【正文】 MEMS和微系統(tǒng)設計 課程的基本目的 ?掌握 MEMS設計的基本過程 ?掌握 mems機電及其耦合分析的基本理論 ?掌握機電結構微器件的性能分析方法 ?了解熱、流體的基本理論 ?了解 MEMS的發(fā)展前沿知識 ?培養(yǎng)對 MEMS的興趣 課程內(nèi)容 ? MEMS概述及 MEMS設計的概述 ? 工藝簡要回顧 ? 系統(tǒng)設計、工藝設計及版圖設計 ? 主要的機械、電子元件及其設計基礎 ? 多域耦合設計：以機電耦合為例子 ? 器件性能的估計 ? 簡單的其他域的元件及其簡要設計要點 ? 設計實例 本章提綱 ?力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 彈簧與電容 ?二階動態(tài)系統(tǒng) ?與測試電路的耦合 Transversal deflection of a beam with a load at the end ? ?xLxIEFw BB?? 36 2????222BBddB dzzb:Iwith: x w dB LB F z (187,1) (187,2) Rectangular beam: 123BB db:I ?(187,3) I := Area moment of inertia of the beam εB := Strain at the surface of the beam F := Force acting at the end of the beam dB := Thickness of beam w := Deflection of beam bB := Width of beam LB := Length of beam EB := Young?s modulus of beam 187 * W. Beitz, . Grote, ?Dubbel, Taschenbuch f252。r den Maschinenbau” * ? ? FdbE LLxw:wBBBBB 3304??? (187,4) ? ?0330 4 wLdbEwFBBBBB ???(187,5) Aria momentum of inertia (188,1) (188,2) Rectangular: 123BB dbI ?(188,3) I := Area moment of inertia of the beam EB := Young?s modulus of the beam FB := Elastic force of the beam at its end w := Deflection of the beam dB, bB, LB, RB := Thickness, width, length, and radius of the beam, respectively 188 More aria momentums of inertia are found in books like: W. Beitz, . Grote, ?Dubbel, Taschenbuch f252。r den Maschinenbau” or . Blevins, ?Formulas for Natural Frequency and Mode Shape“, Krieger, Malaba, FL (1987) ? ? FIELLw:wBBB 330 ?? ? ? 0303 wLIEwFBBB ???bB dB (187,3) Circular: RB 44BRπI ?Trapezoid shaped: dB e bB,1 bB,2 212221213 436 ,B,B,B,B,B,BBbbbbbbdI???? (188,4) 212123 ,B,B,B,BBbbbbde???with: (188,5) ? ?xLdbE Fε BBBBB ?? 26Strain on the surface of a beam loaded at its end x w dB LB F z (189,1) Rectangular beam: (187,3) : (189,2) 189 * W. Beitz, . Grote, ?Dubbel, Taschenbuch f252。r den Maschinenbau” * ? ?xLIE Fdε BBBB ?? 2I := Area moment of inertia of the beam EB := Young?s modulus of the beam F := Force acting at the end of the beam εB := Strain at the surface of the beam w := Deflection of the beam dB, bB, LB : Thickness, width, and length of the beam, respectively Rectangular beam clamped on one side and loaded at the other end x w dB LB F z 01230 200 400 600 800? ?xLdbE Fε BBBBB ?? 26(189,2): x [181。m] ε [‰] 5 0 4 0 3 0 2 0 1 000 200 400 600 800x [181。m] w [181。m] ? ?xLxdbE Fw BBBB?? 32 23(187,1), (187,3): LB = 800 181。m bB = 40 181。m dB = 20 181。m EB = 140 GPa F = 1 mN 190 EB := Young?s modulus of the beam εB := Strain at the surface of the beam F := Force acting at the end of the beam dB, bB, LB, w := Thickness, width, length, and deflection of the beam, respectively Transversal deflection of a beam loaded at the end The strain at the surface of a beam clamped at one end and loaded at the other end in transversal direction is largest at the fixed end. Strain and deflection are not a functions of an initial stress of the beam. Rectangular beam: ? ?xLdbE Fε BBBBB ?? 26(189,2): Strain and deflection are proportional to the force (linear characteristic curve). ? ?xLxdbE Fw BBBB?? 32 23(187,1), (187,3): 191 x w dB LB F z EB := Young?s modulus of the beam εB := Strain at the surface of the beam F := Force acting at the end of the beam dB, bB, LB, w := Thickness, width, length, and deflection of the beam, respectively Transversal deflection of a beam loaded at the end Rectangular beam : Because of the transverse strain the beam gets narrower on the side with tensile stress and wider on the opposite side. (With the exception of the region next to the clamping) Crosssection of the beam: Without load With load bB bB (1 – νB εB) dB 192 x w dB LB F z ? ?xLdbE Fε BBBBB ?? 26(189,2): EB := Young?s modulus of the beam νB := Poisson?s ratio of the beam εB := Strain at the surface of the beam F := Force acting at the end of the beam dB, bB, LB, w: Thickness, width, length, and deflection of the beam, respectively The effect of crystal orientation on elastic properties Only isotropic materials have been considered so far. *. Wortman, . Evans, ?Young?s Modulus, Shear Modulus, and Poisson?s Ratio in Silicon and Germanium“, J. Appl. Phys. 36 (1965) 153 156 Young?s modulus [GPa] of silicon and germanium as a function of the orientation in the (100)plane * However, membranes from monocrystalline silicon are anisotropic. 115 Young?s modulus [GPa] of monocrystalline silicon and germanium as a function of crystal orientation *. Wortman, .