柔性电子器件与制造：第4.1节柔性电子弯曲力学

1、flexible electronics device & manufacturingflexible electronics research centerschool of mechanical science and engineering huazhong university of science and technologychapter4.1bending mechanicsyongan huang, ph.doutline2first failure modecausing tremendous loss in daily lifefailure modes3colum

2、ns can fail if the applied loadexceeds the yield stress of the material. this is a strength failurecolumns can also fail by buckling. this is a stability failurestrength failure4strength failure5mechanical failure is determined by the weakest components ofdevicesthe crack strain of inorganic brittle

3、 material is about 1-2%，andthe metal is also broken after neckingthe freestanding metal film is different from film-on-substrate incrackingfracture6moore, g. electronics 38, 114117 (1965)the s.s. schenectady split apart by brittle fracture while in harbor (1944)vertical stabilizer, which separated f

4、rom american airlines flight 587, leading to a fatal crashfracture in microstructurefracture: utility7stability failure8 buckling is a phenomena of compression members. once the buckling load, or critical load, is reached, the column willinstantly loose stability and “kick out” to one side. once buc

5、kled, the columns ability to carry load is greatly reduced.buckling9buckling10新西兰6.3级地震stressed-out behaviors11stresstensionpressureanxietydepressionstress engineering: bad situations 12 delamination fatigue crows-feet striae gravidarumstress engineering: beneficial applications 13 wrinkle and buckl

6、e are ubiquitous phenomenanature 419, 579(2002)phys.rev.lett.90, 074302(2003)脱氢作用dehydrogenationbuckling patterns of au on pdms14scripta materialia 50, 797(2004)nested buckling of artificial skin15 stiff skin on compliant substrate: a universal modelas a result of ageing, the softdermis contracts, p

7、lacing thesystemundercompressivestress.hierarchicalwrinklingbyinternal stressnature materials 4, 271(2005)nature materials 4, 293(2005)foldable electronics on a pliable substrate16 robustness against bending, stretching, foldingnature nanotechnology 1, 201-207(2008)buckled sphere17cao guoxing, chen

8、xi, c. r. li, z. x. cao, prl100, 2008peel-pick-place18mechanics of flexible electronics19john a. rogers: mechanics is the future of flexible electronicsfeaturesofflexibleelectronics:complexdeformation:bend,buckle, stretch, twistchallenges:radius of curvature as small as 1mmstretchability as large as

9、 50%soft-hard material compound structures20soft-hard material compound structures is the key technologyof flexible electronics (science, 2011)severe mismatch between soft and hard material, so there iscouplingactionduetolargedeformation,temperatureandelectrical fieldsoft material vs hard materialyo

10、ungs modulus： 103-105coefficient of heat conduction ： 103coefficient of thermal expansion ： 10-2soft-substrate and hard filmsource of film stress: thermal stress21the misfit is resulted from the different coefficient of thermalexpansion , so the thermal strain is generated when temperaturechanges0mi

11、sfitfilmsubstratett1tmisfitevsource of film stress: epitaxial stresses22the epitaxial stresses occurs when there is ideal continuitybetween film and substrate外延应力产生示意图filmsubstratemisfitsubstrateaaa111212122223121211100 010001xxxxxyyyyyzzzzzcccecccecccesource of film stress: growth of polycrystal23在

12、薄膜的沉积或生长中，经常可以观测到应力的生长，这是因为薄膜在非平衡状态下的沉积造成的。报告提纲24second foundationlearning the bending mechanicsfilm-on-substrate structures25(a) basic structures of flexible electronics; (b) the size of thin filmfilm-on-substrate structures：bending26a）纯弯结构弯矩和轴向应力分布；b）弯曲示意图the radius of curvature is adopted to deno

13、te the bendingdeformation of flexible electronics. the smaller shows betterdeformability.( )xxryryyyrr 3112vmeh film-on-substrate structures：bending27对基板或薄膜施加一定的预应变或者温度变化，然后再将两者结合在一起，当释放与应变或者温度恢复到室温后，由于基板和薄膜的应变不匹配，会导致膜-基结构会出现弯曲变形。3261121ffsssshvmveheh 221616ssssfffehehvhh rvstoney formula: relations

14、hip between the stress and curvaturestoney formulafilm-on-substrate structures：bending28薄膜和基板中的应力基板和薄膜界面应力 薄膜中： 基板中：xxfxxcompressionbending342fffsxxfffsssttttyttt 14 ,2500500 fsxxfstmtsubstrate ytm 薄膜应力是基板中的应力的100倍以上film-on-substrate structures：bending29the stress of thin film is calculated from the

15、 misfit of the thinfilm and substrate.1, 412felasticffffelasticsssfssvwhereettvyet 00141141ffsffmisfitfsfffssfssvtveteevetvt film-on-soft substrate structures：bending30中性面：在结构中间，没有应变的面如果薄膜的弹性模量远大于基板弹性模量，因此中心面会移向薄膜22212()100%2(1) ,11,112fsfssftosssfffpswherehheeeehhrhree22002002,ffsfffsfsxhxhhxfsffsh

16、xfxx hhhxsfssx hfsfheeedededhhedededeeh rshfhxrfilmsubstrate22122fffsfsfssseexhhh hhhee平衡方程中心面位置film-on-soft substrate structures：bending3110-610-410-210010210-210-1100=hf / hsstrain (2r / (hs+hf) =10000 =100 =1=10000 =100 =1model 1 for =10000model 2 for =10000model 1 for =100model 2 for =100model 1

17、 for =1model 2 for =1上表面的应变film-on-soft substrate structures：bending32in manufacturing, the substrate is located in high temperaturewhen the film-on-substrate is transferred into low temperature,the misfit is resulted from the mismatch of cte. low misfit: equiaxial compression for hemispherical hat

18、large misfit: hemispherical hat to scroll shapestoney公式6smhrescroll shape2221416(1)1smhrv ehat shapefilm-on-soft substrate structures：bending33normalized r is the function of the thickness ratio of film and substrate. scroll shapehat shape6smhrestoney formular：multilayers34尽管薄膜有很多层，但与基底的厚度相比，薄膜的总厚度还

19、是非常小，仍然满足stoney公式的第一条假设。对于n层薄膜stoney公式化为如下形式112221211116sfffffnfnnsshhhrrreh式中下标1，2，n分别代表各层薄膜的编号，为残余应力stoney formula：hypothesis35a)各向同性固体薄膜沉积到较厚基板的膜-基结构，薄膜和基板都是均质，各向同性和线弹性；b)薄膜和基板的厚度要求非常均匀，并且满足 ；c)基板应变和旋转无穷小；d)薄膜所受应力为平面内各向同性或者等轴的，没有平面外的载荷；e)系统曲率是等轴性的，忽略扭转曲率；f)出现的应力和曲率是不随空间变化的。stoney公式广泛应用于计算薄膜的残余应力，

20、但使用时应明确该公式的适用范围， stoney公式采取了如下假设stoney formular：公式的假设36释放假设研究结果 取消假设e：假设e）：系统曲率是等轴性的，忽略扭转曲率 得到双轴stoney公式； 研究了两轴方向作用不同的应力值，以及平面内剪应力； 已应用到裸露或封装的非连续性或周期性“线形”薄膜的分析中； 取消假设d和e中有关等轴性假设； 保留假设d中有关均匀性的假设；d）薄膜所受应力为平面内各向同性或者等轴的，没有平面外的载荷；e）系统曲率是等轴性的，忽略扭转曲率； 允许出现三个独立的曲率和应力部分，以双轴的、不等轴的、直接部分加上一个剪应力或扭转部分形式出现。stoney

21、formular：公式的假设37释放假设研究结果 取消假设d和e中有关等轴性假设 取消假设b的无限小变形假设 保留假设f中有关曲率和应力的空间分布一致性的假设。b）薄膜和基板的厚度要求非常均匀，并且满足 ；f）出现的应力和曲率是不随空间变化的。 对单层、多层、阶梯型薄膜进行了分析； 已经预测了弯曲状态的运动非线性行为和分岔，并得到了实验的验证。 取消假设aa）各向同性固体薄膜沉积到较厚基板的膜-基结构，薄膜和基板都是均质，各向同性和线弹性； 用于研究不同半径的膜-基结构和任意非均匀厚度薄膜的分析； 推导出薄膜应力与系统曲率的解析关系式，当已知了薄膜的厚度分布，通过测量系统的整体曲率就可以精确地

22、推断薄膜的应力。stoney formular：公式的假设38释放假设研究结果 取消假设f（stoney公式假设中最严格的假设）； 在实际情况中，往往都是不均匀分布的，具体研究过程中一并取消假设d和e。f）出现的应力和曲率是不随空间变化的d）薄膜所受应力为平面内各向同性或者等轴的，没有平面外的载荷；e）系统曲率是等轴性的，忽略扭转曲率； 用于非均匀轴对称/非轴对称的应变失配分析，以及薄膜和基板温度动态变化和非均匀分布的情况； 得到非常重要的结论薄膜的应力不是依赖于系统的局部曲率，而是依赖于整个系统的曲率。bending failure of film-on-substrate39three k

23、inds of failures: crack, slipping and delaminationbending failure of film-on-substrate40膜基结构弯曲的曲率半径与最大应变基板曲率的倒数可定性的通过正弦曲线的二次导数获得弯曲形状0sin(/)wwxl2202212shdlwlll弯曲半径为公式中没有包含si的影响，所以可以定义相应的名义弯曲应变为222212nomslrhdlll2snomnomhrbending failure of film-on-substrate41three kinds of failures: crack, slipping an

24、d delaminationsilicon ribbons with 100nm thickness, 20 um widths and 500um lengths on a pet sheet (175um thick) with length l=11.8 mm, coated with an epoxy adhesive layer (1um thick).裂 纹 初 始 于 dl/l=42.4% (rnom2.88um, enom3.04%).裂纹位于丝带中部， dl/l=45.8%时逐渐贯穿整个面bending failure of film-on-substrate42the th

25、ickness play an important role in failure700nm-thick si ribbon，50um-thick petsubstrate，length=11.8mmsi ribbon slips, not crack, on substratedl/l=9.0%，rnom6.26mm, enom0.40%当弯曲释放后，硅带通常不会滑移回去，而已会向上屈曲，并导致局部分层结果表明：系统的弯曲程度不仅仅取决于无机材料的断裂应变，而且取决于界面材料的剪切应力9.0%31.4%50.8%bending failure of film-on-substrate43th

26、e thickness play an important role in failure2.5um-thicksiribbon ， 50um-thick pet，length=11.8mmwhen dl/l=3.4%，si ribbon slipsonsubstrate （ rnom10.2mm,enom0.25% ）when dl/l=53.4%，rnom2.6mm,enom0.98% ， thesiribbondelaminates from substrate结果表明：系统随着硅带厚度增加，会出现分层，而不包含滑移bending failure of film-on-substrate

27、44the length play an important role in failure290nm-thick si ribbon，175um-thickpet ， length=12mm ， 1um-thickepoxy resin(环氧树脂粘结层)figure a: 500um-length si ribbonfigure b: 50um-length si ribbonbending failure of film-on-substrate45modelingcritical straincritical loading粘结层的弯曲刚度远小于基板和薄膜22212shdlll2322,121ssssse hefelvbending failure of film-on-substrate46modeling薄膜粘结层界面的剪切和剥离应力在薄膜边界达到最大值，分别对界面的滑移和剥离起着主要作用max shear stressga为粘结层剪切模量,max peeling stress22max212assag hhdlh ll