Source Dynamics

Typically, in a plasma source, energy for the discharge is provided by a power amplifier which couples power to the plasma either capacitively, inductively or via microwaves. For inductively coupled plasma sources such as the ICPS, both the capacitive and inductive paths are employed. Initially an alternating current is passed through the antenna which creates a near-field time varying magnetic field through the solenoid. If the AC frequency driving the antenna current is below the plasma frequency, (which is often the case), then the near-field emission from the antenna is evanescent and diminishes within the plasma at a characteristic length scale (the plasma skin depth). When the

momentum transfer collisional frequency of the electrons (νm) is greater than

when νm ω the ’collisionless’ skin depthδp is used [60]: δp = c ωpe , δc = r me e2_µ 0ns (3.1)

where c is the speed of light,νm is the collisional frequency given by ( ¯σelngve¯ ),

ns is the sheath density and ωpe is the electron plasma frequency.

The electron plasma frequencies in hydrogen in the ICPS range from 17.8 GHz in the high density region near the antenna to 1.8 GHz in the low density ar- eas downstream at x = 10 cm. The plasma frequencies in argon are higher than hydrogen due to the increased power coupling yielding increased den- sities at a given power. They range between 56.3 GHz under the antenna and 5.6 GHz in the downstream region.

The skin depth of the hydrogen plasma discharge in the ICPS ranges between 20 cm at low plasma densities to 1.6 cm at higher densities. This means the H-mode plasma power coupling is able to penetrate across the diameter of the source tube for hydrogen. However for argon, the skin depth ranges be- tween 5.3 cm at low density and as low as 5 mm at the higher operating power. This means the H-mode argon plasma power coupling is not able to penetrate the source tube at higher powers and the power deposition profile is instead confined to a thin layer near the antenna.

The ratio of the collision frequency to the driving frequency gives an indi- cation of the collisionality within the skin depth during one RF cycle. For the ICPS, this ratio ranges from approximately 1 to 50 for hydrogen in the pressure range from 10 mtorr to 100 mtorr respectively. This places the ICPS measurements in an intermediate collisional skin regime.

In addition to the time varying magnetic field, there is also a capacitive cou- pling of the antenna arising from the time varying applied voltage. At low power, this capacitive potential field is the dominant mode of power coupling to the plasma despite its low efficiency. This coupling results in a low den- sity diffuse plasma throughout the source called the E-mode typically present from 0 W up to 80 W depending on the plasma resistance. As the power is in- creased, the primary power coupling switches to the inductive mode whereby the time varying magnetic field of the antenna gives rise to induced closed-

loop azimuthal electric fields perpendicular to the magnetic field lines [111]:

~_{Eind =−}δA~

δt (3.2)

With A~ as the magnetic vector potential where ~B = ∇ ×A~. The low mass

electrons responding to these high frequency induced electric fields are ac- celerated and undergo collisions dissipating the power from the source. Col- lisional energy transfer of this kind is called ohmic heating and is the pri- mary channel for power deposition in ICP devices operating at higher pow- ers. When the azimuthal currents are the primary sink for the electrons the coupling mode is called H-mode operation and it is highly power effi- cient. The H-mode also typically exhibits a uniform plasma discharge profile with Maxwellian particle distributions making inductively coupled systems ideal for plasma processing applications. The power absorbed by a volume of plasma is related to the azimuthal current density and the effective plasma conductivity by [70]:

Pabs = J_θ2

2σe f f

πVvolδc (3.3)

whereJθis the current density,Vvolis a plasma volume andσe f f is the effective

plasma conductivity:

σe f f =

e0ω2pe

νm+jω (3.4)

wheree0is the electric permittivity of free space. The azimuthal electron flow

induced in the plasma skin layer creates its own magnetic field and along with

the inertial electron induction, the total plasma inductance is defined Lp. It

is clear from Eq. 3.4 that increasing the collisional frequency of the electrons

decreases the conductivity, (equivalent to an increase in the resistivity), of the plasma. Higher resistivity increases the ability of the plasma to absorb

power. The plasma resistance Rp (in ohms) is described as the inverse of the

plasma conductivity containing no imaginary part and can be considered as an in-series resistive component of the plasma:

The plasma resistivity can be increased by increasing the collisional frequency or increasing the plasma inductance. Increasing the plasma resistance is the primary way in which the efficiency of the source can be increased how- ever, increased plasma resistance does not always imply increased ionization. Power may be deposited via inelastic collisions such as atomic orbital exci- tation or power may also be deposited by pumping of rovibrational atomic bond modes if the feedstock gas is molecular.