The term ultra-high vacuum vacuum stands for vacuum with a rest gas pressure of around 10-9 mbar and below. There are couple of essential physical ideas you need to know when you are working with such low pressures. A very important aspect is that a low-pressure rest gas in the vacuum recipient does not flow and behave in the way we are used to from gasses at ambient pressure.
It is very instructive to calculate two quantities for typical UHV pressures: (1) the mean distance the molecules in the system travel before they bump into each other (the so-called mean free path) and (2) the rate at which molecules impinge on a surface in the vacuum system. Both can be calculated by using kinetic gas theory.
The mean free path λ of the molecules is
where ξ is the molecular diameter, P is the pressure of the gas and T is the temperature. The usual units for the pressure in vacuum technology are torr or mbar (1 torr = 1.3332 mbar = 133.32 Pascal). By the way the pressure enters in this equation, we can directly see that the mean free path is going to be very long in UHV. You find that λ for a gas (nitrogen) at ambient conditions is in the order of nm. But since the pressure under UHV conditions is some 12 orders of magnitude lower, the mean free path has to be in the order of km. This means that it is much more likely for the rest gas molecules to hit the walls of the the UHV vessel than to hit each other! It has also consequences for pumping: at ambient pressure we are used to the fact that pressure differences propagate quickly in a gas (like in sound waves or when using a straw for drinking). For UHV this is simply not true anymore. It is the individual molecules we have to think about and, in fact, pumps based on the usual gas flow idea fail to produces UHV.
(2) The rate of impinging molecules R on a surface is
where P is the pressure of the rest gas and M the molecular mass in units of the atomic mass constant. For a pressure of 10-6 mbar (i.e. high vacuum but not yet UHV) and a temperature of 300K we find
As an order of magnitude value, a surface has 1015 atoms per square centimetre. This means that if every rest-gas molecule at the above conditions sticks to a surface the latter will only
stay clean for a second or so. If we are not willing to tolerate more than, say, a percent of contaminating rest-gas molecules on the surface then the pressure has to be in the UHV region.
Finally, a useful thing to define are pumping and leak rates
basic physics behind UHV
