4.5 Plasma Processes 57
The energy transfer in an electric field is a function of the microwave power,
gas pressure and energy input. These are powerful parameters to adjust the conditions for synthesis, and are optimized for the desired chemical reactions and the
product.
In the range of gas pressures usually applied for microwave plasma synthesis,
the mean free path length for free electrons may be in the range from 10
−3 to
10
−2 m leading to an energy of the electrons in the range from a few hundred eV
to more than one keV. The energy transferred to the ions is, at a maximum, close
to 100 meV, which is significantly above the thermal mean value, too. Increasing
the gas pressure leads to a decrease of the mean free path length of the electrons.
As a consequence, the energy uptake in the electrical field is reduced. This has a
number of consequences: In the low-pressure regime, the energy of the electrons
is high enough to ionize the particles; the particles carry positive charges. Even
when in this range electrons and positively charged ions coexist, the probability
for recombination of the positively charged particles with highly energetic electrons is small. In the high-pressure regime, the energy of the electrons is low; the
electrons are unable to ionize the particles, the electrons rather attach at the
surface of the particles; the particles obtain negative electrical charges. In both
regimes, the particles repel each other. In between these two ranges there is a
broad range where the particles carrying positive or negative charges are found;
particles carrying electrical charges of different sign attract each other. This leads
to additional agglomeration of particles of any size. In this range of operating
conditions, products with narrow size distribution are obtained only in cases of
extreme short residence times in the reaction zone and efficient quenching processes after the reaction zone.
charged particles accelerated in the electric field. Hence, the collision frequency
z must be considered [8]
U
Q
m
z
f
z
∝
+
2
2
.
(4.19)
Equation (4.17) does not alter the mass relationship of the energy transfer;
rather, it describes the reduction of the energy transferred to the charged particles due to the collisions with neutral species. Furthermore, this function has
a maximum for the energy transfer at f = z. For f < z the energy transfer
increases, for f > z the energy transfer decreases with increasing gas pressure.
The collision frequency z in the plasma is, to a first approximation, proportional
to the gas pressure. The free path length λ of the electrons limits the maximum
energy U max transferred in an electric field with the field strength E:
U
Q E
max = λ .
(4.20)
As the strength of the electric field in a resonant microwave cavity is in the
range of a few 10
6 V m
−1
≙ 10
4 V cm
−1
, the energy transferred to an electron,
may be, depending on the gas pressure, up to a range of kiloelectron volts.
The energy transfer in an electric field is a function of the microwave power,
gas pressure and energy input. These are powerful parameters to adjust the conditions for synthesis, and are optimized for the desired chemical reactions and the
product.
In the range of gas pressures usually applied for microwave plasma synthesis,
the mean free path length for free electrons may be in the range from 10
−3 to
10
−2 m leading to an energy of the electrons in the range from a few hundred eV
to more than one keV. The energy transferred to the ions is, at a maximum, close
to 100 meV, which is significantly above the thermal mean value, too. Increasing
the gas pressure leads to a decrease of the mean free path length of the electrons.
As a consequence, the energy uptake in the electrical field is reduced. This has a
number of consequences: In the low-pressure regime, the energy of the electrons
is high enough to ionize the particles; the particles carry positive charges. Even
when in this range electrons and positively charged ions coexist, the probability
for recombination of the positively charged particles with highly energetic electrons is small. In the high-pressure regime, the energy of the electrons is low; the
electrons are unable to ionize the particles, the electrons rather attach at the
surface of the particles; the particles obtain negative electrical charges. In both
regimes, the particles repel each other. In between these two ranges there is a
broad range where the particles carrying positive or negative charges are found;
particles carrying electrical charges of different sign attract each other. This leads
to additional agglomeration of particles of any size. In this range of operating
conditions, products with narrow size distribution are obtained only in cases of
extreme short residence times in the reaction zone and efficient quenching processes after the reaction zone.
charged particles accelerated in the electric field. Hence, the collision frequency
z must be considered [8]
U
Q
m
z
f
z
∝
+
2
2
.
(4.19)
Equation (4.17) does not alter the mass relationship of the energy transfer;
rather, it describes the reduction of the energy transferred to the charged particles due to the collisions with neutral species. Furthermore, this function has
a maximum for the energy transfer at f = z. For f < z the energy transfer
increases, for f > z the energy transfer decreases with increasing gas pressure.
The collision frequency z in the plasma is, to a first approximation, proportional
to the gas pressure. The free path length λ of the electrons limits the maximum
energy U max transferred in an electric field with the field strength E:
U
Q E
max = λ .
(4.20)
As the strength of the electric field in a resonant microwave cavity is in the
range of a few 10
6 V m
−1
≙ 10
4 V cm
−1
, the energy transferred to an electron,
may be, depending on the gas pressure, up to a range of kiloelectron volts.