Page 342 - Sami Franssila Introduction to Microfabrication

32

Vacuum and Plasmas

When we talk about vacuum processes, pressures can 32.1 VACUUM-FILM INTERACTIONS
be anything from slightly below atmospheric pressure
down to 10 −11 torr. Reduced pressure processes would Contamination from the gas phase to the surface can be
be a more accurate description, but the word ‘vacuum’ estimated from kinetic gas theory. The impingement rate
is handy. In evaporation, a vacuum of 10 −6 torr is of molecules on the surface is given by
typical; in sputtering, 1 to 10 mtorr is used, depending
√
on system configuration (DC, RF, magnetron). CVD z = P/ 2πmkT (32.3)
process pressures range from atmospheric to ultra-high
vacuum. Units of pressure (and flow) are many, and the where P is pressure, m is mass and T is absolute
reader is referred to conversion tables (Appendix B). temperature.
Transport of ejected atoms or ions from the target If the residual gas is assumed to be nitrogen (m =
to substrate requires vacuum to prevent collisions and 28 amu), then at 10 −6 torr (1.33 × 10 −4 Pa) z = 3.8 ×
2
18
flux divergence. Mean free path (λ, MFP), or the 10 /m s. A monolayer of residual gases will be
distance travelled by atoms between collisions, is a adsorbed on sample surface in a timescale:
useful measure of transport.
t monolayer = N surf /δz (32.4)
√
2
1/λ = 2 × πd n (32.1)
where δ is sticking probability and N surf is the density
of surface sites, which can be taken as approximately
where n is the atom density and d is the molecule 2/3 22 −3
N vol . For silicon, N vol is 5 × 10 cm , and N surf is
diameter. ca. 10 cm . Under the conditions described above,
15
−2
This can be approximated for diatomic molecules monolayer formation time is ca. 1 s under the assumption
−5
at around 300 K as λ (m) ≈ 5 × 10 /P (torr), which of unity δ (which gives a shortest possible monolayer
gives λ ≈ 65 nm for nitrogen (d = 3.75 ˚ A) at room formation time) (Figure 32.1). For oxygen, the sticking
temperature and 1 atm (760 torr) pressure, and 5 cm at coefficient is estimated to be ca. 0.1 (but sticking
1 mtorr pressure. coefficient is strongly temperature-dependent). Residual
The Knudsen number, Kn, relates mean free path and gases are not similar in their effects: oxygen, water
reactor chamber size:
vapour and hydrocarbons are much more problematic
than nitrogen, carbon monoxide, carbon dioxide or
Kn = λ/L (32.2) argon. The sticking coefficient can be tailored by surface
preparation: for instance, HF-last treated surfaces are
where L is the characteristic dimension of the chamber. much more resistant to water adsorption than RCA-1
Kn > 1 is equivalent to collisionless transport across treated surfaces.
the vacuum vessel. This regime is known as molecular Adsorbed species have a characteristic desorp-
flow and the equipment molecular beam epitaxy (MBE), tion time that is exponentially dependent on activa-
refers to the molecular flow regime since it is atoms, not tion energy,
molecules, that are transported in MBE. In the regime
Kn < 0.01, fluid dynamics has to be taken into account. τ = (1/ν) exp(E a /kT) (32.5)

Introduction to Microfabrication Sami Franssila
 2004 John Wiley & Sons, Ltd ISBNs: 0-470-85105-8 (HB); 0-470-85106-6 (PB)