Size effects on the mechanical properties of thin polycrystalline metal films on substrates

An analysis of the effects of the thickness and grain size of polycrystalline thin films on substrates is presented with the objective of linking the film mismatch stress to the underlying characteristic size scales. The model is predicated on the notion that the relaxation of mismatch strain in the film is accommodated by the introduction of dislocation loops whose population, dimensions and interaction energies are controlled by the film thickness and microstructural dimensions. The model is capable of capturing the combined effects of these size scales by accounting for the interaction energies of the constrained dislocation structure, and provides quantitative predictions of the evolution of film stress during thermal excursions. The predictions of the analysis are compared with available experimental results for polycrystalline films of face-centered cubic materials on Si substrates. It is shown that the model correctly predicts the observed influence of film thickness and grain size on stress evolution during thermal excursions. Aspects of strain hardening in thin polycrystalline films with high dislocation densities are also discussed.     

Mechanical properties and microstructures of Al-Cu Thin films with various heat treatments

The relationship between microstructure and mechanical properties has been investigated in Al-Cu thin films. The Cu content in Al-Cu samples used in this study ranges from 0 to 2 wt.% and substrate curvature measurement was used to measure film stress. In thin films, the constraints on the film by the substrate influence the microstructure and mechanical properties. Al-Cu thin films cooled from high temperatures have a large density of dislocations due to the plastic deformation caused by the thermal mismatch between the film and substrate. The high density of dislocations in the thin film enables precipitates to form inside the grain even during a very rapid quenching. The presence of a large density of dislocations and precipitates will in turn cause precipitation hardening of the Al-Cu films. The precipitation hardening is dominant at lower temperatures, and solid solution hardening is observed at higher temperatures in the tensile regime. Pure Al films showed the same values of tensile and compressive yield stresses at a given temperature during stress-temperature cycling.     

Dislocation dynamics simulations of dislocation interactions and stresses in thin films

The dislocation interactions that stop threading dislocations (threads) during relaxation at increasing applied strains in single-crystal thin films are investigated using large-scale three-dimensional dislocation dynamics simulations. Threads were observed to stop via interactions with both threads and misfit dislocations (misfits). Both types of interactions were shown to depend on stress inhomogeneity. Low-stress regions enabled threads to stop in weak thread–misfit interactions even at high average film stresses. Threads were also concentrated in low-stress regions, which facilitated their interaction with other threads. Threads accumulated in thread–thread interactions, and stopped only temporarily in thread–misfit interactions. The mean free path for dislocation motion is shown to be accurately predicted from details of the inhomogeneous stress state arising from the applied strain and the misfit structure. These behaviors are analyzed to present a more complete picture of film strength, strain hardening and relaxation.     

Recent progress in thin film epitaxy across the misfit scale (2011 Acta Gold Medal Paper)

This paper discusses recent progress in thin film epitaxy across the misfit scale through the paradigm of domain matching epitaxy (DME). This epitaxy across the misfit scale is critical for integrating multifunctionality on a chip and creating smart structures for next-generation solid-state devices. There are three sources of strains that are cumulative at the growth temperature, and the relaxation process starts during the growth process. Upon cooling, unrelaxed lattice, thermal and defect strains give rise to net residual strains. In large misfit (ε ? 10%) systems, where lattice misfit strain is predominant, it can be relaxed completely, and then only thermal and defect strains remain upon cooling. In low misfit systems, all three sources contribute to the residual strain upon cooling, as result of incomplete lattice relaxation. The predominant strain relaxation mechanism in thin films is by nucleation of dislocations at the free surface, as the nucleation energy in the bulk is considerably higher. At the free surface, the activation barrier for dislocation nucleation is considerably lower at the steps. Since the step formation energy is lower under a compressive stress compared with tensile stress, it reduces nucleation energy under compressive stress and lowers the critical thickness compared with tensile stresses in thin films. Once the dislocation nucleates, it propagates or glides to the interface to relieve the strain. However, if lattice frictional stress in the film is high, most dislocations may not reach the interface, depending upon the growth temperature and rate. Thus, these two key steps, dislocation nucleation and propagation, play a critical role in the thin film relaxation process. Once the dislocations reach the interface, the atomic structure of the dislocation at the heterointerfaces determines its electronic properties, specifically trapping and recombination characteristics. It is found that the atomic structure of the dislocation is determined by the interplay between strain and chemical free energies. Thus, the dislocations (representing missing or extra planes) play a critical role in the relaxation of thin film heterostructures. This paper focuses on epitaxy across the misfit scale, based upon matching of integral multiples of lattice planes. If the misfit falls between the integral multiples, it is accommodated by the principle of domain variation, where domains alternate to accommodate the misfit. Details of epitaxy from low misfit (～4%) in Ge/Si) to large misfit (～22%) in TiN/Si are shown. In III-nitride/sapphire and II-oxide/sapphire systems, this paper deals with polar orientations, where misfit is uniform in the basal plane, and non-polar orientations, where misfit varies over an order of magnitude in the film plane. It is shown that the DME paradigm is key to the integration of thin film heterostructures across the misfit scale and other complex systems such as vanadium oxide and PZT systems on Si(1 0 0) substrates for the integration of functionalities on a computer chip. Finally, it is shown that the formation of epitaxial and self-assembled nanodots on Si(1 0 0) provides a critical advance, with tremendous implications for information and data storage and related nanomagnetics applications.     

Deformation behavior of thin copper films on deformable substrates

The role of strain hardening for the deformation of thin Cu films was investigated quantitatively by conducting specialized tensile testing allowing the simultaneous characterization of the film stress and the dislocation density as a function of plastic strain. The stress–strain behavior was studied as a function of microstructural parameters of the films, such as film thickness (0.4–3.2 μm), grain size and texture. It was found that the stress–strain behavior can be divided into three regimes, i.e. elastic, plastic with strong strain hardening and plastic with weak hardening. The flow stresses and the hardening rate increase with decreasing film thickness and/or grain size, and are about two times higher in (111)-grains compared to the (100)-grains. These effects will be discussed in the light of existing models for plastic deformation of thin films or fine grained metals.     

形变强化金属材料表面状态特征的疲劳演变研究进展

概述了形变强化技术对金属材料疲劳性能的增强机理,主要归因于残余压应力、加工硬化、微观组织等表面状态特征的协同作用。重点综述了形变强化处理后金属材料表层的残余应力、加工硬化以及微观组织等表面状态特征在热载荷、机械载荷影响下疲劳演变的研究进展,分别总结了热载荷、机械载荷以及热–机械耦合载荷等作用条件下残余应力松弛行为、加工硬化松弛行为以及微观组织的疲劳演变规律与机理,并就热载荷、机械载荷作用下残余应力松弛行为的理论预测模型进行了归纳总结。在此基础上,讨论了关于残余应力、加工硬化以及微观组织等表面状态特征因素之间内在联系的研究进展,并指出了对于上述三者之间的逻辑关系目前研究存在的不足之处,以及尚待解决的问题。最后分析了当前金属材料表面形变强化研究中存在的一些问题与不足,并对表面形变强化抗疲劳制造技术未来的发展趋势进行了展望。     

65Mn弹簧钢在弯曲应力下的松弛行为

用自行设计制造的弹簧应力松弛连续测试系统研究了淬火回火后65Mn弹簧钢的弯曲应力松弛行为.用二阶指数衰减函数对应力松弛曲线进行了拟合,结果表明决定系数很高.用TEM对应力松弛前后试样的组织变化进行了观察,发现松弛试验前为典型的回火马氏体组织,松弛试验后出现了黑白相间的条带组织,并且观察到位错的缠结和塞积.利用热激活理论对应力松弛机理进行了研究,结果表明应力松弛过程的表观激活能随时间逐渐升高,由瞬态松弛阶段的0.24 eV升高到稳态松弛阶段的0.64 eV,由此推断应力松弛瞬态阶段主要发生位错的滑移,而在稳态松弛阶段,位错通过交滑移可以绕过碳化物质点等障碍继续运动,导致塑性应变的进一步增加.     

Void formation in nanocrystalline Cu film during uniaxial relaxation test

Void formation in nanocrystalline Cu thin films with a grain size of 100 nm during uniaxial tensile relaxation experiments is quantitatively studied. Cu thin films with a two-dimensional fiber structure were deposited on heat-resistant polyimide substrates and subject to various subcritical uniform uniaxial tensile strains at an elevated temperature (∼0.3T_m), to observe void formations in nanocrystalline metals with a reduced amount of dislocation-based deformation. Microstructural observations were carried out at several stages of deformation, and the evolutions of void formation in subcritical strain levels are quantitatively discussed. A void formation model is proposed for approximating the nucleation and growth rate of voids. The resulting model shows a reasonable agreement with the observed number density and area fraction of voids for various strain levels and grain sizes. On the basis of the results, the stress and grain size dependences of the void formation process are further discussed.     

Phase-field simulations of thickness-dependent domain stability in PbTiO3 thin films

The phase-field approach is used to predict the effect of thickness on domain stability in ferroelectric thin films. The mechanism of strain relaxation and the critical thickness for dislocation formation from both the Matthews–Blakeslee and People–Bean models are employed. Thickness–strain domain stability diagrams are obtained for PbTiO₃ thin films for different strain relaxation models. The relative domain fractions as a function of film thickness are also calculated and compared with experimental measurements in PbTiO₃ thin films grown on SrTiO₃ and KTaO₃ substrates.     

Stress Study on CrN Thin Films with Different Thicknesses on Stainless Steel

The reliability of a substrate curvature-based stress measurement method for CrN thin films on substrate with fluctuant surface was discussed. The stress error led by the ignorance of substrate thermal deformation was studied. Results showed that this error could be as large as several hundred MPa under general deposition conditions. Stress in the CrN thin films with different thicknesses ranging from 110 to 330 nm on stainless steel was studied by this method, in comparison with conventional results on silicon wafer. The thin films' morphology and structure were investigated and related to the film stress. A significant result of the comparison is that stress evolution in the thin films on steel obviously differs from that on silicon wafer, not only because the two substrates have different coefficients of thermal expansion, which provokes thermal stress, but also the considerable discrepancy in the thin films' grain coarsening rate and structure that induce different intrinsic stresses.     

Surface and defect microstructure of GaN and AlN layers grown on hydrogen-etched 6H–SiC(0001) substrates

Hydrogen-etching of 6H–SiC(0001) substrates removed mechanical polishing damage and produced an array of parallel, unit cell high steps. The initial stage of AlN deposition on these etched substrates occurred via island nucleation, both on step edges and on terraces. Coalesced AlN films did not show scratch-induced undulations observed on the surfaces of AlN films deposited on as-received substrates. The films also had a lower density of growth pits. The majority of threading dislocations (TDs) observed in these films were of a type. Jagged networks of misfit dislocations were seen on the terraces in the 15 nm thick AlN/hydrogen-etched SiC composite. GaN islands nucleated primarily at undulations in AlN layers and at hillocks on the AlN surface of as-received and hydrogen-etched substrates, respectively. Complete coalescence of these islands occurred at thicknesses close to 20 nm, and subsequent growth occurred via the step-flow mechanism. Strain measurements showed more strain relaxation in GaN films grown on the hydrogen-etched substrate. On- and off-axis X-ray rocking curves revealed statistically similar full width at half maximum values for both on- and off-axis reflections, indicating similar densities of TDs in the two types of films. The majority of TDs in GaN epi-layers resulted from defective regions observed contiguous to the GaN/AlN interfaces.     

Bauschinger and size effects in thin-film plasticity

We present an experimental investigation of the effects of surface passivation, film thickness and grain size on the plastic behavior of freestanding Cu thin films. The stress–strain curves of the films are measured using the plane–strain bulge test. Films with a passivation layer on one or both surfaces have an offset yield stress that increases significantly with decreasing film thickness; the yield stress of unpassivated films, by contrast, is relatively independent of film thickness and increases mainly as a result of grain-size strengthening. The stress–strain curves of passivated films show an unusual Bauschinger effect on unloading. This effect is not observed for unpassivated films. Our experimental results suggest that passivation layers prevent dislocations from exiting the films and that they block slip bands at the film–passivation interface. The back stresses associated with these blocked slip bands increase the resistance to forward plastic flow on loading and cause reverse plastic flow on unloading. The effect of the back stresses increases with decreasing film thickness and leads to the observed strengthening of the passivated films. The constraint of a passivating layer on dislocation motion and hence on plastic flow cannot be described by classical plasticity theories, but can be modeled with some strain–gradient plasticity theories. We evaluate the suitability of the strain–gradient plasticity theory developed by Fleck and Hutchinson to describe our experimental results in a continuum framework. Comparison between experimental results and calculations yields very good agreement for the effect of film thickness, but the strain–gradient plasticity model fails to describe the Bauschinger effect observed in passivated films.     

Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques

We present a systematic study of the mechanical properties of different Cu, Ta/Cu and Ta/Cu/Ta films systems. By using a novel synchrotron-based tensile testing technique isothermal stress–strain curves for films as thin as 20 nm were obtained for the first time. In addition, freestanding Cu films with a minimum thickness of 80 nm were tested by a bulge testing technique. The effects of different surface and interface conditions, film thickness and grain size were investigated over a range of film thickness up to 1 μm. It is found that the plastic response scales strongly with film thickness but the effect of the interfacial structure is smaller than expected. By considering the complete grain size distribution and a change in deformation mechanism from full to partial dislocations in the smallest grains, the scaling behavior of all film systems can be described correctly by a modified dislocation source model. The nucleation of dissociated dislocations at the grain boundaries also explains the strongly reduced strain hardening for these films.     

Work-hardening model for polycrystalline metals under strain reversal at large strains

The mechanical behaviours under reversed strain of low carbon steels and aluminium alloys are reviewed and modelled with a simple approach based on the evolutionary laws of two dislocation densities related respectively to the forward and the backward straining. In essence, it is the competition between the annihilation of the dislocations that were created during the prestrain and the storage of newly created dislocations that lead to the observed stagnation of the hardening rate. Textural effects as well as back stresses are shown to extend or to reduce the stress–strain plateau but are not responsible for it.     

部分再结晶对NiFeCoCrMn高熵合金显微组织和拉伸性能的影响

为了调控NiFeCoCrMn高熵合金强度和塑性之间的平衡关系,采用传统的热力学加工技术(冷轧和再结晶),通过不同的再结晶退火工艺得到不同程度的位错强化,并对具有不同再结晶比例的合金进行拉伸性能测试.随着再结晶比例的增加,即应变硬化程度的下降,合金的均匀伸长率和加工硬化率显著提高,但屈服强度和抗拉强度降低.尤其在650℃...     

Work hardening induced by martensite during transformation-induced plasticity in plain carbon steel

Transformation-induced plasticity (TRIP) steels are becoming increasingly exploited for industrial applications because they show high strength and high uniform elongation (ductility). Despite this interest, the relative contributions of the various strengthening and straining mechanisms are often poorly understood. In this study, neutron diffraction is employed to quantify the contribution of different mechanisms to ductility and work hardening for a 0.25 wt.% C steel. Differences in stress–strain response at different temperatures are related to the extent of the transformation of metastable austenite into martensite during deformation. At room temperature (RT) the transformation of austenite occurs gradually with straining, while at ?50 °C the transformation occurs almost from the onset of loading. The associated transformation strain is reduced, comprising nearly half the total strain, lowering the apparent elastic modulus and explaining the relatively low work hardening compared to RT straining. By contrast, deformation at RT after pre-straining at ?50 °C results in larger work hardening than for solely RT straining due to the higher martensite levels introduced at ?50 °C. This is due to composite load transfer to the strong constituent from the soft matrix. The extent of the transformation is quantified as a function of strain at both temperatures as well as its effect on the work hardening and elongation.     

Crystallization process and shape memory properties of Ti–Ni–Zr thin films

The crystallization process of as-deposited Ti–Ni–(10.8–29.5)Zr amorphous thin films was investigated. The Ti–Ni–Zr as-deposited films with a low Zr content exhibited a single exothermic peak due to the crystallization of (Ti,Zr)Ni with a B2 structure. In contrast, a two-step crystallization process was observed in the Ti–Ni–Zr thin films with a high Zr content. Shape memory behavior of Ti–Ni–Zr thin films heat treated at 873–1073 K was investigated by thermal cycling tests under various stresses. The martensitic transformation start temperature increased with increasing Zr content until reaching the maximum value, then decreased with further increasing Zr content. The inverse dependence of transformation temperature on Zr content in the thin films with a high Zr content is due to the formation of a NiZr phase during the crystallization heat treatment. The formation of the NiZr phase increased the critical stress for slip but decreased the recovery strain.     

Microstructural evolution in passivated Al films on Si substrates during thermal cycling

In situ and post-mortem transmission electron microscopy (TEM) observations of thermally cycled Al thin films have been made to identify and characterize the deformation mechanisms that govern the thermo-mechanical response of these films. The early stages of thermal cycling were associated with grain growth, untangling and motion of low angle boundaries and the absorption of dislocations into the metal/oxide interfaces. Comparison with wafer curvature experiments indicate that mechanical saturation is related to the generation of large, relatively clean, columnar grains and that the presence of the capping layer slows the rate at which the as-deposited structure is transformed to this state. The formation of large, defect-free grains facilitated the observation of dislocation sources, the motion of threading dislocations across the Al films, and the interaction of these dislocations with local obstacles and grain boundaries. However, the density and velocity of dislocations were too low to account for the thermal strains being imposed during thermal cycling, and no misfit dislocations were observed at the metal/oxide interfaces. These latter findings point to the possible influence of diffusion-related processes.