Page 344 - Sami Franssila Introduction to Microfabrication

Vacuum and Plasmas 323

Time evolution of pressure can be written as and the ultimate pressure that can be reached is then
given by
dp/dt = (dN/dt)kT/V = −nSkT/V (32.7) p ult = kTnC/S (32.12)
which can be solved to yield 15 −1
If the leak rate is 3.8 × 10 s and 1000 L/s pump
is employed, the base pressure is ca. 1.6 × 10 −5 Pa or
p = p 0 exp(−St/V ) (32.8)
1.2 × 10 −7 torr. Ultimate base pressures are produced by
Pressure drops exponentially over time with character- cryopumps or getter pumps, with values in the range of
istic time τ proportional to V/S. 10 −11 torr. MBE systems operate at such base pressures.
5
Low to medium vacuum (10 –0.1 Pa) can be pro- The theoretical maximum pumping speed is derived
duced by rotary vane pumps, rotary piston pumps, from kinetic theory as
roots blowers and sorption pumps. High vacuum
(0.1–10 −4 Pa) is produced by capture pumps (cryop- S = (A/4)v ave (32.13)
umps, getter pumps) and momentum-transfer pumps
(turbomolecular pumps, diffusion pumps). Capture where A is the inlet area and v ave = (8kT/πm) is the
pumps capture and hold all the gas and therefore they molecular average speed. This represents the case in
need forepumps because of limited holding capacity; which all atoms impinge only in one direction, with no
and they have to be regenerated regularly. Momentum- return flux. Real life pumping speeds of diffusion pumps
transfer pumps, on the other hand, require roughing can be 50% of the theoretical maximum value, but
pumps because they cannot start operation at ambi- rotary pumps fare much worse. Pumping speed is usually
ent pressure. specified for nitrogen, and light gases hydrogen and
helium are difficult to pump. Water vapour is difficult
Crossover is the pressure at which the high vacuum
to remove because its desorption rate is very low.
pump is connected to the chamber. For capture pumps,
this is calculated from torr-litre specification (Pa-L/s), Gases will adsorb on surfaces when energetically
by dividing with the chamber volume. Capture pumps favourable surface sites are available. Adsorbed gases
hold the pumped material, and therefore knowledge of are ‘surface gases’ as opposed to ‘volume gases’. The
chamber volume is essential. Capture pumps often bring latter are related to chamber volume; the former to
the pressure down faster than roughing pumps, because chamber wall area. Large surface area equals large
the pumping speed of a mechanical roughing pump gets quantity of adsorbed gases. The analogy is with water in
worse at lower pressures. a bucket: initially each cup will decrease the water level
Ultimate pressure that can be reached by a pumping in the bucket by a cupful until almost all the water is
system is determined by pumping speed and vacuum removed. When almost all water has been removed, the
remaining water is found in cusps that are smaller than
chamber leak rate. We need the concept of conductance
the cup, and therefore each removal cycle removes less
to estimate this: conductance is flow divided by gas
density difference on the two sides of the vacuum than a cupful. This points to the importance of surface
system. Its unit is thus cubic metre per second. finish in vacuum chamber manufacturing. Pumping can
Conductances add like capacitors in series: be limited by surface gas desorption. It can be helped
by heating or UV radiation.
1/C tot = (1/C 1 ) + (1/C 2 ) (32.9) Ultra-high vacuum (UHV) chamber materials and
surfaces, valves, and all components must be compat-
Maximum conductance is limited by the orifice opening, ible with baking, which is done to outgas the adsorbed
and further limited by tube conductance that leads from species. UHV systems are baked at elevated tempera-
the orifice. tures; MBE systems, for instance, are baked at 200 C
◦
The number of atoms leaking in from the outside is for 24 h, every 30 days.
given by The pressure can be brought down by a multiple-stage
dN/dt = J = −C n (32.10) vacuum system. The sputtering system may have three
levels of vacuum:
For high vacuum, n is equal to the density of the
gas outside the system (approximating high vacuum
– vacuum cassette lock, pumped down to 10 to
with n = 0), which, for STP conditions, is n = 2.4 ×
25
−3
10 m . Identifying flux J as the leak, we get from 100 mtorr by a mechanical pump;
the ideal gas law (Equation 32.6) – transfer chamber, pumped down to 0.01 mtorr by
a turbopump;
pS = kTJ leak = kTnC (32.11) – process chamber, cryopumped to 10 −6 mtorr.