## 5 Plasma Precursors
### Hydrogen
#### 5.1.7 Recombination  
The recombination process for electrons and ions is a very exothermic process, with the energy released depending on the particle's ionization potential. Three types of recombination will be discussed here, namely dissociative, three-body, and radiative electron-ion recombination.  
In the case of molecular gases, the dissociative electron-ion recombination process is the fastest mechanism of electron neutralization. This process follows the mechanism presented in (16) [18].  
\[\mathrm{e}+\mathrm{AB}^{+}\rightarrow(\mathrm{AB})^{*}\rightarrow\mathrm{A}+ \mathrm{B}^{*} \tag{16}\]  
As can be seen by Equation (16), the dissociative recombination process starts with an electron being trapped by a molecular ion. The maintenance of the state of auto-ionization leads to more stable products being produced. The rate of reaction for diatomic and triatomic ions, as is the case for hydrogen, exhibits reaction rate coefficients around the \(10^{-7}\) cm\({}^{3}\)s\({}^{-1}\) mark [19].  
The dissociative recombination equations in the case of hydrogen plasma are shown in (17) and (18). The threshold voltage levels for Equations (17) and (18) is 0.01 eV [87].  
\[\mathrm{H}_{2}^{+}+\mathrm{e}\rightarrow\mathrm{2H} \tag{17}\]  
\[\mathrm{H}_{3}^{+}+\mathrm{e}\rightarrow\mathrm{H}_{2}+\mathrm{H} \tag{18}\]  
Three-body recombination, also known as ternary association, is a intermolecular reaction where three particles collide, resulting in the formation of a bound state between two of the particles, while the third particle escapes freely. In plasma cleaning systems, three-body recombination plays a crucial role in maintaining the efficiency and effectiveness of the cleaning process.  
In the context of plasma cleaning, three-body recombination helps to neutralize charged particles, reducing the overall plasma density and preventing potential damage to the surface being cleaned. This process ensures that the plasma remains stable and effective in breaking down contaminants into volatile compounds, which are then evacuated from the chamber. However, three-body recombination can reduce the overall ionization level in the plasma, affecting the efficiency of cleaning by decreasing the number of reactive species available for surface interactions. To mitigate this, plasma cleaning systems are often designed to operate at lower pressures, minimizing three-body collisions and sustaining a higher density of ionized particles for effective contaminant removal [93].  
The three-body recombination competes with dissociative recombination at high electron concentrations exceeding \(10^{13}\) cm\({}^{-3}\). At a 1 eV electron temperature, three-body recombination only in case of electron densities being exorbitantly high exceeding \(10^{20}\) cm\({}^{-3}\). The excessive energy in this case is transferred to the third body, the electron [18].  
The third process of recombination, radiative electron-ion recombination, is an electron-ion process that is slow compared with the other processes, the reason being that a photon needs to be emitted during the interaction of an electron and an ion [18]. The process shown in Equation (19).  
\[\mathrm{e}+\mathrm{A}^{+}\rightarrow\mathrm{A}+\hbar\omega \tag{19}\]  
where  
\(\mathrm{e}\) represents a free electron;  
\(\mathrm{A}^{+}\) represents a positive ion;  
\(\mathrm{A}\) represents the resulting neutral atom or molecule;  
\(\hbar\) is the reduced Planck constant;  
\(\omega\) is the angular frequency of the emitted photon.  
It is important to note that this process has a low cross section of \(10^{-21}\) cm\({}^{2}\) and is only a key player if molecular ions are present and mechanisms such as three-body recombination are suppressed. This mechanism is therefore not very relevant in the case of hydrogen plasmas [18].