ODF intensities were calculated and then plotted against film thickness.

compressive for 12 mm film thickness, while for the entire 30 μm film thickness, this reversed. Some of these aspects are deliberated further in the Discussion section. GIXRD measurements, Figure 7, came up with additional information on shear anisotropy. These measurements were obtained from diamond films grown to different thicknesses. The incident angle, ω, and corresponding penetration depth, κ, were suitably adjusted to cover the entire film thickness (appearance/disappearance of Si peak, as in Figure 3, was used as verification). At the higher film thicknesses, of 21 and 30 μm, τϕ was negative until 150° ϕ and positive for 150° > ϕ < 330°: an interesting transition in the positive or negative τϕ at an approximate angle of 30° with S1 (Figure 1a). It also needs to be noted that average positive and negative τϕ were nearly identical. An indirect implication of the large out-of-plane shear stresses is seen in Figure 8. At the beginning, Figure 8a, substrate was near (100) single-crystal silicon. This appeared smooth under backscattered imaging. After film delamination and rupture, on the other hand, the silicon substrate had clear shear markings and “turned” polycrystalline, see Figure 8b. The shear markings had two interesting features. First, they had an approximate morphological angle of ϕ = 30°; the same angle where τϕ was observed to reverse sign (Figure 7). Second, shear markings were associated with presence of misorientations, see Figure 8d. In EBSD data, local misorientaions can be measured as kernel average misorientation or KAM values. KAM represents misorientations by each measurement point and its immediate neighbors (six in case of the hexagonal grid used in this study). In the original substrate (Figure 8c), KAM was below 0.5°, the measurement uncertainty of the EBSD system. After film delamination (Figure 8d), on the other hand, KAM values increased; higher KAM regions defining the ϕ = 30° shear markings. EBSD measurements also brought out differences in microstructure with film thickness, see Figure 9. At the beginning

Figure 5a shows the bulk crystallographic textures in IPF notation. Texture changes (Figure 5a) can be further described in terms of changes in the volume fractions of the ideal fibers (Figure 5b) and relative texturing or anisotropy (Figure 5c). As the film thickness increased from 12 to 21 μm, ND//⟨110⟩ (or (110) pole) increased, while ND//⟨100⟩ and ⟨311⟩ dropped. For all the stages of film growth, (111) remained a relatively insignificant orientation. Changes in volume fraction accompanied changes in texture indices and maximum ODF intensities. Both increased with an increase in film thickness. In a word, film growth enhanced texturing or anisotropy. To bring out its effects on anisotropy of residual stresses, conventional d-sin2ψ stresses were measured for the available crystallographic poles. Figure 6 collates residual stress measurements, for different poles, with standard d-sin2ψ. The d-sin2ψ stress measurements demand sufficient peak intensities at extreme ψ-tilts, and reliable measurements were possible only for three crystallographic poles: (111), (110), and (311). Both in-plane normal stresses (σ11, 1/2(σ11 + σ22) + σ12, σ22) (see Figure 6a) and out-of-plane shear stresses (τ13, + 1√2 (τ13 + τ23)τ23) (see Figure 6b) were measured. They also had striking differences. Average and standard deviations of normal (σϕ) stresses dropped with increase in film thickness. [Standard deviations can be taken as a measure of rotational (ϕ rotations) anisotropy.] For the out-of-plane shear (τϕ), on the other hand, a significant increase was noted for (111) pole. For the other two poles, the values remained nearly the same. Though X-ray texture revealed that (111) was a minority texture component, it is apparent that a strong, and anisotropic, τϕ for (111) was also responsible for the GIXRD estimated (Table 1) significant gain in out-of-plane shear. The drop and increase in average/ standard deviation values were not truly monotonic, and there were interesting differences in the sign of the estimated stresses. For example, (110) and (311) σϕ were, respectively, tensile and 1518



Article

ratios were modified (11 μm and 5.1 aspect ratio), and they became inclined at an approximate angle of 30° with the ND. Such a change in morphology is not unexpected,36,37 but possible correspondence to intrinsic stresses and out-of-plane shear needs further deliberation.

4. DISCUSSION Single crystal silicon wafers remain the most common substrate for growth of heteroepitaxial diamond films.11,12,16,17 As summarized by Paul W. May,38 substrate material (such as silicon) should be capable of forming a carbide layer. The thin carbide interfacial layer not only promotes growth of heteroepitaxial diamond film but also supports its adhesion by (partial) relief of stresses at the interface. The stresses are expected from the fact that the CVD/MPCVD processing takes places at elevated temperatures, and the silicon substrates undergo contraction during cooling. The resultant compressive stresses were stated38 to be significant and can lead to bowing/cracking, delamination, and even rupture of the diamond film. This manuscript provides an alternate origin for the aforementioned stresses and the resultant failure. It is important to discuss the present results before deliberating on the mechanisms/models for the observed delamination/rupture. Intrinsic stresses are through ‘accumulation of crystallographic defects’.19 This has been generalized11 as an inverse function of grain size, but directly proportional to the constrained relaxation of the lattice constant. The latter is determined by point of closest approach between neighboring atoms. Presence of crystallographic defects, namely dislocations and grain boundaries, can thus affect the intrinsic stresses. Present data showed a clear change in the intrinsic stresses: from mildly compressive (−0.28 GPa) to significantly tensile (Figure 4b). This is counterintuitive, especially viewed against a clear drop in estimated dislocation densities (Figure 4a). It is to be noted that a similar gradient in dislocation density has also been reported,39 qualitatively, through careful transmission electron microscopy study. Raman analysis did not reveal presence of nondiamond phases, another expected11,12 source for intrinsic stresses. Grain boundaries are shown11,12,40 to be the source of tensile intrinsic stresses. At different locations, Figure 9, probabilities of finding in-plane grain boundaries were similar: approximately one boundary per μm. Information on Raman peaks came from a spot/depth size of approximately 1 μm. The 30° inclined boundaries, over such depth, will offer approximately twice the grain boundary volume and thus are expected to have a higher constrained relaxation.11 Inclined or lateral boundaries thus appear to be the plausible explanation for the observed increase in intrinsic stresses (Figure 4b). The Raman measures the so-called intrinsic stresses.10,12 However, XRD estimates the stress tensors or the distortion in the unit cell itself.12,22 The stresses in the diamond film, both intrinsic stresses (Figure 4b) and the anisotropic shear (Figures 6b and 7) were in GPa. This was at least an order of magnitude more than the yield stresses of the silicon substrate. Naturally, this (strain partitioning from film to substrate) resulted in the plastic deformation of the substrate material and was clearly revealed by the EBSD (see Figure 8). It is also clear that the increase in the intrinsic stresses did coincide with increased anisotropy in residual shear stresses (Figure 7). An explanation for the latter may exist in the developments of crystallographic texture and/or grain morphology. As in Figure 5, and also shown in previous studies,36,37,41,42 growth created more anisotropy or texturing. Grains of different

Figure 6. Residual stress components: (a) σϕ [eq 5] and (b) τϕ [eq 6], for films grown to different thicknesses. Measurements were obtained for (220), (111), and (311) poles at ϕ = 0, 45, and 90°. Standard deviations on the residual stress estimates are shown with appropriate error bars.

Figure 7. GIXRD estimates for τϕ [eq 6] versus ϕ rotation for films grown to different thicknesses. Respective ω values were selected to cover the entire film thickness κ (eq 7). The figure clearly shows unbalanced or anisotropic residual shear stresses.

(12 μm film thickness), the diamond grains (5 μm average size and aspect ratio, major versus minor axes, of approximately 2.1) were parallel to the normal direction (ND − film normal). With an increase in film thickness, the crystal size and aspect 1519



Article

Figure 8. (a) Single crystal silicon substrate before the film deposition. (b) Polycrystalline silicon substrate after film (32 μm thickness) delamination. In (a) and (b), single and polycrystalline natures were confirmed through X-ray (peak profiles) and electron (EBSD estimated IPFs) diffraction. Local misorientation (KAM) maps of the Si substrate (c) before and (d) after film delamination. (c) and (d) Both topological (forescatter detector data in gray scale) and KAM information (in color), while (a) and (b) contain orientation (IPF) information in color. (For interpretation of color, reader may consult the web version.)

Figure 9. Cross-sectional electron micrograph, after FIB polishing, with EBSD images. The latter were taken close to the silicon−diamond interface (dotted line) and near the top (film) surface. EBSD images were obtained using IPF notation. (For for interpretation of color, reader may consult the web version.)

crystallographic orientations were reported10,43 to have differing magnitude of in-plane residual stresses. For example, (100) and (111) were shown43 to possess the lowest and highest

stresses, respectively. This study had revealed close to 165 GPa stress for (111) σ11 (Figure 5a) at a film thickness of 12 μm. For thicknesses >12 μm, however, this component reduced 1520



Article

At the initial stages of vapor deposition, grains are expected to be present as ‘isolated’ islands arising from separate nucleation events.18,45 They are also stipulated18,44,45 to exert compressive residual stresses. The classical model of Nix− Hoffman45 considers coalescence of individually nucleated islands. The angle of the resulting grain boundary is expected to arise from a tension balance between surface and grain boundary energies. The coalescence process thus leads to developments of tensile or lateral stresses. Concurrent developments in compressive and lateral stresses, especially the unbalanced components, can lead to out-of-plane shear stresses. When such shear stresses are too intense and exceed the interfacial bonding, both film delamination/rupture of films and plastic deformation of substrate can take place. Phenomenological evidence on growth morphology, its relation with growth selection41,42 and/or from crystallite coalescence,18,44,45 and the relationship between morphological, crystallographic, and stress state demand further explorations. The role of anisotropic residual shear stress on the delamination/rupture of the present diamond films, however, remains convincing and statistically reliable. This study hints at an alternate model to more ‘convention’ approaches6,38 of film rupture: a model expanding the role of “lateral” stresses26 through out-of-plane anisotropic shear.

to only 7−27 GPa. It needs to be noted that volume fraction of (111) (Figure 5b) did not change noticeably with film growth (Figure 5b). The interesting pattern of stress relaxation in (111) σ11 was reproducible; though an explanation appears baffling. It is almost impulsive to attribute increased anisotropy in τϕ (Figure 6b) to stronger texturing (Figure 5c). Literature provides excellent information on residual stress developments in thin films: stress developments with processing conditions,11,12 a possible relationship between stress and microstructure,3,5,7,9,14,20 and the role of stresses on film delamination/rupture4−9 with plausible analytical models for the same.18,44,45 Usual observations16,17 state a change of stress state, with increase in film thickness, from compressive to tensile, even indicating developments in “lateral”26 stresses. In tensorial terms, such “lateral” stresses are out-of-plane shear. Though ‘limited’7 data on residual shear stresses in diamond films are available, the significance was never highlighted. The present study highlights noticeable developments in anisotropic out-of-plane shear stresses, and the latter tries to establish correlations with substrate microstructure developments and delamination/rupture of the film. Previous literature on polycrystalline diamond films39,46 also reported plastic deformation of the silicon substrate through X-ray peak broadening46 and transmission electron microscopy observations.39 The present study not only brings in comprehensive evidence of plastic deformation in silicon substrate but also relates the same with clear evidence of shear markings. As in Figure 8, such markings were present on the silicon substrate as intense strain localizations. An anisotropic shear residual stress in the elastically harder diamond film is expected to leave signatures of plastic strain on the silicon substrate. It is indeed interesting to note that a 30° (with x-axis) angle between positive and negative τϕ (Figure 7) also corresponds to the morphological patterns of shear markings in silicon substrate (Figure 8). An exhaustive range of literature exists on the subject of mechanical stability of polycrystalline films.6−9,24,47 The extreme instability, or the film rupture, has been related to (i) total stress (thermal plus intrinsic stresses),4,6,8 (ii) in-plane hoop stress,7 (iii) elastic plus surface energy considerations,8 and (iv) intense normal and shear stresses.4 All of these models are discussed with reference to the present data. Thermal stresses were estimated from appropriate (see Appendix) numerical equations as −1.32 GPa. As in Table 2, the total stresses are thus expected to change from −1.6 GPa (12 μm film thickness) to a maximum of +1.57 GPa. The so-called debonding stress of +1.57 GPa appears to be significantly lower than values reported (3.94 and −5.93 for untreated and treated substrates)6 for debonding of diamond films on titanium substrate.6 Cracking of free-standing diamond film was also linked to stress gradient.7 In the present study, as verified from Raman peak shifts at different locations, stress gradients were “minor”. Elastic plus surface energy considerations stipulate a critical film thickness for catastrophic failure.8 Any thicknessdependent failure can, arguably, be fitted into such a model. On the other hand, finite element modeling has shown4 that concentrations of ‘intense’ normal and residual shear stresses can lead to film instability through interfacial spalling. A local stress concentration may exceed be-bonding strength and result in failure. One may thus ‘fit’ the present observations with models (iii) and (iv), but that does not explain or relate to the microstructural observations.

5. SUMMARY • Clear delamination/rupture of the diamond films and fracture of silicon substrate were noted beyond a film thickness of 30 μm and a corresponding deposition time of 30 h. • Increasing film thickness was associated with a shift in Raman peak and changes in X-ray line profiles. These were expanded in terms of intrinsic stress and dislocation densities. The former showed a change from relative minor compressive stress (−0.28 GPa) to significant tensile stress (+2.89 GPa), as film thickness increased from 12 to 30 μm. On the other hand, increasing film thickness reduced the estimated dislocation densities by nearly 1.6 times. • With an increase in film thickness, clear patterns of residual stresses were noted through standard sin2ψ and multiple {hkl} GIXRD. These can be summarized as (1) (i) In plane σϕ: both average values and rotational anisotropies dropped noticeably. (2) (ii) Out-of-plane τϕ: Strong developments for (111) pole, both average and anisotropy values increased substantially. As estimated through GIXRD, τϕ changed from positive to negative at an approximate angle of 30° with x-direction. • Delamination of polycrystalline diamond films led to a rupture of silicon substrate. The severe plastic deformation of the substrate had two effects: (1) (i) A single-crystal Si substrate was converted to polycrystalline in nature. (2) (ii) The presence of clear shear markings or strain localizations at approximately 30° with x-direction. • A change in growth morphology of the diamond films was observed. Near the substrate, the diamond grains were growing perpendicular to the substrate, while such grains had an approximate inclination of 30° at higher film thicknesses. Observations on significant intrinsic tensile 1521



■

■

stresses were rationalized from 30° inclined boundaries. Such microstructures will offer approximately twice the grain boundary volume and hence are expected to enforce a higher constrained relaxation to the Raman spectra. This has been stipulated as the source of intrinsic tensile stresses observed experimentally. • Different models on film delamination/rupture were deliberated. Though some of these models, especially thickness-dependent developments in elastic plus surface energy and the presence of intense normal/shear stresses, may rationalize the observed rupture, they do not address the microstructural developments in the film and substrate. This study proposed an alternate model: a model based on anisotropic out-of-plane residual shear stresses. When such stresses exceeded interfacial bonding, delamination/rupture of the films and corresponding substrate shear markings resulted.

APPENDIX ΔεEd (1 − υd)

(11)

where Ed is Youngs modulus of diamond (1080 GPa), and υd is Poisson’s ration for diamond (0.1). Misfit strain (Δε) was estimated from the coefficients of thermal expansions of diamond (αd) and silicon substrate (αs) as T1

Δε =

∫T 2

[αd(T ) − αs(T )]dT

(12)

Temperature-dependent formulations for αd and αs were taken from refs 6 and 48, respectively. Integration was done from a deposition temperature of 850 °C (T1) until ambient (T2: 30 °C). The numerical calculation returned a thermal stress value of −1.32 GPa. The total stresses, thermal plus intrinsic (Table 2), then change from −1.6 to +1.57 GPa as the film thickness increased from 12 to 30 μm.

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b01328.

■

summary of deposition time periods and corresponding values of the film thicknesses (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91 022-2576 7621. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Freund, L. B.; Suresh, S. Thin Film Materials, Stress, Defect Formation and Surface Evolution; Cambridge University Press: Cambridge, U.K., 2003. (2) Laribi, M.; Mesrati, N.; Vannes, A. B.; Treheux, D. Surf. Coat. Technol. 2003, 166, 206. (3) Tamboli, S. H.; Puri, V.; Puri, R. K. Appl. Surf. Sci. 2010, 256, 4582. (4) Gunnars, J.; Alahelisten, A. Surf. Coat. Technol. 1996, 80, 303. (5) Liu, E.; Blanpain, B.; Celis, J. P.; Roos, J. R.; Alvarez-Verven, G.; Priem, Th. Surf. Coat. Technol. 1996, 80, 264. (6) Chandra, L.; Chhowalla, M.; Amaratunga, G. A. J.; Clyne, T. W. Diamond Relat. Mater. 1996, 5, 674. (7) Li, C.; Li, H.; Niu, D.; Lu, F.; Tang, W.; Chen, G.; Zhou, H.; Chen, F. Surf. Coat. Technol. 2007, 201, 6553. (8) Knuyt, G.; Vandierendonck, K.; Quaeyhaegens, C.; Van Stappen, M.; Stals, L. M. Thin Solid Films 1997, 300, 189. (9) Telling, R. H.; Field, J. E. Int. J. Refract. Hard Met. 1998, 16, 269. (10) Fan, Q. H.; Fernandes, A.; Pereira, E.; Gracio, J. Diamond Relat. Mater. 1999, 8, 645. (11) Windischmann, H.; Epps, G. F.; Cong, Y.; Collins, R. W. J. Appl. Phys. 1991, 69 (4), 2231. (12) Rats, D.; Bimbault, L.; Vandenbulcke, L.; Herbin, R.; Badawi, K. F. J. Appl. Phys. 1995, 78 (8), 4994. (13) Tamulevičius, S.; Valkonen, M. P.; Laukaitis, G.; Lindroos, S.; Leskela, M. Thin Solid Films 1999, 355-356, 430. (14) Vink, T. J.; Somers, M. A. J.; Daams, J. L. C.; Dirks, A. G. J. Appl. Phys. 1991, 70 (8), 4301. (15) Soares, M. R.; Belmonte, M.; Silva, R. F. J. Appl. Phys. 2003, 94 (9), 5633. (16) Kim, J. G.; Yu, J. Scr. Mater. 1998, 39 (6), 807. (17) Shang, N. G.; Lee, C. S.; Lin, Z. D.; Bello, I.; Lee, S. T. Diamond Relat. Mater. 2000, 9, 1388. (18) Spaepen, F. Acta Mater. 2000, 48, 31. (19) Thornton, J. A.; Hoffman, D. W. Thin Solid Films 1989, 171, 5. (20) Fu, Y.; Du, H.; Sun, C. Q. Thin Solid Films 2003, 424, 107. (21) Van Houtte, P.; De Buyser, L. Acta Metall. Mater. 1993, 41 (2), 323. (22) Welzel, U.; Ligot, J.; Lamparter, P.; Vermeulen, A. C.; Mittemeijer, E. J. J. Appl. Crystallogr. 2005, 38, 1. (23) Withers, P. J.; Bhadeshia, H. K. D. H. Mater. Sci. Technol. 2001, 17, 355. (24) Atar, E.; Sarioglu, C.; Demirler, U.; Sabri, K. E.; Cimenoglu, H. Scr. Mater. 2003, 48, 1331. (25) Verlinden, B.; Driver, J.; Samajdar, I.; Doherty, R. D. ThermoMechanical Processing of Metallic Materials, Pergamon Materials Series; Cahn, R.W., Ed.; Elsevier: Amsterdam, 2007. (26) Krishnamurthy, R.; Srolovitz, D. J. Acta Mater. 2004, 52, 3761. (27) Baczmanski, A.; Braham, C.; Seiler, W.; Shiraki, N. Surf. Coat. Technol. 2004, 182, 43. (28) Vermeulen, A. C.; Detlev, G. Proceedings from the European residual stress conference ECRS-7, Berlin, Germany, September 13− 15, 2006; Trans Tech: Switzerland, 2006. (29) Bunge, H. J. Texture Analysis in Materials Science; Butterworths: London, 1982. (30) Van-Houtte, P. MTM-FHM Software Manual; Katholieke Universiteit Leuven: Belgium, 1995. (31) Borbely, A.; Groma, I. Appl. Phys. Lett. 2001, 79 (12), 1772. (32) Khatirkar, R.; Vadavadagi, B.; Haldar, A.; Samajdar, I. ISIJ Int. 2012, 52 (5), 894. (33) Yerra, S. K.; Verlinden, B.; Van-Houtte, P. on crystallographic texture of as-drawn doped-W wires. Mater. Sci. Forum 2005, 495-497, 913. (34) Van Houtte, P.; Li, S.; Seefeldt, M.; Delannay, L. Int. J. Plast. 2005, 21, 589. (35) Raveendra, S.; Kanjarla, A. K.; Paranjape, H.; Mishra, S. K.; Mishra, S.; Delannay, L.; Samajdar, I.; Van Houtte, P. Metall. Mater. Trans. A 2011, 42, 2113. (36) Wild, Ch.; Herres, N.; Koidl, P. J. Appl. Phys. 1990, 68 (3), 973.

For numerical estimation of thermal stress, eq 116 was used:

σd =

Article

ACKNOWLEDGMENTS

Support from the National Facility of Texture & OIM (a DSTIRPHA facility at IIT Bombay) is acknowledged. Financial support from Department Science and Technology (DST, India) is gratefully acknowledged. 1522



Article

(37) Thompson, C. V.; Carel, R. Mater. Sci. Eng., B 1995, 32, 211. (38) Paul, W.; May, P.; Trans, R. Philos. Trans. R. Soc., A 2000, 358, 473. (39) Michler, J.; von Kaenel, Y.; Stiegler, J.; Blank, E. J. Appl. Phys. 1998, 83 (1), 187. (40) Vlasov, I.; Ralchenko, V.; Zakharov, D.; Zakharov, N. Phys. stat. sol. (a) 1999, 174, 11. (41) Mohapatra, D. R.; Jain, L.; Rai, P.; Hazra, K. S.; Samajdar, I.; Misra, D. S. Chem. Vap. Deposition 2011, 17, 107. (42) Van der Drift, A. Philips Res. Rep. 1967, 22, 267. (43) Zhang, Y.; Zhang, J.-M.; Ji, V. Phys. B 2007, 389, 372. (44) Janssen, G. C. A. M. Thin Solid Films 2007, 515, 6654. (45) Nix, W. D.; Clemens, B. M. J. Mater. Res. 1999, 14 (8), 3467. (46) Jeong, J.h.; Kwon, D.; Lee, W. S.; Baik, Y. J. J. Appl. Phys. 2001, 90 (3), 1227. (47) Vinci, R. P.; Zielinski, E. M.; Bravman, J. C. Thin Solid Films 1995, 262, 142. (48) Okada, Y.; Tokumaru, Y. J. Appl. Phys. 1984, 56 (2), 314.

1523


Rupture of Polycrystalline Diamond Film: Defining Role

Recommend Documents