1 Review of your last-time homework: Thanking about 1.What is MEMS by your thinking? try to give your own definition. try your best to use four English words with their capitals in the order of M, E, M and S For example: Miniaturized Everything Making Sense 2. Why people use MEMS? i.e. the advantage of MEMS 3. Who is the greatest Korean MEMS researcher (include all the Korean people in all over the world) to your best knowledge? 4. How MEMS can be put into volume production? i.e. make big money 5. Which kind of MEMS work you are the most interested in?

2 Miniaturized Everything Making Sense Multifunction Enclosed Micro Systems Micro Engineered Multiple Sciences … …

3 The most important material basis of MEMS: single crystalline silicon is not only an ideal electronic material but also a nearly ideal mechanical material Key parameters: density=2330 (kg/m 3 ), E=1.7E11 (Pa), Poisson ratio  0.3 Diamond crystal of silicon vs cubic crystal of metal A little bit anisotropic but not serious A good character related to less-fatigue (means a very long working life) subject to that max stress adequately lower than the rupture stress (1.6GPa ? 500MPa ?) Not like poly-crystalline metal, SC-silicon is with its yield higher than rupture 。 In Chinese: 宁折不弯

4 Stress represents internal force of solid-state body. It may be caused by external force, e.g. a steel bar is forced into bending. But, without external force, stress may be still existing, e.g. residual stress in SiN thin film Mismatch of material parameter also causes stress, e.g. thermal stress of SiO 2 on Si Stress is not so simple as a vector, in fact it is a second rank tensor and, can be expressed with a 3 by 3 matrix of

5 All the components can be categorized as Normal stress and Shear stress

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7 Strain is a relative deformation of a solid-state body

8 Sometimes, stress causes strain, sometimes no In contract, strain always causes stress When stress and strain is in a linear relationship, Hook’s law can express this relationship Here E is Young’s modulus, with its unit the same as stress (Pa) Let’s understand what E means?

9 For normal stress vs normal strain: Here is Poisson ratio, defines the transverse deformation vs the elongation deformation For shear stress vs shear strain: Here G is shear modulus and we have:

10 This kind of thing is so boring. I hate it! Knowing and understanding something is OK!

11 Now we talk about important “beam” in MEMS There are two important kinds of beam: “clamped-clamped beam” and “cantilever beam” A beam can bend under a force-moment

12 Two important things

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14 Now we investigate “Cantilever Beam” Which Chinese people have been familiar to Most of Chinese people know “cantilever” because of a lot of diving champions from China

15 Typical example is AFM and SPM probes

16 （ 311 ）  （ 100 ） （ 411 ） 0.5  m Li Xinxin has a patent technique to fabricate the cantilever-tip probes

17 “ Millipede” by IBM

18 Cantilever-mass accelerometers Pyrex glass Device wafer Cap wafer Stopper MassBeam BCB Lead wire Damping gap 1g peak

19 Commercial Seismic sensor Our MEMS sensor

20 How to design the cantilever?

21 xL 0 T

22 TCS ： -0.12%/ o C TCO ： 0.02%/ o C/FS Car Collision Sensor

23 Uniform acceleration

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25 xL 0 T

26 Homework: Resemble the case of trapezoid cross section in Page 47-48, try to calculate the moment of inertia of a “T”-shaped cross-sectional beam a1 a2 b1 b2