Chemistry Reference
In-Depth Information
Because the relation
i
e
,
ret
V
s
often
the measured total probe current is differentiated instead of the electron retarding
current.
i
+
,
sat
is valid for low and medium values of
V
−
6.1.3.2 Plasmas with Anisotropic EEDF
In case of an anisotropic EEDF in an axisymmetric discharge a Legendre polynomial
expansion of the EEDF has to be performed. The coefficients
f
i
of this expansion
follow from the second derivatives of probe characteristics measured with a one-sided
planeprobeindifferentorientations[10,28-30].Meanenergyanddensityofelectrons
follow from
f
0
and the drift velocity is derived from
f
1
[11,31,32]. A generalized theory
of electron retardation by Langmuir probes in anisotropic plasmas with no assumed
symmetry is performed in [33] by expansion of the EEDF into a series of spherical
harmonic functions.
6.1.3.3 Determination of the Second Derivative of the Probe Characteristic
The second derivative of the probe characteristic may be obtained by modulation
of the probe current superposing an alternating voltage
v
mod
(
on the steady probe
bias. The amplitude of one of the harmonics of the current is proportional to the
derivative [4,10,18,34,35]. Presently often numerical techniques are used to differen-
tiate the probe characteristic after measurement. One possibility is the non-recursive
digital or FIR filtering of the characteristic recorded point by point at equidistant
voltage values. Here each current value is replaced by a linear combination of itself
and some neighboring current values [26], details in [36,37]. The distortion of the
second derivative of the characteristic by the electrical or numerical differentiation
is described by the convolution of the true derivative with an apparatus function
[35-39]. Further differentiating techniques are listed in [11].
t
)
6.1.3.4 Probe Measurements in rf-Discharges
Technological plasmas often are generated by rf-discharges. Due to the varying
plasma potential in these discharges an rf-current occurs in the probe circuit which is
rectified at the nonlinear probe characteristic leading to distortions of the character-
istic. The evaluation described here of such disturbed characteristics gives incorrect
plasma parameters. Especially the electron temperature may be strongly overesti-
mated. To avoid this problem the probe tip is forced to follow the varying plasma
potential either by driving the probe with an rf-voltage (active rf-compensation)
[40-43], or by increasing the impedance between probe and ground (introducing of
blocking filters or self-resonant inductors connected in series to the probe tip) and
decreasing the probe to plasma sheath impedance using an additional compensation
electrode(passiverf-compensation)[44-47].Theblockingelementshavetobeplaced
to the probe tip as near as possible, but at least inside the metallic rf-reactor to avoid
a big capacitively rf-current from probe tip connection to ground. Unfortunately
often the rf-compensation is incomplete and a certain rf-perturbation remains. The
evaluation of the characteristic has to be modified in this case [39,48,49]. Also
rf-distortions of the probe characteristic are described by the convolution of the true
characteristic with an apparatus function. Because this function is not a bell-shaped
