介觀材料力學(xué)

1、材料的介觀力學(xué)性能評價及尺度效應(yīng)材料的介觀力學(xué)性能評價及尺度效應(yīng)參考書目：參考書目：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 連續(xù)介質(zhì)理論連續(xù)介質(zhì)理論分子動力學(xué)分子動力學(xué)介觀介觀什么是介觀？什么是介觀？3材料介觀

2、力學(xué)性能評價的意義材料介觀力學(xué)性能評價的意義微米尺寸材料的廣泛應(yīng)用微米尺寸材料的廣泛應(yīng)用MEMSCuOSGSiNTaNIntel 90 nm interconnect集成電路集成電路互連導(dǎo)線互連導(dǎo)線4塊體塊體材料強度隨晶粒尺寸的變化材料強度隨晶粒尺寸的變化材料材料介觀介觀力學(xué)性能？力學(xué)性能？微米尺寸下微米尺寸下材料安全選擇材料安全選擇與與性能預(yù)測性能預(yù)測的需要的需要材料介觀力學(xué)性能評價的意義材料介觀力學(xué)性能評價的意義5強度強度材料力學(xué)材料力學(xué)性能指標性能指標延性延性韌性韌性承載能力承載能力可發(fā)生變形的能力可發(fā)生變形的能力抵抗斷裂的能力抵抗斷裂的能力強度強度延性延性韌性韌性疲勞！疲勞！6提綱提綱

3、1. 金屬薄膜的準靜態(tài)力學(xué)性能金屬薄膜的準靜態(tài)力學(xué)性能2. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能3. 微小柱狀單晶試樣的力學(xué)性能微小柱狀單晶試樣的力學(xué)性能7彈性模量彈性模量：彈性變形的抗力：彈性變形的抗力1. 宏觀材料的力學(xué)性能評價宏觀材料的力學(xué)性能評價強強 度度：承載能力：承載能力塑塑 性性：變形能力：變形能力韌韌 性性：變形功：變形功 能量概念能量概念硬硬 度度：材料軟硬程度：材料軟硬程度萬能材料實驗機萬能材料實驗機常用試樣形貌常用試樣形貌8塊材壓入測試簡介塊材壓入測試簡介1. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能納米壓入儀測量納米壓入儀測量布氏硬度壓痕布氏硬度壓痕布氏布氏：穩(wěn)定：

4、穩(wěn)定/壓痕大壓痕大洛氏硬度壓痕洛氏硬度壓痕洛氏洛氏：壓痕小：壓痕小/不穩(wěn)定不穩(wěn)定維氏維氏：兼有：兼有布氏布氏和和洛氏洛氏的優(yōu)點的優(yōu)點9加載加載卸載卸載薄膜薄膜基體基體1. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能納米壓入儀測量納米壓入儀測量10H 硬度硬度A 壓頭接觸面積壓頭接觸面積Ef 薄膜彈性模量薄膜彈性模量壓頭接觸面積函數(shù)壓頭接觸面積函數(shù)1. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能納米壓入儀測量納米壓入儀測量11不足：不足：基體影響基體影響壓頭周圍材料堆積或塌陷壓頭周圍材料堆積或塌陷尺寸效應(yīng)問題尺寸效應(yīng)問題殘余應(yīng)力影響殘余應(yīng)力影響1. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性

5、能納米壓入儀測量納米壓入儀測量121. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能懸臂梁法懸臂梁法屬于薄膜彎曲實驗方法屬于薄膜彎曲實驗方法131. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能懸臂梁法懸臂梁法MEMS中的微懸壁梁中的微懸壁梁聚焦離子束聚焦離子束（FIB）加工）加工MEMS用微米尺寸懸臂梁試樣用微米尺寸懸臂梁試樣141. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能懸臂梁法懸臂梁法屈服應(yīng)力屈服應(yīng)力- -懸臂梁厚度關(guān)系曲線懸臂梁厚度關(guān)系曲線151. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能 懸臂梁法懸臂梁法可能原因：可能原因：殘余應(yīng)力殘余應(yīng)力基體影響基體影響壓頭滑動壓頭滑動1

6、61. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能 微橋法微橋法171. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能單軸拉伸單軸拉伸獲得材料應(yīng)力獲得材料應(yīng)力- -應(yīng)變應(yīng)變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間介質(zhì)層溶去中間介質(zhì)層溶去基板溶去基板邊緣損傷、卷曲邊緣損傷、卷曲裝樣困難裝樣困難試樣規(guī)整試樣規(guī)整制備復(fù)雜制備復(fù)雜簡單易行簡單易行數(shù)據(jù)可靠數(shù)據(jù)可靠181. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能單軸拉伸單軸拉伸膜基系統(tǒng)拉伸曲線膜基系統(tǒng)拉伸曲線柔性基板柔性基板310Cu聚酰亞胺聚酰亞胺19微小力實驗機微小力實驗機：P = + 250 N +

7、1 N； l = + 50 mm + 5 m薄膜薄膜夾頭夾頭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. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能單軸拉伸單軸拉伸201. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能單軸拉伸單軸拉伸t ：薄膜厚度：薄膜厚度 尺寸效應(yīng)尺寸效應(yīng)柔性基板柔性基板21Cu薄膜薄膜/聚

8、酰亞胺聚酰亞胺 晶粒尺寸晶粒尺寸 vs 薄膜厚度薄膜厚度磁控濺射薄膜沉磁控濺射薄膜沉積設(shè)備積設(shè)備t = 60 nmt = 340 nmt = 700 nm02004006008000306090 t (nm)d (nm)10152025300153045 d (nm)Frequency (%)t = 60 nm020040060001020 d (nm)Frequency (%)t = 700 nm221. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能單軸拉伸單軸拉伸表面、界面處位錯受約束表面、界面處位錯受約束231. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能 延性延性自由膜自由膜：一旦頸

9、縮，快速斷裂：一旦頸縮，快速斷裂Stiff substrate硬基底附著膜硬基底附著膜：基底脆斷：基底脆斷軟基底附著膜軟基底附著膜：可使薄膜延性完全表現(xiàn)：可使薄膜延性完全表現(xiàn)延性評價方法延性評價方法 ？241. 金屬薄膜的靜態(tài)力學(xué)性能金屬薄膜的靜態(tài)力學(xué)性能微裂紋統(tǒng)計及實時電阻法微裂紋統(tǒng)計及實時電阻法裂紋萌生臨界應(yīng)變：裂紋萌生臨界應(yīng)變： C薄膜表面微裂紋百分數(shù)統(tǒng)計薄膜表面微裂紋百分數(shù)統(tǒng)計實時電阻法測試實時電阻法測試05101520253035050100150200C(R-R0) / R0 (%)Strain (%)0102030405001020304050C Strain (%)Cracks

10、 density (% / m2)25實時電阻法測定臨界應(yīng)變實時電阻法測定臨界應(yīng)變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臨界應(yīng)變臨界應(yīng)變-屈服強度關(guān)系屈服強度關(guān)系Cu薄膜延性尺寸效應(yīng)薄膜延性尺寸效應(yīng)26微裂紋統(tǒng)計法測定臨界應(yīng)變微裂紋統(tǒng)計法測定臨界應(yīng)變應(yīng)變應(yīng)變薄薄膜膜厚厚

11、度度20%30%40%60 nm275 nm700 nm10um薄膜越薄，薄膜越薄，應(yīng)變越大，應(yīng)變越大，貫穿型大貫穿型大裂紋越多裂紋越多27不同薄膜厚度不同薄膜厚度微裂紋統(tǒng)計法測定臨界應(yīng)變微裂紋統(tǒng)計法測定臨界應(yīng)變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兩種方法結(jié)果對比兩

12、種方法結(jié)果對比微裂紋測定與實時電阻測定結(jié)果相近微裂紋測定與實時電阻測定結(jié)果相近金屬薄膜延性評價方法金屬薄膜延性評價方法28Flexible substrate(Polymer)Rigid substrate(Silicon)Good understanding of the fatigue properties are very important !2. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能附著膜附著膜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. 金屬薄膜的疲勞性能金屬薄膜的疲勞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. 金屬薄膜的疲勞性能金屬薄膜的疲勞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. 金屬薄膜的疲勞性能金屬薄膜的疲勞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. 金屬薄膜的疲勞性能金屬薄膜的疲勞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. 金屬薄膜的疲勞性能金屬薄膜的疲勞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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性

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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板362. 金屬導(dǎo)線的力學(xué)性能評價金屬導(dǎo)線的力

19、學(xué)性能評價試樣制備試樣制備1）光刻2）顯影3）濺射掩膜基體光刻膠Cu膜4）二次顯影微米級線寬微米級線寬37“工工”字型試樣字型試樣2. 金屬導(dǎo)線的力學(xué)性能評價金屬導(dǎo)線的力學(xué)性能評價試樣形貌試樣形貌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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板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. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板42Damage mechanismLow cycle region:Burst to electrical openHigh cycle region:Formation of damage bands2. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板43Damage bands in high cycle regionGrain extrusionTEM imageExtrusion of grain arraysDifferent from all the previous reports !2. 金屬薄膜的疲勞性能金屬薄膜的疲勞性能剛性基板剛性基板44AFM analysesTwo dimension AFM image70.37nm 0.005.