介观材料力学

1、材料的介观力学性能评价及尺度效应材料的介观力学性能评价及尺度效应参考书目：参考书目：L. B. Freund and S. Suresh, Thin Film Materials: Stress, Defect Formation,and Surface Evolution Cambridge University Press, Cambridge,2003(2) W. D. Nix, Metall. Trans. A 20 (1989) 2217.2Size10-3 10-6 10-6 10-8 10-3 连续介质理论连续介质理论分子动力学分子动力学介观介观什么是介观？什么是介观？3材料介观

2、力学性能评价的意义材料介观力学性能评价的意义微米尺寸材料的广泛应用微米尺寸材料的广泛应用MEMSCuOSGSiNTaNIntel 90 nm interconnect集成电路集成电路互连导线互连导线4块体块体材料强度随晶粒尺寸的变化材料强度随晶粒尺寸的变化材料材料介观介观力学性能？力学性能？微米尺寸下微米尺寸下材料安全选择材料安全选择与与性能预测性能预测的需要的需要材料介观力学性能评价的意义材料介观力学性能评价的意义5强度强度材料力学材料力学性能指标性能指标延性延性韧性韧性承载能力承载能力可发生变形的能力可发生变形的能力抵抗断裂的能力抵抗断裂的能力强度强度延性延性韧性韧性疲劳！疲劳！6提纲提纲

3、1. 金属薄膜的准静态力学性能金属薄膜的准静态力学性能2. 金属薄膜的疲劳性能金属薄膜的疲劳性能3. 微小柱状单晶试样的力学性能微小柱状单晶试样的力学性能7弹性模量弹性模量：弹性变形的抗力：弹性变形的抗力1. 宏观材料的力学性能评价宏观材料的力学性能评价强强 度度：承载能力：承载能力塑塑 性性：变形能力：变形能力韧韧 性性：变形功：变形功 能量概念能量概念硬硬 度度：材料软硬程度：材料软硬程度万能材料实验机万能材料实验机常用试样形貌常用试样形貌8块材压入测试简介块材压入测试简介1. 金属薄膜的静态力学性能金属薄膜的静态力学性能纳米压入仪测量纳米压入仪测量布氏硬度压痕布氏硬度压痕布氏布氏：稳定：

4、稳定/压痕大压痕大洛氏硬度压痕洛氏硬度压痕洛氏洛氏：压痕小：压痕小/不稳定不稳定维氏维氏：兼有：兼有布氏布氏和和洛氏洛氏的优点的优点9加载加载卸载卸载薄膜薄膜基体基体1. 金属薄膜的静态力学性能金属薄膜的静态力学性能纳米压入仪测量纳米压入仪测量10H 硬度硬度A 压头接触面积压头接触面积Ef 薄膜弹性模量薄膜弹性模量压头接触面积函数压头接触面积函数1. 金属薄膜的静态力学性能金属薄膜的静态力学性能纳米压入仪测量纳米压入仪测量11不足：不足：基体影响基体影响压头周围材料堆积或塌陷压头周围材料堆积或塌陷尺寸效应问题尺寸效应问题残余应力影响残余应力影响1. 金属薄膜的静态力学性能金属薄膜的静态力学性

5、能纳米压入仪测量纳米压入仪测量121. 金属薄膜的静态力学性能金属薄膜的静态力学性能悬臂梁法悬臂梁法属于薄膜弯曲实验方法属于薄膜弯曲实验方法131. 金属薄膜的静态力学性能金属薄膜的静态力学性能悬臂梁法悬臂梁法MEMS中的微悬壁梁中的微悬壁梁聚焦离子束聚焦离子束（FIB）加工）加工MEMS用微米尺寸悬臂梁试样用微米尺寸悬臂梁试样141. 金属薄膜的静态力学性能金属薄膜的静态力学性能悬臂梁法悬臂梁法屈服应力屈服应力- -悬臂梁厚度关系曲线悬臂梁厚度关系曲线151. 金属薄膜的静态力学性能金属薄膜的静态力学性能 悬臂梁法悬臂梁法可能原因：可能原因：残余应力残余应力基体影响基体影响压头滑动压头滑动1

6、61. 金属薄膜的静态力学性能金属薄膜的静态力学性能 微桥法微桥法171. 金属薄膜的静态力学性能金属薄膜的静态力学性能单轴拉伸单轴拉伸获得材料应力获得材料应力- -应变应变最直接最直接的方法的方法自由膜自由膜微加工微加工柔性基板柔性基板粘揭粘揭溶去中间介质层溶去中间介质层溶去基板溶去基板边缘损伤、卷曲边缘损伤、卷曲装样困难装样困难试样规整试样规整制备复杂制备复杂简单易行简单易行数据可靠数据可靠181. 金属薄膜的静态力学性能金属薄膜的静态力学性能单轴拉伸单轴拉伸膜基系统拉伸曲线膜基系统拉伸曲线柔性基板柔性基板310Cu聚酰亚胺聚酰亚胺19微小力实验机微小力实验机：P = + 250 N +

7、1 N； l = + 50 mm + 5 m薄膜薄膜夹头夹头0123010203040 pure polymer Film/polymer systemStrain (%) Tensile load F (N)0.00.51.01.52.0050010001500 t = 60 nm 100 nm 275 nm 470 nm 700 nm Strain (%)Stress (MPa)1. 金属薄膜的静态力学性能金属薄膜的静态力学性能单轴拉伸单轴拉伸201. 金属薄膜的静态力学性能金属薄膜的静态力学性能单轴拉伸单轴拉伸t ：薄膜厚度：薄膜厚度 尺寸效应尺寸效应柔性基板柔性基板21Cu薄膜薄膜/聚

8、酰亚胺聚酰亚胺 晶粒尺寸晶粒尺寸 vs 薄膜厚度薄膜厚度磁控溅射薄膜沉磁控溅射薄膜沉积设备积设备t = 60 nmt = 340 nmt = 700 nm02004006008000306090 t (nm)d (nm)10152025300153045 d (nm)Frequency (%)t = 60 nm020040060001020 d (nm)Frequency (%)t = 700 nm221. 金属薄膜的静态力学性能金属薄膜的静态力学性能单轴拉伸单轴拉伸表面、界面处位错受约束表面、界面处位错受约束231. 金属薄膜的静态力学性能金属薄膜的静态力学性能 延性延性自由膜自由膜：一旦颈

9、缩，快速断裂：一旦颈缩，快速断裂Stiff substrate硬基底附着膜硬基底附着膜：基底脆断：基底脆断软基底附着膜软基底附着膜：可使薄膜延性完全表现：可使薄膜延性完全表现延性评价方法延性评价方法 ？241. 金属薄膜的静态力学性能金属薄膜的静态力学性能微裂纹统计及实时电阻法微裂纹统计及实时电阻法裂纹萌生临界应变：裂纹萌生临界应变： C薄膜表面微裂纹百分数统计薄膜表面微裂纹百分数统计实时电阻法测试实时电阻法测试05101520253035050100150200C(R-R0) / R0 (%)Strain (%)0102030405001020304050C Strain (%)Cracks

10、 density (% / m2)25实时电阻法测定临界应变实时电阻法测定临界应变0510152001020304050Strain (%) 60nm 100nm 275nm 470nm 705nm (R-R0)/R0%020040060080005101520600800100012001400y (MPa) Critical strain (%)t (nm) Critical strain Yield strength不同薄膜厚度不同薄膜厚度临界应变临界应变-屈服强度关系屈服强度关系Cu薄膜延性尺寸效应薄膜延性尺寸效应26微裂纹统计法测定临界应变微裂纹统计法测定临界应变应变应变薄薄膜膜厚厚

11、度度20%30%40%60 nm275 nm700 nm10um薄膜越薄，薄膜越薄，应变越大，应变越大，贯穿型大贯穿型大裂纹越多裂纹越多27不同薄膜厚度不同薄膜厚度微裂纹统计法测定临界应变微裂纹统计法测定临界应变0204002040Cracks density (% m-2) t = 60 nm 100 nm 275 nm 340 nm 705 nm Strain (%) c0200400600800051015Critical strain (%)t (nm) Electrical resistivity method Microcrack analyzing method两种方法结果对比两

12、种方法结果对比微裂纹测定与实时电阻测定结果相近微裂纹测定与实时电阻测定结果相近金属薄膜延性评价方法金属薄膜延性评价方法28Flexible substrate(Polymer)Rigid substrate(Silicon)Good understanding of the fatigue properties are very important !2. 金属薄膜的疲劳性能金属薄膜的疲劳性能附着膜附着膜29Polymer substrate (Stretchable)Tension-tension fatigue (Microforce tester)Key point: Subtracti

13、ng or avoiding the influence of deformed substrate 3 % elastic deformationP = 250 N + 1 mNpolyimide 2. 金属薄膜的疲劳性能金属薄膜的疲劳性能柔性基板柔性基板30Previous methods on fatigue lifetime (Nf) measurementShortcomings: complicated and structurally instable at definition pointStrain range change (Kraft et al. 2001)Extrus

14、ion density counting (Volkert et al. 2008)NfLoad-controlledSaturatedEx-situ measurement2. 金属薄膜的疲劳性能金属薄膜的疲劳性能柔性基板柔性基板31100101102103104015304560Nf(R-R0)/R0 (%)N (Cycles)Suggestion of a much more simple methodFatigue lifetime for microcrack nucleation (Verified by SEM)Relative change in ERCuIn-situ mea

15、surement2. 金属薄膜的疲劳性能金属薄膜的疲劳性能柔性基板柔性基板32Thin Cu and Al films: Nf CurvesFollowing the well-known Coffin-Manson relationship1021031041050.40.50.60.70.80.91 123Cu films 1.35 m 3.75 m (%)Nf (Cycles) 100 nm 175 nm 700 nm1021031041050.40.50.60.70.80.91 12Al films (%)Nf (Cycles) 800 nm 340 nm 80 nmAl films

16、(80nm-800nm)Cu films (100nm-3.75 m)2. 金属薄膜的疲劳性能金属薄膜的疲劳性能柔性基板柔性基板33Thin Cu films: thickness dependent NfThe thinner is the film, the longer is the NfFatigue lifetimeYield strength & ductility2. 金属薄膜的疲劳性能金属薄膜的疲劳性能柔性基板柔性基板34Comparing with others resultsShorter than others experimental results103104

17、1051060.50.60.70.80.91 12Cu films 200 nm 100 nm Wang et al. (2008) (%)Nf (Cycles) Present results 175 nm 100 nm1021031041051060.11Kraft et al. (2002) 3.1 m 1.5 m 1.1 mWang et al. (2008) 3 m Present results 1.35 m 3.75 m (%)Nf (Cycles)Cu filmsNano-thick Cu filmMicro-thick Cu films2. 金属薄膜的疲劳性能金属薄膜的疲劳性

18、能柔性基板柔性基板35In-situ testing in a SEM chamberThermal fatigueTime variant resistance and TBased on the resistance-temperature relationship, ?T (?) can be determinedMonig, et al., Rev. Sci. Ins. 75 (2004) 4997Electrical open: Nf? = ? x ?TMismatch in TEC2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板362. 金属导线的力学性能评价金属导线的力

19、学性能评价试样制备试样制备1）光刻2）显影3）溅射掩膜基体光刻胶Cu膜4）二次显影微米级线宽微米级线宽37“工工”字型试样字型试样2. 金属导线的力学性能评价金属导线的力学性能评价试样形貌试样形貌10mm10mm100um1mm5mm3mm38Previous work on the Thermal fatigue of Cu thin filmsNf vs ?T and ? Damage morphology Park et al., Thin Solid Films 504 (2006) 321Volkert et al., Thin Solid Films 515 (2007) 3253

20、300 nm-thick Cu1.5 m GS200 nm-thick Cu0.5 m GSIn all the previous reports, the Cu films have a thickness 200 nm and an average grain size 500 nm, within this region dislocation is operativeSo, how about the thermal fatigue of more thinner and more finer Cu films ?2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板39Thick

21、ness: about 60 nmGrain size: about 55 nmResistance and temperature Measurement60 nm-ultrathin Cu films/lines ( 5,10,15 m wide)A single layer of grain along the thickness051015202530556065707580406080100120140Resistance Time ms Temperature oC j = 3.2 26.5 MA/cm22. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板40Current

22、density dependent T and Nf510152025300306090120T (K)Current density (MA/cm2) 5 m 10 m 15 m510152025050010001500200025003000Time to failure (min)Current density (MA/cm2) 5 m 10 m 15 mj vs T j vs NfT j NfSize effect: the wider is the line, the longer is Nf 2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板41Two-stage fati

23、gue lifetime curves 1041051061070.010.110100T (K) 15 m 10 m 5 mhigh cycle regionlow cycle region (%)Nf (cycles) 10210410610810100.010.11 Mechanical fatigue of bulk Cu (grain size 55 m) Present 60 nm-thick Cu line (10 m wide) Thermal fatigue of 200nm Cu lines (%)Nf (cycles) Mechanical fatigue of 3m C

24、u filmLow cycle region ( j 10 MA/cm2)Thermally controlled damage Mechanically controlled damage 2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板42Damage mechanismLow cycle region:Burst to electrical openHigh cycle region:Formation of damage bands2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板43Damage bands in high cycle regionGrain extrusionTEM imageExtrusion of grain arraysDifferent from all the previous reports !2. 金属薄膜的疲劳性能金属薄膜的疲劳性能刚性基板刚性基板44AFM analysesTwo dimension AFM image70.37nm 0.005.