|
|
The rate at which molecules bombard a surface given above, means that at atmospheric pressure and room temperature, about 8x1023 molecules hit every cm2 of surface per second. This number is too large to imagine, let us relate it to the number of atom in a surface, S ~ nb2/3 where nb is the number of atoms per cubic centimeter in the solid. We use an approximate sign because S depends on the crystallographic direction in crystals, and on surface topography. Now, nb = NA x d/M where NA is the Avogadro number (6.02 x 1023 molecules/mol), d is the density in grams/cm3 and M the molecular mass (in atomic units, where M(Al) = 27. Typically, d/M = 0.1 so that a good estimate for the bulk density is nb ~ 6 x 1022 molec./cm3 and, therefore, a typical density of surface molecules is: S ~ 1.5 x 1015 molec./cm2 We can now compare the impingement rate with the number of molecules on the surface: F / S ~ 2.6 x 105 /s P(Torr) This means that at 1 atmosphere, ~760 Torr at sea level, each molecule on the surface is hit 200 million times a second, or once every 5 nanoseconds. We need to compare that time to that typically needed to do an experiment, say 20 minutes. During this time, we do not want a significant number of molecules to hit the surface since they may stick or produce other changes. If we need to have only a 10 % chance that a surface molecule is hit during this time, the impingement rate has to be smaller by a factor of about 200 minutes/ 5 nanosecond, or 2.4 1012. This requires a pressure smaller than an atmosphere by this factor, or about 3 x 10-10 Torr. If the molecules do not stick on the surface every time they hit, the vacuum requirements are relaxed. That is, if the sticking probability is 0.1, one can do with a vacuum of 3 x 10-9 Torr. UHV is typically considered to be below 10-9 Torr. Even at the best vacuum normally used in surface science experiments, ~10-11 Torr, there are still plenty of molecules in the gas phase, about 300 hundred thousand per cm3. In interstellar space, the density of molecules can be as low as a few per cm3, corresponding to about 10-16 Torr. Vacuum doesn’t really mean that there is nothing Lowering a pressure around the sample into the UHV region does not produce a pristine surface. This is because there is always gas adsorbed on the surface that, because of its low vapor pressure or sublimation rate, will not be desorb in a reasonable time. Typical gases are water vapor, that can be removed by moderate baking if the sample integrity allows it, and hydrocarbon contaminants from atmospheric pollution. The hydrocarbon contamination is ubiquitous and cannot removed by baking. It is important to note that any surface exposed to the atmosphere, even if otherwise little reactive like gold, is covered by a contaminant hydrocarbon layer. This means that to study elemental surfaces one must first produce them or clean them in the vacuum environment. Among the methods to produce surfaces in vacuum are cleaving, fracturing, and growth by condensation. Cleaning methods include flashing at high temperatures and erosion with energetic ions (sputtering). The achievement of UHV requires specialized equipment and strict procedures. The usual mode of operation of UHV systems is with the walls of the experimental chamber at room temperature. Some setups have been made with the surfaces at cryogenic temperatures, but this are not widespread because of a complicated operation. Standard, room-temperature UHV systems have to be not only leak proof in the conventional sense, but should not contain materials that are permeable to gases, like rubber gaskets. Achievement of UHV requires the removal of water vapor from the inside walls. This requires baking to temperatures of about 100oC or higher, with shorter bake out times needed at the higher temperatures. This is because desorption rates vary exponentially with temperature: rd(T) = f(T) e-E/kT where E is the desorption energy. f(T) is a slowly varying function of T. The exponential term dominates the T dependence. At room temperature (kT= 0.025 eV) we get, for a desorption energy of 0.5 eV, typical of water, e-20 ~ 2x10-9. Increasing the temperature to 150 C (kT=0.036 eV), we get e-13.9 = 10-6, an increase of nearly three orders of magnitude. Small changes in temperature mean large changes in desorption rate Heating to stimulate desorption limits the materials that can be used in the construction of the experimental chamber and in what goes inside the chamber. The baking temperature is limited to about 250o C or less by diffusion through the walls of the chamber, and deterioration of the materials used in the experiments. The need of baking dictates avoidance of materials with low vapor pressure, like plastics or oils. If any such materials are essential for the experiment, their surface area must be kept to a minimum to achieve UHV. To illustrate the importance of reducing to a minimum high vapor pressure substances, consider that at 10-10 Torr, the number of molecules in the gas phase is large, 3.3x106/cm3 at room temperature. That means that in a typical experimental volume of 50 liters, the total number of molecules is 1.7x1011. This number is enormous in absolute terms, but small compared to the number of molecules in a small, 1 cm2 patch, ~1015 molecules. A small stain or fingerprint can contain 1018 molecules, or 10 million times more than in the gas phase. Cleanliness is of outmost importance in UHV
Vacuum pumps used for UHV are typically of four types:
The last two types actually remove gas from the vacuum system and require a forepump (roughing pump) to maintain their outlet pressure low (typically below 0.1 Torr). The flux of molecules removed by the pump is Qp = S P where the factor S is called the pumping speed, and is usually independent of P in the UV range. S is measured in liters per second. The gas removed by the pump is equal to the decrease in number of molecules in the gas phase, -V dP/dt and Qi the gas flux entering the gas phase from leaks and from desorption from walls. S P = Qi - V dP/dt If Qi can be considered constant, we obtain by integration: P = Peq + (P(0)-Peq) e-S t/V Where Peq = Qi/S is the final (equilibrium pressure) and P(0) the initial pressure. The time constant, V/S is typically of the order of seconds, after which the evolution of the pressure is given by the evolution of Qi (outgassing from surfaces if, as is the case in well kept systems, leaks are negligible). The limit in the lowest attainable vacuum is almost always determined by outgassing (gas desorption) and rarely by inadequate pumping speeds. This is because outgassing rates can vary by many orders of magnitude whereas pumping speed is limited by the size of the system. Even a perfect pump, a hole connected to a perfect vacuum, has a pumping speed of about 12 l/s. per cm2 of hole area. Essentially, the ability to remove gases is limited by their arrival rate to the pumping surface. Since outgassing is proportional to the area of the walls which, for a given geometry, is proportional to the maximum opening available for pumping, it follows that the ultimate pressure achievable should not depend on system size, on first approximation. There are other factors that in practice determine the minimum attainable pressure, like leaks and diffusion of gas through gaskets and even the walls, and gas released from the vacuum pumps. This can be regurgitation of gas previously pumped (like in ion, sorption or cryogenic pumps) or gas that "back-streams" from the discharge side of the pump in diffusion or turbo-molecular pumps.
We have seen that in surface studies, the degree to which a pressure is acceptable is acceptable is given by the rate at which gas molecules hit the surface. For some applications, one requires that the chance of a collision between gas phase molecules is small. The number of collisions suffered by a molecule traversing a pathlength L of gas at density n is given by: Nc = s n L Where s is the collision cross section (area) of the molecule. The product nL is called the column density and is usually given in molecules/cm2. The size of a molecule is an ill-defined quantity; if measured by molecular collisions at thermal energies, one can obtain s of the order of 7x10-15 cm2, valid to within a factor of 2 for most molecules. The mean free path is the average distance the molecule travels between collisions, and can be obtained by setting Nc = 1 in the equation above:
In the UHV range, the mean free path is of the order of tens of kilometers and, therefore, larger than almost any human made vacuum system. In UHV it is safe to neglect intermolecular collisions in the gas phase
|
|
Copyright 2002, by Raśl Baragiola, University of Virginia. All rights reserved. |
