MEMS及纳米接触研究
摘要
本文系统的研究了MEMS的主要工作原理、工艺方法、主要存在的问题，重点讨论了严重影响MEMS性能、阻碍MEMS进入市场的纳米接触问题，并从物理力学领域出发，根据物质结构和固体物理学理论，详细分析了纳米接触的实质，提出一种工程实用的纳米接触力计算方法，为MEMS的结构设计提供理论依据，分析了AFM针尖同试样面的纳米接触力，为AFM实现原子操纵研究提供理论基础。主要工作如下：
1)分析了影响MEMS性能的粘附现象，提出了粘附现象的实质为物质间的纳米接触问题，并阐述了纳米接触问题的研究方法为量子力学法、分子动力学法和连续介质法，介绍了分子动力学和连续介质法的研究现状。
2)系统分析了MEMS的压容原理、压阻原理、静电原理、压电原理、隧道原理和形状记忆合金原理等工作原理：介绍了MEMS的平面加工工艺、体硅加工工艺、LIGA技术、准分子激光加工技术、分子操纵技术等MEMS工艺，提出了MEMS有待进一步研究的领域。
3)介绍了双原子势函数，重点分析了Lennard-Jones势，推导出Lennard-Jones势中的A、B常数的表达式，计算出双原子间引力最大位置和力平衡位置，阐述了微观连续介质的理论基础——Hamaker假设。
4)通过分析双原子间引力，发现Hamaker假设在距离近时不成立的现象；通过分析相对误差，得到Hamaker假设的定义域为接触距离大于7倍的原子半径的结论；计算了双原子的斥力，得到Hamaker假设的合力定义域为接触距离大于10倍的原子半径的结论。分析了Hamaker常数和数字密度，得到Hamaker常数和数字密度均随距离变化的结论。
5)提出了Hamaker假设的距离修正理论，首次对Hamaker假设进行了修正。分析了距离修正系数，并计算了修正系数对多原子修正时的误差变化规律，得到计算微观物质间作用力的连续介质法的计算式。
6)介绍了晶体结构和空间点阵，发现Hamaker假设模型中存在原子空隙，导致Hamaker假设1和Hamaker假设2存在矛盾，并由此介绍了W-S模型。
7)通过分析双原子模型，推导出体心立方体和面心立方体的引力、斥力空隙修正系数；进一步分析空隙修正系数发现，当距离趋向无穷远时，空隙修正系数等于W-S单元体积和原子体积比值的平方，由此得到Hamaker假设仅在距离无穷远处才成立的结论。
8)分析了W-S模型连续介质法对不同距离的原子修正时的误差变化规律，提出Hamaker假设的空隙修正理论，对Hamaker假设进行了第二次修正。提出纳米接触的W-S模型连续介质法的计算式。
9)建立了面心立方体结构的刚性平面同单原子之间作用力的离散模型，用离散法推导出单原子同刚性平面间的作用力表达式，通过大量仿真，从量上证实了对合力起作用的原子主要是接触区域附近的少数原子的结论。
10)用W-S模型连续介质法推导出单原子同刚性平面的作用力表达式，并同离散法得到的单原子——刚性平面作用力比较，通过仿真，比较两者的相对误差，
MEMS及纳米接触研究
得到两种方法结果误差很小的结论，从而完善了W一S模型微观连续介质法的理
论基础。
11)用w一S连续介质法推导出AFM球型针尖同试样面的作用力，经过仿真
计算，并同实验结果比较，发现修正结果很明显，进一步验证了W一S模型连续
介质法的正确性。
12)推导出AFM圆锥针尖、四棱锥针尖、抛物面体针尖同试样面作用力的
表达式。通过比较引力、斥力的相对误差，得到圆锥、四棱锥和抛物面体针尖同
试样面的纳米接触力分别在接触距离大于2、2.5、3.5倍的原子距离时，可以不
考虑斥力对合力的影响的结论。仿真了三种常见的AFM针尖同试样面的粘着力。
13)基于分析力学的虚功原理，讨论了微悬臂梁的弹性力同粘着力间的粘
着稳定性;分析了非稳定平衡位置对微梁状态的影响;通过增加微梁刚度的方法，
分析了微梁为避免粘着现象发生，其结构尺寸所具有的关系，并给出了触点分别
为抛物面型、圆锥型和四棱锥型时的仿真结果，为工程实际微梁的结构设计提供
理论基础。
14)讨论了悬臂梁的动力响应，通过对微梁连续体的离散化，用有限元理
论仿真出悬臂梁末端同基座的粘附现象。
关键词:MEMS，纳米接触，粘着力，AFM，Hamaker假设，微观连续介质理
论
The principles, fabrication methods and problems of micro-electromechanical system (MEMS) are studied in this paper, with emphasis on the nano-contact that affects the MEMS performance and prevents the MEMS from going into market. Firstly, according to the physical mechanics principle, on the basis of the principle of substance structure and solid physics, the nano-contact is analyzed carefully. Secondly, an engineering practical calculation way of the nano-contact is put forwarded. Finally, the adhesion between the tip and the sample of the atomic force microscopy (AFM) is discussed. The main works and conclusions include:1) The analysis of the "stick" phenomenon. The conclusion, which "stick" problem belongs to the nano-contact problems, is drawn. The research ways of the nano-contact problem are introduced, and emphasized on the molecule dynamic and continuum medium mechanics.2) The introduction of the principles of capacitive principle, piezoresistive principle, electrostatics principle, piezoelectric principle, stunning principle and shape memory alloy principle. The fabrication processes of the MEMS are discussed, and emphasized on the silicon surface sacrificial, bulk silicon fabrication, LIGA technology and molecule manipulating technology. The fields of the MEMS, which demand further study, are put forwarded.3) The introduction of the double electron potential, with emphasis on the classical Lennard-Jones potential. The A and B constants of the Lennard-Jones potential are obtained, and followed by the key positions of the balance spot and the attract force biggest spot. The Hamaker hypothesis is discussed.4) The discover of the atomic attract force, which is got on the continuance medium method of the Hamaker theory, is not in agreement with the classical Lennard-Jones potential. The conclusions, which the Hamaker homogeneous hypothesis only holds true for the long distance between the two micro-substances, is obtained. The attract force domain of definition of the Hamaker theory: h∈(7r,∞) is obtained. The same phenomenon in the repulsive force is found by the same method. Synthesizing the attraction and repulsive force, The domain of definition of the Hamaker theory: h∈(10r,∞), which includes the repulsive force, is put forward after analyzing the rule of relative error. In addition, the Hamaker constant and digit density are analyzed. The conclusion, which the Hamaker constant and digit density are varied with the contact distance, is obtained.5) The Hamaker hypothesis distance revision theory is put forward, which is the first revision of the Harnake. hypothesis. The distance revision factors, k_1 and k_2, are obtained. Both of their relative errors and absolute errors are discussed. The micro continuum medium contact force equation is gotten.6) The crystal structure and space point lattice are discussed. The atom gap, which exits in the Hamaker model, Is discovered. The contradiction between the Hamaker 1
and the Hamaker 2 is obtained. So the Wigner-Seitz model is put forward.7) By analyzing the double electron model, the gap revision factors of attract force and repulsive force with body center cube and face center cube are obtained. A surprised phenomenon, the air-gap revision factors are equal to the square of Wigner-Seitz size divided by the atom size when the distance tends to infinity, is discovered, and followed by the conclusion that the Hamaker theory does not hold until the distance between the substances becomes infinite and the number density is equal to the Wigner-Seitz unit.8) The error rules of the Wigner-Seitz model continuum medium method are analyzed which vary with the distance. The principle of the Hamaker hypothesis gap revision is set up. The Hamaker hypothesis is revised secondly. The nano-contact Wigner-Seitz model calculation equation is gotten.9) The discrete model of the single atom and rigid plane with the face center cube is found. The force equation between the single atom and rigid plane is obtained on discretion way. The several simulation
1)分析了影响MEMS性能的粘附现象，提出了粘附现象的实质为物质间的纳米接触问题，并阐述了纳米接触问题的研究方法为量子力学法、分子动力学法和连续介质法，介绍了分子动力学和连续介质法的研究现状。
2)系统分析了MEMS的压容原理、压阻原理、静电原理、压电原理、隧道原理和形状记忆合金原理等工作原理：介绍了MEMS的平面加工工艺、体硅加工工艺、LIGA技术、准分子激光加工技术、分子操纵技术等MEMS工艺，提出了MEMS有待进一步研究的领域。
3)介绍了双原子势函数，重点分析了Lennard-Jones势，推导出Lennard-Jones势中的A、B常数的表达式，计算出双原子间引力最大位置和力平衡位置，阐述了微观连续介质的理论基础——Hamaker假设。
4)通过分析双原子间引力，发现Hamaker假设在距离近时不成立的现象；通过分析相对误差，得到Hamaker假设的定义域为接触距离大于7倍的原子半径的结论；计算了双原子的斥力，得到Hamaker假设的合力定义域为接触距离大于10倍的原子半径的结论。分析了Hamaker常数和数字密度，得到Hamaker常数和数字密度均随距离变化的结论。
5)提出了Hamaker假设的距离修正理论，首次对Hamaker假设进行了修正。分析了距离修正系数，并计算了修正系数对多原子修正时的误差变化规律，得到计算微观物质间作用力的连续介质法的计算式。
6)介绍了晶体结构和空间点阵，发现Hamaker假设模型中存在原子空隙，导致Hamaker假设1和Hamaker假设2存在矛盾，并由此介绍了W-S模型。
7)通过分析双原子模型，推导出体心立方体和面心立方体的引力、斥力空隙修正系数；进一步分析空隙修正系数发现，当距离趋向无穷远时，空隙修正系数等于W-S单元体积和原子体积比值的平方，由此得到Hamaker假设仅在距离无穷远处才成立的结论。
8)分析了W-S模型连续介质法对不同距离的原子修正时的误差变化规律，提出Hamaker假设的空隙修正理论，对Hamaker假设进行了第二次修正。提出纳米接触的W-S模型连续介质法的计算式。
9)建立了面心立方体结构的刚性平面同单原子之间作用力的离散模型，用离散法推导出单原子同刚性平面间的作用力表达式，通过大量仿真，从量上证实了对合力起作用的原子主要是接触区域附近的少数原子的结论。
10)用W-S模型连续介质法推导出单原子同刚性平面的作用力表达式，并同离散法得到的单原子——刚性平面作用力比较，通过仿真，比较两者的相对误差，
MEMS及纳米接触研究
得到两种方法结果误差很小的结论，从而完善了W一S模型微观连续介质法的理
论基础。
11)用w一S连续介质法推导出AFM球型针尖同试样面的作用力，经过仿真
计算，并同实验结果比较，发现修正结果很明显，进一步验证了W一S模型连续
介质法的正确性。
12)推导出AFM圆锥针尖、四棱锥针尖、抛物面体针尖同试样面作用力的
表达式。通过比较引力、斥力的相对误差，得到圆锥、四棱锥和抛物面体针尖同
试样面的纳米接触力分别在接触距离大于2、2.5、3.5倍的原子距离时，可以不
考虑斥力对合力的影响的结论。仿真了三种常见的AFM针尖同试样面的粘着力。
13)基于分析力学的虚功原理，讨论了微悬臂梁的弹性力同粘着力间的粘
着稳定性;分析了非稳定平衡位置对微梁状态的影响;通过增加微梁刚度的方法，
分析了微梁为避免粘着现象发生，其结构尺寸所具有的关系，并给出了触点分别
为抛物面型、圆锥型和四棱锥型时的仿真结果，为工程实际微梁的结构设计提供
理论基础。
14)讨论了悬臂梁的动力响应，通过对微梁连续体的离散化，用有限元理
论仿真出悬臂梁末端同基座的粘附现象。
关键词:MEMS，纳米接触，粘着力，AFM，Hamaker假设，微观连续介质理
论
The principles, fabrication methods and problems of micro-electromechanical system (MEMS) are studied in this paper, with emphasis on the nano-contact that affects the MEMS performance and prevents the MEMS from going into market. Firstly, according to the physical mechanics principle, on the basis of the principle of substance structure and solid physics, the nano-contact is analyzed carefully. Secondly, an engineering practical calculation way of the nano-contact is put forwarded. Finally, the adhesion between the tip and the sample of the atomic force microscopy (AFM) is discussed. The main works and conclusions include:1) The analysis of the "stick" phenomenon. The conclusion, which "stick" problem belongs to the nano-contact problems, is drawn. The research ways of the nano-contact problem are introduced, and emphasized on the molecule dynamic and continuum medium mechanics.2) The introduction of the principles of capacitive principle, piezoresistive principle, electrostatics principle, piezoelectric principle, stunning principle and shape memory alloy principle. The fabrication processes of the MEMS are discussed, and emphasized on the silicon surface sacrificial, bulk silicon fabrication, LIGA technology and molecule manipulating technology. The fields of the MEMS, which demand further study, are put forwarded.3) The introduction of the double electron potential, with emphasis on the classical Lennard-Jones potential. The A and B constants of the Lennard-Jones potential are obtained, and followed by the key positions of the balance spot and the attract force biggest spot. The Hamaker hypothesis is discussed.4) The discover of the atomic attract force, which is got on the continuance medium method of the Hamaker theory, is not in agreement with the classical Lennard-Jones potential. The conclusions, which the Hamaker homogeneous hypothesis only holds true for the long distance between the two micro-substances, is obtained. The attract force domain of definition of the Hamaker theory: h∈(7r,∞) is obtained. The same phenomenon in the repulsive force is found by the same method. Synthesizing the attraction and repulsive force, The domain of definition of the Hamaker theory: h∈(10r,∞), which includes the repulsive force, is put forward after analyzing the rule of relative error. In addition, the Hamaker constant and digit density are analyzed. The conclusion, which the Hamaker constant and digit density are varied with the contact distance, is obtained.5) The Hamaker hypothesis distance revision theory is put forward, which is the first revision of the Harnake. hypothesis. The distance revision factors, k_1 and k_2, are obtained. Both of their relative errors and absolute errors are discussed. The micro continuum medium contact force equation is gotten.6) The crystal structure and space point lattice are discussed. The atom gap, which exits in the Hamaker model, Is discovered. The contradiction between the Hamaker 1
and the Hamaker 2 is obtained. So the Wigner-Seitz model is put forward.7) By analyzing the double electron model, the gap revision factors of attract force and repulsive force with body center cube and face center cube are obtained. A surprised phenomenon, the air-gap revision factors are equal to the square of Wigner-Seitz size divided by the atom size when the distance tends to infinity, is discovered, and followed by the conclusion that the Hamaker theory does not hold until the distance between the substances becomes infinite and the number density is equal to the Wigner-Seitz unit.8) The error rules of the Wigner-Seitz model continuum medium method are analyzed which vary with the distance. The principle of the Hamaker hypothesis gap revision is set up. The Hamaker hypothesis is revised secondly. The nano-contact Wigner-Seitz model calculation equation is gotten.9) The discrete model of the single atom and rigid plane with the face center cube is found. The force equation between the single atom and rigid plane is obtained on discretion way. The several simulation
引文
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