PLASMA KEY PARAMETERS

Bulk power

The plasma bulk power P_B is volume averaged RF power dissipated by the electrons:

with I_k: harmonics of discharge (plasma current)

R_B: plasma resistance

Plasma resistivity

The plasma resistivity R_B (ohmic part of the plasma bulk resistance) is:

with: n_e: electron density

        n_eff: effective electron collision rate

        m_e: electron mass

        l: effective length of plasma (approx. electron gap)

        A: electrode area

Electron collision rate

The collision rate of electrons n_e (please see Figure 2.4) depends on:

• Power and pressure (recipe)

• Gas mixture (recipe)

• Impact of electrons on chemistry

• Feedback from chemistry via cross sections and relative concentration of species

and can be calculated for magnetic field B = 0: 

The electron collision rate is sensitve to many influences.

Electron density

For magnetically enhanced plasmas, the scaling law of electron density is given by

Please see M. A. Lieberman, A.J. Lichtenberg, Principles of plasma discharges and materials processing, John Wiley & Sons, Inc., 2005.

Note: The plasma parameters electron density and electron collision rate
only can be calculated by using a broad band measurement because
the inertia effects of the electrons occur only at higher frequencies
(higher harmonics). A separation of these parameters from the plasma
resistivity at lower frequencies as used by the Hercules^� N (narrow
band measurement) is not possible.

Resonance Frequency

The resonance frequency is the serial resonance of the bulk 'inductance' and the sheath capacitance and is a property of the plasma. The lower the difference between generator and resonance frequency the higher the dissipated RF power in the plasma bulk. A changed generator frequency influences the resonance conditions of the serial oscillator!

If the resonance frequency is more then six times larger than the generator frequency the resonance frequency is setting to the six times larger value.

Uniformity Edge

The parameter Uniformity edge is described by the ratio of the geometric dimensions of the chamber and the skin depth and is frequency depended.

Nonlinearity

The parameter nonlinearity describes the ability of the plasma to generate harmonics. The value is usually in the range from 0.05 to 0.25. The nonlinearity is used the calculate the resonance frequency and vice versa. Regularly the nonlinearity is set to 1/8.

RF Fundamentals

The RF Fundamental is the RF current at generator frequency. This parameter indicates variation of the hardware or the RF sub-circuit (electrode system, matchbox, ...).

V1_{RMS_mV}

This parameter shows the amplitude of the sensor signal and is required in order ot checkr functionality of sensor.