金属互连电迁移噪声的分形特征

为了研究金属互连电迁移失效机理并寻找新的电迁移表征参量，应用分形理论，通过电子扩散轨迹分形维数，将电迁移噪声时间序列分形维数与晶粒间界分形维数相联系，确定了噪声时间序列分形维数在电迁移演变中的变化趋势.研究结果表明，在金属互连电迁移前期，晶粒间界形貌越来越复杂，致使噪声时间序列的分形维数逐渐增大；成核后，由于空位凝聚成空洞，晶粒间界形貌变得较成核前规则，致使噪声时间序列的分形维数减小；成核时刻是其折点.实验结果证明理论分析的正确性，噪声时间序列的分形维数可望作为金属互连电迁演变的表征参量.     

金属互连电迁移噪声的相关维数研究

针对金属铝互连中噪声信号随电迁移过程变化规律及其所反映的内部失效机理问题，提出将相关维数用于对电迁移噪声时间序列的分析.通过对互连电迁移噪声实验数据的相关维数计算，发现随着电迁移的进行，金属铝互连噪声由随机性成分占主导变为确定性成分占主导，反映出噪声由随机信号转变为混沌动力学信号.应用散射理论解释上述现象，在金属互连电迁移中，空位扩散阶段噪声主要产生机制是空位随机散射；在空位聚集到空洞成核这一过程中，噪声产生机制逐渐从随机散射转变到弹道混沌腔输运机制为主.通过与传统表征参量的对比，证明相关维数可用于预测金 关键词： 电迁移 噪声 相关维数 混沌     

金属互连电迁移噪声的多尺度熵复杂度分析

针对传统频域方法用于分析金属铝互连中的噪声信号的局限性,本文采用多尺度熵方法分析电迁移噪声时间序列.结果表明在电迁移早期,噪声信号较不规律,复杂度较大;随空洞成核的发生,噪声信号规律性增强,复杂度明显减小,反映出随电迁移过程的进行系统的混乱度不断减小.通过与传统表征参量的对比,证明多尺度熵能够对电迁移失效过程进行表征. 关键词： 电迁移 噪声 多尺度熵 复杂度     

Al互连线和Cu互连线的显微结构

利用电子背散射衍射(EBSD)技术，测量了由反应离子刻蚀工艺(RIE)制备的Al互连线和大马士革工艺(Damascene)制备的Cu互连线的显微结构，包括晶粒尺寸、晶体学取向和晶界特征.分析了Cu互连线线宽，及Al和Cu互连线退火工艺对互连线显微结构及电徙动失效的影响.     

Effect of thermal fluctuations on the coarsening dynamics of 2D hexagonal system

The dynamics of ordering in a 2D hexagonal system was investigated through the Cahn-Hilliard-Cook model. At low thermal noise amplitudes, pinning forces acting on grain boundaries dominate the dynamics and the coarsening evolves logarithmically in time. As noise amplitude increases, fluctuations becomes large enough to unlock dislocations located along grain boundaries and the grain boundary motion is driven by curvature. The grain boundary relaxation leads to a grain structure with Lifshitz's configurations. In this case the dynamic is also logarithmic as a consequence of the pinning of triple points.     

超大规模集成电路互连电迁移自由体积电阻模型

将晶核析出的Avrami 方程应用于描述超大规模集成电路中金属Al薄膜互连电迁移过程中电阻的演变. 根据电子散射理论，晶界电阻主要起源于晶界处空位或者空洞对电子的散射. 为了描述这些离子的特征，引入了自由体积的概念，将晶界处电子散射这个复杂的过程简化用自由体积的有效散射截面来描述，从而建立了自由体积与电阻变化的定量关系，统一描述了电迁移过程中不同阶段的电阻变化. 数值模拟结果表明，在第一个空洞成核时刻电阻会发生急剧变化，这一结果已被实验所证实. 关键词： 电迁移 Al互连 电阻变化     

The structural properties of Al doped ZnO films depending on the thickness and their effect on the electrical properties

In this study, the structural and electrical properties of AZO films with different film thickness deposited by r.f. magnetron sputtering were interpreted in relation with film growth process. The result shows that the grain size increases during film growth, which is accompanied by decrease of compressive stress, indicating the enhancement of crystallinity. The relationship between grain size and compressive stress follows the same tendency for the samples regardless of deposition temperature, which implies the strong dependencies between the grain size and the compressive stress. The XPS analysis shows that the defects such as chemisorbed oxygen and segregated Al₂O₃ cluster at grain boundary are reduced with increase of film thickness or deposition temperature, leading to increase of carrier concentration and mobility. The mobility increase is accompanied by grain size increase and compressive stress reduction, indicating the influences of grain boundary and crystallinity on the mobility.     

回转体边界层转捩区声辐射的预报方法研究

基于边界层理论和转捩区声辐射理论,利用Liepmann理论Krane偶极子声源改进模型,在研究回转体表面的压力梯度和声衍射损失对转捩区声辐射影响的基础上,改进了回转体边界层转捩区声辐射的预报方法。结果表明:与零压力梯度相比,逆压梯度下的转捩区将导致更高的噪声辐射,利用改进方法预报的噪声级与实验值的一致性较好。     

Effects of energy dissipation on anisotropic materials

A model and its simulations are presented to describe the effects of energy dissipation on anisotropic systems. When the current electromigration is constant, energy dissipation depends on lattice constants, resistivity, and the angles along the longitudinal and transversal directions. It is shown that an orientation variation of the grain can significantly influence the energy dissipation for some anisotropic materials. Based on calculations for the grain model, the mechanism of grain growth and microstructure evolution under electromigration is explained. Theoretical implications about material selection and reliability are derived.     

Grain Boundary Resistivity and Electrically Induced Grain Boundary Migration (EIGM) in Metallic Bamboo Microstructures

As VLSI conductor line dimensions continue to decrease, electrotransport properties increasingly effect device lifetimes. Grain boundaries are intimately linked to these processes, providing paths of varying diffusivity, and as mobile defects themselves. Haessner et al. [6] make a challenging finding in experiments with thin gold films: based on calorimetric data, in order to account for the velocity of grain boundaries migrating in high electric current densities, the force on the atoms of a grain boundary would have to be two orders of magnitude larger than what the accepted theory for bulk ions predicts. The failure is attributed to the simplicity of the model which does not account for possible variations of the resistivity and effective valance charge that could occur in the vicinity of a grain boundary. In this paper, expressions are developed for the electron wind force on the atoms near grain boundaries, and they are written in terms of thermodynamic variables: the boundary specific volume expansion and specific resistivity. The enhancement of the wind force of the boundary atoms over the bulk wind force is calculated using published data. This model allows for more than an order of magnitude enhancement in gold, and Haessner's observation is rationalized.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.     

Magnetic field dependence of conductance and conduction noise of an artificial grain boundary junction in a La0.67Ba0.33MnO3 epitaxial thin film

A single artificial grain boundary in La_0.67Ba_0.33MnO₃ (LBMO) thin film has been prepared by depositing the film on a bicrystal substrate using laser ablation technique. We investigated the magnetic field dependence of magnetoresistance and conductance-voltage characteristics of the grain boundary at 77 K. A decrease of nonlinearity of current-voltage characteristics was observed upon application of magnetic field. The results are explained by assuming the presence of two different types of parallel conducting channels (metallic and highly resistive) across the grain boundary. The analysis of the results reveals that the application of magnetic field suppresses magnetic disorders at the grain boundary region and increases metallic conduction channels across the grain boundary. The temperature dependence of the conduction noise of the bicrystal grain boundary was measured at 0 and 1.5 kG magnetic field and compared with a microbridge on the LBMO film having no grain boundary. The presence of the grain boundary was found to enhance noise by one order of magnitude. The noise of a bicrystal grain boundary showed a decrease in the presence of 1.5 kG magnetic field for T<210 K. This decrease of noise confirms that the application of a magnetic field induces more metallic channels across the grain boundary.     

Copper Segregation to the Σ5 (310)/[001] Symmetric Tilt Grain Boundary in Aluminum

New insight into the atomic segregation of copper to an aluminum grain boundary has been obtained using multiple, complementary atomic resolution electron microscopy techniques coupled with ab-initio electronic structure calculations. The copper segregation is site specific and changes the structure of the boundary by occupying interstitial sites. Minor elemental constituents in materials can have profound effects on their engineering performance. This change in structure can be associated with these strong effects. The observed structural change will alter the mass transport behavior of the boundary and has implications for the understanding of electromigration mechanisms.     

基于微观结构的Cu互连电迁移失效研究

提出了一种基于微观晶粒尺寸分布的Cu互连电迁移失效寿命模型. 结合透射电子显微镜和统计失效分析技术, 研究了Cu互连电迁移失效尺寸缩小和临界长度效应及其物理机制. 研究表明, 当互连线宽度减小, 其平均晶粒尺寸下降并导致互连电迁移寿命降低. 小于临界长度的互连线无法提供足够的空位使得铜晶粒耗尽而发生失效. 当互连长度大于该临界长度时, 在整个电迁移测试时间内, 部分体积较小的阴极端铜晶粒出现耗尽情况. 随着互连长度的增加该失效比例迅速增大, 电迁移失效寿命减小. 当互连长度远大于扩散长度时, 失效时间主要取决于铜晶粒的尺寸, 且失效寿命和比例随晶粒尺寸变化呈现饱和的波动状态. 关键词： Cu 互连 电迁移 微观结构     

Speech enhancement based on the discrete Gabor transform and multi-notch adaptive digital filters

This paper presents a new method to speech enhancement based on time-frequency analysis and adaptive digital filtering. The proposed method for dual-channel speech enhancement was developed by tracking frequencies of corrupting signal by the discrete Gabor transform (DGT) and implementing multi-notch adaptive digital filter (MNADF) at those frequencies. Since no a priori knowledge of the noise source statistics is required this method differs from traditional speech enhancement methods. Specifically, the proposed method was applied to the case where speech quality and intelligibility deteriorate in the presence of background noise. Speech coders and automatic speech recognition (ASR) systems are designed to act on clean speech signals. Therefore, corrupted speech signals by the noise must be enhanced before their processing. The method uses a primary input containing the corrupted speech signal while a reference input containing the noise only. In this paper, we designed MNADF instead of single-notch adaptive digital filter and used DGT to track frequencies of corrupting signal because fast filtering process and fast measure of the time-dependent noise frequency are of great importance in speech enhancement process. Therefore, MNADF was implemented to take advantage of fast filtering process. Different types of noises from Noisex-92 database were used to degrade real speech signals. Objective measures, the study of the speech spectrograms and global signal-to-noise ratio (SNR), segmental SNR (segSNR), Itakura-Saito distance measure as well as subjective listing test demonstrated consistently superior enhancement performance of the proposed method over traditional speech enhancement method such as spectral subtraction. Combining MNADF and DGT, excellent speech enhancement was obtained.     

Dye laser model with pump and quantum fluctuations; colored noise

A single mode dye laser model with two stochastically fluctuating forces representing pump and quantum fluctuations is discussed. In extension to a previous paper we investigate the different influences ofcolored pump noise andwhite quantum fluctuations on the laser light statistics. The corresponding two-variable Fokker-Planck equation is solved by means ofmatrix continued fractions. A comparison to the model with two white noise forces is also included. We focus especially on the intensity correlation time enhancement observed for low noise strengths which seems to be the result of a competition between (multiplicative) pump noise and (additive) quantum noise. An increase in correlation time of the colored pump noise causes the intensity correlation time enhancement to disappear.     

Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established. Solving multi-phase field models for thin interface layer thickness conditions, the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt% camphor model alloy bi-crystals are investigated. The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed. The obtained results are shown below. In the competitive growth of convergent bi-crystals, when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large, the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite, blocking the unfavorably oriented dendrite, and the grain boundary is along the growth direction of the favorably oriented dendrite. When the pulling speed becomes small, the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite, eliminating the favorably oriented dendrite. In the process of competitive growth of divergent bi-crystal, when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small, the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains, and as the orientation angle of unfavorably oriented dendrites becomes larger, the unfavorably oriented grains are more likely to have stable secondary dendritic arms, which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space, but the grain boundary direction is still parallel to favorably oriented dendrites. In addition, the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes, this blocking of the tertiary dendritic arms has a random nature, which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.     

利用Pr_(70)Cu_(30)晶界扩散改善烧结钕铁硼废料矫顽力的研究

钕铁硼磁体制备过程中出现的部分块体废料由于矫顽力较低,性能难以满足使用要求.本文主要通过晶界扩散技术来提高废料磁体的矫顽力.采用Pr_(70)Cu_(30)合金作为扩散介质,对烧结钕铁硼废料磁体进行了晶界扩散处理,研究了扩散温度、扩散时间和回火时间对扩散后的磁体性能的影响.结果显示,800℃下扩散3 h,磁体的矫顽力从原来的7.88 kOe(1 Oe=79.5775 A/m)提升至11.55 kOe,提升幅度为46.6%,同时剩磁没有明显降低.扩散后回火对矫顽力的提升有一定的作用.800℃下扩散4h后的磁体在500℃回火3h后,最高矫顽力可达11.97 kOe,比原磁体废料提高了51.9%,接近成品磁体的水平.显微组织分析证实了晶界扩散的作用.扩散处理后的磁体中,主相晶粒间形成了连续晶间相,起到有效的磁隔离作用,有利于矫顽力的提高.研究还发现,Pr_(70)Cu_(30)晶界扩散虽然可以使磁体腐蚀电位上升,但也会增加腐蚀电流密度,不利于磁体抗腐蚀性的改善.本文工作对于提高材料的成品率具有重要意义.