Residual Stress In Thin Films Research Articles

AlN as an actuation material for MEMS applications: The case of AlN driven multilayered cantilevers

This paper treats a wide range of subjects related to the use of AlN as actuation layer in MEMS, from its deposition conditions to accurate interferometric device characterization and physical parameters extraction. The case of AlN driven multilayered cantilevers has been considered. Parameters such as Young's modulus associated to the (0 0 2) orientation of the crystallites, residual thin film stresses, thermal expansion coefficient α and piezoelectric coefficient d 31 have been calculated using non approximated equations able to take into account multiple film stacking. The well oriented thin films exhibit approximately the same properties as the bulk material.

A direct method of determining complex depth profiles of residual stresses in thin films on a nanoscale

A cantilever method of determining complex depth profiles of residual stresses is presented by means of a 840 nm thin Ni film on a Si substrate. The technique developed is based on the fabrication of a micro-cantilever and the subsequent gradual reduction of film thickness using a focused ion beam workstation. The deflection as a function of film thickness is measured directly from SEM images, and the stress distribution in the thin film is determined by means of a straightforward calculation procedure. The method can be applied to crystalline as well as amorphous materials and permits stress profiles on a nanoscale to be determined.

Fabrication, caractérisation et modélisation de micropoutres multimorphes intégrant un film piézoélectrique d'AlN comme actionneur

Cet article presente les potentialites de films d'AlN piezoelectriques comme elements actionneurs pour les MEMS. Le cas de micropoutres constituees d'un empilement de differents films (electrode/AlN/electrode/substrat Si) est presente. Un dispositif interferometrique de type Twyman-Green permet de quantifier precisement les deformees et les deplacements ce qui permet de calculer, a l'aide des equations non simplifiees, differentes grandeurs physiques des films d'AlN, par exemple le module d'Young lie a l'orientation (002) des cristallites, les contraintes residuelles consecutives au mode d'elaboration, le coefficient de dilatation α ainsi que le coefficient piezoelectrique d31. On retrouve sensiblement les valeurs du materiau massif.

Nanoparticulate origin of intrinsic residual stress in thin films

The formation of grains in thin films generates intrinsic residual stress. In this work, we present a model of intrinsic residual stress calculation based on the size-dependent phase transitions of the nanograins. Evaporated thin films are produced by condensation from the vapor on the substrate. It is assumed that the starting nanograins grow from the liquid phase. It is well established that the melting temperature of nanoparticles is a function of their size. By assuming that the intrinsic stress originates from the volume change of the nanograins, and taking into account relaxation processes, the generated intrinsic residual stress in the films is evaluated. The results of the model are compared quantitatively with experimental data obtained from Ta, Mo, Pd and Al films deposited on Si. This model also gives a theoretical interpretation of Thornton and Hoffman’s modelling of the stress-temperature diagram of thin films.

High-temperature residual stresses in thin films characterized by x-ray diffraction substrate curvature method

A new x-ray technique to determine temperature dependencies of macroscopic stresses in thin films by characterizing the substrate curvature is introduced. The technique is demonstrated on polycrystalline TiN and Al thin films deposited on Si(100) wafers. The structures are thermally cycled in the temperature range of 25-400 degrees C using a newly developed heating chamber attached to a commercial x-ray diffractometer. The curvature of the freestanding samples was determined by the rocking curve measurement of substrate Si 400 reflections at different lateral positions of the samples, and the stresses are calculated using Stoney's formula. The results show that the magnitude of the stress is in good agreement with the results obtained by other techniques. For the practical application of the technique, the sample mounting and the temperature control are of great importance.

A Novel Micro Tensile Testing Instrument with Replaceable Testing Specimen by Parylene Passivation Technique

AbstractThis study has successfully demonstrated a novel tensile testing approach to mount the thin film test specimen onto the MEMS instrument using microfabrication process. The MEMS instrument consists of thermal actuator, differential capacitance sensor, supporting spring. The thermal actuator applies tensile load on the test specimen to characterize the Young's modulus and the residual stress of thin films. As compare with the existing approaches, the problems and difficulties resulting from the alignment and assembly of thin film test specimens with the testing instrument can be prevented. Furthermore, the parylene passivation technique of MEMS fabrication process allows the changing of testing film materials easily. In application, the present approach has been employed to determine the Young's modulus and the residual stress of Al films.

A Direct Method of Determining Complex Depth Profiles of Residual Stresses in Thin Films on a Nanoscale - Mechanics of Residually Stressed Systems

AbstractThe basic ideas behind the calculation procedure of the developed ion beam layer removal method (ILR method) to determine complex depth profiles of residual stresses are explained. In order to give the readers an understanding of the mechanics of films on substrates and the corresponding stresses in cantilevers fabricated from such systems, the equations necessary for the calculations are explained by means of a residually stressed model system.

Mechanical cross-characterization of sputtered inconel thin films for MEMS applications

The characterization of Young's modulus, Poisson's ratio, linear coefficient of thermal expansion and residual stress of thin films is a critical issue for the design and development of MEMS. As inconel thin films have a relatively large thermal expansion coefficient together with a high electrical resistivity, they are good candidates for thermal actuators in MEMS. This work focuses on the determination of the mechanical properties of inconel thin films ranging from 0.4 up to 1.2 μm sputtered on a (100) silicon substrate. The atomic composition (6% Fe, 80% Ni, 14% Cr) of these films, close to that of inconel 600 alloys, has been determined by XRF analysis. A wafer curvature measurement technique is used to determine the residual stress and the linear thermal expansion coefficient. We measure residual stress between 152 and 342 MPa. The value of the linear thermal expansion coefficient is discussed but is found to be around 10 ppm/K −1. We perform bulge testing on micro machined square membranes to determine together the Young's modulus and residual stress of 0.4 μm films. Values of 166 GPa and 296 MPa are obtained, respectively. These results obtained by bulge testing are eventually compared with measurements made by nanoindentation. Good correspondence is found between the different methods.

Rapid determination of stress factors and absolute residual stresses in thin films

A methodology is presented that allows the determination of experimental stress factors in thin films on the basis of static diffraction measurements. The approach relies on the characterization of thin films deposited on a monocrystalline substrate serving as a mechanical sensor. Rocking-curve measurements of the symmetrical reflections of the substrate are used to determine the substrate curvature and subsequently the macroscopic stress imposed on the film. The elastic strain in the film is determined by lattice-spacing measurement at different sample tilt angles. The calculated experimental stress factors are applied to thin films deposited on other types of substrates and are used to determine the absolute magnitude of the residual stress. The approach is applied to nanocrystalline TiN and CrN thin films deposited on Si(100) and steel substrates, characterized using a laboratory-type θ/θ goniometer.

Analysis of Residual Stress in Thin Film Using Laser Scanning Method

The residual stresses in a polymeric thin film deposited on Si wafer induced during cooling from a cure temperature down to room temperature are investigated. The laser scanning method and the boundary element method (BEM) are employed to investigate the residual stresses. A 3 μm thick polyimide film is deposited on a relatively thick Si wafer. The normal stress across thickness of the thin film is estimated from wafer curvature measurements to be 20MPa . The boundary element method is employed to investigate the whole stresses in the film. The numerical result for the normal stress across thickness of the film, σ xx , shows good agreement with the experimental result obtained by using the laser scanning method. The singular stress is observed near the interface corner. Such residual stresses are large enough to initiate interface delamination to relieve the residual stresses.

Measurement of Residual Stresses in Thin Films by Two-Dimensional XRD

This paper introduces the recent progress in two-dimensional X-ray diffraction as well as its applications in residual stress analysis in thin films. The stress measurement with twodimensional x-ray diffraction can be done with low incident angle and is not limited to the peaks with high two-theta angles like the conventional method. When residual stresses of thin films are measured, a low incident angle is preferred to maximize the diffraction signals from the thin films surfaces instead of from the substrates and matrix materials. Since one stress measurement at one fixed incident angle is possible, stress gradients in depth can be measured by series of incident angles. Some experimental examples are given to show the stress measurement at low and fixed incident angle.

Stress Factors and Absolute Residual Stresses in Thin Films Determined by the Combination of Curvature and sin²ψ Methods

A new method is presented which allows the determination of experimental stress factors in anisotropic thin films on the basis of static diffraction measurement. The method is based on the simultaneous characterization of macroscopic stress and elastic strain in thin film using substrate curvature and sin2ψ methods, respectively. The curvature of monocrystalline substrate with known mechanical properties is determined using rocking curve measurements on substrate symmetrical reflections. The experimental stress and strain values are used to calculate stress factors for the specific film as a function sample tilt angle and reflection measured. The approach represents a relatively simple recipe to determine residual stress magnitude in thin films on the absolute scale. The procedure is demonstrated on polycrystalline Cu thin film deposited on Si(100).

Strain–energy method for determining residual stresses in anodised thin films

Residual stresses in thin films are usually evaluated either by measurement of elastic strains in the film or from the curvature or deflection of a film coated substrate material (the Stoney technique). Both methods are prone to serious measurement errors particularly for thinner films or smaller curvatures or deflections. The Stoney technique is popular because the analysis does not require the elastic modulus of the film. However, residual stress can be determined more accurately using the film modulus. A simple strain–energy analysis using this modulus has been developed to investigate residual stresses in boric acid–sulphuric acid (BSA) anodised films, based on bending measurements of thin coupons. The method is an improvement over Stoney's equation because the square root of the thickness of the film, rather than the thickness itself, is involved, therefore reducing one of the larger sources of error. The modulus of the film was determined from nanoindentation measurements. The strain–energy method allows analysis of residual stress development in the coupons as functions of film thickness and time. The results show that the residual stress in BSA anodised films formed on high strength Al–Cu alloy is highly tensile with stress levels up to 400 MPa. The effects of coupon geometry on stress development were also studied and were found to influence the final levels of residual stress developed. These results have implications for the measurement of residual stresses by beam deflection methods.

Gradient residual stress induced elastic deformation of multilayer MEMS structures

Multilayered structures are widely used as sensing or actuating components in MEMS devices. Since the thin films of multilayered structures are always subject to residual stresses, it is important to model the relation between these residual stresses and the resultant elastic deformation. The main purpose of this paper is to explore two different approaches to addressing this issue when the residual stress in each thin film is not necessarily uniform throughout the thickness. These two approaches are first briefly introduced and then used to arrive at identical solutions for a monolayer cantilever and a bilayer cantilever, both with arbitrary residual strain distributions throughout the thickness. The analytical formulas for a bilayer cantilever are further verified by the numerical simulation of a special case. After the discussion on the errors induced by assuming the gradient residual strains in the bilayer cantilevers are uniform, the relation between the bending plane and the neutral plane in bilayer cantilevers is also explored. Finally, we present an approach to characterizing residual stresses in thin films by using micromachined bilayer cantilevers in conjunction with the theory developed in this paper.

D023 Residual stresses in thin films characterized by the combination of SIN2Ψ and curvate methods: possibilities and limitations

D023 Residual stresses in thin films characterized by the combination of SIN²Ψ and curvate methods: possibilities and limitations

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.

P12 薄膜光導波路内の光伝播特性に及ぼす薄膜残留応力の影響(OS2)

P12 薄膜光導波路内の光伝播特性に及ぼす薄膜残留応力の影響(OS2)

306 半導体レーザ発光特性に及ぼす薄膜残留応力の影響(学生賞I)

306 半導体レーザ発光特性に及ぼす薄膜残留応力の影響(学生賞I)

Measurement of residual stress in multilayered thin films by a full-field optical method

Wafer level thin film residual stress is generally determined by a full-field optical method, which converts the measured curvatures into the stress using Stoney formula. During the fabrication of the IC and MEMS devices, however, multilayered thin films are often generated on both sides of the wafer simultaneously. By extending the Stoney formula, this paper presents a method for measuring residual stress in the multilayered films on the wafer. In the method, only the back film layers of the wafer need to be etched in turn and corresponding curvature radii is measured by the full-field optical method. The residual stress of each film layer may then be obtained by the radii using the extended Stoney formula. By comparing the proposed method with the existing method using the traditional Stoney formula, it is shown that the proposed method is more simple and economical for practical applications. The extended Stoney formula was verified by Coventorware. Experiments show that the proposed method is simple and accurate for process monitoring.

Residual stresses in titanium nitride thin films deposited by direct current and pulsed direct current unbalanced magnetron sputtering

This work presents a study on the effect of deposition parameters on the residual stresses developed in titanium nitride (TiN) thin films deposited onto cemented carbide (WC-Co) substrates. Depositions were conducted by reactive unbalanced magnetron sputtering of a single titanium target. Six different conditions were selected, varying parameters such as bias (0, − 50 or − 100 V), power applied to the target (direct current or pulsed direct current) and, in the cases where substrate bias was zero, substrate condition (ground or floating). Pulsed power was applied at a frequency of 50 kHz and with a reverse pulse time of 1 μs. Residual stresses were evaluated through X-ray diffraction, using the sin 2 ψ method. Results confirmed the effect of substrate bias on the residual stresses of thin films. Additionally, it was possible to observe that by pulsing the power to the target, residual stress varies as a consequence of the increased ion energy.