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Dear Jim: Thank you for your question. Let me begin by stating some basic facts (http://www.britannica.com): Basic plasma physics Plasma formation Apart from solid-state plasmas, such as those in metallic crystals, plasmas do not usually occur naturally at the surface of the Earth. For laboratory experiments and technological applications, plasmas therefore must be produced artificially. Because the atoms of such alkalies as potassium, sodium, and cesium possess low ionization energies, plasmas may be produced from these by the direct application of heat at temperatures of about 3,000 K. In most gases, however, before any significant degree of ionization is achieved, temperatures in the neighbourhood of 10,000 K are required. A convenient unit for measuring temperature in the study of plasmas is the electron volt (eV), which is the energy gained by an electron in vacuum when it is accelerated across one volt of electric potential. The temperature, W, measured in electron volts is given by W = T/12,000 when T is expressed in kelvins. The temperatures required for self-ionization thus range from 2.5 to 8 electron volts, since such values are typical of the energy needed to remove one electron from an atom or molecule. Because all substances melt at temperatures far below that level, no container yet built can withstand an external application of the heat necessary to form a plasma; therefore, any heating must be supplied internally. One technique is to apply an electric field to the gas to accelerate and scatter any free electrons, thereby heating the plasma. This type of ohmic heating is similar to the method in which free electrons in the heating element of an electric oven heat the coil. Because of their small energy loss in elastic collisions, electrons can be raised to much higher temperatures than other particles. For plasma formation a sufficiently high electric field must be applied, its exact value depending on geometry and the gas pressure. The electric field may be set up via electrodes or by transformer action, in which the electric field is induced by a changing magnetic field. Laboratory temperatures of about 10,000,000 K, or 8 kiloelectron volts (keV), with electron densities of about 1019 per cubic metre have been achieved by the transformer method. The temperature is eventually limited by energy losses to the outside environment. Extremely high temperatures, but relatively low- density plasmas, have been produced by the separate injection of ions and electrons into a mirror system (a plasma device using a particular arrangement of magnetic fields for containment). Other methods have used the high temperatures that develop behind a wave that is moving much faster than sound to produce what is called a shock front; lasers have also been employed. Methods of describing plasma phenomena The behaviour of a plasma may be described at different levels. If collisions are relatively infrequent, it is useful to consider the motions of individual particles. In most plasmas of interest, a magnetic field exerts a force on a charged particle only if the particle is moving, the force being at right angles to both the direction of the field and the direction of particle motion. In a uniform magnetic field (B), a charged particle gyrates about a line of force. The centre of the orbit is called the guiding centre. The particle may also have a component of velocity parallel to the magnetic field and so traces out a helix in a uniform magnetic field. If a uniform electric field (E) is applied at right angles to the direction of the magnetic field, the guiding centre drifts with a uniform velocity of magnitude equal to the ratio of the electric to the magnetic field (E/B), at right angles to both the electric and magnetic fields. A particle starting from rest in such fields follows the same cycloidal path a dot on the rim of a rolling wheel follows. Although the "wheel" radius and its sense of rotation vary for different particles, the guiding centre moves at the same E/B velocity, independent of the particle's charge and mass. Should the electric field change with time, the problem would become even more complex. If, however, such an alternating electric field varies at the same frequency as the cyclotron frequency (i.e., the rate of gyration), the guiding centre will remain stationary, and the particle will be forced to travel in an ever-expanding orbit. This phenomenon is called cyclotron resonance and is the basis of the cyclotron particle accelerator. The motion of a particle about its guiding centre constitutes a circular current. As such, the motion produces a dipole magnetic field not unlike that produced by a simple bar magnet. Thus, a moving charge not only interacts with magnetic fields but also produces them. The direction of the magnetic field produced by a moving particle, however, depends both on whether the particle is positively or negatively charged and on the direction of its motion. If the motion of the charged particles is completely random, the net associated magnetic field is zero. On the other hand, if charges of different sign have an average relative velocity (i.e., if an electric current flows), then a net magnetic field over and above any externally applied field exists. The magnetic interaction between charged particles is therefore of a collective, rather than of an individual, particle nature. At a higher level of description than that of the single particle, kinetic equations of the Boltzmann type are used. Such equations essentially describe the behaviour of those particles about a point in a small-volume element, the particle velocities lying within a small range about a given value. The interactions with all other velocity groups, volume elements, and any externally applied electric and magnetic fields are taken into account. In many cases, equations of a fluid type may be derived from the kinetic equations; they express the conservation of mass, momentum, and energy per unit volume, with one such set of equations for each particle type. Now here is a little factoid (http://sciam.com/news/112100/1.html) Instant Plasma Physicists in the U.S. and France have found a new technique for whipping up instant gases of ionized atoms at temperatures nearing absolute zero. These ultracold plasmas are useful for study in that they probably resemble the plasmas churning within white dwarf stars and massive planets, such as Jupiter (see image). Until recently, researchers were unable to create plasmas so cold--making this latest feat, reported in yesterday's issue of Physical Review Letters, all the more remarkable. These ultracold plasmas differ from their warmer, though still officially "cold," cousins in that they are held together solely by the attraction between the ions and electrons they contain. Thomas Gallagher of the University of Virginia, Pierre Pillet of the National Center for Scientific Research in Orsay, France, and their colleagues happened on the new instant plasma recipe while working with so- called Rydberg atoms. Researchers can create these atoms by exciting an outer electron to a distant orbital. So swollen with energy, a Rydberg atom becomes enormous; the diameter of a cesium Rydberg atom, for instance, can reach 1,600 angstroms. Gallagher and Pillet cooled rubidium or cesium atoms using lasers and trapped them, then exciting their electrons to a Rydberg state. They discovered that when the density of these atoms was high enough, the cloud spontaneously turned into a plasma. In other words, the highly excited electrons lost their weak affiliations with individual ions. Trapped cold atoms don't normally undergo such transformations. Thus, Gallagher believes that the small percentage of hot Rydberg atoms found in their trap played a key part--by colliding with the cold atoms and by increasing the rate of ionization, caused by thermal photons. Still, the researchers estimate that the collisions and ionization amount to only 10 percent of the energy needed to produce the plasma. So their next round of experiments will look for the rest. Here is some bibliography Setsuo Ichimaru, Statistical Plasma Physics, Vol. 1. Basic Principles, Vol. 2. A. Mikhailovskii, Electromagnetic Instabililties in an Inhomogeneous Plasma, IOP, 1992. M. Sugawara, Plasma Etching: Fundamentals and Applications, Oxford, 1998. Microlithography: Science and Technology, J. R. Sheats and B. W. Smith, eds.,Y. P. Raizer and J. E. Allen, Gas Discharge Physics, AIP, 1997. C. K. Birdsall, and A. B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill, 1985, 1991. The NRL Plasma Formulary has been the mini-Bible of plasma physicists for the past 20 years. It is an eclectic compilation of mathematical and scientific formulas, and contains physical parameters pertinent to a variety of plasma regimes, ranging from laboratory devices to astrophysical objects. The Formulary was originally developed at NRL by Dave Book (currently at the Naval Postgraduate School). His conscientiousness and perseverance have made the Formulary one of the most widely used `tomes' in plasma physics. The new custodian of the Formulary is Joe Huba. He is responsible for its maintenance and future revisions. Any questions, suggestions, comments, etc. can be directed to him via e-mail (huba@ppd.nrl.navy.mil). The formulary and its components are available in Postscript, PDF, and TeX formats. Now, let me consider another aspect ( http:/ /csep10.phys.utk.edu/astr162/lect/light/ionization.html ) Planck Radiation Law The primary law governing blackbody radiation is the Planck Radiation Law, which governs the intensity of radiation emitted by unit surface area into a fixed direction (solid angle) from the blackbody as a function of wavelength for a fixed temperature. The Planck Law can be expressed through the following equation. The behavior is illustrated in the figure shown above. The Planck Law gives a distribution that peaks at a certain wavelength, the peak shifts to shorter wavelengths for higher temperatures, and the area under the curve grows rapidly with increasing temperature. The Wien and Stefan-Boltzmann Laws The behavior of blackbody radiation is described by the Planck Law, but we can derive from the Planck Law two other radiation laws that are very useful. The Wien Displacement Law, and the Stefan-Boltzmann Law are illustrated in the following equations. The Wien Law gives the wavelength of the peak of the radiation distribution, while the Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by the blackbody (which is the area under the Planck Law curve). Thus, the Wien Law explains the shift of the peak to shorter wavelengths as the temperature increases, while the Stefan- Boltzmann Law explains the growth in the height of the curve as the temperature increases. Notice that this growth is very abrupt, since it varies as the fourth power of the temperature. So, if you decided to try the experiment, you could use a radiation thermometer to measure the actual temperature at the moment of the arcing The Low Pressure, Cold Plasma State The most commonly encountered plasma in CVD applications is the capacitive or "RF diode" plasma. A simplified view of such a reactor might look like this http://www.batnet.com/enigmatics/semiconductor_processing/CVD_Funda mentals/ plasmas The plasma is excited and sustained by applying a voltage --typically AC or RF, 60 Hz to many MHz -between the two electrodes. The "capacitive" moniker arises from the nature of the coupling to the plasma. The plasma forms "sheaths", regions of very low electron density, with solid surfaces: the RF voltage appears mostly across these sheaths as if they were the dielectric region of a capacitor, with the electrode and the plasma forming the two plates. The system pressure is typically between about 100 mTorr and 10 Torr. The electrodes are typically cylindrical, with the separation between the two electrodes usually small compared to the electrode diameter. The electrode "gap" is an important parameter; it varies from about 0.5 cm to 10 cm, generally getting smaller for higher pressure operation. Typical gaps are a few hundred times the mean free path, so electrons undergo many collisions but do not have time to transfer their energy to the neutral gas. However, practical limitations on chamber size generally lead to increasing ratios, and "hotter" plasmas, at higher pressures. In practice, typical electron temperatures are around 5 eV. Electron temperature varies weakly with other parameters: it is dominated by the requirement that the electrons provide enough ions to keep the plasma going. Plasma Density The ion density is equal to the electron density in the plasma, to ensure overall balance of charge: the density of electrons and ions is just known as the plasma density. [This is true for "electropositive" plasmas, in which the only significant ions are positive. "Electronegative" plasmas result when attachment of electrons to form negative ions is important; such plasmas have very different properties. They are particularly important in etching applications, but less frequently encountered in deposition.] About 100 eV is required to produce an ion in a typical low- pressure plasma, when all the losses due to collisions, excitation/de- excitation, and inefficient energy transfer are accounted for. The ions are mainly lost by diffusion to the walls in a low-pressure plasma. The ion density is set by the balance between the input power, which heats the electrons and provides energy to ionize, and the loss of ions to the walls. Plasma density in typical capacitive plasmas is very "low": the fractional ionization is only about 0.01% (1 molecule in 10,000 is ionized). Fractional excitation can be much higher, since excitation and dissociation usually require less energy than ionization. The electrons are distributed in a vaguely Maxwellian fashion, as exp(-E/kTe); thus there are many more electrons with energies of e.g. 8 or 10 eV, able to dissociate, than there are at 16-25 eV driving ionization processes. Substance dissociation ionization energy (eV) energy (eV) H2 4.5 15.4 O2 5.2 12 Sheath Formation As noted above, electropositive plasmas form sheaths of low electron density -also known as dark spaces from their visual appearance -- near solid surfaces. At right we show the plasma in a potential diagram, similar to an energy band diagram for a semiconductor device. Ions roll "down hill" in the sheath regions, acquiring energy which is dissipated when the strike the walls. Electrons float bubble-like upwards, and are thus confined by the potential away from the sheath regions, which therefore have few electrons. Occasionally an ion striking the wall surface knocks off an electron --a secondary-- which then is accelerated into the plasma by the sheath electric field. An electrically isolated object in the plasma will have a sheath around it, since the mobile electrons are lost more readily by diffusion to the surface, giving the plasma a net positive charge until a sheath forms to ensure charge balance. Such sheaths have a potential of typically 10-25 volts. The sheath potential in a capacitive plasma is much larger: it varies during the RF cycle, with peak values of several hundred volts often present. In consequence, the substrate surface in a plasma is likely to be bombarded with ions, whose kinetic energy varies from a few 10's to several hundred eV, along with the usual flux of neutral molecules, and lots of neutral but reactive radicals. The actual potential across the sheaths varies with time in order to add up to the applied RF voltage (very little voltage typically appears across the plasma itself). The plasma is always more positive than either of the electrodes, as otherwise electrons would rapidly escape from the plasma. Thus one sheath grows and the other sheath shrinks as we proceed through the RF cycle. At t=0 in the example at right, the top electrode has a "floating" sheath with only a few volts across it, allowing electron current to flow (to neutralize the ions that struck the surface during the remainder of the cycle), while the bottom electrode has a sheath with e.g. 240 V potential drop, causing energetic ion bombardment of the surface. A half cycle later (t=1/2) the sheath on the bottom electrode is small, and that on the top electrode is large. In the following webpage you can find a software program for numerical simulation http://ptsg.eecs.berkeley.edu/ in different conditions, for example: ES1, XES1: An electrostatic 1 dimensional, periodic many-particle (PIC) code. Can be magnetized. Described in detail in Plasma Physics via Computer Simulation, by Birdsall and Langdon, McGraw-Hill 1985 and Adam Hilger 1991 (which has the ES1 disk with it). Input files runs on PC's, or on X-11 windows equipped computers. Finally, in the this link you could find a nice set of equations that I am reproducing here. http:/ /www.rzg.mpg.de/~dpc/RFS_LECTURES_Nov_96/Equations.html I hope this will help you Cheers Jaime Valencia
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