Plasmas: mean free paths

In a cascade process, one incident electron (e ) collides with a neutral atom ((S)) to produce a second electron and an ion ( ). Now there are two electrons and one ion. These two electrons collide with another neutral atom to produce four electrons and three ions. This process continues rapidly and — after about 20 successive sets of collisions — there are millions of electrons and ions. (The mean free path between collisions is very small at atmospheric pressures.) A typical atmospheric-pressure plasma will contain 10 each of electrons and ions per milliliter. Some ions and electrons are lost by recombination to reform neutral atoms, with emission of light. 

Plasma-arc diamond deposition is produced at a higher pressure than in a microwave plasma (0.15 to 1 atm). At such pressure, the average distance traveled by the species between collisions (mean free path) is reduced and, as a result, molecules and ions collide more frequently and heat more readily. 

Figure 3. Electron mean free path as a function of electron kinetic energy through organic materials. Key V, PMMA , poly(p-xylene) O, plasma polymerized fluorocarbon , barium stearate 0, cadmium arachidate and A, carbon. (Reproduced, with permission from Ref. 35.)...

In looking at plasmas in the most general way, we can categorize phenomena in terms of characteristic parameters. For example, a simple gas can be dealt with in terms of a mean-free path, mean collision frequency, or mean thermal energy. If the mean-free path is less than the dimensions of the vessel holding the gas, it can be treated as a continuum. Otherwise, we would have to look at free molecular flow. In contrast, a plasma has many more characteristic parameters than a simple gas. 

The different regions are delineated by the Debye length (d), the mean-free path (X), and the Larmor radius rL). In a plasma, there can be many mean-free paths, since there are many different types of particles (different neutral species, electrons and ions). Of primary interest are the mean-free paths for collisions between electrons and heavy particles (Xe) and ions and heavy particles (Xd). 

It is also of interest to consider a typical plasma used for CVD. If we have p 250 mTorr, we will likely have Te 20,000°K. Then, the electron mean-free path and the electron-heavy particle collision frequency can be estimated and we recognize that the collision frequency is much higher than the highest frequency typically used in a plasma CVD reactor (13.56 MHz). Therefore, electrons will experience many collision during each applied field cycle. 

Plasma Frequency. If E(co) varies with frequency as in Eq. (8.1.20), and if its wavelength X = 2nc/co is large compared to the mean free path between electron-electron (or electron-ion core) collisions, [co(f)] 1, then... 

Collision frequencies, mean free paths, and cross sections. Collision processes are central to the description of chemical reactions in the plasma. The mean free path /Ia/b of particle A is the mean distance this particle travels before encountering particle B. AA/b is related to the mean velocity of particle A and to the mean collision frequency between A and B. 

At normal deposition pressures, the mean free path of the gas molecules is 10" -10" cm and is much smaller than the dimensions of the reactor, so that many intermolecular collisions take place in the process of diffusion to the substrate. An understanding of the growth is made particularly difficult by these secondary reactions. In a typical low power plasma, the fraction of molecular species that is radicals or ions is only about 10" , so that most of the collisions are with silane. An important process is the formation of larger molecules, for example... 

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