4.2 Why is UHV required for surface studies ?
Ultra high vacuum is required for most surface science experiments for two principal reasons :
To put these points in context we shall now look at the variation of various parameters with pressure
The gas density is easily estimated from the ideal gas law :
n = ( N / V ) = P / (k T) [ molecules m^{3} ]
where : 
P  pressure [ N m^{2} ]

The average distance that a particle (atom, electron, molecule ..) travels in the gas phase between collisions can be determined from a simple hardsphere collision model (see, for example, Atkins' Physical Chemistry)  this quantity is known as the mean free path of the particle, here denoted by l , and for neutral molecules is given by the equation :

[m] 
where : 
P  pressure [ N m^{2} ]

One of the crucial factors in determining how long a surface can be maintained clean (or, alternatively, how long it takes to buildup a certain surface concentration of adsorbed species) is the number of gas molecules impacting on the surface from the gas phase.
The incident flux is the number of incident molecules per unit time per unit area of surface.
(Note  the flux takes no account of the angle of incidence, it is merely a summation of all the arriving molecules over all possible incident angles)
For a given set of conditions (P,T etc.) the flux is readily calculated using a combination of the ideas of statistical physics, the ideal gas equation and the MaxwellBoltzmann gas velocity distribution.
Step 1 : it can be readily shown that the incident flux, F , is related to the gas density above the surface by

[ molecules m^{2} s^{1} ] 
where : 
n  molecular gas density [ molecules m^{3} ]

Step 2 : the molecular gas density is given by the ideal gas equation, namely
n = N / V = P / (kT) [ molecules m^{3} ]
Step 3 : the mean molecular speed is obtained from the MaxwellBoltzmann distribution of gas velocities by integration, yielding

[ m s^{1} ] 
where : 
m  molecular mass [ kg ]

Step 4 : combining the equations from the first three steps gives the HertzKnudsen formula for the incident flux

[ molecules m^{2} s^{1} ] 
Note
The gas exposure is measure of the amount of gas which a surface has been subjected to. It is numerically quantified by taking the product of the pressure of the gas above the surface and the time of exposure (if the pressure is constant, or more generally by calculating the integral of pressure over the period of time of concern).
Although the exposure may be given in the SI units of Pa s (Pascal seconds), the normal and far more convenient unit for exposure is the Langmuir, where 1 L = 10^{6} Torr s . i.e.
(Exposure/L) = 10^{6} x (Pressure/Torr) x (Time/s)
The sticking coefficient, S , is a measure of the fraction of incident molecules which adsorb upon the surface i.e. it is a probability and lies in the range 0  1 , where the limits correspond to no adsorption and complete adsorption of all incident molecules respectively. In general, S depends upon many variables i.e.
S = f ( surface coverage , temperature, crystal face .... )
The surface coverage of an adsorbed species may itself, however, be specified in a number of ways :
Note :
We can also ask,
How long will it take for a clean surface to become covered with a complete monolayer of adsorbate ?
This is dependent upon the flux of gas phase molecules incident upon the surface, the actual coverage corresponding to the monolayer and the coveragedependent sticking probability ... however , it is possible to get a minimum estimate of the time required by assuming a unit sticking probability (i.e. S = 1) and noting that monolayer coverages are generally of the order of 10^{15} per cm^{2} or 10^{19} per m^{2} . Then
Time / ML ~ ( 10^{19} / F ) [ s ]
All values given below are approximate and are generally dependent on factors such as temperature and molecular mass.
Degree of Vacuum 
Pressure 
Gas Density 
Mean Free Path 
Time / ML 





Atmospheric 
760 
2 x 10^{25} 
7 x 10^{8} 
10^{9} 
Low 
1 
3 x 10^{22} 
5 x 10^{5} 
10^{6} 
Medium 
10^{3} 
3 x 10^{19} 
5 x 10^{2} 
10^{3} 
High 
10^{6} 
3 x 10^{16} 
50 
1 
UltraHigh 
10^{10} 
3 x 10^{12} 
5 x 10^{5} 
10^{4} 
We can therefore conclude that the following requirements exist for :
Collision Free Conditions 
⇒ 
P < 10^{4} Torr 
Maintenance of a Clean Surface 
⇒ 
P < 10^{9} Torr 
For most surface science experiments there are a number of factors necessitating a high vacuum environment :
It is clear therefore that it is the last factor that usually determines the need for a very good vacuum in order to carry out reliable surface science experiments.