Measurement Of Stress In Thin Films Research Articles

A Theoretical Analysis for Arbitrary Residual Stress of Thin Film/Substrate System With Nonnegligible Film Thickness

Abstract Stoney formula is widely used in advanced devices to estimate the residual stress of thin film/substrate system by measuring surface curvature. Many hypotheses including that thin film thickness is ignored are required, thus bringing significant error in characterizing the inhomogeneous residual stress distribution. In this article, arbitrary residual stresses on thin film/substrate structures with nonnegligible film thickness are modeled and characterized. We introduce nonuniform misfit strain and establish the governing equations including mismatched strain, displacements, and interfacial stresses based on the basic elastic theory. The parameterization method and the method of constant variation are used in the process of equation decoupling. The expressions between displacements, surface curvatures, and misfit strain are determined through decoupling calculations. By substituting misfit strain, residual stresses are expressed by parametric equation related to surface curvature. It further indicates that there is a “non-local” part between the film stress and curvature at the same point. Compared to neglecting the film thickness, the proposed method eliminate relative errors up to 58.3%, which is of great significance for stress measurement of thin films and substrates.

Internal Stress Prediction and Measurement of Mid-Infrared Multilayer Thin Films.

We present an experimental method for evaluating interfacial force per width and predicting internal stress in mid-infrared band-pass filters (MIR-BPF). The interfacial force per width between the two kinds of thin-film materials was obtained by experimental measurement values, and the residual stress of the multilayer thin films was predicted by the modified Ennos formula. A dual electron beam evaporation system combined with ion-assisted deposition was used to fabricate mid-infrared band-pass filters. The interfacial forces per width for Ge/SiO2 and SiO2/Ge were 124.9 N/m and 127.6 N/m, respectively. The difference between the measured stress and predicted stress in the 23-layer MIR-BPF was below 0.059 GPa. The residual stresses of the four-layer film, as well as the 20-layer and 23-layer mid-infrared band-pass filter, were predicted by adding the interface stress to the modified Ennos formula. In the four-layer film, the difference between the predicted value and the measured stress of the HL (high–low refractive index) and LH (low–high refractive index) stacks were −0.384 GPa for (HL)2 and −0.436 GPa for (LH)2, respectively. The predicted stress and the measured stress of the 20-layer mid-infrared filter were −0.316 GPa and −0.250 GPa. The predicted stress and the measured stress of the 23-layer mid-infrared filter were −0.257 GPa and −0.198 GPa, respectively.

Using Digital Image Correlation on SEM Images of Strain Field after Ion Beam Milling for the Residual Stress Measurement of Thin Films.

The residual stress of thin films during the deposition process can cause the components to have unpredictable deformation and damage, which could affect the service life and reliability of the microsystems. Developing an accurate and reliable method for measuring the residual stress of thin films at the micrometer and nanometer scale is a great challenge. To analyze the residual stress regarding factors such as the mechanical anisotropy and preferred orientation of the materials, information related to the in-depth lattice strain function is required when calculating the depth profiles of the residual strain. For depth-resolved measurements of residual stress, it is strategically advantageous to develop a measurement procedure that is microstructurally independent. Here, by performing an incremental focused ion beam (FIB) ring-core drilling experiment with various depth steps, the digital image correlation (DIC) of the specimen images was obtained. The feasibility of DIC to FIB images was evaluated after the translation test, and an appropriate procedure for reliable results was established. Furthermore, the condition of the film in the function of residual stress was assessed and compared to elucidate the applicability of this technology.

Influence of curvature induced stress on first principle calculation and the reliability of 4H-SiC (0001) thermally grown SiO2 gate oxide

Gate oxide films on silicon carbide (SiC) markedly affect the performance of SiC metal-oxide-semiconductor field effect transistors (MOSFETs). We used current-voltage (I–V) measurements to investigate the influence of curvature induced stress/strain on the breakdown electric field and the charge-to-breakdown (QBD) at SiO2/SiC, defined here as time-zero dielectric breakdown and time-dependent dielectric breakdown, respectively. The curvature of the epitaxy wafers was characterized by a thin film stress measurement system. The compression/tensile curvature decreased EBD and QBD during the dry thermal oxidation process. Furthermore, first-principle calculations suggested that the energy levels of the samples were related to the lattice constants of the SiC crystal, indicating that stress mainly affected the SiO2/SiC interface. We suggest that a “stress free” oxide film might be the best choice for SiC-MOSFET applications.

Depth-graded Mo/Si multilayer coatings for hard x-rays.

This manuscript presents the first systematic study of non-periodic, broadband Mo/Si multilayer coatings with and without B4C interface barrier layers for hard x-ray applications with large field of view. The photon energy of operation in this work is 17.4 keV, the Mo Kα emission line. The coatings involve layers with varying thicknesses in the nanometer scale and the behavior at the layer interfaces plays a crucial role in their performance. Reflectivity measurements and modeling at 8.05 keV and 17.4 keV, Transmission Electron Microscopy (TEM), as well as thin film stress measurements, are employed to examine and optimize the reflective performance of these coatings and the physics of their constituent layers and interfaces. Mo/Si with B4C barrier layers on the Mo-on-Si interface is shown to produce the highest reflectivity among all design configurations considered in this work.

Residual Stresses in Cu/Ni Multilayer Thin Films Measured Using the Sin2ψ Method

Residual stresses in multilayer thin films are of substantial importance to the service life of advanced engineering systems. In this investigation, the residual stresses in magnetron sputtered Cu/Ni multilayer thin films were characterized using x-ray diffraction (XRD) and the sin2ψ method. The influence of layer thickness on residual stress was explored for films with alternating Ni and Cu layers with equal layer thicknesses ranging from 10 nm to 100 nm. To address peak broadening and overlapping, the Gaussian Mixture Model (GMM) and Expectation Maximization (EM) algorithm were employed, and the peak position was determined using the Center of Gravity (CoG) method. Results showed tensile residual stress in both the Cu and Ni layers and a prominent layer thickness dependence. The stress in the Ni layers increased from roughly 880 MPa to 1550 MPa with decreasing layer thickness from 100 nm to 10 nm. In the Cu layers, the stress remained relatively constant at ~250 MPa and then substantially decreased for the 10 nm thickness. The findings confirm that the XRD-based approach can be applied for residual stress measurement in nanoscale multilayer thin films, provided that peak broadening and overlapping issues are addressed. Furthermore, the residual stress in metal multilayers is strongly dependent on layer thickness.

Influence on curvature induced stress to the flatband voltage and interface density of 4H-SiC MOS structure

Gate oxide film on Silicon carbide (SiC) severely affects the performance of SiC metal-oxidesemiconductor field effect transistor (MOSFET). The authors investigated the influence of curvature induced stress/strain to flatband voltage (Vfb) and interface density (Dit) on SiO2/SiC by Capacitance-voltage (C-V) measurement. The curvature of epitaxy wafers has been identified by the Thin Film Stress Measurement system. The compress/tensile curvature led to increase of the positive Vfb shift (negative fixed charge) of SiO2 and the interface density of SiO2/SiC during dry thermal oxidation process. In addition, the transverse optical (TO) phonon wavenumber of the samples related with the curvature of the film, indicating that stress mainly affected the interface of SiO2/SiC. According to the experimental result, the authors suggested that a “free” stress oxide film might be a best choice for the application of SiC-MOSFET.

Self-contained in-vacuum in situ thin film stress measurement tool.

A fully self-contained in-vacuum device for measuring thin film stress in situ is presented. The stress was measured by measuring the curvature of a cantilever on which the thin film was deposited. For this, a dual beam laser deflectometer was used. All optics and electronics needed to perform the measurement are placed inside a vacuum-compatible vessel with the form factor of the substrate holders of the deposition system used. The stand-alone nature of the setup allows the vessel to be moved inside a deposition system independently of optical or electronic feedthroughs while measuring continuously. A Mo/Si multilayer structure was analyzed to evaluate the performance of the setup. A radius of curvature resolution of 270 km was achieved. This allows small details of the stress development to be resolved, such as the interlayer formation between the layers and the amorphous-to-crystalline transition of the molybdenum which occurs at around 2 nm. The setup communicates with an external computer via a Wi-Fi connection. This wireless connection allows remote control over the acquisition and the live feedback of the measured stress. In principle, the vessel can act as a general metrology platform and add measurement capabilities to deposition setups with no modification to the deposition system.

Real-Time Stress Measurement in SiO2 Thin Films during Electrochemical Lithiation/Delithiation Cycling

Oxide coatings have been shown to improve the cyclic performance of high-energy density electrode materials such as Si. However, no study exists on the mechanical characterization of these oxide coatings. Here, thin film SiO2 electrodes are cycled under galvanostatic conditions (at C/9 rate) in a half-cell configuration with lithium metal foil as counter/reference electrode, with 1 M LiPF6 in ethylene carbonate, diethyl carbonate, dimethyl carbonate solution (1:1:1, wt%) as electrolyte. Stress evolution in the SiO2 thin film electrodes during electrochemical lithiation/delithiation is measured in situ by monitoring the substrate curvature using a multi-beam optical sensing method. Upon lithiation SiO2 undergoes extensive inelastic deformation, with a peak compressive stress of 3.1 GPa, and upon delithiation the stress became tensile with a peak stress of 0.7 GPa. A simple plane strain finite element model of Si nanotube coated with SiO2 shell was developed to understand the mechanical response of the core-shell type microstructures under electrochemical cycling; measured stress response was used in the model to represent SiO2 constitutive behavior while Si was treated as an elastic-plastic material with concentration dependent mechanical properties obtained from the literature. The results reported here provide insights and quantitative understanding as to why the highly brittle SiO2 coatings are able to sustain significant volume expansion (300%) of Si core without fracture and enhance cyclic performance of Si reported in the literature. Also, the basic mechanical properties presented here are necessary first step for future design and development of durable Si/SiO2 core shell structures or SiO2-based electrodes.

Residual Stress Measurement in Micro-region Using Digital Image Correlation Method

The residual stress of the zirconia film on a stainless steel substrate is measured using the digital image correlation (DIC) method. A lattice structure is milled by focused ion beam (FIB) and used as the deformation carrier. An annular groove is etched by FIB in order to release the residual stress. The DIC method is used to calculate the deformation caused by the release of residual stress and the residual stress is derived by mechanics equations. The results demonstrate that this method can be extended for micro-region residual stress measurement of other thin films on substrates.

Residual stress measurement in thin films using a slitting method with geometric phase analysis under a dual beam (FIB/SEM) system

Stress generated during thin film deposition is a critical issue for many applications. In general, the possible origins of the residual stress include intrinsic and extrinsic stresses. Since high residual stresses can cause detrimental effects on the film, such as delamination and wrinkle, it is of great importance to quantify the residual stress for the optimal design and the evaluation of its mechanical behavior. In this study, a method combining focused ion beam (FIB) milling and geometric phase analysis (GPA) is developed to assess the residual stress of thin films. The procedures of the residual stress measurement using this method include grating fabrication and slot milling by FIB, high-resolution scanning electron microscope (SEM) imaging of the grating before and after stress relaxation, and deformation analysis by GPA. The residual stress can be inferred from the released deformation using the reference displacements of the finite element model. As an application, this method was utilized to measure the residual stress in a TiAlSiN film, and the measured result is in good agreement with that obtained by the curvature method. In order to analyze the measurement error, the influence factors of Ga+ bombardment and the deposited platinum layer on the stress calculation are also discussed in detail.

Residual stress and mechanical property measurements in amorphous Si photovoltaic thin films

The mechanical reliability and efficiency of thin film photovoltaics attached to structural members depends on the initial state of residual stresses in the films. In this work, predictions for the mechanical and functional failure of photovoltaic films co-cured with carbon fiber composite laminates were made possible by quantifying the mean and gradient residual stresses and the failure properties of the individual layers in thin film inorganic photovoltaics consisting of an amorphous silicon (Si) p–n junction diode, a zinc oxide (ZnO) Transparent Conductive Oxide (TCO) layer (each 1μm thick), a Kapton™ layer, and a thick aluminum substrate. The mean residual stresses (−466±118) MPa in the Si monolayer and the Si/ZnO bilayer (−661±93) MPa were calculated from the geometrical details of straight and telephone cord type buckling delaminations induced to the p–n junction layer and its combination with the TCO layer, respectively. Curvature measurements provided the residual stress gradient of the Si monolayer as 274±20MPa/μm and the stress gradient profile in the Si/ZnO bilayer. The tensile strength of freestanding amorphous Si monolayer and Si/ZnO bilayer strips was measured as 425±75MPa and 109±23MPa, respectively. These microscale tension experiments also showed that there is weak adhesion between the Si and the mechanically weak ZnO layers. The aforementioned experimental results were employed to predict the onset of fragmentation of the ZnO layer and the initiation of functional degradation of the photovoltaic films that were co-cured with 0° carbon fiber composite laminates, at 0.3% and 0.9% applied strain, respectively, which was in very good agreement with experimental measurements at the composite level.

Stress Analysis of Free-Standing Silicon Oxide Films Using Optical Interference

ABSTRACTWe report a method for stress measurement and analysis in silicon oxide thin films using optical interference. Effects of design and fabrication on stress have been studied by fabricating submicron-thick slabs of oxide anchored at one end and extending over a reflective surface. Optical interference occurs between reflections from the surface and the oxide slab, giving rise to light and dark fringes that may be imaged with a microscope. Analysis of the interference pattern at different wavelengths gives the radius of curvature and means of stress mapping. The accuracy exceeds non-interferometric profilometry using optical or confocal microscopes, and it can be more quantitative than scanning electron microscopy. This nondestructive profilometry method can aid the stress optimization of silicon oxide or other transparent thin films to achieve specific mechanical characteristics in MEMS devices.

A simple method for residual stress measurements in thin films by means of focused ion beam milling and digital image correlation

Hydrogenated amorphous carbon (a-C:H) coatings contain substantial residual stresses which particularly influence the failure behaviour of the coating system. However, measuring their residual stresses with conventional methods is not trivial. In this work, a simple method is presented to determine residual stresses of thin films locally by using stress relaxation tests by means of focused ion beam (FIB) milling and digital image correlation (DIC). It is shown, that the H-bar geometry, as it is used for TEM lamella preparation, is especially suitable for such measurements. Displacements due to relaxation of residual stresses are tracked using DIC and the stresses are obtained by correlation with finite element analysis. The method is applied to determine residual stresses of two a-C:H coatings processed with different deposition processes and parameters. It was found, that the coatings differ in their mechanical properties as well as in their residual stress state. The proposed method offers therefore a simple way for analysing residual stresses in thin amorphous coatings.

Observations in the H-Pd{111} System via Stress and EQCM Measurements

The under-potential deposition (UPD) & absorption of hydrogen in thin film palladium (45–75 nm) was investigated electrochemically utilizing both EQCM and thin film stress measurement techniques. The total frequency change during H absorption (desorption) as measured by EQCM is attributed to both an increase (decrease) in mass, Δfm, as well as the associated thin film stress evolution, Δfs. In order to deconvolute these two contributions, the changes in the Pd{111} thin-film stresses were measured directly by a high-resolution cantilever curvature-based stress monitoring technique. Mass incorporation and stress generation due to hydrogen absorption were recorded during cyclic voltammetric scans of increasingly cathodic potentials as well as during chronoamperometric holds in the hydrogen UPD region. The combination of stress measurements and mass uptake of hydrogen in the purely elastic regime provided a measure of a biaxially constrained partial molar volume of hydrogen in the Pd thin films, = 0.44 cm3/mol. Additionally, the occurrence of hysteresis and dramatic changes in slope of stress vs. H concentration during loading and unloading of thin films is explained in the context of elastic-plastic transitions that occur in the film.

Residual stress measurement in thin films at sub-micron scale using Focused Ion Beam milling and imaging

Residual stress evaluation in thin films at the sub-micron scale was achieved in the present study using a semi-destructive trench-cutting (ring-core) method. Focused Ion Beam was employed to introduce the strain relief by milling the slots around an “island” and also to record the images for strain change evaluation by digital image correlation analysis of micrographs. Finite element simulation was employed to predict the curves for strain relief as a function of milling depth, and compared with the experimental measurements, showing good agreement. An empirical mathematical description of the curves was proposed that allows efficient data analysis for residual stress evaluation.

Residual stress measurement in thin films using the semi-destructive ring-core drilling method using Focused Ion Beam

In the present study, residual stress evaluation in thin films was achieved using a semi-destructive trench-cutting method. Focused Ion Beam (FIB) was employed to introduce the strain relief by ring-core milling, i.e. creating a trench around an “island”. Either SEM or FIB imaging can be used to record sequences of images for strain change evaluation by Digital Image Correlation (DIC) analysis of micrographs. A regular array of shallow holes was drilled on a thin overlayer of Pt (∼100nm) deposited on to the film prior to patterning and trenching, in order to reduce the damage introduced by the ion beam during imaging and to assist the DIC strain evaluation by adding traceable markers. Finite Element (FE) simulation was also carried out to predict the curves for strain relief as a function of milling depth, and compared with the experimental measurements, which show good agreement with each other. An empirical mathematical description of the curves was proposed that allows efficient residual stress evaluation in thin solid films.

Direct stress measurements in thin polymer films

Stresses in thin polymer films were quantitatively determined by measuring the deflection of a cantilever cut from a film-covered silicon nitride membrane using a focused ion beam. Spin-cast high molecular weight films showed a surprisingly high residual stress, which by far exceeded the tensile strength of the bulk polymer. Thermal annealing relaxed these stresses suggesting two relaxation mechanisms, both of which are much faster than the reptation time.

Design and development of a novel paddle test structure for the mechanical behavior measurement of thin films application for MEMS

A new technique was developed for studying the mechanical behavior of thin films on substrate applications for micro-electro-mechanical system (MEMS). The test structure was designed on novel “paddle” cantilever beam coated thin film specimens with dimensions of a few hundred to 50 nm. This beam has a triangle shape that provides a uniform plane strain distribution. Standard clean room processing was used to prepare the paddle sample. The experiment can be operated using the electrostatic force to deflect the “paddle” cantilever beam and measure the mechanical response of the sample with surface deposited thin film. A capacitance measurement is used to observe the deflection of the cantilever plate on the other side of the sample with respect to the electrostatic force on the one side. The measured strain was then converted through this capacitance measurement to conduct mechanical behavior studies on the coated thin film. Both system performance experiments and calculations were studied to verify the design concepts. The residual thin film stress measurements were performed and compared with the calculated results from three different forces exerted on the “paddle” cantilever beam, including the force due to the film, compliance force, and electrostatic force.

Effect of the pre-gate oxide cleaning temperature on the reliability of GOI and devices performances in deep submicron CMOS technology

This paper reports the impacts of the pre-gate oxide cleaning on the statistic fluctuations of a deep submicron CMOS devices’ saturation current, leakage current, threshold voltage, and gate oxide integrity (GOI) in detail. These statistic distributions are based on a foundry’s batch production line. This study concludes that the pre-gate oxide hot water clean enhances silicon surface’s micro-roughness and stress effects, thus are responsible to the higher fluctuations of devices performance distributions. Similar results were found in the GOI of the thin gate oxide. The micro-roughness and stress effects of silicon surface were evaluated systematically through atom force microscope (AFM) and thin film stress measurement system, and their mechanisms are interpreted comprehensively with schematic models.