TimeDomain CVD, Inc.

Alternative Discharges: Fields and Waves

Magnetic Fields and Plasmas: Magnetrons, MERIE, ECR

 

An electron moving in a magnetic field experiences a force perpendicular to its direction of motion.
Since the force is always perpendicular to the velocity, the electron travels in a circle "around" lines of magnetic field. Changes in the electron velocity change the radius of the orbit but not the period: the electrons all rotate at the Larmor frequency, whatever their velocity.   B (Gauss) 100 280 MHz 1000 2.8 GHz
If the pressure is low enough for electrons to complete their orbits without scattering, an electromagnetic field at the Larmor frequency will be in phase with the electrons (resonance) and add energy on each cycle. This is the principle of the cyclotron accelerator, and of Electron Cyclotron Resonance (ECR) plasmas. (Note in the figure that the electric field is directed opposite to the electron motion in order to achieve acceleration, since the electron charge is negative.)
Imposition of magnetic fields on a plasma "traps" the electrons: they are forced to circle around the field lines rather than diffusing freely to the walls. (The ions have much larger Larmor orbits and shorter mean free paths, so they less influenced by the field.) The probability that a hot electron will ionize a molecule is increased due to the increased path length. Magnetized plasmas can be sustained at pressures of a few mTorr, where conventional capacitive plasmas are difficult to ignite: this is the principle of magnetron sputtering and magnetically-enhanced RIE (MERIE). Magnetized plasmas tend to have large variations in plasma density, since the strength of the magnetic field varies from place to place. Large variations in plasma potential may also result: the electrons have a hard time moving across the field lines, and thus can't easily move around to compensate for variations in potential. Such inhomogeneities have important implications for plasma damage.

Inductive Plasmas

 

Wrap a soilenoidal coil around a dielectric chamber (e.g. a quartz tube), and apply an RF voltage. The current flow in the coil generates a magnetic field in the vertical (z) direction:
This time-varying magnetic field creates a time-varying azimuthal electric field (wrapping around the axis of the solenoid). The field strength is proportional to the radial distance and the frequency.
The azimuthal electric field induces a circumferential current in the plasma. The electrons thereby accelerated gain energy, creating enough hot electrons to sustain the plasma through ionization.
Once the plasma forms, the magnetic fields are screened by the induced currents, just as in a metal: in operation, the magnetic field penetrates into the chamber to a depth determined by the magnetic skin depth, which is in turn set by the plasma conductivity and thus by the plasma density and the pressure.

Starting an inductive plasma presents a problem: until the plasma is present, there aren't any free electrons to respond to the induced electric field, thus no power dissipation and no plasma. This problem often solves itself: since there's no plasma, there's not much power dissipation in the coil. With a good matching network, the reactive power stored in the inductance grows quite large, resulting in a large voltage across the coil. Some of this voltage is capacitively coupled to the inner wall of the chamber, creating an electric field. When the field is large enough, conventional breakdown occurs, leading to a plasma supported by the usual capacitive coupling, albeit in an unusual geometry: the system is said to be operating in capacitive mode. As power is increased, the plasma density grows high enough to support induced circumferential currents, and the system switches (often abruptly) to a true inductive mode, typically signified by a sudden increase in brightness of the plasma.

Inductive plasmas generate electrons and ions more efficiently than capacitive plasmas, and can achieve electron densities of 10^12 /cm3 at pressures of a few mTorr, as much as 100 times higher than comparable capacitive plasmas. The inductive plasma has a relatively low plasma potential, and results in little ion bombardment of surfaces. By intentionally applying an RF bias voltage to the substrate, one can modify the ion bombardment energy with almost no effect on plasma density. Biased inductive reactors allow independent adjustment of plasma parameters and ion bombardment energy to a much greater extent than dual frequency or conventional single-frequency capacitive reactor designs.

Electromagnetic Fields in Plasmas

 

Electromagnetic fields at low frequencies can't propagate in a plasma, but are reflected. At high frequencies the plasma electrons can't respond and fields travel freely. The boundary between these regimes is the plasma frequency. Waves with frequency near the plasma frequency penetrate slightly into the plasma.
The plasma frequency varies from about 100 MHz to a few GHz for typical laboratory plasma densities. (The rarefied plasma of the ionosphere reflects low frequency electromagnetic waves, allowing AM radio stations to reach listeners far beyond their line of sight.)
It is interesting to note that the phase velocity of a wave propagating in the plasma is "infinite" at a frequency just above the plasma frequency, and slows back to the speed of light as the frequency increases. The group velocity (the actual speed at which a signal is carried) is zero at fp and increases with increasing frequency above.

Microwave Plasmas

 

Use of a high frequency electromagnetic wave (a microwave) allows direct heating of plasma electrons without reflection by the plasma.
In order for the wave to continuously add energy to the plasma, collisions must occur. Otherwise, the energy received by an electron each half-cycle is taken back by the field on the next half-cycle. The frequency of collisions increases with pressure.
As a consequence, for any particular frequency, there's an optimum operating pressure for maximum power transfer.
Microwave plasmas are usually implemented as an evacuated dielectric tube placed within a microwave resonator.
The size of the cavity must be adjusted to support a resonance at the desired operating frequency. If the plasma volume is small, its effects on the resonant frequency are modest and one can estimate the required dimensions from the unperturbed values. For example, the lowest mode of a "tall" cavity (height > radius) is a TE(111) mode, with frequency shown at right.	d = height; a = radius; p11 = first zero of derivative of first Bessel function

Microwave plasmas are "electrodeless" (no metal parts need touch the plasma) and thus have very low plasma potential, and no sputtering or contamination. They are compact and can achieve high plasma densities. They are widely used for remote generation of active species. However, it is difficult to create large area plasmas with good uniformity using microwave excitation.

 

Plasma: Table of Contents