Crystal grown in solution would be an equilibrium growth technique, or solidifying crystals out of a melt would be another one.
With MBE you can produce materials that are metastable. This means that if you looked at a phase diagram they would not normally exist. So in that sense the are out of equilibrium and since at some very long time should transform to another structure. That works out fine for many devices since they can be metastable for extremely long times.
Traditional MBE the atoms from the cell are usually evaporated, and the molecules have relatively low kinetic energies. But you can have other types of MBE using a plasma source, gas source etc. Laser MBE or pulsed laser deposition the materials ablated and the plume is a plasma and can have kinetic energy that are extremely large. In the second case, the atomic species are very far from equilibrium, also those very energetic atoms have a lot of energy when they hit the substrate. So depending on the specific type of MBE you can quibble about how far from equilibrium the process is.
If you think about the substrate in the chamber and you wanted to produce an amorphous material you might consider cryogenically cooling the substrate and most of the energy of the atoms and the surface would be coming from the velocity (kinetic energy) of the impinging atom.
At room temperature there is a little more energy, but KT/q is about 26 milli electron volts, so the surface atoms and crystal lattice is vibrating some and with the kinetic energy of the impinging atoms there is some movement of atoms on the surface. If you heat up to several hundred degrees, then there is a lot of energy for atoms to run around on the surface and find places where they can form a nice crystal, for example the atom may move around until it finds an atomic step and stick there extending the step in a nice crystalline way. This is called step growth. Of course as you heat up the substrate you also have to worry more about the vapor pressures of the various elements and you might start losing elements with lower vapor pressure. So it is a balancing act.
There are different modes of crystal growth, for example you might form little islands and as the different islands move together they could be at different orientations and you can get defects. Maybe you anneal the defects out by raising the temperature, or you play games to get step growth after forming a nucleation layer with little islands. For example starting growth a low temperature to get nucleation and the growth started, and then raising the temperature and getting step growth later.
You rotate the substrate so the atoms land more uniformly on the substrate. You get better uniformity across the wafer. The atoms that land on the substrate move around, but not that far, so if you have more atoms landing in an area you may get a thicker film there.
There are other growth methods that are much faster than a micron an hour, and growth methods that are much slower. For MBE, you can probably think of it in terms of the flux of atoms you are sending out from the source.
If you calculate the amount of material being evaporated by weight, and then the area of the cone of atoms that leave the small aperture in the source, and then see how percentage of that area is the area being deposited on, you will find that it is not much. Deposit too fast you may not get good growth. A micron an hour is ball park figure for MBE.
