The voltage necessary to initiate a discharge is roughly a
function of the product of the spacing between electrodes and the
pressure. The minimum voltage occurs at a product of about 1 Torr-cm.
At higher pressures, the discharge voltage increases, making it
difficult to start the plasma if the electrode spacing is large.
At very low pressure (or more properly pressure-distance
product), there are too few collisions and electrons traverse the
chamber and strike the walls without ionizing. Again the voltage for
initiating the discharge increases. For typical chamber geometries,
it is very difficult to initiate a capacitive discharge at pressures
less than 10-20 mTorr, though it is often possible to
"strike" the discharge at higher pressure and then operate
at only a few mTorr. This high breakdown voltage is exploited in
making dark space shields, grounded plates placed within a
few mm of a powered electrode to localize the plasma above the
The electron and ion diffusivity increase just like neutral
diffusivities as roughly (1/P). [The diffusion of electrons and ions
is, however, coupled; we'll discuss this ambipolar diffusion
later.] Thus at pressures of 10's of mTorr, electrons diffuse
readily and the plasma tends to spread through the reactor; at
pressures of a few Torr and above plasmas are generally confined
to the regions where the electric fields heat the electrons.
Paschen curve :
breakdown voltage vs. P-d product for air
ref: Basic Data of Plasma Physics, S. Brown,
American Inst. of Physics Press
Time and Frequency
What frequency of excitation should one apply to the electrodes to
create a plasma? What difference does it make?
DC or AC? As we've noted, electrons and
ions are lost primarily to the walls at pressures of a few Torr or less,
rather than to recombination in the gas phase. For chamber sizes of a few
cm (shortest length) the electrons are gone in ┼ 20-100 Ásec. Thus:
f < 10 KHz "DC": plasma off between cycles
f > 100 KHz "AC": plasma on continuously
AC or RF?
Typical ion velocities are similar to typical molecular thermal
velocities, on the order of 10^5 cm/s. For a typical sheath
thicknesses of 0.5 - 2.5 mm, ion transit times are ┼ 0.5 - 2.5 Ásec.
f < 1 MHz ions cross the sheath in < 1 RF cycle, follow
instantaneous sheath potential
f > 10 MHz ions takes many RF cycles to cross the sheath, see
At low frequencies, ion energies can vary from very small values (when
the sheath is small ) to
energies equal to the peak RF voltage. At 13.56 MHz, the range in ion
energies is much reduced, because the ions gain energy over several RF
calculated for Ar plasma; reference: van Roosmalen et.
al., Dry Etching for VLSI 1991
Keeping it Going
The plasma is sustained by hot electrons which strike molecules
to knock off another electron, creating an ion. At very low
frequencies (< 10 KHz) the mechanism for creating these hot
electrons is very similar to that operating in DC plasmas: the large
sheath voltage present at the cathode accelerates the secondary
electrons, which gain enough energy to ionize molecules in the
plasma. This is an inefficient process: very large sheath voltages
(400-700 V) are required, and much of the electron energy is
dissipated in non-ionizing collisions.
As frequency increases into the MHz
range, two new mechanisms for transferring energy to electrons
become important. First, the change in sheath sizes with each RF
cycle requires that charge move back and forth through the plasma --
that is, that a displacement current flow must exist. This
displacement current, like any other current, encounters some
resistance as it flows in the plasma, and leads to a voltage and
thus heat dissipation through P = V*I. Since the current is
proportional to frequency, and the power is proportional to the
square of the current, the amount of power dissipated scales as the
square of the frequency.
Displacement current heating takes place in the bulk plasma, and
is most important at high pressures and large electrode gaps.
The motion of the sheath is itself significant: a 1 cm wide
sheath growing and shrinking 10,000,000 times per second must be
moving at about 10^7 cm/second! Such a velocity is quite comparable
to electron thermal velocities. Electrons in the plasma can
"scatter" from the sheath and gain energy. Naturally, they
can also give up energy to the sheath when it is moving away from
them, but the number of electrons encountering the sheath is higher
when it moves into the plasma than when it moves out.
Sheath reflection is localized near the moving sheath edge, and
is especially important for low pressure plasmas (10's to 100's of
mTorr). It also scales as the square of the frequency.
The Mystery Number: It is very common for an excitation
frequency of 13.56 MHz to be employed in plasma processing. This
frequency, and some of its harmonics, are reserved for industrial as
opposed to communications use by the FCC. While there is no underlying
physical reason to prefer 13.56 MHz as opposed to, say, 12 MHz or 14.5
MHz, the powerful influence of the economics of scale has made power
supplies and matching networks more widely available at lower cost for
this standard frequency than for others nearby.
Reactor Geometry: Electrode Areas
In many practical reactors, one electrode is "grounded"
-- connected to the chamber wall, which is normally connected to
"true" ground for safety reasons. In this case, the area
of one electrode is much larger than that of the other.
In such reactors, it is empirically found that most of the RF
potential appears across the sheath near the smaller electrode.
Simple theoretical arguments predict a dependence on the fourth
power of the electrode area, but a quadratic dependence is more
typically observed in practice.
As a consequence, larger peak ion energies are observed on a
substrate mounted on the smaller electrode. This configuration is
sometimes referred to as a "reactive ion etch"
configuration, and distinguished from the "plasma etching"
configuration with either substrates mounted on the large area, or
equal area electrodes.
Many plasma CVD processes operate at a high enough pressure (a
few Torr) that the plasma is mostly contained between the
electrodes, so that they are effectively symmetric reactors, even if
the wall area is actually large.
RF Power and Multiple Frequency Excitation
In a conventional reactor, we can increase the RF power to get a
higher ion bombardment energy, but the plasma density will also
increase. We can't adjust these two parameters independently.
An additional degree of flexibility can often be obtained by
providing more than one frequency of excitation of a capacitive
plasma. A typical approach is shown schematically at right. Two
separate power supplies are employed, each attached to one
electrode. Filtering is employed to minimize the interaction between
the two signals: in this case, we've shown an inductor that grounds
the top electrode at 100 KHz, while appearing to be a high impedance
for a 13 MHz signal. Similarly, a capacitor is used to ground the
lower electrode for high frequency signals. Alternative
configurations where both supplies are connected to the same
electrode can also be employed.
To a fair approximation, the high frequency power controls the
plasma density, due to the more efficient displacement current and
sheath heating mechanisms mentioned above.
The low frequency excitation influences the peak ion bombardment
energy, as discussed previously.
Therefore, the user has some ability to separately adjust the ion
bombardment energy and the plasma density, which is not very easy
with a single excitation energy. Reactors of this design have found
applications in both CVD and plasma etching.