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Small Scale Effect

Small Scale Effect . From macro to nano …. Scaling laws of small. Laws of physics make the small world look different. Some small scale phenomena Surface tension. Surface tension force for 100 µm opening = 5.7 µN Typical force for 100 µm device is 10 nN

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Small Scale Effect

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  1. Small Scale Effect

  2. From macro to nano…

  3. Scaling laws of small • Laws of physics make the small world look different.

  4. Some small scale phenomenaSurface tension • Surface tension force for 100 µm opening = 5.7 µN • Typical force for 100 µm device is 10 nN • Surface tension over 500x greater!

  5. Some small scale phenomenaLaminar flow • Reynolds Number (Re)scales as length. • Typical Reynolds Number for 100 µm device is Re ~ 0.1 • Onset of turbulence is at Re ~ 2000

  6. Some small scale phenomenaSurface area/volume • Surface area to volume is large at small scales. • Mass flow saturates quickly in small volumes. • Equilibrium can be reached very quickly. • Mass flows through small devices quickly. • Hard to maintain concentration gradient. • Micro-scale systems must • utilize physical barriers (cell • walls) to maintain • concentration gradients. • Surface contamination is a • serious issue at small scales.

  7. Some small scale phenomenaLoss of continuity • At sizes below ~50 µm, granularity of nature becomes relevant. • Many bulk-scale physical laws no longer accurate. • Typical grain size is ~10 µm. • Affects physical, thermal and • electrical properties. • Mean free path of N2 at atmosphere • is 60 nm. Affects dynamics in air. Example: Paschen effect.

  8. Micromachining Materials • Substrates: • • Silicon • • GaAs • • Other elemental or compound semiconductors • • Metals (bulk and foils) • • Glasses • • Quartz • • Sapphire • • Ceramics • • Plastics, polymers and other organics

  9. Silicon Crystallography

  10. Cubic Lattices • Simplest arrangements of atoms in three dimension in which the unit cell is a cubic volume • Simple Cubic (sc) structure has an atom located at each corner of the unit cell • Body Centered Cubic (bcc) has an additional atom at the center of the cube • Face Centered Cubic (fcc) unit cell has atoms at the eight corners and on the six faces.

  11. Cubic Lattices • How is the arrangement of atoms in Silicon? • Silicon has fcc + (1/4x, 1/4y, 1/4z) fcc structure

  12. Si crystal structure

  13. Planes and directions • Lattice vector R= r*a+ s*b+ t*c, r, s & t are integers • We can define a plane in a crystal lattice with three integer, called Miller indices

  14. Planes and directions [0 1 0 ] [1 0 0 ] [1 1 0 ]

  15. Czochralski Method (CZ)

  16. Si-Wafer fabriaction

  17. Floating Zone Method (FZ)

  18. 懸浮帶區法(FZ法)

  19. CZ法和FZ法比較

  20. CZ法和FZ法比較

  21. 晶圓的備製

  22. 晶塊修整

  23. Miller indices indicated by ground edges called “flats”. “n”-type and “p”-type refer to “doping”. N means “negative” (phosphorous) and P means “positive” (boron).

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