Elastic anisotropy effect on indentation-induced thin film interfacial delamination

Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green’s function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films.     

Stress in Thin Films;Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transvers isotropy is expected,owing to the limited dimenionlity .The usually applied models for the calculation of elstic constants of polycrystals from single crystal elastic contants(so-called grain interaction models)erroneously predict macroscopic isotropy for an(untextured) thin film.This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically anisotropic behaviour (shown by non-linear sin^2φ plots).A new grain interaction model,predictin the macroscopically anisotropic behaviour of thin films,is proposed.     

Low-temperature epitaxy of silicon by electron beam evaporation

In this paper we report on homoepitaxial growth of thin Si films at substrate temperatures T_s = 500-650 °C under non-ultra-high vacuum conditions by using electron beam evaporation. Si films were grown at high deposition rates on monocrystalline Si wafers with (100), (110) and (111) orientations. The ultra-violet visible reflectance spectra of the films show a dependence on T_s and on the substrate orientation. To determine the structural quality of the films in more detail Secco etch experiments were carried out. No etch pits were found on the films grown on (100) oriented wafers. However, on films grown on (110) and (111) oriented wafers different types of etch pits could be detected. Films were also grown on polycrystalline silicon (poly-Si) seed layers prepared by an Aluminum-Induced Crystallisation (AIC) process on glass substrates. Electron Backscattering Diffraction (EBSD) shows that the film growth proceeds epitaxially on the grains of the seed layer. But a considerably higher density of extended defects is revealed by Secco etch experiments.     

Growth of GaN films with controlled out-of-plane texture on Si wafers

GaN films were deposited on Si (400) wafers by a pulsed laser deposition technique, and it was shown that out-of-plane texture of the film is controllable although the film and the substrate do not have any interface epitaxy. The texture of the film can be set either in c-axis or a-axis direction, thereby achieving polar or nonpolar film surfaces as desired. The GaN film and Si substrate were found to be separated by a thin amorphous interface layer consisting of Si, Ga, and O atoms, that can enhance the bonding between GaN and Si. This study shows the possibility of depositing GaN films on Si wafers at low cost and the potential of integrating Si based electronics with GaN based optoelectronics.     

Simple recurrence matrix relations for multilayer anisotropic thin films

Generalized Abelès relations for one anisotropic thin film [E. Cojocaru, Appl. Opt. 36, 2825-2829 (1997)] are developed for light propagation from an isotropic medium of incidence (with refractive index n(0)) within a multilayer anisotropic thin film coated onto an anisotropic substrate. An immersion model is used for which it is assumed that each layer is imaginatively embedded between isotropic gaps of zero thickness and refractive index n(0). This model leads to simple expressions for the resultant transmitted and reflected electric field amplitudes at interfaces. They parallel the Abelès recurrence relations for layered isotropic media. These matrix relations include multiple reflections while they deal with total fields. They can be applied directly to complex stacks of isotropic and anisotropic thin films.     

Describing isotropic and anisotropic out-of-plane deformations in thin cubic materials by use of Zernike polynomials

Isotropic and anisotropic out-of-plane deformations induced by thin-film residual stress on thin cubic materials are studied. By transforming the compliance tensor, an analytical expression can be derived for the biaxial stiffness modulus for all directions in any given cubic crystal plane. A modified Stoney's equation, including both isotropic and anisotropic terms, can be formulated to predict the anisotropic out-of-plane deformation. The isotropic and anisotropic deformations are then described using the Zernike polynomials U21 and U22, respectively. Experimental results from (100) and (110) silicon wafers confirm the model by quantitatively comparing the changes in Z21 and Z22 coefficients due to thin-film stress.     

Reactive magnetron sputtering from a composite target for large area BaPbO3 thin film electrode

Radio frequency reactive magnetron sputtering from a composite target made of PbO pellets uniformly positioned on a metallic Ba disc has been utilized for BaPbO₃ electrode deposition on 150 mm Si wafers. The reactive sputtering process has been analyzed in relation to sputtering parameters for composite targets with different percentage of PbO coverage. The process optimization method for in situ crystallized BaPbO₃ thin film fabrication has been emphasized. The growth of BaPbO₃ films has been discussed from the viewpoint of the BaO-PbO phase diagram and thermodynamics of Ba_n + 1Pb_nO_3n + 1 (n = 1, 2, ∞) phase formation. The microstructure analysis of the deposited films has been performed with atomic force microscopy and wide-angle X-ray diffraction (XRD) techniques. The grazing angle XRD measurements reveal the formation of a Ba₂PbO₄ phase in the film fabricated at 450 °C. The Ba₂PbO₄ phase content decreases with decreasing substrate temperature. The BaPbO₃ film deposited at a substrate temperature of 430 °C on naturally oxidized (001) Si wafers shows an electrical resistivity of 1.13 mΩ·cm. The BaPbO₃ films deposited on SiO₂ (native oxide)/Si wafer do not exhibit a preferred orientation whereas use of (111) Pt/SiO₂/Si substrate results in highly (111)-oriented films.     

Stress and strain in titanium nitride thin films

Titanium nitride (TiN) films, with thickness ranging from 0.02 µm to 1.9 µm, were grown by reactive unbalanced magnetron sputter deposition on silicon substrates. The average film stress is highly compressive in thin films and less compressive in thicker films.Two films, with thicknesses of 0.53 µm and 1.63 µm, were subjected to detailed X-ray diffraction (XRD) analysis. Sin²Ψ analysis was performed, both on films attached to the substrate, as well as on free-standing flakes of the film. The flakes were obtained by dissolving the substrate. Sin²Ψ analysis, both on the films attached to the substrate as well as on the flakes, did not yield straight lines. By combining the sin²Ψ measurements on films attached to the substrate with the sin²Ψ measurements on the flakes we were able to distinguish between a residual deformation of the lattice and the deformation due to the biaxial stress. Following this procedure the stress obtained from wafer curvature and from XRD strain measurements coincides.A residual strain parallel to the growth direction of the crystallites with the <111> direction parallel to the growth direction combined with a changeover in film texture from <001> parallel to growth direction to <111> parallel to growth direction leads us to propose a model explaining the dependence of stress on film thickness in TiN thin films.     

Effects of elastic anisotropy on the surface stability of thin film/substrate system

The surface stability of thin film/substrate system is an important problem both in the film synthesis and reliability of micro electrical and mechanical system (MEMS). In this work, the elastic anisotropy effect on surface stability of thin film/substrate system was considered. The theoretical analysis indicates that elastic anisotropic influence could play an important role in the surface stability of thin film/substrate system. And the anisotropy effect should be considered both in the thin film synthesis process and its service reliability. In addition, there exists an nondimensional parameter k for cubic crystalline thin film materials in evaluating the anisotropic effect. When k is larger than one unit, the surface stability will be weakened by anisotropic effect; vice versa. The method used in present work could be easy extended to multi-layered thin film/substrate system and help us to consider the elastic anisotropy effect.     

Measurement of thermal stress in Pd2Si film on Si(111) by absorption edge contour mapping

The film stress due to thermal mismatch between the Si(111) substrate and the overlying epitaxial Pd₂Si thin film has been measured by a novel technique named absorption edge contour (AEC) mapping using synchrotron radiation. The thermal expansion coefficient for Pd₂Si has been determined to be 23 × 10⁻⁶K⁻¹. Stress relaxation was observed after prolonged annealing at temperatures greater than 200°C.     

Extracting thin film hardness of extremely compliant films on stiff substrates

A previously reported method for extracting the thin film hardness from nanoindentation into a film on an elastically mismatched substrate was applied to four different cases of extreme mismatch in elastic properties: Parmax, Ultem, Polysulfone and Perfluorocyclobutyl polymer thin films on Si substrates. All of these cases represent extremely compliant films on a stiff substrate, where the ratio of film shear modulus to substrate shear modulus ranged from 0.008 to 0.036. Analyzing the nanoindentation data into these film/substrate systems poses a significant limitation when using the Oliver and Pharr method as the hardness increases rapidly with indentation depth. Therefore, a method involving the measured contact stiffnesses to more accurately determine the correct contact areas was used to extract the true hardness of the polymer thin films. The results indicate that our method is able to remove the substrate effects as well as the complications arising from pile-up and surface roughness to yield a wide plateau in hardness despite the extreme elastic mismatch conditions.     

The growth and transformation of Pd2Si on (111), (110) and (100) Si

Thin Pd films on (111), (110), (100) and amorphous Si substrates form [001] fiber textured Pd₂Si in the temperature range 100°–700°C. The degree of texture is a function of substrate orientation, increasing in the order amorphous Si, (100) Si, (110) Si and (111) Si. Only on the (111) Si substrate is the Pd₂Si film epitaxially oriented. Temperature-dependent growth on this orientation can be characterized by [001] textured growth, epitaxial azimuth orientation at the Si interface and progressive layer by layer formation of the mosaic crystal to the thin film surface.During Pd deposition, rapid non-diffusion-controlled growth of epitaxial Pd₂Si on (111) Si occurs at substrate temperatures of 100° and 200°C. An unidentified palladium silicide of low crystallographic symmetry forms during Pd deposition onto a 50°C substrate. The diffusion-controlled growth of Pd₂Si on (111) Si follows a t^0.5 dependence. The velocity constant is

$\text{k = 7 × 10}{}^{\mathrm{?2}}\text{exp}\text{?}\text{29200±800}\text{RT}\text{cm}{}^2\text{/}\text{sec}$

Palladium deposited on 100°C (111) Ge substrates reacts during deposition to form epitaxially oriented Pd₂Ge. However, growth of this phase at higher temperatures results in a randomly oriented film. The transformation of Pd₂Ge to PdGe is kinetically controlled. After a 15 min anneal at 560°±10°C in N₂ only PdGe is detectable on (111) Ge.The high temperature stability of thin film Pd₂Si is controlled by time- temperature kinetics. For a given annealing cycle, the nucleation and growth rates of the PdSi phase are inversely related to the crystalline perfection of Pd₂Si. Decreasing transformation rates follow the order (100), (110), (111) Si. formation of thin film Pd₂Si occurs by the formation of PdSi and subsequent growth of Si within the PdSi phase. After a 30 min N₂ anneal, initial transformation occurs at 735°C on (100) Si, 760°C on (110) Si and 840°C on (111) Si. Extended high temperature annealing produces a two-phase structure of highly twinned and misoriented Si and small PdSi grains that penetrate as much as 3 μm into the Si.     

Catalytic synthesis of ZnO nanorods on patterned silicon wafer—An optimum material for gas sensor

ZnO nanorods have been synthesized over etch-patterned Si (110) wafer using annealed silver thin film as growth catalyst. The growth of ZnO nanorods were performed by a two-step process. Initially, the deposition of Zn thin film was done on the annealed silver catalyst film over etch-patterned Si (110) substrate by thermal evaporation, and then annealed at 800°C in air. The etching of the patterned Si (110) wafers was carried out by 50% aqueous KOH solution. The samples were investigated by optical microscopy, scanning electron microscopy, X-ray diffraction, Raman spectroscopy and room temperature photoluminescence spectroscopy. ‘V’ shaped grooves with no undercut were formed after etching due to the anisotropic nature of the KOH etchant. The etch-patterned wafer was used to provide larger surface area for ZnO growth by forming ‘V’-grooves. This ZnO film may be predicted as a very good material for gas sensor.     

Mechanical properties of amorphous and microcrystalline silicon films

Hydrogen-free amorphous silicon (a-Si) films with thickness of 4.5-6.5 μm were prepared by magnetron sputtering of pure silicon. Mechanical properties (hardness, intrinsic stress, elastic modulus), and film structure (Raman spectra, electron diffraction) were investigated in dependence on the substrate bias and temperature. The increasing negative substrate bias or Ar pressure results in simultaneous reducing compressive stress, the film hardness and elastic modulus. Vacuum annealing or deposition of a-Si films at temperatures up to 600 °C saving amorphous character of the films, results in reducing compressive stress and increasing the hardness and elastic modulus. The latter value was always lower than that for monocrystalline Si(111). The crystalline structure (c-Si) starts to be formed at deposition temperature of ∼ 700 °C. The hardness and elastic modulus of c-Si films were very close to monocrystalline Si(111). Phase transformations observed in the samples at indentation depend not only on the load and loading rate but also on the initial phase of silicon. However, the film hardness is not too sensitive to the presence of phase transformations.     

Residual stress in piezoelectric poly(vinylidene-fluoride-co-trifluoroethylene) thin films deposited on silicon substrates

The residual stress and its evolution with time in poly(vinylidene-fluoride-co-trifluoroethylene) (P(VDF-TrFE) (72/28)) piezoelectric polymer thin films deposited on silicon wafers were investigated using the wafer curvature method. Double-side polished silicon wafers with minimized initial wafer warpage were used to replace single-side polished silicon wafers to obtain significantly improved reliability for the measurement of the low residual stress in the P(VDF-TrFE) polymer thin films. Our measurement results showed that all the P(VDF-TrFE) films possessed a tensile residual stress, and the residual stress slowly decreased with time. Our analysis further indicates that the tensile stress could arise from the thermal mismatch between the P(VDF-TrFE) film and the silicon substrate. Besides possible viscoelastic creep mechanism in thermoplastic P(VDF-TrFE) films, microcracks with widths in the range of tens of nanometers appeared to release the tensile residual stress.     

The effects of film thickness variations on the residual stress distributions in coated Cr thin films

Generally, the residual stress of thin film coatings is calculated using Stoney's equation. However, variables in the manufacturing of the coated film, such as crystalline particle size and the unevenness of the thickness of the film, cause the radius of curvature of the beam to vary all over the beam. The cantilever beam curves not only in the axial direction but also in the transverse direction. Therefore, the residual stress in a film coating comprises not only axial residual stress but also transverse residual stress, and its distribution is also not uniform. Under such conditions, Stoney's equation must be modified. In this study, Si was used as a substrate in the production of cantilever beam specimens. Chromium thin films of various thicknesses were coated onto the Si substrates. The 3D digital image correlation technique was used to measure the out‐of‐plane displacement of the specimens at various positions. Then the modified Stoney's equation was used to obtain the axial and transverse residual stress at each measurement point to study the effect of variations in the thickness of the thin film on the magnitude and uniformity of the distribution of the residual stresses. Three thin film thicknesses 1, 2, and 3 μm were studied, and three specimens for each thickness were used. For each specimen, axial and transverse residual stresses were obtained at nine test points, and the equivalent residual stress was calculated. The results of this study reveal that as the difference between the thicknesses of the coating increased, average equivalent residual stress decreased and the distribution of stresses became more uniform. By comparing the corresponding results for the 1‐ and 3‐μm‐thick films revealed that the confidence levels in the average value and uniformity of the equivalent residual stress distribution, which increased with thickness, were 92.81% and 80.57%, respectively.     

Epitaxial growth of gallium nitride by ion-beam-assisted evaporation

The epitaxial growth of gallium nitride thin film was obtained on the inclined Si(111) substrates by the process of ion-beam-assisted evaporation (IBAE) at the low temperature of 500 °C. The film composition determined by Rutherford backscattering spectrometry shows that the synthesized film is a stoichiometric nitride. The epitaxial quality of GaN film is enhanced by minimizing the bombardment-induced film damage by decreasing the ion flux. However, the crystallinity of the GaN film becomes very poor when the ion flux is not sufficient to densify the film. The optimum flux ratio of N⁺₂ to Ga and the energy of incident N⁺₂ ions for the epitaxial growth were found to be 3.4 and 50 eV, respectively. The GaN film deposited on the 4 °-inclined Si (111) with respect to substrate surface shows much better crystalline quality compared with that on the 0 ° inclined Si(111) due to many stable nucleation sites. A thin amorphous layer exists at the interface between GaN and Si(111) substrate and acts as a buffer zone enabling the subsequent epitaxial growth of GaN by relaxing the large misfit strain (23%) in the early stage of film growth. The epitaxial GaN film shows an orientational relation with the Si(111) substrate.     

Using thin film stress to produce precision, figured X-ray optics

We are studying the possibility of producing precision, aspherical mirrors for X-rays and visible light. Our study examines the use of ultrastructure processing to replace mechanical methods of material removal. The method starts with a chemically-mechanically polished, flat silicon wafer. The aim is to preserve atomic scale smoothness of the surface wafer while the wafer is bent to a desired figure. We report measurements of the mechanical properties of various stressing layers. This involves measuring the deformation of several thin silicon wafers coated with chemically vapor deposited nickel and boron films of known thickness. We have found that, under normal conditions, the film does not add to the microroughness of the substrate on either the front or the back surfaces. Film and substrate thicknesses, however, vary by as much as 10%. This is the present limit on figure accuracy. We have developed a model that describes bending of B/Si and Ni/Si structures. The model relates stress and Young's modulus to the measured thickness of the film, and the thickness and curvature of the substrate. This approach is used to measure the stress and Young's modulus for boron and nickel films. The Young's modulus E_f was 3.05 x 10¹² Pa for the boron films and 1.4 x 10¹⁰ Pa for the nickel films. From the relationship developed and verified for predicting the radii of curvature of the substrate, if may be possible to define a film thickness pattern which would provide a desired optical figure.     

An integral formulation for steady-state elastoplastic contact over a coated half-plane

 A boundary-domain integral equation for a coated half-space (elastically isotropic homogeneous substratum, possibly anisotropic coating layer) is developed. The half-space fundamental solution is used, so that the discretization is limited to the potential contact zone (boundary elements), the potentially plastic part of the substratum and the coating layer (domain integration cells). Steady-state elastoplastic analysis is implemented within this framework, for plane-strain conditions, for solving rolling and/or sliding contact problems, where at the moment the contact load comes from either a purely elastic contact analysis or is of Hertz type. The constitutive integration is of implicit type. In order to improve accuracy and computational efficiency, infinite elements are used. Comparison of numerical results with other sources, when available, is satisfactory. The present formulation is also used to compute the contact pressure for an isotropic (or anisotropic) coating on an isotropic homogeneous half-space indented by an elastic punch. Received 29 May 2001     

Crystallographic properties of four-fold grain K3Li2Nb5O15 thin films

The structural properties of a potassium lithium niobate (KLN; K₃Li₂Nb₅O₁₅) thin film deposited by rf-magnetron sputtering on a Pt/Ti/SiO₂/Si(100) substrate were investigated. The crystalline structures of the Pt under layer and KLN thin films were examined using θ-2θ, θ-rocking, and mesh scan X-ray diffraction (XRD). The XRD results revealed that the Pt under layer was a strong (111) direction orientated poly crystal. Unlike the Pt under layer film, the KLN(001) peak was found to consist of two separate peaks, one with a broad full width half maximum (FWHM) and the other with a narrow FWHM, indicating that the KLN film had a single crystalline structure. The surface and cross-section morphology were investigated using a scanning electron microscope (SEM). Accordingly, from the results of the SEM and XRD experiments, it was concluded that the KLN film was composed of small single crystals, which had a four-fold symmetry morphology with a c-axis normal to the substrate.