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One of the key aspects of low-temperature reactive plasma processing is the enhanced chemistry offered by plasma-chemical reactions driven by energetic electrons. In low- temperature plasmas the neutral gas temperature is typically around, or just above, room temperature and so reactions with an energy threshold are driven by electrons. Negative ions in plasmas are generally formed via electron attachment to neutral species:

e−+ A→ A−∗ →A−+ ∆E (3.1)

where an unstable intermediate state, (A−)∗, is formed. ∆Erepresents the internal energy of A, the electron energy and electron affinity, Eaff, of A. This energy can be released

via photon emission (radiative attachment) or through a collision with a third body. However, these reactions are both relatively unlikely in low-pressure plasmas due to small cross sections and low density conditions. The most probable formation mechanism for negative ions in low-pressure, low-temperature plasmas is the dissociative attachment of small molecules [96]:

e−+ AB → AB−∗ →A−+ B (3.2)

The formation of stable negative ions in this way can occur if A has a positive electron affinity, Eaff >0. If Eaff <0 then A− will be unstable and consequently undergo autode-

tachment: A−→A + e−, hence stable negative ions exist only for strongly electronegative gases.

In the first step of equation 3.2, any excess energy cannot be carried away as a colli- sional loss because the electron is captured. For this reason, dissociative electron attach- ment is a resonant process and so the energy range is relatively narrow. The measured cross section for the production of oxygen negative ions as a function of electron temper- ature is shown in figure 3.1, which can be seen to peak at around Te≈6.5 eV. The shape

of this peak is typical of a resonant process. The second maximum beyond 15 eV is due to polar dissociation (p. 250 in [28]) and isn’t significant for most low-pressure discharges due to the high electron energy threshold.

It is also possible for negative ions to form via charge transfer reactions, such as

A−+ B→A + B− (3.3)

which is favoured if B has a higher electron affinity than A. This process can also pro- duce negative molecular ions. For example, in oxygen discharges, O−₂ and O−₃ can be

3. NEGATIVE IONS IN REACTIVE MAGNETRON SPUTTERING

Figure 3.1. Total measured cross section of oxygen negative ion production in O2 by

electron impact. Reproduced from p. 251 in [28].

formed via charge transfer reactions of excited metastable oxygen [97] and ozone with O−, respectively.

However, it is generally accepted that dissociative electron attachment is the pri- mary volumetric formation mechanism of negative ions in low-pressure plasma dis- charges [96]. Dissociative electron attachment can also occur when the molecule, AB, is in an excited metastable state. For the case of oxygen, attachment to metastable O2

(A3_Σ+

u, C3∆u, c1Σ−u) is thought to be particularly important during the afterglow of

pulsed discharges as the drop in electron temperature favours this reaction over dissocia- tive attachment to the oxygen ground state which has a higher threshold energy [98]. It has also been suggested by Ding et al.[99] that attachment to high Rydberg states of O2

is also important.

Attachment cross sections can also be strongly influenced by the rotational and vibra- tional modes of the molecule. This is particularly true for hydrogen and deuterium, where the cross section for dissociative electron attachment for the vibrational mode ν = 1 is a factor of 104 _{smaller than forν = 4 [96]. Furthermore, the increased internal energy of the}

excited molecule means that the threshold electron energy is reduced when compared with dissociative attachment reactions involving the molecular ground state. The combination of these two effects results in dissociative electron attachment to hydrogen molecules being the fully dominant process for negative ion formation in hydrogen discharges [100]. This has implications for hydrogen/deuterium negative ion sources which are routinely used to generate neutral beams for use in thermonuclear fusion research [101]. These effects have also been reported for oxygen, but the effects are not as remarkable as those observed for hydrogen [96].

3. NEGATIVE IONS IN REACTIVE MAGNETRON SPUTTERING

Negative ions can be lost via several different reaction pathways involving collisions with electrons or heavy particles. For example, electron impact detachment,

e−+ A− →A + 2e−, (3.4)

can be an important loss channel of negative ions, however, only for high electron tem- peratures. The peak of the cross section for this reaction is typically centred around an electron temperature that is a factor of 10−20 higher than electron affinity, Eaff [28],

due to the Coulomb repulsion between the negative ion and electron. A more proba- ble loss mechanism of negative ions in a low-pressure discharge is positive-negative ion recombination:

A−+ B+→A + B∗. (3.5)

At large separation distances, the potential energy of the A− + B+ _{state lies above the}

A + B∗ state. However, due to the attractive Coulomb force between the negative and positive ions, the potential energy of the A− + B+ _{state decreases with the nuclear}

separation distance, eventually dropping below that of the A + B∗ state at a distance, Rx. Following Lieberman (p. 257 in [28]), the energy separation between these two states

can be estimated by

∆E ∼ EizB

n2 − EaffA (3.6)

whereEizB is the ionization energy of B,nis the principal quantum number of B∗andEaffA

is the electron affinity of A. For A taken to be atomic oxygen (O) and B to be argon (Ar), EaffA ≈ 1.5 eV and EizB ≈ 16 eV, and assuming a principal quantum number, n ≈3, ∆E

is found to be relatively small with a value of approximately 0.3 eV. Due to the typically small values of ∆E, the nuclear separation distance at which the potential energies of the two states in equation 3.5 intercept (Rx) can be large, resulting in ion-ion recombination

possessing a significant cross section.

Another important negative ion destruction mechanism in oxygen discharges is the associative detachment of negative atomic oxygen with neutral oxygen:

O−+ O→(O−₂)∗ →O2+ e− (3.7)

where the intermediate (O−₂)∗state autodetaches. The ground state of O−₂ is stable against autodetachment as it lies below the O2 ground state, however, many of the excited states

of O−₂ sit above the neutral ground state and readily undergo autodetachment (p. 260 in [28]). This results in equation3.7having a large reaction rate constant even at thermal energies where kadet∼3×10−16m3s−1.

3. NEGATIVE IONS IN REACTIVE MAGNETRON SPUTTERING

3.2.1.1 Global models

To model the complex chemical processes in plasma discharges, so-called global models

are often employed. Although the spatial distributions of plasma parameters are assumed rather than calculated, or ignored completely for the case of zero-dimensional models, global models can provide a valuable insight to the evolution and scaling of plasma parameters in complex multi-species discharges. An alternative to global models are particle-in-cell (PIC) simulations, which present several advantages over the former. For example, the rate coefficients used in global models are calculated assuming a Maxwellian distribution of electrons, while PIC simulations are able to model the distributions. How- ever, PIC models are very computationally expensive and, despite the assumptions made, global models can be used to ascertain correlations between various plasma parameters. A global model uses volume-averaged quantities and constitutes a system of conservation equations for all species to be considered. For instance, the evolution of the density of species A can be written in the form of a first order differential equation,

dnA

dt = formation terms−destruction terms−wall loss term. (3.8) An example of a formation term for negative ions would bekattnenA where katt is the

reaction rate coefficient for attachment of electrons to neutral species A,nAis the number

density of A and ne is the electron number density. Additionally, quasi-neutrality of the

charged species must also be satisfied;

X

i

Zn+_i =X

j

Zn−_j +ne (3.9)

where n+_i is theith positive ion species, n−_j is thejth negative ion species. As the power absorbed by the discharge is coupled almost exclusively to electrons in low-pressure, low- temperature plasmas, the evolution of the electron temperature Te can be obtained by

examining power balance. Following the text by Lieberman and Lichtenberg [28], the power balance in the discharge must also be considered by equating the power absorbed by the discharge, Pabs, to the power lost via collisions and at surfaces. By summing over

all heavy neutral and ion species (j andj+_{, respectively) the power balance equation can}

be written as Pabs V = X j eE(j) c k (j) iz njne+k (j+₎ w e(Ee+Ei)n(j+₎ (3.10)

where Ec is the collisional energy loss for each electron-ion pair created for the neutral

j, Ee,i is the kinetic energy lost at a surface for electrons (e) and ions (i), k

j

iz is the

ionization rate coefficient of the neutral j and k_wj+ is the rate coefficient for wall losses of the positive ion j+_{. Negative ion energy losses to the walls are often neglected when the}

3. NEGATIVE IONS IN REACTIVE MAGNETRON SPUTTERING

discharge is active as the low-temperature negative ions generated in the plasma volume are generally confined to the discharge bulk by wall sheaths. However, the positive ion flux to the walls is partially dependent upon the negative ion content in the discharge [102]. In the afterglow, the situation is different and, given enough time, the sheaths at the chamber walls eventually collapse, allowing negative ions to be transported to plasma- facing surfaces. This feature of pulsed discharges is discussed further in section§3.2.2. The reader is referred to Ch. 10 of [28] for a much more thorough description of electronegative plasma equilibria.