Plasma key parameters provided by Plasmetrex sensors

Model / Method

Process condition

Plasma resistivity

The plasma resistivity is the normalized plasma bulk resistance 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

Very good correlation to deposition rate !

Hercules N

NEED

high

pressure

Effective,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 

The dependence for no magnetic field B = 0:  

The electron collision rate is sensitve to many influences.

Hercules C

SEERS

low pressue

Electron density, spatially avaraged

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.

Hercules C

SEERS

low pressure

Asymmetry

The asymmetry of the plasma discharge is defined as the ratio of sheath voltage at the chamber wall to the sheath voltage at the wafer.

Equivalent to DC Bias, not any longer available due to usage of ESC.

A change of asymmetry means always moving charge carriers inside the chamber
- The faster the asymmetry changes, the larger the short time DC current.
- Change of asymmetry --> DC current --> Charging --> Breakdown --> Particle
Larger asymmetry means larger ion energy at the RF driven electrode.

Hercules C

SEERS

low pressure

SheathHeating of electrons

is the net energy gain of electron per RF cycle through maximum energy of electrons. Heating or cooling (net gain or loss) of all electrons during one RF cycle in plasma body, close to boundary sheath, given by the energy flux density, defined as: Extraction of the electron heating in the sheath by a plasma physical  model.

Averaging in time provides the so called SheathHeating.

Resonance Frequency is the serial resonance of

- plasma bulk 'inductance' depending on collision rate and density
- sheath capacitance (depending on RF voltage and density)
- inductance of the wafer chuck grounding in particular if moveable.

Therefore an important peculiarity of PECVD chambers is involved in the combined plasma and chamber model. The resonance frequency varies usually only in case of equipment faults and of heavy process changes.

Hercules N

NEED

high

pressure