56 4 Gas-Phase Synthesis of Nanoparticles
charged particles is inversely proportional to the mass of the charged particles.
The amount of energy transferred depends not at least on the free path length of
the electrons, which depends on the gas pressure. This leads to a function exhibiting a maximum of the energy transfer. The maximum of this energy transfer
function is found under conditions where the microwave frequency and collision
frequency are equal. Figure 4.14 displays this function for three different frequencies of the microwaves as a function of the collision frequency, which is proportional to the gas pressure. Additionally, the course of the maximum of the energy
transfer is plotted. It is remarkable that this function decreases with increasing
collision frequency.
Figure 4.14 Energy transferred in a
microwave plasma to an electrically charged
particle as a function of the collision
frequency and the microwave frequency. The
maximum energy is transferred when the
collision frequency is equal to the microwave
frequency; additionally, the course of the
maximum of the energy transfer is indicated.
0
2
4
6
8
10
collision frequency or pressure [a.u.]
0
0.1
0.2
0.3
0.4
0.5
energy
transferred
[a.u.]
Microwave frequency [a.u.]
1
2
4
Transfer maximum
Box 4.8 Energy Transfer in a Microwave Plasma
In an oscillating electrical field with the frequency f, the energy U transferred
to a particle with the electric charge Q and the mass m is given by.
U
Q
mf
∝
2
.
(4.18)
As the mass of the electrons is a few thousand times smaller than the mass of
the ions, the energy is transferred primarily to the electrons, and not to the
heavy ions. Equation (4.18) is valid for one charged particle in an oscillating
electrical field. In a plasma, the free electrons interact with ions, dissociated
gas and precursor molecules, and neutral gas species. Therefore, collisions
between charged and uncharged particles limit the mean free path of the
charged particles is inversely proportional to the mass of the charged particles.
The amount of energy transferred depends not at least on the free path length of
the electrons, which depends on the gas pressure. This leads to a function exhibiting a maximum of the energy transfer. The maximum of this energy transfer
function is found under conditions where the microwave frequency and collision
frequency are equal. Figure 4.14 displays this function for three different frequencies of the microwaves as a function of the collision frequency, which is proportional to the gas pressure. Additionally, the course of the maximum of the energy
transfer is plotted. It is remarkable that this function decreases with increasing
collision frequency.
Figure 4.14 Energy transferred in a
microwave plasma to an electrically charged
particle as a function of the collision
frequency and the microwave frequency. The
maximum energy is transferred when the
collision frequency is equal to the microwave
frequency; additionally, the course of the
maximum of the energy transfer is indicated.
0
2
4
6
8
10
collision frequency or pressure [a.u.]
0
0.1
0.2
0.3
0.4
0.5
energy
transferred
[a.u.]
Microwave frequency [a.u.]
1
2
4
Transfer maximum
Box 4.8 Energy Transfer in a Microwave Plasma
In an oscillating electrical field with the frequency f, the energy U transferred
to a particle with the electric charge Q and the mass m is given by.
U
Q
mf
∝
2
.
(4.18)
As the mass of the electrons is a few thousand times smaller than the mass of
the ions, the energy is transferred primarily to the electrons, and not to the
heavy ions. Equation (4.18) is valid for one charged particle in an oscillating
electrical field. In a plasma, the free electrons interact with ions, dissociated
gas and precursor molecules, and neutral gas species. Therefore, collisions
between charged and uncharged particles limit the mean free path of the