Small Scale Effect

From macro to nano…

Scaling laws of small

Laws of physics make the small world look different.

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!

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

Some small scale phenomena Surface 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.

Some small scale phenomena Loss 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.

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

Silicon Crystallography

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.

Cubic Lattices

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

Si crystal structure

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

Planes and directions

[1 0 0 ][0 1 0 ]

[1 1 0 ]

Czochralski Method (CZ)

Si-Wafer fabriaction

Floating Zone Method (FZ)

懸浮帶區法 (FZ法 )

CZ法和 FZ法比較

CZ法和 FZ法比較

晶圓的備製

晶塊修整

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).