Roland A. - PVD for microelectronics (779636), страница 13
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Their flux isonly a few percent of the ion flux anyway, and they move very rapidlythrough the sheath. One result of this is that the sheath is dark becausethere are few electrons available to excite the atoms and ions present.Strictly speaking, the sheath is not completely dark, but the emitted lightlevels are significantly below that of the bulk plasma.PLASMA SYSTEMS57The Child-Langmuir Law is relevant for virtually all cases of currentflow either across a sheath or between two grids or apertures and can beeasily derived from Poisson's equation [3.4].Plasmas also have a characteristic length, known as a Debye length,which is given byL =(3.4)4,rrnee2where n e is the electron density, e is the electron charge, and k T is the electron temperature (described below).
The Debye length can be thought of asa self-shielding distance for an electrical disturbance of a plasma. If asmall potential is applied to some surface in a plasma, the movement ofcharge will be such that most of the potential is shielded within one Debyelength.
In a practical example, if a grid or an array of holes was present ona metal surface in a plasma, electrically the grid would appear as a solidsurface if the Debye length was larger than the hole radius. If the Debyelength was significantly smaller than the holes, then the plasma would penetrate the holes. Converting the Debye length into useful units, the aboveequation can be rewritten asL(cm) = 7 4 3 ( T ) ./2(3.5)where T is the electron temperature in eV and n is the electron density inelectrons/cm -~.Example: A typical high-density plasma has a density of 1012/cm 3.If the electron temperature is 2 eV, the Debye length is 1 • 10 -3cm, or 10 microns.
A lower-density plasma of 109/cm 3 with anelectron temperature of 5 eV would have a Debye (self-shielding)length of 0.05 cm.There are three primary species of particles in a plasma: ions, electrons,and gas atoms. In the bulk of the plasma, the electron and ion densities, n eand n/, are identical. Experimentally, techniques may measure either theelectron density or the ion density, although measurements of the electrondensity are more common and more accurate. For this reason, usually theelectron density is given as the plasma density even though it means exactly the same as the ion density.
The electrons, which are much more mobile than the ions due to their low mass, become thermally equilibrated anddevelop a "temperature" or energy dependence that can be characterizedR. POWELL AND S. M. ROSSNAGEL58by a Maxwell-Boltzmann distribution (Fig 3.4). This is given by the relation [3.4]f (v) = Aexp- 1~2(mykT2))(3.6)withm )1/2A = n2"rrkTwhere m is the electron mass and v is the electron velocity. The peak in thisdistribution is generally called the electron temperature, although the average energy is 3/2 of the peak in the distribution. Even though this is actually an energy, the "k" in k T is assumed, and the electron temperature isgiven in electron volts (eV). A typical value for a processing plasma mightbe 2 eV, and rarely would the electron temperature exceed 10 eV.The use of terms and units in plasma technology can be somewhat confusing and ambiguous.
The electron temperature is almost always described in energy units (eV, where 1 eV = 1.6 • 10 -19 joule) and virtuallynever in the form of degrees K. A simple rule of thumb is that a l-eVFIG. 3.4M a x w e l l - B o l t z m a n n electron energy distribution.PLASMA SYSTEMS59plasma temperature is about equal to 11,600 K. Another ambiguous termwith plasmas is the description of ion or electron energies in terms of volts,rather than in energy units such as eV or joules. Since all electrons have asingle charge and virtually all of the ions also have a single charge, whenthese particles are accelerated over some voltage, they attain the samenumber of eV in kinetic energy as the acceleration voltage. So, their kinetic energy in eV is equal to the acceleration voltage in volts, and the general tradition is to simply describe the energy in terms of volts.The ions in a plasma are significantly colder than the electrons.
This isdue to the large numbers of collisions that each ion has with the background gas atoms. The cross sections for these elastic collisions as well ascollisions where an electron can be transferred (known as charge exchange collisions) are large. Since there are 100 to 10,000 neutral gasatoms for each ion, the gas temperature dominates the ion temperature,and this stays at a few hundred degrees C, which is equivalent to 1/10 ofan eV or less.3.2 Plasma PotentialSince the electrons are so light and so energetic compared to the ions,many aspects of plasma calculations or models assume that the ions arevirtually immobile. In the bulk of the plasma, since the electrons are somobile, the loss rate for electrons from the plasma edge is greater than theloss rate for ions.
This results in a slight positive charging of the plasma,setting up a small positive potential that retards the rate of electron loss tobe the same as the ion loss rate. The plasma potential is virtually alwayspositive in this situation and is typically positive on the order of the electron temperature in voltage.
Virtually all processing plasmas have a fairlyuniform plasma potential, and it is almost always a few volts positive ofthe most positive potential exposed to the plasma, which is either theanode or the grounded chamber walls that function as the anode.3.3 Floating PotentialAn electrically isolated object immersed in a plasma receives a flux of bothelectrons and ions.
Since current flow away is inhibited, the net currentflow to the object must be zero. However, since electrons move so muchmore rapidly than ions, the object may develop a net negative charge andpotential, which limits the flow of electrons to be equal to the ion flow.60R. POWELL AND S. M. ROSSNAGELThis negative potential is known as the floating potential and is typically2 to 3 times the electron temperature (in voltage).Note: While the plasma potential and the floating potential are related to theelectron temperature, there are other factors that preclude a direct calculationof the electron temperature from measurements of these potentials.
In general, low electron temperatures correlate with small plasma and floating potentials. The topic of direct plasma probe measurements is well treated in[3.1, 3.4, 3.6].3.4 Flux to the SheathThe bulk of the plasma is at a uniform potential, and only small, localvariations in potential or density can occur. In many ways, the plasmafunctions as a gas of charged particles that are randomized by collisions.Near the edge of the plasma, though, small potentials may extend into theplasma. This potential is on the order of one-half of an electron temperature (in volts, now) and typically perturbs the edge regions of theplasma (on the order of a Debye length or two) in the region between thedark space of the sheath and the bulk of the plasma.
In this region, ionscan be weakly attracted by this potential difference and drawn to the edgeof the sheath. The ions attain what is known as the ion acoustic velocity,which is(3.7)where M is the ion mass. This can be converted into useful units asV~,,,,, ~ou.,,i~ = 9.8 x 10 5(3.8)where T is the electron temperature in eV, W is the mass of the ion inAMU, and the velocity is in cm/sec.Example" For a 2-eV p l a s m a of argon (40 AMU), this leads toV - 2.2 • l0 s cm/sec.PLASMA SYSTEMS61This is called B o h m p r e s h e a t h d i f f u s i o n and was first understood byBohm in the late 1940s. The flux to the sheath edge is then just the ion density (which is also the electron density) times the ion acoustic velocity, typically with a factor of 0.6 [3.5]:(3.9)j = 0.6neV(ionacoustic )which, converted into mA/cm 2, becomesj= 8.9 • 10 -11 n e(3.10)where n e is the density in electrons/cm 3, ire is the electron temperature ineV, and W is the atomic weight of the ion in AMU.Example: For a Ar (W = 40 AMU) plasma density of 1011/cm3 andan electron temperature of 2 eV, the current density to the sheathedge is j = 2 mA/cm 2.This ion flux is then accelerated by the sheath potential and bombardsthe cathode/target surface or the anode surface.
The net ion energy for thecathode/target is the difference between the plasma potential (typically afew volts positive) and the cathode potential, which is generally severalhundred volts negative (Fig. 3.5). In practice, the plasma-potential contribution is usually ignored for the cathode.
For the anode (or the chamberwalls if they are the anode), the ion's energy is just due to the plasma potential. This bombardment is generally ignored in practical systems, although it can be important in high-density plasma etch tools.3.5 DC and RF PlasmasHistorically, DC diode plasmas were first used for sputtering and sputterdeposition applications. DC diodes are limited in practical terms either bylow ion currents and high voltages or by operating pressures that are toohigh to allow significant deposition rates. A key problem is that the crosssection for ionization of the background gas by the secondary electronsemitted from the cathode is small and effectively decreases as the electronenergy increases (Fig.
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