【作者】 何亮；

【导师】 杜磊；

【作者基本信息】 西安电子科技大学 ， 物理电子学， 2011， 博士

【摘要】 自集成电路问世至今，金属互连电迁移现象一直是制约电路可靠性提升的重要因素之一。随着微电子器件持续小型化，集成电路封装不断密集化，金属互连薄膜的截面积越来越小，其承受的功率密度急剧增加，因此，由电迁移导致的互连失效已成为当今集成电路可靠性研究中最关键的问题。如何对电迁移现象进行敏感、准确且全面的表征是电迁移失效研究中的基础与根本。随着互连工艺的不断进步，对可靠性要求的不断提高，传统表征方法表现出了一定的局限性，例如，中期失效时间（MTTF）方法虽能通过统计学原理同时测定大量样品，但却无法通过失效机制对个别样品进行表征；原位检测方法虽然直观明了，但需对测试样品进行特殊的处理或制备，难以如实反映实际电路工作状态下的电迁移失效；阻抗测试方法简单易行，能有效反映空洞成核的发生，却对电迁移早期损伤与潜在损伤并不敏感。因此，需要探索能更加直接地反映电迁移失效机制且更加灵敏的表征技术与参量。噪声作为一种新型表征手段，在电子材料与元器件的可靠性研究中正在得到越来越广泛的应用，主要原因在于：1.它的测试是非破坏性的；2.它具有高的灵敏性；3.测试方法简单，不要求昂贵的测试仪器；4.建立噪声模型的步骤相对简单。本文将噪声表征应用于金属互连电迁移失效研究，提出了低阻互连噪声测试系统，建立了晶界噪声自由体积模型，进行了金属互连电迁移老化实验，提取了电迁移噪声频谱表征参量，分析了表征参量所反映的失效机理，在此基础上，认识到电迁移过程是一种复杂的动态失效过程，其噪声信号中常常带有非高斯性、非平稳性、复杂性、奇异性、浑沌性等特征，因此，采用了若干时间序列分析方法，对电迁移进行了多个角度且更加全面、深入的分析与表征。本文的主要的创新点及成果体现在：1.针对传统噪声测试系统在电迁移低阻样品测试方面的不足，建立了电迁移低阻样品双放大器串联噪声测试系统。新系统的一级放大采用超低噪声前置放大器，保证能够采集到幅度较小的样品噪声，其良好的频率响应特性确保了样品噪声的低频段不产生畸变；二级放大器具有良好的放大增益，确保样品噪声能够被准确采集，放大器串联的形式使得系统总背景噪声幅值与一级放大器背景噪声相当，有效降低了背景噪声对样品噪声的干扰。2.对电迁移噪声与电迁移主导缺陷—晶界的相互关系进行了探讨，明确了随电迁移过程的进行，晶界噪声逐渐成为主导噪声，在此基础上，将晶界等效为二维散射平面，借助自由体积概念，建立了晶界自由体积噪声模型。模型结果显示，电迁移噪声主要受晶界自由体积散射截面积S (v f)、晶界宽度、单位面积自由体积膨胀V/A等参数影响。参考晶界电子风力增强因子表达式，提出晶界噪声增强因子的概念并给出表达式，计算结果显示相对于电子风力在晶界处增大1-2个数量级，晶界处的噪声增强达到4个数量级，显示了噪声参量的高灵敏度。3.采用新提出的低阻噪声测量系统，设计了电迁移老化实验并进行了噪声测试，对测试结果进行了频谱分析，结果显示频谱幅值在电迁移前期常常呈震荡增大趋势，空洞成核时刻产生跳变，之后随空洞的生长信号可能产生低频段衰减畸变；频率指数则在空洞成核前在0.8-1.5的范围之内缓慢增大（或震荡增大），空洞成核时期突变至1.5以上。另外，频谱参量对于外部应力的变化（温度、电流密度）也非常敏感。4.证明了电迁移噪声信号具有分形特性，分形维数能够有效地区分电迁移过程的各个阶段，反映电迁移导致缺陷类型的变化及电迁移噪声产生机制的变化。通过盒子维与渗流理论将噪声时间序列分形维数与晶粒间界分形维数相联系，通过对噪声维数的表征，描述了晶界形貌随电迁移过程的演变。通过相关维数对电迁移噪声的随机性与确定性进行了表征，确定了噪声由电迁移前期的随机信号转变为电迁移后期的混沌动力学信号，反映了噪声产生机制由空位随机散射转变为空洞类弹道混沌腔输运机制。另外，通过相关维数是否收敛，可预测电迁移失效的发生。5.根据熵在刻画系统所处状态的无序性或混乱度方面的重要作用，采用多尺度熵分析方法对电迁移信号的复杂度特性进行了表征。结果表明：电迁移早期，噪声信号较不规律，其复杂度较大；电迁移空洞成核阶段，噪声信号规律性增强，复杂度明显减小。通过噪声信号的多尺度熵与热力学熵关系，表明系统混乱度以及内部微观状态数也随电迁移过程的进行而减少。更多还原

【Abstract】 Since integrate circuit was invented, electromigration in metal interco nnection hasalways been an important restrictive factor for circuit reliability upgrade. Nowadays,Microelectronics devices continue miniaturization, circuit packaging tends to denseness,the section area of interconnection is smaller and smaller, the power density it takesincreases dramatically, thereby, interconnection failure caused by electromigration hasbeen the key issue in integrated circuit reliability research.How to characterize electromigration with sensitivity, accuracy, all-sided tokenparameters is the basis of electromigration research. With the advancement of technicsand reliability requirement, traditional token methods presents some limitations, such as,the mean time to failure(MTTF) can deal with a batch of samples but can not charac terindividual sample through failure mechanism; in-situ test method is intuitionistic, butthe samples need special preparation, it can not be used to reflect electromigration inworking statement; resistance test is simple and convenient, it can reflect the voidnucleation, however, it is insensitive to electromigration forepart damage and latentdefects. Therefore, new token techniques and parameters which more sensitive anddirectly relate to electromigration failure mechanism are needed.Noise as a new token method, was used more and more extensive in electronicmaterial and devices reliability research. The main advantages lie on:1) noise isnon-destructive;2) noise has a higher sensitivity;3) noise testing is simple, and theequipments don’t cost a lot;4) the establishment of noise models are relatively easier.This paper applied noise to electromigration failure characterize, presented a lowresistance interconnection noise test system, established a grain boundary free volumenoise model, executed electromigration aging experiment, extracted electromigrationnoise frequency spectrum parameters, analysed electromigration failure mechanism.Furthermore, electromigration process is a complicated dynamic process, its noisepresents some special properties, such as nonnormality, instability, complexity,singularity and chaos etc.. In order to characterize electromigration morecomprehensive and deeper, several time series analysis methods were also adopted. Themain innovation and production of this paper lies on:1．Aimed at the shortage of traditional noise testing system in low-resistance test, anew double-amplifiers-in series electromigration noise testing system was proposed. The first amplifier adopted extremely low noise voltage amplifier, to ensure lowresistance noise can be collected. Its great frequency response makes sure lowfrequency noise do not aberrant. The second amplifier has a great magnifyingcoefficient, which ensures noise can be collected accurately. Two amplifiers in seriesmakes sure the total background noise equals to the first amplifier’s background noise,which weakened the interference of background noise effectively.2. Discussed the relationship between noise and electromigration dominantdefect-grain boundary, confirmed grain boundary noise becomes the dominant noisealong with electromigration process. Grain boundary was equivalent to a two-dimensionscattering flat, combined with free volume conception, a grain boundary free volumenoise model was established. Based on the model, electromigration noise is mainlydetermined by free volume scatter section area S (v f), grain boundary width, freevolume expansion per unit area of grain boundary V/Aetc.. Referring to theelectron wind enhancement factor, grain boundary noise enhancement factor wasproposed, the calculation showed the enhancement of noise at grain boundary reaches to4orders, comparing the1~2orders enhancement of electron wind force, theenhancement of noise at grain boundary is more remarkable.3. Based on the new electromigration noise testing system, designedelectromigration aging experiment and executed noise testing. The results showed noiseamplitude increases periodically at electromigration prophase, once void nucleationoccurs, it increases sharply, with void growth, noise shows aberrance at low-frequencyband. Frequency exponent increases slowly(or increases periodically) within the range0.8-1.5before void nucleation, once void nucleation, it breaks1.5. Besides, frequencyspectrum parameters are also sensitive to exterior stress (temperature,currentdensity)change.4. Verified electromigration noise is fractal signal, fractal dimension candistinguish every phase during electromigration process, reflect the change of defecttypes and noise generation mechanism. Through Bouligand dimension and percolationtheory, noise time series fractal dimension and grain boundary fractal dimension werebonded, through noise dimension token, grain boundary appearance change duringelectromigration can be obtained. Correlation dimension was adopted to characterizethe stochastic or determinate of electromigration noise, the results showed the noisechanged from stochastic signal to chaotic dynamic signal during electromigrationprocess, indicated the noise generation mechanism changes from stochastic dispersion to ballistic chaotic cavity transport. Furthermore, by judging the convergent ofcorrelation dimension, electromigration failure can be predicted.5. Entropy plays an important role in characterizing system irregular or disorderdegree. Multiscale entropy was adopted to analyze electromigration noise complexity.The result showed: at the early stage, electromigration noise is more irregular, noisecomplexity is greater; as void nucleation occurs, electromigration noise becomes moreregular, the complexity decreases obviously. Through the relationship between noisemultiscale entropy and system thermodynamics entropy, It reflects that the disorderdegree of electromigration system decreases continually.更多还原