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By combining the well-known grid reflection method with a digital image correlation algorithm and a geometrical optics model, a new method is proposed for measuring the change of curvature of a smooth reflecting substrate, a common reporter of stress state of deposited layers. This tool, called Pattern Reflection for Mapping of Curvature (PReMC), can be easily implemented for the analysis of the residual stress during deposition processes and is sufficiently accurate to follow the compressive-tensile-compressive stress transition during the sputtering growth of a Ag film on a Si substrate. Unprecedented resolution below 10âˆ'5 mâˆ'1 can be reached when measuring a homogeneous curvature. A comparison with the conventional laser-based tool is also provided in terms of dynamical range and resolution. In addition, the method is capable of mapping local variations in the case of a non-uniform curvature as illustrated by the case of a Mo film of non-uniform film thickness under high compressive stress. PReMC offers interesting perspectives for in situ accurate stress monitoring in the field of thin film growth. [ABSTRACT FROM AUTHOR]

We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses. [ABSTRACT FROM AUTHOR]

Applying the principle of minimum potential energy in an invariant plane reference frame, we obtain a concise curvature-strain equation for large size thick multilayered wafer, which incorporates strain due to nonlinear deformation. This equation manifests itself as Stoney's or other famous formulas for specific cases, and clarifies their relations and physical origins. We find nonlinear deformation greatly suppresses wafer bending and verify this effect experimentally in 2–4 in. GaN/sapphire systems. Such mechanical analysis provides a foundation of curvature control which is crucial in wafer fabrication for electronics and photonics. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Continued downscaling of functional layers for key enabling devices has prompted the development of characterization tools to probe and dynamically control thin film formation stages and ensure the desired film morphology and functionalities in terms of, e.g., layer surface smoothness or electrical properties. In this work, we review the combined use of in situ and real-time optical (wafer curvature, spectroscopic ellipsometry) and electrical probes for gaining insights into the early growth stages of magnetron-sputter-deposited films. Data are reported for a large variety of metals characterized by different atomic mobilities and interface reactivities. For fcc noble-metal films (Ag, Cu, Pd) exhibiting a pronounced three-dimensional growth on weakly-interacting substrates (SiO2, amorphous carbon (a-C)), wafer curvature, spectroscopic ellipsometry, and resistivity techniques are shown to be complementary in studying the morphological evolution of discontinuous layers, and determining the percolation threshold and the onset of continuous film formation. The influence of growth kinetics (in terms of intrinsic atomic mobility, substrate temperature, deposition rate, deposition flux temporal profile) and the effect of deposited energy (through changes in working pressure or bias voltage) on the various morphological transition thicknesses is critically examined. For bcc transition metals, like Fe and Mo deposited on a-Si, in situ and real-time growth monitoring data exhibit transient features at a critical layer thickness of ~2 nm, which is a fingerprint of an interface-mediated crystalline-to-amorphous phase transition, while such behavior is not observed for Ta films that crystallize into their metastable tetragonal β-Ta allotropic phase. The potential of optical and electrical diagnostic tools is also explored to reveal complex interfacial reactions and their effect on growth of Pd films on a-Si or a-Ge interlayers. For all case studies presented in the article, in situ data are complemented with and benchmarked against ex situ structural and morphological analyses.

Phase change materials are attractive materials for non-volatile memories because of their ability to switch reversibly between an amorphous and a crystal phase. The volume change upon crystallization induces mechanical stress that needs to be understood and controlled. In this work, we monitor stress evolution during crystallization in thin GeTe films capped with SiOx, using optical curvature measurements. A 150 MPa tensile stress buildup is measured when the 100 nm thick film crystallizes. Stress evolution is a result of viscosity increase with time and a tentative model is proposed that renders qualitatively the observed features.

In-situ wafer curvature measurements and ex-situ ion-beam layer removal method are used to evaluate residual stress depth profiles in a 1.8 μm thick Al x Ga 1 − x N heterostructure on Si(111) by evaluating substrate surface curvatures and deflections of stepwise ion-beam milled micro-cantilevers, respectively. Both approaches reveal oscillatory stress depth gradients which correlate excellent in their depth alternations. Differences are found locally in the magnitudes of the stress concentrations, especially in the regions with relatively large stresses, inhomogeneous microstructures and at relatively small thicknesses. The discrepancies are interpreted by local stress relaxations in the growing heterostructure, like dislocation formation and overgrowth by differently stressed regions. [ABSTRACT FROM AUTHOR]

This paper reports on the comparison of residual stresses in AlN thin films sputter-deposited in identical conditions on Si (100) (110) and (111) substrates. The deposited films are of polycrystalline wurtzite structure with preferred orientation along the (002) direction. AlN film on the Si (111) substrate showed a vertical columnar structure, whereas films on Si (100) and (110) showed tilted columnar structures. Residual stress in the AlN films is estimated by x-ray diffraction (XRD), infra-red absorption method and wafer curvature technique. Films residual stress are found compressive and values are in the range of − 650 (± 50) MPa, − 730 (± 50) MPa and − 300 (± 50) MPa for the AlN films grown on Si (100), (110) and (111) substrates, respectively, with different techniques. The difference in residual stresses can be attributed to the microstructure of the films and mismatch between in plane atomic arrangements of the film and substrates. [ABSTRACT FROM AUTHOR]

Aluminium nitride (AlN) thin films are being extensively used for diverse applications. However, its use significantly depends on the minimization residual stress generated during the deposition process. This paper reports the evolution of residual stress in sputter deposited AlN thin films on Si (100) substrates with varying thickness. The deposited films were found to be polycrystalline wurtzite structure with orientations along (100) for low value of thickness (300 nm and 430 nm) and (002) preferred oriented for thicker films (630 nm and 830 nm). Residual stresses in the AlN films were estimated by x-ray diffraction, infra-red absorption and wafer curvature techniques. Determined Residual stresses were found to be matching well with each other and were compressive in nature. Residual stresses in the AlN thin films were found to decrease (from −2.1 GPa to −0.6 GPa) with the increase in film thicknesses. [ABSTRACT FROM AUTHOR]

Heavily boron doped silicon layer is being used to control the thickness of the bulk micro-machined micro-electro-mechanical system (MEMS) based structures. Residual stress generated due to the doping may affect the functioning and reliability of the MEMS devices. This paper presents a model for estimation of the diffusion induced residual stress by wafer curvature technique. Boron diffusion induced residual stresses in the silicon (100), (110) and (111) wafers are found to be 475 MPa, 963 MPa and 957 MPa respectively. [ABSTRACT FROM AUTHOR]

Polycrystalline thin films often have residual stress that is affected by the growth conditions (temperature, deposition rate, etc.) and material parameters. Real-time wafer curvature measurements from many groups have enabled the stress evolution with thickness and its dependence on processing conditions to be quantitatively determined for a large number of systems. Based on these results, we have developed a model for the stress evolution that focuses on the processes that occur at the evolving grain boundary between adjacent grains. The model includes parameters to predict the dependence of the stress on the diffusivity, growth rate, grain size and morphology. In this manuscript, we review the physical basis for this model and compare its predictions with two sets of measurements. In the first case, we consider the evolution of stress in films grown on patterned substrate in which the morphology of the film is known precisely, allowing for direct comparison with the model. In the second case, we consider the steady-state stress as a function of the deposition rate in electrodeposited films. [ABSTRACT FROM AUTHOR]

Mesoporous silicon can be used as isolating substrate for the integration of radiofrequency (RF) passive devices. The higher is the porous silicon (PS) thickness, the better are the RF performances. However, an increase of PS thickness induces a raise of strain in the substrate. In this work, the strain of 6 inches PS substrates which has been generated during electrochemical etching and post anodization annealing steps are studied. It is shown that, if the anodization process is not well-controlled, the consequences can be cracks of the PS layer or a high wafer curvature which prevents device from integration with a standard process. It is also demonstrated that different kinds of defects due to PS stress can be also observed on full wafer PS layers and localized PS substrates as well. [ABSTRACT FROM AUTHOR]

Bioceramic coatings, including calcium phosphate coatings composed of hydroxyapatite (HA), represent a common surface modification for metallic bone implants. In view of the mismatch in material properties between the ceramic coating material and the metallic substrate material, this study aimed to evaluate the residual stress within an HA-coating deposited using RF magnetron sputtering via two different analyses, based on either the Stoney formula (i.e. based on curvature measurements of the substrate [Stoney, 1909]) or the sin 2 ψ method (i.e. based on X-ray diffraction patterns of the coating). Additionally, the effect of HA-coating thickness (i.e. 1 or 4 μm) on residual stress and surface topography was addressed. We hypothesized that: (i) both methods to determine residual stress would show similar results, and (ii) residual stress would vary between coating thicknesses. The curvature measurements showed low residual stress values (ranging from − 60 to 80 MPa) and indicated relaxation upon post-deposition heat treatment at 650 °C. Similarly, lattice-based measurements of residual stress showed relaxation of HA coatings upon post-deposition heat treatment. Coating thickness variation in the micrometer scale showed no major effects on residual stress magnitude. For reasons of accuracy and similarity to the actual conditions, determination of residual stress via lattice-based techniques is preferable. [ABSTRACT FROM AUTHOR]

Abstract: During the heteroepitaxial growth of a thin film on a thick substrate, important stresses arise in the grown material and may influence the physical properties of the film. The residual stresses result in a bending of the substrate/film system. In this work the evaluation of the wafer curvature and the residual stress along different crystallographic directions of the wafer was proposed. Performed by an interferometric optical profilometer, optical microscope and X-ray diffraction analysis, the curvature of the wafer along the [110] and [1−10] wafer directions was observed for hetero-epitaxial Cubic Silicon Carbide (3C-SiC) on Si (001) films. As a consequence of the stress generated during hetero-epitaxy, due to the difference in thermal expansion coefficient and lattice mismatch between the two materials, an asymmetric wafer curvature was observed. [Copyright &y& Elsevier]

Abstract: Residual stress is a longstanding problem in thin film growth that affects film performance and limits the range of applicability. A better understanding of why this stress develops and how it depends on the growth conditions and material properties would improve our ability to predict it and control it. We describe a kinetic model we have developed that explains stress evolution in terms of a dynamic competition between tensile and compressive stress generation mechanisms. The balance between them changes as the microstructure evolves from isolated islands, through coalescence and into a uniform film, leading to the sequence of stress states observed during growth. The model further predicts that the stress in the steady-state depends on the dimensionless parameter D/LR where D is the diffusivity, R is the growth rate and L is the grain size. Calculations from the model in both the high and low mobility regime are compared with real-time measurements of stress using wafer curvature in different systems The discussion addresses limitations of the model and other issues that are not covered such as surface roughness and energetic particle deposition. [Copyright &y& Elsevier]

Thermomechanical stresses in metallic films are a root cause for material fatigue which limits the lifetime of electronic devices. Since the yield stress of metals is temperature dependent, plastic deformations during thermal cycling are in- creased at elevated temperature. This effect reduces the reliability of electronic parts. In order to investigate this problem, a 20 μm thick copper film was deposited on a silicon wafer. After annealing at 400°C, the sample was exposed to thermal cycles in the temperature range between room temperature and 600°C. The different values for the coefficient of thermal expansion of copper and silicon lead to a curvature of the sample. The wafer curvature was measured by a multilaser beam method. On the basis of the experimental results, a new theoretical model was developed that describes the stress evolution in the film during thermal cycling. In this investigation, the relation between wafer curvature and film stress is calculated by analogy to a model by Freund which is an improvement to the well-known Stoney formula. In addition to the elastic response, the new model considers plasticity of the copper film as well as temperature dependence of creep. It is demonstrated that the model can describe the experiment well and thus thermomechanical stress in copper films. [ABSTRACT FROM AUTHOR]

A theoretical model based on two-body contact theory is established to simulate the contact pressure distribution arising from wafer curvature which is caused by film stress during CMP process. Both wafer and pad deformations during the contact process are considered. The profiles of the contact pressure distribution for wafers with different curvature radius are simulated. The influences of wafer curvature on mean removal rate and within wafer removal rate nonuniformity (WIWNU) are simulated and compared with the experimental data. According to the two-body contact model, when the pad is in contact completely with the wafer, the profile of the contact pressure has almost the same trend whether the wafer has an upward or a downward curvature. The mean value of the contact pressure will increase with increasing of radius of downward curvature. WIWNU will decrease with increasing pre-polish wafer bow from concave (upward curvature) to convex (downward curvature). The results from the simulation correlated with the experimental data and demonstrated the validity of the model. The results are helpful for controlling and reducing the wafer to wafer removal rate nonuniformity and within wafer removal rate nonuniformity in CMP. [ABSTRACT FROM AUTHOR]

Abstract: Stress in a thin film on a flexible substrate induces a curvature of the substrate. Usually the substrate is orders of magnitude thicker than the film, leading to small and purely elastic deformation of the substrate. In this case, the Stoney equation yields the stress in the film from the measured curvature of the substrate. The Stoney equation contains thickness of film and substrate and the elastic properties of the substrate. Typically the elastic properties of the substrate are specified by E (Young''s modulus), and ν (Poisson''s ratio). E and ν provide a valid description for elastically isotropic substrates, e.g. polycrystalline steel strips, as used by Stoney in 1909. Today the Stoney equation is still used for relating substrate curvature to film stress. However, in the majority of thin film stress measurements by means of substrate curvature, Si wafers are used as the substrate. Silicon wafers are cut from single crystals and are thereby elastically anisotropic. In the present paper, a modified form of the Stoney equation, well known for elastic isotropic substrates, is derived for Si(001) and Si(111) wafers, using the elastic stiffness constants of silicon, c ij , instead of the orientation averaged values E and ν, which do not have a meaning for elastically anisotropic single crystal materials. Curvature measurements of thin films on Si(001) and Si(111) wafers are presented. The difference in film-stress-induced curvature of Si(001) and Si(111) wafers is discussed. [Copyright &y& Elsevier]

Abstract: This paper examines the surface stress associated with the electrochemical desorption of 4-mercaptobenzoic acid (4-MBA) from (111) textured Au in aqueous 0.1molL−1 KOH. Self-assembled monolayers of varying coverage were adsorbed onto the Au electrode surface from a 0.1molL−1 aqueous KOH solution containing 1mmolL−1 4-MBA. Adsorption follows Langmuir kinetics and fully formed monolayers, corresponding to 0.29 coverage with respect to the Au surface, are formed in about 120min. XP spectra confirm the formation of the Au–S bond while FTIR spectra indicate that the 4-MBA is orientated with the carboxylate pointed away from the surface. The one-electron reductive desorption of 4-MBA occurs at a potential of −0.9 to −1.0V vs. SSE, depending on coverage, and causes a surface stress change in the tensile direction, indicating that 4-MBA adsorption induces a compressive surface stress to the Au. At short immersion times and low monolayer coverage, the surface stress increases with coverage as the stress response is primarily governed by the Au–S bond density. SAM desorption following longer immersion times produces large stress changes with little corresponding change in SAM coverage. We attribute the additional compressive stress to stabilization of the Au–S bonding regions and the coulombic repulsion between neighboring molecules, both associated with ordering of the 4-MBA on the Au surface. [Copyright &y& Elsevier]

Abstract: Polycrystalline thin films on substrates usually are in a “stressed” state. In the present paper, recent results on stress in polycrystalline films will be reviewed. For Cr and CrN films, it has been shown that the stress is not uniform over the thickness of the film. High tensile stresses are observed near the substrate-film interface. Lower tensile stresses are observed further away from the interface. Moreover, it has been shown that the tensile stress is generated at the grain boundaries. In the case for which the deposition of the film is accompanied by an ion bombardment, a compressive stress is generated. The tensile and compressive stresses in these films are independent and additive. This description, however, does not hold for all high melting point films, notably not for TiN. For c-BN films, the challenge is to form these metastable films and at the same time control the compressive stress within an acceptable range. Here some promising results have been obtained. For low melting point films, some new deposition experiments have been performed and new theories have been formulated. Here the situation is still less clear than with the high melting point films. [Copyright &y& Elsevier]

Continued downscaling of functional layers for key enabling devices has prompted the development of characterization tools to probe and dynamically control thin film formation stages and ensure the desired film morphology and functionalities in terms of, e.g., layer surface smoothness or electrical properties. In this work, we review the combined use of in situ and real-time optical (wafer curvature, spectroscopic ellipsometry) and electrical probes for gaining insights into the early growth stages of magnetron-sputter-deposited films. Data are reported for a large variety of metals characterized by different atomic mobilities and interface reactivities. For fcc noble-metal films (Ag, Cu, Pd) exhibiting a pronounced three-dimensional growth on weakly-interacting substrates (SiO2, amorphous carbon (a-C)), wafer curvature, spectroscopic ellipsometry, and resistivity techniques are shown to be complementary in studying the morphological evolution of discontinuous layers, and determining the percolation threshold and the onset of continuous film formation. The influence of growth kinetics (in terms of intrinsic atomic mobility, substrate temperature, deposition rate, deposition flux temporal profile) and the effect of deposited energy (through changes in working pressure or bias voltage) on the various morphological transition thicknesses is critically examined. For bcc transition metals, like Fe and Mo deposited on a-Si, in situ and real-time growth monitoring data exhibit transient features at a critical layer thickness of ~2 nm, which is a fingerprint of an interface-mediated crystalline-to-amorphous phase transition, while such behavior is not observed for Ta films that crystallize into their metastable tetragonal β-Ta allotropic phase. The potential of optical and electrical diagnostic tools is also explored to reveal complex interfacial reactions and their effect on growth of Pd films on a-Si or a-Ge interlayers. For all case studies presented in the article, in situ data are complemented with and benchmarked against ex situ structural and morphological analyses. [ABSTRACT FROM AUTHOR]

Phase change materials are attractive materials for non-volatile memories because of their ability to switch reversibly between an amorphous and a crystal phase. The volume change upon crystallization induces mechanical stress that needs to be understood and controlled. In this work, we monitor stress evolution during crystallization in thin GeTe films capped with SiOx, using optical curvature measurements. A 150 MPa tensile stress buildup is measured when the 100 nm thick film crystallizes. Stress evolution is a result of viscosity increase with time and a tentative model is proposed that renders qualitatively the observed features. [ABSTRACT FROM AUTHOR]