The effect of grain size and film thickness on the thermal expansion coefficient of copper thin films

Cu thin films underwent thermal cycling to determine their coefficient of thermal expansion (CTE). The thermal stress of the Cu thin films with various microstructures (different grain size and film thickness) was measured using a curvature measurement system. The thermal expansion coefficients of the films were obtained from the slope of the stress-temperature curve with the knowledge of the Young's modulus and Poisson's ratio. The change in thermal stress with temperature of the Cu thin films tended to decrease with increasing grain size, resulting in an increase in the CTE. The thickness of Cu thin film had little effect on the thermal stress or the CTE.     

The effect of linear thermal expansion on the temperature coefficient of resistance of double-layer thin metallic films

A general theoretical expression for the temperature coefficient of resistance of double-layer thin metallic films, based on the well known Fuchs-Sondheimer model, is derived. This expression includes the linear thermal expansion coefficients and Poisson's ratios of the double layers and the substrate, also the film dimensions and temperature coefficient of resistance of the double-layer thin film, with and without the thermal expansion of both the film layers and the substrate. Numerical calculations are carried out for gold-silver double-layer films deposited on a glass substrate, where variations in the temperature coefficient of resistance depending on thermal expansion are studied as a function of reduced film thickness. The computed numerical results, using the derived new expression for the temperature coefficient of resistance of the double-layer thin metallic films, show that the thermal expansion decreases the value of the temperature coefficient of resistance.     

Modeling of relaxation of viscoelastic stresses in multi-layered thin films/substrate systems due to thermal mismatch

Assume the ratio of the total axial rigidity of thin films to that of the substrate is smaller than 0.02, an approximate closed-form solution for viscoelastic stresses in multi-layered thin films/substrate systems due to thermal mismatch is derived. This is achieved by utilizing the analogy between the governing field equation of elasticity and the Laplace transform with respect to time of the viscoelastic field equation. Based on two solutions, simplified solutions for relaxation of residual stresses distributed in multiple layers of thin films deposited on a thick substrate are obtained. The effect of the thickness, thermal expansion coefficient, Young's modulus, and viscosity coefficient of the substrate and thin films on the relaxation of residual stresses is considered. This simplified solution can be applied to some special cases such as one layered or periodic multi-layered thin films on a thick substrate.     

用热弯实验方法决定导电薄膜的热膨胀系数

研究了热-力载荷下薄膜/基板复合梁的弯曲问题,导出了薄膜的热膨胀系数与试样表面的温度和变形之间的关系式;提出一种测量导电薄膜的热膨胀系数的方法,并用热弯实验测SnO₂膜的热膨胀系数。      

Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry

Abstract

This paper reports on the application of a phase shifting interferometry technique for the concurrent measurement of the thermal expansion coefficient α_f and the elastic modulus E_f /1 - V_f of Ta₂O₅ thin film. The Ta₂O₅ films were prepared by ion beam sputter deposition. The stresses in the thin films were measured with the phase shifting interferometry technique using two types of circular discs with known thermal expansion coefficients, Young's moduli and Poisson's ratios. The temperature-dependent stress behaviour of Ta₂O₅ films was obtained by heating samples in the range from room temperature to 70°C. The internal stresses of Ta₂O₅ thin films deposited on the BK-7 and Pyrex glass substrates were plotted against the stress measurement temperature, showing a linear dependence. From the slopes of the two lines in the stress versus temperature plot, the thermal expansion coefficient and the elastic modulus of Ta₂O₅ thin film are then calculated.     

Quantitative characterization of the composition, thickness and orientation of thin films in the analytical electron microscope

Compositional variations in thin films can introduce lattice-parameter changes and thus create stresses, in addition to the more usual stresses introduced by substrate-film mismatch, differential thermal expansion, etc. Analytical electron microscopy comprising X-ray energy-dispersive spectrometry within a probe-forming field-emission gun scanning transmission electron microscope (STEM) is one of the most powerful methods of composition measurement on the nanometer scale, essential for thin-film analysis. Recently, with the development of improved X-ray collection efficiencies and quantitative computation methods it has proved possible to map out composition variations in thin films with a spatial resolution approaching 1-2 nm. Because the absorption of X-rays is dependent on the film thickness, concurrent composition and film thickness determination is another advantage of X-ray microanalysis, thus correlating thickness and composition variations, either of which may contribute to stresses in the film. Specific phenomena such as segregation to interfaces and boundaries in the film are ideally suited to analysis by X-ray mapping. This approach also permits multiple boundaries to be examined, giving some statistical certainty to the analysis particularly in nano-crystalline materials with grain sizes greater than the film thickness. Boundary segregation is strongly affected by crystallographic misorientation and it is now possible to map out the orientation between many different grains in the (S)TEM.     

Coatings for wear and lubrication

In this paper we review the recent advances in the tribological uses of r.f.-sputtered and ion-plated films of solid film lubricants (laminar solids, soft metals, organic polymers) and wear-resistant refractory compounds (carbides, nitrides, silicides). The sputtering and ion-plating potentials and the corresponding coatings formed are evaluated relative to the friction coefficient, wear endurance life and mechanical properties. The tribological and mechanical properties of each kind of film are discussed in terms of film adherence, coherence, density, grain si morphology, internal stresses and thickness and substrate conditions such as temperature, topography, chemistry and d.c. biasing. The ion-plated metallic films in addition to improved tribological properties also have better mechanical properties such as tensile strength and fatigue life.     

General expression for the temperature coefficient of resistivity of polycrystalline semi-metal films

After calculating the different contributions to the resistivity of a thin film, a general expression for the temperature coefficient of resistivity in a polycrystalline semi-metal film is derived by taking into consideration the influence of internal size effects on the film resistivity in terms of the Mayadas-Shatzkes function, thermal strains and the difference in the thermal expansion coefficients between the film and its substrate. A comparison with experimental data, in the temperature range 77 to 500 K, over grain size range 30 to 200 nm, for antimony films, 200 nm thick, is made. Good agreement has been found between experiments and the theoretical equations we proposed.     

Sc2W3O12薄膜制备及其负热膨胀性能

采用脉冲激光沉积法制备了斜方相Sc₂W₃O₁₂薄膜。利用X射线衍射仪(XRD)和场发射扫描电镜(FESEM)对Sc₂W₃O₁₂靶材和Sc₂W₃O₁₂薄膜组分、表面形貌和靶材断面形貌进行表征, 研究衬底温度与氧分压对薄膜制备的影响。采用变温XRD和热机械分析仪(TMA)分析了Sc₂W₃O₁₂陶瓷靶材和薄膜的负热膨胀特性。实验结果表明: 经1000℃烧结6 h得到结构致密的斜方相Sc₂W₃O₁₂陶瓷靶材, 其在室温到600℃的温度范围内平均热膨胀系数为-5.28×10^-6 K^-1。在室温到500℃衬底温度范围内脉冲激光沉积制备的Sc₂W₃O₁₂薄膜均为非晶态, 随着衬底温度的升高, 薄膜表面光滑程度提高; 随着沉积氧压强增大, 表面平整性变差。非晶膜经1000℃退火处理7 min后得到斜方相Sc₂W₃O₁₂多晶薄膜, 在室温到600℃温度区间内, Sc₂W₃O₁₂薄膜的平均热膨胀系数为-7.17×10^-6 K^-1。     

Microplasticity phenomena in thermomechanically strained nickel thin films

Magnetron sputtered Ni thin films on both oxidised Si (100) and α-Al₂O₃ (0001) substrates of thickness 150–1000 nm were tested thermomechanically with a wafer curvature system, as well as in situ in a transmission electron microscope. The films on oxidised Si have a {111}-textured columnar microstructure with a mean grain size similar to the film thickness. On (0001) α-Al₂O₃ a near single crystal epitaxy with two growth variants is achieved leading to a significantly larger grain size. The thermomechanical testing was analysed in terms of the room temperature/high temperature flow stresses in the films and the observed thermoelastic slopes. It was found that the room temperature flow stresses increased with decreasing film thickness until a plateau of ∼1100 MPa was reached for films thinner than 400 nm. This plateau is attributed to the present experiments exerting insufficient thermal strain to induce yielding in these thinner films. At 500 °C the compressive flow stresses of the films show a competition between dislocation and diffusion mediated plasticity. A size effect is also observed in the thermoelastic slopes of the films, with thinner films coming closer to the slope predicted by mismatch in thermal expansion coefficients. It is put forward here that this is due to a highly inhomogeneous stress distribution in the films arising from the grain size distribution.     

共聚低热膨胀聚酰亚胺薄膜的制备与表征

以4,4′-(六氟异丙烯)二酞酸酐(6FDA)为含氟二酐,4,4′-二氨基-2,2′-双三氟甲基联苯(TFMB)为含氟二胺,通过引入分子结构相对对称的刚性单体1,2,4,5-均苯四甲酸二酐(PMDA)进行共聚合成了5种含氟比例不同的透明聚酰亚胺薄膜,并对其性能进行了表征。分析表明:引入刚性单体共聚后薄膜的热稳定性和耐热性有所提高;薄膜的介电常数随着PMDA含量的上升而增加;共聚薄膜在可见光领域的透光率低于均聚薄膜;拉伸实验显示在添加少量PMDA后,薄膜的拉伸强度和弹性模量有所增大,但当PMDA含量过高时其力学性能反而下降;随着PMDA含量的增加,薄膜的热膨胀系数明显降低。     

The domain switching and structural characteristics of PLZT bulk ceramics and thin films chemically prepared from the same acetate precursor solutions

Lead lanthanum zirconate titanate (PLZT) ferroelectrics were produced in bulk ceramic and thin-film form from the same acetate precursor solutions in order to compare their electrical and physical properties. Bulk ceramics were hot pressed from chemically coprecipitated powders, and thin films were fabricated by spin coating on silver foil and platinum-coated silicon wafer substrates. A number of PLZT compositions were investigated, including ferroelectric memory materials near the morphotropic phase boundary with 2% La, memory and slim-loop ferroelectric x/65/35 (La/Zr/Ti) compositions with up to 12% La, as well as some antiferroelectric thin-film materials. Internal film stress from thermal expansion mismatch between films and substrates was found to contribute to differences in electrical properties and Curie temperatures between the thin film and bulk materials, as were interface layers between the films and substrates, mechanical clamping from the substrates and grain size.     

Polyimide/sepiolite nanocomposite films: Preparation, morphology and properties

Polyimide/sepiolite nanocomposite films have been prepared via an in situ polymerization method. The process involves the dispersion of sepioite in N,N-dimethylacetamide, polycondensation of 2,2′-bis [4-(3,4-dicarboxyphenoxy) phenyl] propane dianhydride and 4,4′-oxydianiline in the presence of sepiolite suspension to form poly(amic acid), and the thermal imidization of poly(amic acid)/sepiolite nanocomposite. The morphology, thermal and mechanical performance, and water absorption of nanocomposite films were systematically studied with various sepiolite contents. The results indicated that sepiolite was dispersed homogeneously at a nanometer scale in polyimide matrix. Owing to such nanodispersion of sepiolite, the polyimide/sepiolite nanocomposite films exhibit dramatic improvements on the mechanical properties and the coefficient of thermal expansion while fine thermal stability and low water absorption capacity were also maintained. When the sepiolite content increased to 16% the polyimide/sepiolite nanocomposite film achieved as much as 41% and 94% increase on the tensile strength and modulus respectively, and 50% decreased in coefficient of thermal expansion.     

Study of adhesion of carbon nitride thin films on medical alloy substrates

The adhesion improvement of biocompatible thin films on medical metal alloy substrates commonly used for joint replacement implants is studied. Diamond-like carbon (DLC) and carbon nitride (CN) thin films are, because of their unique properties such as high hardness, wear resistance and low friction coefficient, candidates for coating of medical implants. However, poor adhesion on substrates with high thermal expansion coefficient limits their application. We deposited CN films by pulsed DC discharge vacuum sputtering of graphite target on CoCrMo and Ti6Al4V substrates. Surface nitridation of the substrate, changing the deposition parameters and use of interlayer led to improved adhesion properties of the films. Argon and nitrogen gas flow, thickness of the film and frequency of the deposition pulses had significant influence on the adhesion to the substrate. Properties of deposited films were analyzed using Scanning Electron Microscopy, Raman spectroscopy and tribology tests.     

Residual stresses in thin polymer films cause rupture and dominate early stages of dewetting

In attempting to reduce the size of functional devices, the thickness of polymer films has reached values even smaller than the diameter of the unperturbed molecule. However, despite enormous efforts for more than a decade, our understanding of the origin of some puzzling properties of such thin films is still not satisfactory and several peculiar observations remain mysterious. For example, under certain conditions, such films show negative expansion coefficients or show undesirable rupture although energetically they are expected to be stable. Here, we demonstrate that many of these extraordinary effects can be related to residual stresses within the film, resulting from the preparation of these films from solution by fast evaporation of the solvent. Consequently, depending on thermal history and ageing time, such films show significant changes even in the glassy state, which we quantify by dewetting experiments and corresponding theoretical studies. Identifying the relevance of frozen-in polymer conformations gives us a handle for manipulating and controlling properties of nanometric thin polymer films.     

Galvanomagnetic Properties of Bi<Subscript>95</Subscript>Sb<Subscript>5</Subscript> Thin Films on Substrates with Different Thermal Expansions

Results of an investigation of galvanomagnetic properties of Bi₉₅Sb₅ block thin films on substrates with different coefficients of thermal expansion covered with polyimide are presented. The difference between thermal expansions of the film material and the substrate was found to have a strong effect on the films’ galvanomagnetic properties. Analysis of the properties of the films using the two-band model showed that the concentration and mobility of the charge carriers in the Bi₉₅Sb₅ films are related to the coefficient of thermal expansion of the substrate material.     

添加剂的膨胀系数对Y-TZP力学性能的影响

通过在Y-TZP中加入不同膨胀系数的玻璃相添加剂,低温烧结得到了具有不同力学性能的试样.建立了薄晶界应力模型,定性地计算了晶界应力,讨论了添加剂的热膨胀系数对Y-TZP陶瓷晶界应力及力学性能的影响.发现小膨胀系数的添加剂使晶界获得压应力,有利于获得较高断裂韧性的Y-TZP陶瓷.     

Effect of surface tension and coefficient of thermal expansion in 30 nm scale nanoimprinting with two flexible polymer molds

We report on nanoimprinting of polymer thin films at 30?nm scale resolution using two types of ultraviolet (UV)-curable, flexible polymer molds: perfluoropolyether (PFPE) and polyurethane acrylate (PUA). It was found that the quality of nanopatterning at the 30?nm scale is largely determined by the combined effects of surface tension and the coefficient of thermal expansion of the polymer mold. In particular, the polar component of surface tension may play a critical role in clean release of the mold, as evidenced by much reduced delamination or broken structures for the less polarized PFPE mold when patterning a relatively hydrophilic PMMA film. In contrast, such problems were not notably observed with a relatively hydrophobic PS film for both polymer molds. In addition, the demolding characteristic was also influenced by the coefficient of thermal expansion so that no delamination or uniformity problems were observed when patterning a UV-curable polymer film at room temperature. These results suggest that a proper polymeric mold material needs to be chosen for patterning polymer films under different surface properties and processing conditions, providing insights into how a clean demolding characteristic can be obtained at 30?nm scale nanopatterning.     

Inkjet printing of conductive Ag lines and their electrical and mechanical characterization

This paper aims to investigate the effects of the substrate, the printed line thickness and the sintering temperature on the electrical resistivity, Young's modulus and hardness of inkjet-printed Ag thin films. Electrical resistivity was determined from the four-point method and Young's modulus and hardness were evaluated from nanoindentation test. Several models for evaluating Young's modulus and hardness were used and compared to account for the influence of substrates. It is noted that Ag lines on glass have higher resistance and resistivity than those on polyimide (PI) since Ag lines on glass and PI have tensile and compressive residual thermal stresses, respectively, due to the difference of coefficient of thermal expansion between Ag lines and substrates. Young's modulus of Ag films on glass can be predicted by the modified King and Bec models considering the substrate effect, but these models offer unstable results for Ag films on PI. Young's modulus and hardness of Ag films increase with the sintering temperature, and they are little affected by the film thickness when fully sintered.     

Stability of NiO membranes on photostructurable glass substrates for micro solid oxide fuel cells

NiO thin films with thicknesses in the range of 100 to 900 nm were deposited by spray pyrolysis onto photostructurable glass substrates and, ultimately, free-standing membranes with diameters of 100, 200 and 300 µm were fabricated using these thin films. The membranes are intended to act as simplified anodes or anode current collectors in micro solid oxide fuel cells (µSOFCs) and their differential pressure and thermal stability were characterized. The membranes tolerated a differential pressure between 13,700 and 158,600 Pa. Smaller membranes showed more pressure tolerance than larger membranes. A membrane diameter of 100 µm and a film thickness of 400-500 nm turned out to be a promising geometry for µSOFC membranes. All membranes survived temperatures higher than the intended operating temperature of µSOFCs (350-600 °C). We attribute the good thermal stability to the match of the thermo-mechanical properties of the substrate and the NiO thin films for the lower temperature regime and the substrate softening at higher temperatures releasing stresses in the thin films. Furthermore, the thermal expansion of the substrate is close to thermal expansion of materials used in SOFCs and circular geometries can be realized using wet etching.