丁建宁
论文题目：多晶硅微机械构件材料力学行为及微机械粘附问题研究
作者简介：丁建宁，男，1966年03月出生，1998年09月师从于清华大学温诗铸教授，于2001年06月获博士学位。
摘 要
微机电系统（Microelectromechanical Systems，MEMS）和纳机电系统（Nanoelectromechanical Systems，NEMS）是机械科学技术的前沿领域。由于尺寸效应和表面效应等因素的影响，在微尺度下的机械设计不能直接套用传统的机械设计理论和分析方法。微型机械研究发展至今，人们已经能够制造出各种微器件，然而，要将各种微器件有效地组合成具有一定功能的微机电系统就需要发展微机械设计理论。目前在微型机电系统研究中存在许多急需解决的有关微机械设计的基础问题，如微摩擦学、微热力学、微流体力学和材料的微观力学和微机构学等。这些问题已严重限制了微机电系统的发展，必须开展微型机械设计的基础研究[14]。
在微型机械中，由于表面积与体积之比相对增加，表面效应增强，再加上微机械中构件间的间隙很小，因而微构件间的表面作用力影响较大，其时对微构件的作用力分析不同于宏机械构件间的受力分析，在宏机械研究中忽略的一些因素在微机械中必须考虑。另外，当构件缩小到一定的尺寸范围时将出现材料强度尺寸效应，材料性能和构件的力学行为将发生很大变化。因此，表面效应和尺寸效应是微型机械研究中众多需要解决的基础问题中急待解决的两个关键问题。两种效应相互关联，由于尺寸的微小化导致表面效应的增强，而与表面有关的物理参量又会影响到尺寸效应的发挥，很难将两者单独开来进行研究。两种效应在微型机械设计研究中具体体现在对于反映微构件材料变形、损伤特性的微机械构件材料力学行为的研究和反映微机械工作可靠性、稳定性的微机械粘附问题的研究[18]。基于以上分析，本文较早提出对这相互关联的两个问题展开研究。论文着重通过实验分析了由于尺寸微小化而导致的多晶硅微构件力学性能、变形和断裂损伤特性的变化及其主要影响因素，又从理论上分析了微构件的受力状态以及产生表面效应和强度尺寸效应的物理机制，并进一步基于表面物理，分析典型微构件间的相互作用力，探讨微机械产生粘附的物理机制，提出了一些新的见解。论文的主要研究工作和创新成果如下：
1． 发展了研究多晶硅微构件的弯曲力学特性的纳米硬度计弯曲法，并利用自行研制成功的电磁—线圈力驱动的微拉伸装置研究了多晶硅微构件拉伸力学特性，得到了一系列有价值的实验数据：首先在对涂层-基体系统压痕法研究材料力学性能的基础上[30]，阐明由于产生相变，使得压痕法测试数据不能用于微悬臂梁的形变特性研究[37]；进而提出采用纳米硬度计弯曲法来研究多晶硅微悬臂梁的力学特性[20]，并对其测量原理以及对测量数据的影响因素和可能产生的误差进行了详细的分析讨论[11]。提出了采用压入载荷与压入深度平方的关系曲线来描述涂层-基体系统[1]，从而得到有关薄膜涂层的纯变形特性，为正确评定薄膜的力学性质提供依据[15]。同时指出还需要考虑微悬臂沿宽度方向的挠曲[21]。经过这些修正，得到有关多晶硅微悬臂梁形变特性可靠的力学性能数据[23]。在对弯曲形变特性研究的基础上，进一步提出运用纯拉伸法来研究多晶硅薄膜微构件的拉伸形变特性。基于电-磁-力原理，对电磁-线圈组件的结构进行优化设计，从而研制了一种电磁—线圈力驱动器并将其应用于微拉伸装置[16]。该电磁力驱动器在实现微进给领域有明显的优点，具有很好的线性，低滞后性，无摩擦，能进行直接控制等特点，同时利用光纤传感器来测量构件的拉伸形变。在此基础上探寻了合适的拉伸试件制作和测量方法，然后由实验测得的应力—应变本构关系得到多晶硅薄膜微构件的微拉伸弹性模量，测试结果表明，微多晶硅薄膜拉伸构件发生的破坏明显是脆性断裂，在断裂前未出现屈服、颈缩和塑性变形[22、4]。最后从理论上进一步提出织构理论模型，理论与实验分析结果表明，根据<110> 织构取向模型得到的理论弹性模量数值与实验值非常接近，从而从理论上证实了本微拉伸实验的可靠性，从实验中也验证了织构理论模型的合理性[31]。从而掌握了多晶硅微构件的形变特性，为微型机械构件的变形分析提供了可靠的数据。
2． 对微尺度下多晶硅薄膜微构件的强度随构件尺寸变化的规律进行了比较系统的研究：运用材料脆性破坏的统计理论分析了多晶硅微悬臂梁的断裂失效强度，得到弯曲强度随构件尺寸的增加而减小的尺寸效应[7]。然后利用微拉伸装置研究了多晶硅薄膜的拉伸强度的尺寸效应，得到拉伸强度随体积、表面积、截面积、长度和宽度变化的统计规律[8]。从理论和实验上着重分析了试件宽度对拉伸强度的影响，从而指出Toshiyuki tsuchiya等学者得出的微构件的拉伸强度与宽度无关的结论不可靠。最后进一步运用威布尔统计分布研究了拉伸强度的统计分布规律[24]。从弯曲强度和拉伸强度的尺寸效应反映出多晶硅薄膜微构件强度的尺寸效应表现为微结构和试件微尺寸的双重约束，提出尺寸效应可由强度随参量表面积与体积之比值的变化来反映[13]。得到的有关多晶硅薄膜微悬臂梁和拉伸构件的弯曲强度和拉伸强度数据以及有关的统计参量可用于微机械构件的设计[26]。
3． 运用断裂力学理论对多晶硅微构件的断裂损伤特性进行了分析研究，提出表面粗糙度是引起多晶硅微构件断裂失效的主要原因，并研究了表面施加OTS膜后对微机械构件力学性能的影响：在对多晶硅微构件的形变、强度特性和强度的尺寸效应研究的基础上，进一步对尺寸微小化后的微构件断裂损伤机制进行了研究[36]。运用原子力显微镜（AFM）、透射电子显微镜（TEM）和场发射扫描电子显微镜（SEM）对多晶硅薄膜的微结构进行分析。进一步研究得到多晶硅薄膜的断裂韧性，采用极大似然法来估计断裂失效起源，并结合断口分析，对多晶硅薄膜材料的断裂物理进行了研究[24]。表明多晶硅薄膜发生的是解理断裂，在宏构件研究中往往忽略的表面粗糙度的影响在微机械构件材料力学性能的研究中已变得非常重要，该影响可运用断裂力学进行合理的解释[38]。对微机械构件施加OTS膜后，明显提高了试件的拉伸强度。这一结果表明，采用微机械构件表面施加OTS膜，不仅能有效改善表面的摩擦磨损，减低粘附（sticking），而且能有效地提高微机械构件的力学性能。微机械构件损伤特性的表面效应研究结果为今后的材料设计提供依据。
4． 结合微构件材料力学性能的研究，分析了表面张力以及Casimir力对微构件的粘附和稳定性的影响，给出了多晶硅微悬臂梁和微腔的抗粘附结构尺寸参数设计依据：首先分析了影响微机械构件粘附的作用力，表明在大气环境或有液体的环境下，表面张力对微机械构件的粘附起主要作用，而在真空条件下，需考虑量子力（Casimir力）的影响，Casimir力将显著影响微构件的运动、微结构的稳定性和装置的可靠性[9]。在考虑Casimir力的影响时，须考虑表面形貌、材料导电性能和温度的影响[32]。在修正Casimir力的作用下，分析了典型的微腔薄膜结构，对实际粗糙模型和理想光滑模型的形变研究表明，系统结构的稳定性和粘附问题可利用一个无量纲常数K来表达[2、3]。无量纲常数K的物理意义表明微机械结构的粘附和稳定性与构件材料性质和结构的几何参数有关。其次，探讨了不同表面力作用下的抗粘附结构参数设计。得到了表面张力作用下稳定的抗粘附多晶硅微悬臂梁结构参数设计和Casimir力作用下稳定的抗粘附多晶硅薄膜微腔结构尺寸参数设计[6]。结果表明，微悬臂梁和薄膜微腔结构产生的粘附与材料的弹性特性、材料的表面特性、构件的长度、厚度和构件与基体之间的间隙有关，而与构件的宽度无关[39]。本文首次给出了不同间隙和表面力作用下典型的多晶硅微悬臂梁结构参数设计图和薄膜微腔结构参数设计图[34]。这些结果可以应用于微型机械的设计，对于建立微型机械设计的理论体系具有重要意义。
关键词：微型机械，弹性模量，弯曲强度，拉伸强度，断裂韧性，粘附
*
文摘中所列参考文献数字代表所附的“发表论文目录”中的相应论文
Abstract
Microelectromechanical Systems (MEMS) and/or Nanoelectromechanical Systems (NEMS) is a newly rising interdisciplinary technology. The mechanical design of MEMS and/or NEMS is one of the frontiers of mechanical engineering. The traditionary mechanical design methods and theories can not be used in MEMS design due to surface effect and size effect. The up-to-date development of the study of MEMS has brought about varies kinds of micro-components. When these micro-components are used to build up a microelectromechanical system to obtain a definite function, the theory of MEMS design should be developed. There are some existing problems of the fundamental design issues of MEMS about microtribology, microthermodynamics, microhydrodynamics, micromechnics of materials and micromechanisms. These problems have heavily restricted the development of MEMS, and the fundamental design issues of MEMS should be studied as quickly as possible [14].
As the influences of surface forces on the micromachines are very large due to the surface effect with an increase in the ratio of surface area to volume and the small clearance between micro-components, the analysis of forces on micromachines is different from that on marcomachines. Some neglected influences in marcomachines should be considered in the design of micromachines. On the other hand, the change of material properties and mechanical behavior should be considered duo to the size effect on material strength. Obviously, the surface effect and the size effect are two key problems of many fundamental design issues to be studied in MEMS. These two kinds of effect affect each other and they can not be studied separately. So, the two representative problems about the understanding of the mechanical behavior of MEMS materials and the unwanted typical “sticking” phenomenon in MEMS should be theoretically and experimentally studied [18]. As discussed above, the study of these two relating problems are firstly brought forward in this dissertation and this dissertation takes up two key points among the existing problems in the development of MEMS, the mechanical behavior of MEMS materials and the stiction phenomenon in MEMS, for investigating theoretically and experimentally in detail. New micromechanical models and approaches are proposed. The specific works finished and main innovative contributions of this dissertation are as follows:
Firstly, a novel, direct and convenient method for micromechanical property measurements by beam bending using a nanoindenter has been developed, and a microtensile test device with a magnet-solenoid actuator and a fibre-optical displacement sensor has been designed and constructed to investigate the tensile mechanical properties of polysilicon films. Based on the investigation of mechanical properties of coating/substrate system by nanoindentation [30], the data obtained from nanoindentation are certified unsuitable to be used in the study of deformation of microcantilever because of the emergence of phase transformation under indentation [37]. Thus, a method for micromechanical property measurements by beam bending using a nanoindenter has been demonstrated [20]. A systematic analysis of the measurement principle and influences has been made [11]. In order to achieve the net deformation properties of a thin coating, both load-penetration depth and load-penetration depth squared plots have been demonstrated to be necessary if a more complete understanding of coating/substrate system behavior is to be gained [1], which has been suggested to be a rule to evaluate the mechanical properties of thin solid films[15]. In the meantime, in the deflection of microbeams, the influence of the indenter tip pushing into the top of the microbeams and the curvature across its width must be considered [21]. With these influences considered, the mechanical properties of microcantilever deformation can be obtained [23]. In order to investigate the mechanical properties of microstructures under purely tensile pulling procedures, the optimum configuration and geometry for a magnet-solenoid force actuator has been presented, enabling its application to the design of microtensile test device [16]. The electromagnetic force actuators have distinct advantages for applications involving very small displacements, which include linear operation, low hysteresis, no friction and direct electrical control. The magnet within a coil has a low stiffness relative to the mechanism and will readily be self-align to the primary translation axis and so all but eliminate crossaxis forces. This low stiffness coupling also reduces the transmission of mechanical vibration between the stage and the frame. The displacement of the sample is measured with two groups of optical fibers bundled together having a realizable accuracy of 50nm in stable thermal conditions. This microtensile test device is used to measure the mechanical properties of polysilicon films. During the test, the tensile stress linearly increases with the displacement of the precise stage, and the stress curve manifests no yield point until fracture. The specimen has no necking, and no plastic deformation is observed. The Young's modulus are obtained by calculating the slope of the stress-strain curve using a least-squares fit [22、4]. The Young’s modulus of polysilicon films are also calculated by either the isotropic model of Reuss-Voigt model, Shtrik-Hashin model or texture model. The bounds for the {110} in-plane elastic constants are modeled to be in good agreement with the results of the tensile experiments. It has been found that the measured average values of Young’s modulus by tensile tests falls within the theoretical bounds of texture model [31]. The test data accounts for the uncertainties of the reported Young’s modulus mean values obtained for polysilicon. This data may be used in the future reliability design of polysilicon MEMS.
Secondly, the size effect of the typical manufactured component on bending strength of polysilicon microcantilever beams and tensile strength of polysilicon thin films has been systematically investigated. Statistical analysis of bending strength [7] and tensile strength [8] for various specimen sizes predict the size effect of specimen length, width，cross-section area，surface area, and volume. Especially，the size effect of specimen width on tensile strength has been theoretically and experimentally studied. It shows that the result concluded by Toshiyuki tsuchiya, which was stated that statistical analysis of tensile strength predicted no size effect of specimen width, is incorrect. The Weibull distribution probability function is adopted to represent such tensile strength variations for polysilicon brittle materials [24]. Statistical analysis of the specimen size effects on the tensile strength predicts the size effects on the length, the surface area and the volume of the specimens due to microstructural and dimensional constrains. The fracture strength increases with the increase of the ratio of surface area to volume. In such cases the size effect can be traced back to the ratio of surface area to volume as the governing parameter [13]. The test data accounts for the uncertainties in mechanical properties and may be used in the future reliability design of polysilicon MEMS [26].
Thirdly, the rupture physics and crack origin of polysilicon thin films are analyzed by means of AFM, SEM and TEM [36]. The maximum-likelihood method is also applied to analyze the fracture origin of polysilicon films combining with the cross-section photo of fracture face [24] .The fracture behavior indicates that the fracture origin of polysilicon thin films is located on the surface of the specimens. The surface roughness is proved to be the main fracture origin of polysilicon thin films for the first time and the effect of surface roughness on tensile strength has been theoretically and experimentally studied, which can be expressed by fracture mechanics [38]. For brittle materials the strength is governed by the maximum flaw size, typically at the surface. Clearly the processing route and resulting surface roughness have a strong influence on strength. The valley is a stress concentration and a flaw at the surface. Furthermore, the mechanical properties of polysilicon thin films coated with OTS film are also investigated. It is found that tensile strengths of polysilicon thin films are enhanced greatly when they are coated with OTS films. It is clearly that not only the tribology properties and anti-stiction properties of microstructures can be improved but also the mechanical properties of microstructures can be enhanced. These results would work as guidance for the design of MEMS materials.
Lastly, base on the investigation of the mechanical properties of microstructures the influence of capillary forces on sticking of a surface micromachined polysilicon microcantilever in ambient environment or the rinse liquid and the influence of quantum mechanical effect such as the Casimir effect on sticking and stability of a micro polysilicon membrane strip cavity structure in vacuum are investigated. Mechanical stability and sticking are the troublesome problems in microfabrication and operation processes when separations of components in MEMS are in the sub-micrometer regime. Some mechanical effect, including quantum mechanical effect should be taken into account for solving the problems. Capillary forces will play a dominant role on sticking in ambient environment or the rinse liquid. On the other hand, the magnitude of Casimir force is significant when the membranes work in vacuum without the effect of capillary forces. The Casimir effect may play an important role if the separations are small enough [9]. The corrections of roughness, conductivity, and temperature to the Casimir force must be considered for accurate account of their effects [32]. With nothing other than the Casimir force loading the strip, there exist a stable static equilibrium state and an unstable static equilibrium state, depending on the value of a dimensionless constant K [2、3]. The membrane strip will collapse if the value of K is larger than the critical value. Thus, the influence of capillary forces and the Casimir effect on sticking and stability of microstructures are investigated [6]. The study on the design of anti-sticking structures under different forces shows that sticking and stability of microcantilevers and micro membrane strip cavities has something to do with Young’s modulus of materials, surface properties, length of structures, thickness of structures and separation between the fixed surface and the deflecting component. But, it is independent of width of structures [39]. A map of the size design of anti-sticking structures has been proposed for the first time, which provides a way to check if a system with given dimensions and material properties will be in a stable equilibrium [34]. These results are expected to be useful for the design of MEMS, and of significance for establishing a framework of the design theory of MEMS.
Key words: micromachines, Young’s modulus, bending strength, tensile strength, fracture toughness, sticking
*
Please note that the numbers appeared in this abstract correspond to
the article numbers appeared in the Publication List.
