S Brand

R A Abram

M A Kaliteevski

Tailor-made surface plasmon polaritons above the bulk plasma frequency: a design strategy for indium tin oxide

Keywords: numbers: 41.20 Jb, 42.70 Qs, 73.20 Mf, 78.68 +m

A simple phase-matching approach is employed as a design aid to engineer surface plasmon polariton states at the interface of an indium tin oxide layer on the top of a Bragg reflector. By altering the details of the reflector, and in particular the ordering of the layers and the thickness of the layer adjacent to the indium tin oxide, it is possible to readily adjust the energy of these states. Examples of structures engineered to give rise to distinctive features in the reflectivity spectra above the bulk screened plasma frequency for states of both possible polarizations are presented.

Introduction

Surface plasmon-related excitations, which may have advantageous or deleterious consequences, depending on circumstances, have most often been studied at interfaces involving silver or gold but Rhodes et al have experimentally demonstrated the presence of both bulk and surface plasmon polaritons (SPPs) in indium tin oxide (ITO) on a glass substrate [1,2].

ITO is currently particularly useful as an electrode in a variety of optoelectronic devices and other oxides, such as ZnO, may become important for such applications. The existence of SPPs in conducting oxide films was confirmed by Michelotti et al [3] in the case of ITO, although they were unable to detect their signature in an alternative series of conducting oxide ZnO:Al films, and additional results on ITO have more recently been reported by Losego et al [4]. All of these reflectivity experiments were carried out employing a standard prism-coupling technique in order to access the SPP states using TM-polarized light in which the electric field is polarized in the plane of incidence. There are no associated SPPs at the interface of these simple conductor/substrate structures with the orthogonal TE polarization in which the electric field is polarized parallel to the interface as these are precluded by the boundary conditions.

However, we have recently demonstrated theoretically that both TM-and TE-polarized optical Tamm states or SPPs should be observable above the plasma frequency ( p ) in a system in which the conducting film is on the surface of a Bragg relector, and further, that such states can be revealed without the use of prism coupling [5]. In that work, however, we considered only an idealised conductor with a frequency-dependent permittivity of the form ( ) ( )

2 1 / p c i ε ω ω ω ω ω = - +
, where c is the loss-associated collision frequency term. In this work we consider a system employing a permittivity consistent with the experimental work on ITO of Rhodes et al [2] and Michelotti et al [3], and give a more detailed analysis of the conditions under which the SPPs are observable. Brief and more extended reviews of SPPs can be found in the works of Barnes et al [6] and Pitarke et al [7] respectively.

Background considerations

In previous work Kaliteevski et al [8] showed that in order to obtain an eigenmode or surface state at an interface between a metal (on the left) and Bragg reflector (on the right) it is necessary to fulfil the condition that r left r right = 1 where r left , r right represent electric field amplitude reflection coefficients for light travelling from right to left, and left to right respectively at a virtual interface within the Bragg reflector considered to be an infinitesimal distance from the metal interface. In the simplest cases this means that r = r left = r right = ± 1.

The specific case where r -1 was considered in that work, corresponding to the situation in which the phase of the complex reflection coefficient is approximately which occurs when considering reflection from a metal at an energy well below the plasma frequency and near the centre of the photonic band gap (PBG) of a Bragg reflector with a high refractive index layer adjacent to the metal. In this case the existence of the PBG ensures that states at energies within the PBG are confined by the Bragg reflector on one side of the interface and the evanescent nature of the state below the plasma frequency in the metal does so on the other. Subsequent experiments demonstrated the existence of such states at the interface of a gold/GaAs-AlGaAs Bragg reflector structure [9] . The alternative situation in which r + 1, and hence the phase change is approximately zero for both reflections was considered in our more recent work [5] dealing with surface states above the plasma frequency but within the PBG of the Bragg reflector: in that case the layer adjacent to the metal had the lower refractive index (leading to r right = +1) and total internal reflection at the interface with the metal is responsible for the existence of the state. Similar arguments were utilised earlier by Kavokin et al [10] who considered lossless modes at the interface between two different periodic dielectric structures.

More generally, it follows that the requirement for a surface state can be stated as

0 left right φ φ + = ( + integer × 2 ) (1)
where left φ and right φ are the respective phases of the two complex amplitude reflection coefficients and this leads to a complete family of more general phase matching situations in which surface states may be found. Although eqn. ( 1) does not give any information concerning the detailed form of the resultant surface state it represents a very simple and useful criterion as an aid to the design of structures exhibiting such states.

In what follows we consider the case of an ITO layer on a Bragg reflector, as illustrated in figure 1, and show that such structures can be designed to exhibit SPP features above the (screened) ITO plasma frequency in both TE and TM polarisations. For ITO we take the permittivity to be essentially of the form given by Rhodes et al [2] :

( ) ( ) 2 1 p c i ω ε ω ε ω ω ω ∞ = - + (2)
ε ω ε ∞ ∞ = = = h eV, 0.118 c ω = h eV).
For the purposes of the current calculations a Bragg reflector consisting of SiO 2 and TiO 2 layers is employed. In general the refractive index of these materials is complex and depends upon frequency (see e.g. Lee and

Yao [11]) but in the infra-red regime considered in the present work we take that of SiO 2 to be 1.47 and use a value of 2.37 for TiO 2 .

We note that as well as the experimental justification supplied by Sasin el al [9] in the near infra red region, the additional results of Guo et al [12], who considered the GHz response of microstrip transmission lines, confirms the general utility of the phase-matching approach for the design and manipulation of optical Tamm states.

Phase calculations

The phase associated with reflection from the ITO layer, left φ , depends on the thickness of the ITO layer, the refractive index of the top layer in the Bragg stack, the angle of incidence and the energy and polarization of light considered. In the case of a finite thickness ITO layer it also depends on the refractive index in the region following the ITO, which is taken to be air.

As an illustration of the value of left φ , associated with reflection from the ITO, we show in figures 2 a), b) results for both TM and TE polarizations as a function of energy at a particular fixed angle. For these calculations a high index TiO 2 layer is at the top of the Bragg reflector:

results for left φ with the lower index material at the interface with ITO are different in detail but of the same form. As the phase depends on the thickness of the ITO layer we show results calculated via the standard Fresnel equations for an infinite system as well as for a finite structure with an arbitrary 200 nm layer of ITO followed by air. In the latter case the phase is evaluated using a transfer matrix calculation. Results are shown for both a lossless ( c = 0) representation of the ITO permittivity as well as with the full equation ( 2) loss term included.

In the case of TM polarization the standard Fresnel equation calculation without losses for the ITO (curve FNL in figure 2 (a)) shows predictable behaviour. At high energy, corresponding to light at high frequency and consequently in a regime with relatively high refractive index (albeit with 1 n < ), the set angle of 20°is below both the critical angle, C , and the Brewster angle, B , and the phase left φ = 0. However, when the energy/frequency is reduced far enough, ( ) ε ω is such that the refractive index is reduced to the point where B = 20°and the phase jumps discontinuously to 180°: this occurs at an energy 1.252 eV, when n 0.86. At a slightly smaller energy 1.235 eV, when n 0.81, the corresponding frequency of the light is such that the critical angle is reduced to C = 20°, the set angle, and the phase then drops rapidly below 180°as the energy is reduced further, tending to the expected value of 0°at an energy corresponding to the plasma frequency of 1.123 eV and continuing to fall towards -180°far below this energy. It is in the regime of energy above the bulk plasma frequency but below the energy for which C equals the angle of incidence that SPPs of the type we are considering can potentially be seen. In the simpler case of TE polarization with no losses, the Fresnel result is that 0 left φ = until the energy corresponds to that for C = 20°and the phase then gradually shifts down towards -180°. The results are somewhat modified for the finite width ITO structure and with losses included but all results are very similar in the neighbourhood of and below that corresponding to the plasma frequency.

We now consider an illustration of results for right φ , the phase associated with reflection from the Bragg reflector. We take the reflector to be formed from 188 nm layers of SiO 2 and 116 nm layers of TiO 2 on a SiO 2 substrate (refractive index = 1.47). The structure is designed to have a photonic band gap centred at 1.123 eV at normal incidence and this results in a photonic band gap between 0.95 1.29 eV (for a Bragg reflector of infinite extent). φ is relatively small close to the centre of the gap and hence equation ( 1) can be satisfied at some energy near p ω h , which explains the choice of low index material at the interface in our earlier work [5], although the detailed considerations were slightly different due to the simpler form of ( ) ε ω in that report.

(a). Results: TM SPPs above the plasma frequency

Despite the arguments made in Section 3, it is possible to produce structures that support SPPs in which the Bragg reflector is such that the top layer is formed from the high index TiO 2 material. In fact there is some advantage in choosing to position the high index material at the interface with ITO because that reduces the critical angle at that interface and enhances the confinement of the SPP. The general form of right φ as shown in figure 3 a) does produce an unfavourable arrangement for the satisfaction of equation ( 1) if that particular reflector is employed but an appropriate phase shift can be produced if the thickness of the top layer is increased, a reflector with a PBG centred at a lower energy is employed or some combination of both adjustments is made. To illustrate this point we choose to utilise a reflector designed to have a PBG of 1 eV and maintain a quarter-wave TiO 2 layer bordering the ITO. In θ , within the TiO 2 ). The phase-matching approach and also the semiinfinite ITO/Bragg reflector structure result obtained using the complex photonic bandstructure method described in Brand et al [5] both predict the energy of the SPP to be 1.229 eV when the loss term is neglected, in excellent agreement with the reflectivity result. The previous results were chosen to understand the underlying nature of the SPP states more clearly but relate to an unrealistic situation with regard to the ITO loss term. Consequently we now consider a more realistic scenario in which the full loss term of equation ( 2) is included and the corresponding results are therefore representative of what would be expected in an actual experiment. This necessitates the use of much thinner ITO layers, otherwise there is insufficient penetration of light to access the state at the ITO/Bragg reflector interface. Figure 6 shows the calculated reflection coefficient at the same external angle in air as used previously, 54.3

e θ =
°, for a range of ITO layer thicknesses. The structure is otherwise as before. In the case of very thin layers an obvious feature is present very close to the centre of the PBG (the structure has been designed such that the feature will appear at the centre of the gap at the chosen angle) at an energy corresponding to that of the screened bulk plasmon. As w is increased the dip in the reflection coefficient becomes more prominent, shifts to higher energy and we see a near zero reflection coefficient when the ITO layer width is w = 120 nm. The dip continues to move towards the energy of the SPP as the thickness of the ITO layer is increased but the effects of the high loss term eventually dominate the reflectivity, the penetration of the light to the ITO/Bragg reflector interface is suppressed and the initial strong feature in the reflectivity vanishes. We note that when a large loss term is present and a much broader feature is obtained than in the previous idealised calculations, we no longer expect the minimum in the reflection coefficient to coincide with the SPP energy although it does approach this value as the ITO thickness is increased before finally disappearing. For comparison, results are also displayed for the situation with a Bragg reflector and no ITO over-layer and also for a bare 120 nm ITO layer on a SiO 2 substrate. We note that the shift in the reflection minimum away from the bulk plasmon value and towards that of the SPP as the ITO thickness is increased is similar to that demonstrated by Rhodes et al [2] except that in their case the shift was downwards towards a more conventional lower energy SPP and prism coupling was required in order to obtain the results.

(b). Results: TE SPPs above the plasma frequency

In the case of TE polarization the general form of figure 2 b), indicates that the phase left φ is negative above the critical angle at the ITO/dielectric interface irrespective of the details concerning ITO layer thickness, loss term and dielectric material. Also, the results of figure 3 b) illustrate that the phase right φ is always positive at energies above the PBG centre when a low index quarter-wave layer is present at the top of the Bragg reflector. Thus equation (1) should be easily satisfied if the low index material in the Bragg reflector is adjacent to the ITO. To examine this case in more detail we reverse the ordering of the final layer compared to the calculations in the previous section, but otherwise employ the same basic 20 layer-pair Bragg reflector with PBG centred on 1 eV.

To begin, we first confirm that the expected localized TE SPP exists above the bulk screened plasmon energy, and for the purposes of our calculations we choose an external air/ITO interface angle of incidence of e = 50°(this external air/ITO interface angle corresponds to an internal SiO 2 angle 31.4 i θ = °). The semi-infinite ITO/Bragg reflector calculation [5] gives the resultant SPP energy to be 1.202 eV, whereas the phase-matching approach indicates that the solution is to be expected at 1.203 eV. These results can be compared with the transfer matrix reflection coefficient plot of figure 7 which shows a sharp dip at an energy of 1.203 eV. In order to obtain definitive results we have employed an artificially reduced loss term of 0.01 c and an associated large ITO thickness of 1210 nm, which ensures good localization of the SPP and a sharp feature in the reflectivity plot. The associated electric field intensity plot, calculated via the transfer matrix approach, is shown in figure 8 and this clearly demonstrates that the feature is due to an SPP localized at the ITO Bragg reflector interface. At the SPP energy the value of the refractive index (with loss term neglected) of the ITO is 0.698 with a corresponding external critical angle in the air at the air/ITO interface of ec = 44.3°, below that of the external angle considered, 50 e θ = °. Thus it is again necessary to employ a carefully chosen balance of ITO layer thickness and loss term in order to reveal the nature of the SPP while avoiding a situation in which the evanescent field at the air/ITO interface is such that the SPP cannot be effectively accessed. Again, as expected, calculations confirm that the SPP moves to lower or higher energy when the value of d is increased or decreased respectively. It can also be observed in figure 7 that there is a minor dip in the reflection plot at about 1.26 eV. The transfer matrix calculation of the associated E-field intensity at this energy reveals a peak at the centre of the ITO layer, as opposed to localization at the ITO/BR interface. The position of the feature shifts to higher energy as the ITO layer thickness is decreased and vice versa as the confinement of the associated state is altered.

We have also computed results for a realistic situation with the full loss term included.

Figure 9 illustrates the calculated reflection coefficient for TE polarization as a function of energy for a range of ITO layer thicknesses. The external angle of incidence is 50°. For this polarization the feature associated with the bulk plasmon at 1.123 eV is weaker and less sharp than in the TM case for the smaller ITO layer thicknesses but a very distinctive reflectivity minimum associated with the presence of the SPP develops as the ITO thickness increases up to 260 nm. The energy at this minimum is just under 1.2 eV, very close to the idealised value of 1.203 eV obtained from the previous essentially loss-free calculations. We note that the feature becomes less prominent as the ITO layer becomes thicker and penetration to the ITO/Bragg reflector interface is reduced.

Conclusions

We have demonstrated that significant features are to be expected in the reflectivity spectra of indium tin oxide layers on a Bragg reflector as a consequence of surface plasmon polaritons at the interface. It is not necessary to employ a prism coupling technique, as is normally required, in order to observe the effects of the presence of these states although additional distinctive features (not described in this work) can be seen in that case. By an appropriate choice of structure, the design of which is aided by consideration of the simple phase matching condition 0 left right φ φ + = , the SPP energy can be easily adjusted and, in particular, can be positioned above the bulk screened plasmon energy. This is in contrast to the normal situation without the reflector where the SPP is found below the bulk plasmon energy.

In addition, the position of the SPP can be readily shifted by an appropriate choice of ITO layer thickness and that of the material forming the dielectric layer at the top of the reflector.

Although the particular conditions employed have been designed to enhance the distinctive nature of the reflectivity response presented, the general features described should be observable over a range of experimental conditions and the general design approach is applicable to other systems.

  Figures 3 a), b)show right φ as a function of energy for a structure consisting of 20 layer pairs on a SiO 2 substrate as a function of the thickness, d, and composition of the final layer. The results are calculated using a standard transfer matrix approach. By altering the material of the top layer and also the thickness of this final layer it is possible to adjust right φ to have any desired value in the range ± at a chosen energy within the PBG. When the top layer in the reflector is composed of low refractive index material with phase at the centre of the PBG is 0°and alternatively, when a quarter-wave layer of the high refractive index material is present the phase at the centre of the PBG is right φ = ±180°(which are equivalent values). We note that in the PBG region, when incoming light is totally reflected, the change in phase at a given frequency in response to a change in width is directly related to the change in optical path length due to the related round-trip distance. At normal incidence there is, of course, no distinction between the results for TE and TM polarization. At a more general angle of incidence the photonic band gap region shifts to higher energies and there is a difference in the detailed results for the two polarizations. Note that the centre of the PBG can be shifted relative to the plasma frequency of the ITO by altering the structure of the Bragg reflector. Thus there is considerable flexibility with regard to the adjustment of the phase right φ associated with the Bragg reflector at any particular energy through the choice of the PBG or angle of incidence or polarization. This flexibility can be employed to tailor-make a structure to satisfy equation(1) at a chosen energy for a particular metallic surface layer and given polarization.The general form of the results in figure2 a), b) indicate that in order to obtain a SPP well-confined by internal reflection at the ITO/Bragg reflector interface, the phase left φ will be relatively small in magnitude, irrespective of polarization. If the loss term is neglected then left φ can be large, approaching when the angle of incidence (20°here) is just above the critical angle in the case of TM polarization, but in such a case confinement will be poor, so angles of incidence significantly larger than C despite the smaller left φ are to be preferred. When losses are included left φ is always relatively small near, but above, the plasma frequency, having a negative value in the case of TE and a positive value in the case of TM polarization. Thus it is clear that the situation in which the high index, quarter-wave material of the Bragg reflector is at the interface provides an unfavourable scenario for the formation of SPPs near the plasma frequency if the band gap is centred at the plasma frequency: Figure3a) shows that the phase right φ ±180°in this region and with left φ small, equation (1) cannot be satisfied. On the other hand, figure 3 b) demonstrates that right

  this case the respective thicknesses of the TiO 2 and SiO 2 layers are 131 nm and 211 nm and the normal incidence PBG is from 0.85 eV 1.15eV, largely below 1of incidence the PBG is effectively shifted to higher energies, the plasmon energy falls further within the PBG and equation (1) can more easily be satisfied above the plasma frequency. This is illustrated in figure4which shows a sharp feature in the (power) reflection coefficient associated with the SPP at 1.230 eV. In order to demonstrate the existence of this state clearly, the collision term has been artificially reduced to 0.01 c ω , the incident angle at the external air/ITO interface, e θ , has been chosen as 54.3°(this external air/ITO interface angle corresponds to the internal TiO 2 angle 20 i θ = °employed in constructing figure 2) and a relatively thick, w = 1650 nm ITO layer is used. Under these circumstances the SPP energy effectively corresponds to the position of the narrow minimum and we can compare this with the predicted energy of the SPP found from equation (1) (note that left φ and right φ are evaluated at the internal angle, i

Figure 4 2 tanE

 42 also shows the reflection coefficient associated with the 40-layer Bragg reflector on the SiO 2 substrate without the ITO cap layer to make it clear that the SPP feature lies just below the PBG edge. If the value of d is increased then the SPP moves to lower energy and vice versa. The form of the variation in the SPP energy as a function of Bragg reflector top layer width was presented in Kaliteevski et al[8] without discussing the specific form of the individual phase variations.In order to demonstrate the detailed form of the SPP we reduce the loss term to 0.001 c ω , extend the thickness of the ITO to w = 2700 nm and also consider a 1000 nm thick region of the air to the left of the ITO. A plot of the resultant component of the electric field intensity ( ) tangential to the interface as calculated from the transfer matrix approach is shown in figure5. This clearly reveals the characteristic properties of a surface state localized at the ITO/Bragg reflector interface. We note that at the SPP energy, the value of the refractive index (with loss term neglected) of the ITO is 0.795 with a corresponding external critical angle at the air/ITO interface of ec = 52.6°, below that of the external angle 54.3 e θ =°considered. If the thickness of the ITO is increased we find that there is eventually insufficient penetration of the light through the ITO due to the evanescent nature of the electromagnetic field at the air/ITO interface, and it becomes more difficult to observe the feature due to the SPP at the ITO/Bragg reflector interface.

Figure captions FIG. 1 FIG. 3 1 /FIG. 8 A

 captions1318 Figure captions

  Figure 2


Mihai Draghici

Eugen Stamate

Properties of highly electronegative plasmas produced in a multipolar magnetic-confined device with transversal magnetic filter

Keywords: negative ions, ion-ion plasma, Ar/SF 6 plasma, plasma diagnostics PACS

Highly electronegative plasmas were produced in Ar/SF 6 gas mixtures in a DC discharge with multipolar magnetic confinement and transversal magnetic filter.

Langmuir probe and mass spectroscopy were used for plasma diagnostics. Plasma potential drift, the influence of small or large area biased electrodes on plasma parameters, the formation of the negative ion sheath, and etching rates by positive and negative ions have been investigated for different experimental conditions.

Reducing the electron temperature below 1 eV the density ratio of negative ion to electron exceeded 100 even for very low amounts of SF 6 gas. The plasma potential drift could be controlled by proper wall conditioning. A large-electrode biased positively had no effect on plasma potential for density ratios of negative ion to electrons larger than 50. For similar electronegativities or higher a negative ion sheath could be formed by applying a positive bias of a few hundred volts.

I. Introduction

Electronegative plasmas produced by attaching mobile low-energy electrons to create heavy negative ions are very attractive for both fundamental research and plasma processing applications [1,2]. Recent reports include the discrete and modal focusing effects for negative ions in three-dimensional plasma sheath lenses [3,4] that can be used for negative ion beam extraction [START_REF] Stamate | Ion beam extraction by discrete ion focusing[END_REF], and mass spectrometry [START_REF] Stamate | [END_REF]. Highly electronegative discharges, also called ion-ion plasmas [7][8][9], are seen as a promising solution for electric propulsion [10][11][12][13], and neutral beam development [14]. Positive ion sheath formed when applying a negative bias with respect to plasma potential, V pl , has been extensively investigated starting with the pioneering work of Langmuir. Recently, there is also a growing interest in electron sheath [15] and its transition to anodic glow [16][17][18]. However, there is very limited understanding of the negative charge sheath formed by both electron and negative ion. Electronegative plasmas produced in argon and sulphur hexafluoride (SF 6 ) are used to etch silicon [19], silicon nitride [20], silicon carbide [21][22][23][24] and titanium carbide [25] with high etch rates and without film residues. Nevertheless, problems associated with charge accumulation at the trench bottom during high-aspect-ratio etching by positive ions have led a systematic research on silicon etching by negative ions [26][27][28][29]. The goal was to use the benefit of a considerably lower charging potential during negative ion neutralization on the substrate. Negative ion etching with low energies and low charging potentials is also attractive for low damage processing required in node technologies below 50 nm [30]. So far, despite of good theoretical coverage [31][32][33][34][35] and a large variety of methods for negative ion diagnostic including optical emission [36], photodetachment [37], Langmuir probe [38][39][40][41][42][43], thermal probe [44], propagation of the ion acoustic waves [45][46][47] and Thomson scattering [48] there are still important basic questions related to highly electronegative discharges that need to be answered.

The aim of this paper is to clarify some physical aspects related to highly electronegative discharges, including plasma potential drift, the influence of small or large area biased electrodes on plasma parameters, the formation of the negative ion sheath, and etching rates and surface roughness by positive and negative ion impact. Experiments are performed in Ar/SF 6 plasma produced in a multipolar magnetically confined discharge with transversal magnetic filter.

II. Experimental

The reactor chamber has a cylindrical geometry and it is schematically illustrated in figure 1(a). The experiments were performed using Ar/SF 6 gases and the DC plasma was produced between a negatively biased filament, and a grounded anode. An inner metallic cylinder, C 1 , could be polarized at a certain potential U W and it was used to study the possibility of tuning the plasma potential. Moreover, C 1 could be heated up to a few hundred degrees using a vacuum compatible heating system sandwiched between C 1 and an additional cylinder, C 2 , electrically insulated from the wall. The pressure inside the main chamber during the measurements was 3 mTorr and the discharge voltage 150 V. A transversal magnetic filter divides the chamber into two regions: source plasma (SP) and target plasma (TP) [49][50][51]. It was made of permanent magnets (2000 Gauss at the surface) placed in rectangular pipes situated 45 mm apart. Cooling water was flowing through the filter during plasma operation to avoid damage of the magnets by excessive heating.

The magnetic field between two consecutive pipes was about 500 Gauss. The magnetic filter reduces the electron temperature, T e , by increasing the diffusion time of the electrons in SP. Consequently, the negative ion production becomes much more efficient in TP. The magnetic confinement at the walls is obtained with an array of permanent magnets which are fixed at the outer side of the cylinder.

A mass spectrometer Hiden EPIC Series 1000 was used to record and monitor both positive and negative ion species. The plasma parameters were measured using two Langmuir cylindrical probes: one situated in SP, which has a fixed position and the other in TP, which can be moved in radial direction. The electrical probe circuit and the details of the "Test Function" procedure for extracting the bulk and hot electron densities (n e and n eh ) and temperatures (T e and T eh ) and the negative ion parameters (n ni and T ni ) are presented in detail elsewhere [39,40]. Special care was devoted to avoid recording erroneous probe characteristics affected by contaminations effects reported for reactive plasmas [52,53]. It has been shown that the DC discharges with magnetic confinement exhibit three groups of electrons, namely the anisotropic primary electrons emitted by filament and accelerated to an energy correlated to the discharge voltage in a very thin sheath surrounding the cathode (filament) [54]. The isotropic hot electrons resulted from primary electrons after repetitive scattering in the magnetic confinement near the walls and consecutive ionization with the buffer gas and the bulk, cold isotropic electrons, resulted by ionization. For simplicity, this paper presents the total electron density as the sum of hot and bulk density while the effective temperature, T eff , obtained by integrating the electron energy distribution function, T eff =2/3 e , is used as a common parameter for electron temperature where e is the average electron energy. To prevent the primary electrons from reaching the TP and suppressing instabilities occurring in the electronegative regime, a stainless steel mesh with 1×1 mm grid size was placed between the filament and the transversal magnetic filter. The mesh also increases considerably the life time of the filament by reducing its etching.

III. Results and discussion

Figure 2 presents (a) the ratio of the negative ions to electrons x = n ni /(n e +n eh ), (b) the positive ion density and (c) the effective electron temperature as function of SF 6 flow rate for two different discharge currents, 150 mA and 500 mA in both SP and TP regions for a constant Ar flow of 2 sccm. Higher T eff and n i values in SP result in a less efficient negative ion production, while T eff lower than 1 eV in TP leads to x larger than 100 for SF 6 flows over 0.2 sccm. This fact is well correlated with the cross section of F -, 5 SF - and 6

SF -, which are very large for T eff <1 eV [55]. For 150 mA and a SF 6 flow of 0.5 sccm, we could obtain a negative ion to electron density ratio of 300 in a continuous operation regime without filtering out the electrons. This proves that this type of discharges with a transversal magnetic filter is very efficient in producing almost electron free plasmas (ion-ion plasmas) at densities below 10 16 m -3 . Figure 3 illustrates the mass spectrometry results for the negative ion species produced in TP, namely the dependence of the measured peaks of F -, 5 SF -and 6 SF -as a function of the flow rate of SF 6 for 150 mA and 500 mA discharge current. When the discharge current is increased, the maxima shift toward larger SF 6 flow rates and they become higher for higher discharge currents. The most efficiently produced specie is F -, while 6 SF -has the lowest efficiency.

The plasma potential for different flow rates of Ar and SF 6 while keeping the flow ratio constant at 8 is presented in figure 4 (a). Due to fast adsorption at the walls and also possible deposition of various species of ions and radicals produced in Ar/SF 6 plasma, one finds a drift of V pl toward negative values, which depends on the flow rate of SF 6 . Keeping the discharge "on" further lowers V pl to values that reduce the effective applied voltage with respect to ground (anode) below the threshold of about 40 V necessary to sustain the plasma. The time dependence of x parameter corresponding to data shown in figure 4 (a) is presented in figure 4 (b). After running continuously the plasma only in Ar gas for a few hours the plasma potential is reversibly getting back to the initial starting value and the next curve corresponding to different Ar and SF 6 flow rates was measured. One can see that a high value of a few hundreds for the ratio of the negative ions to electrons is obtained only for SF 6 flow rates larger than of 0.125 sccm. This suggests the role of an accumulation process that can take place at the walls but also in the volume as the heavy SF 6

molecules are evacuated at lower rates than Ar. The rather constant values of x in time shows that the plasma potential drift has no major influence on the production mechanism of negative ions. However, the drift of V pl spoils the benefit of very large x available in a continuous mode of operation, not pulsed as in ion-ion plasma produced in afterglow discharges, which is desired in many applications and basic studies.

To verify the influence of the walls state over the potential drift, we performed a very good cleaning process of the chamber and repeated the measurements. In figure 4 (a) the plasma potential drift after 30 min is larger than 30 V for 0.25 sccm SF 6 flow rate. According to figure 4 (c) after cleaning the chamber, the plasma potential remains at the constant value of 0.32 V in the first 30 min and decreases to only -1.2 V after 120 min, in spite of the fact that the SF 6 flow rate is 4 times higher. To confirm that the change in sign of V pl does not result in significant changes of plasma parameters the plasma density was also included in figure 4 (c). The density was slightly increasing in time due to walls conditioning by plasma heating after switching on the discharge.

The mesh placed in front of the cathode had an essential role in extending the lifetime of the filament from about 10 minutes to several hours and also to improve the discharge stability. In spite of this advantage, the mesh was also affected by a faster contamination taking place at high temperatures by discharge species including sulphur.

In order to clarify the role of physical adsorption at the walls, plasma potential relaxation was also studied, and this process is illustrated in figure 5. For these measurements, Ar and SF 6 were introduced into the chamber and the plasma was produced until the plasma potential became -20 V. Then the SF 6 was stopped and the measurements were performed only in Ar plasma. Heating the metallic inner cylinders C 1 and C 2 to 150 ºC, one can see that some species adsorbed on the walls are released and the plasma potential goes back faster toward the initial positive value, showing that the adsorption is also responsible for the plasma drift.

Plasma sources are often used for positive ion beam extraction where the ion energy can be adjusted by controlling the potential difference between V pl and the extraction bias. In our experiment one possibility of such control is to bias the inner metallic cylinder, C 1 , so as the plasma potential to follow the potential of the most positive electrode or section of the wall [START_REF] Chen | Lecture Notes on Principles of Plasma Processing[END_REF]. This possibility is valid for electropositive plasmas, which contain very mobile negative charges (electrons) with respect to positive ions, but it needs to be tested for electronegative discharges. For this reason, we studied the dependence of V pl as a function of the bias applied to the inner cylinder U W for different SF 6 flows and it is shown in figure 6 (a) where the values in branches correspond to x . An interesting fact is the presence of a jump at a certain U W bias, which is mainly determined by the SF 6 flow rate or x . For small biases applied to the cylinder, the plasma potential is almost constant. Then, depending on the SF 6 flow rate, V pl jumps and becomes approximately equal to U W bias as one would expect and the increases linearly with U W . When the SF 6 flow rate is increased to 0.1 sccm (x =60) no jump is noticed for U W biases less than 50 V. The corresponding ion densities are illustrated in figure 6 (b) and show a large increase for lower SF 6 flows. It is evident that the fast electron and the ion flux change when biasing C 1 and this change can also be discontinuous. For example, a sharp increase in the near-wall potential associated with self trapping of fast electrons in plasma volume was reported by Demidov et al. [START_REF] Demidov | [END_REF]. The jump can also be related to a change in the current closure to the anode as reported by Dorf et al. in [15]. Experiments with conducting walls performed by Stangeby and

Allen [58] revealed the current amplifier effect when changing the wall potential, a situation that is different from the present one where the target plasma has a diameter larger than its length. Thus, further investigations are necessary in order to correlate the jump in figure 6 with a detailed phenomenology. We checked T eff before and after the jump and the radial profile measurements for Ar plasma are presented in figure 7. There are no large differences between the curves corresponding to before (U W =10 V) and after the jump (U W =25 V), proving that the jump does not affect the electron temperature.

The radial profile measurements of the plasma potential show also that this parameter is constant. These results demonstrate that one cannot control the plasma potential in a highly electronegative discharge by biasing positively a large electrode exposed to plasma. This limits the possibility to control the energy of negative ions extracted from plasma using V pl , but favours the applicability of these plasmas for negative ion etching, where a large surface (the wafer) needs to be biased positively as to provide the anisotropic flux of negative ions necessary for directive etching without affecting the plasma potential.

It was recently demonstrated that a negatively biased electrode interfacing an insulator, for example, one side conductive electrode, or a conducting surface surrounded by an insulator, creates in plasma a potential structure that in certain conditions exhibits discrete and modal focusing effects [3,4]. If the applied bias is positive with respect to plasma potential then the same phenomenology affects the negative ions. Based on it, some new applications have been developed related to negative ion diagnostics [59],

negative ion extraction [START_REF] Stamate | Ion beam extraction by discrete ion focusing[END_REF] and mass spectrometry [START_REF] Stamate | [END_REF]). Since these applications are using negative sheath formed at positively biased electrodes of sizes significantly lower than the plasma volume, it become important to know in what conditions one can create such sheath in electronegative plasmas and how these structures influences the plasma parameters. The I-V characteristics measured in Ar plasma only for V≥ 0 (V pl =-1.5 V) using a planar probe (PP) of 10 mm in diameter mounted in the TP are illustrated in figure 8.

The family of I-V characteristics recorded with PP exhibits different regions. After a fast increase of the current with the applied voltage up to 10 V and a saturation-like region where the current increases slowly and almost linear with the voltage, the current jumps suddenly to high values corresponding to the so-called glow discharge or anodic-glow [16][17][18]60]. The voltage applied to the probe, for which the glow discharge appears, decreases with the increase of the plasma density (larger discharge currents) as expected from Townsend theory. Due to this behaviour it is difficult to create thick negative sheath of electrons at pressures from 1 to 100 mTorr, a range that is very interesting both for applications and basic research. By replacing the electrons with heavy negative ions, one expects a clear change in the negative sheath structure as well as in the formation of the anodic-glow. For example, figure 9 shows the I-V characteristics in Ar/SF 6 plasma (V pl =-1.5 V) measured on the planar probe for different SF 6 flow rates and Ar flow of 2 sccm for a discharge current of 500 mA. The density ratio of negative ions to electrons, x , is included in parenthesis for each curve. Thus, the ignition bias for the anodic glow shifts from 80 V for x =9 to 320 V for x =34 and there is now glow ignition for x >37 up to 400 V. This fact is directly correlated with a decrease in electron density resulted from negative ion production and proves that one can create a thick negative sheath dominated by negative ions for x >50. Moreover, it suggests that it should be possible to implement a model for correlating the ignition bias of the anodic-glow with x as a method for negative ion diagnostics in low electronegative discharges. As shown in figure 6 a large electrode biased positively affects plasma parameters for x <50, but it is expected that a smaller electrode to have a limited influence. To verify this hypothesis we have measured V pl and x as a function of SF 6 flow for 2 sccm of Ar by placing the cylindrical probe LP1 at 20 mm from the planar electrode when PP was grounded (0 V) or biased at 200 V. The 200 V bias was applied only for SF 6 flows that inhibited the glow ignition, respectively x >50 or SF 6 flows larger than 0.1 sccm. The result is shown in figure 10 and demonstrates that one can form a negative sheath to a small electrode with respect to chambers walls with negligible changes of the plasma parameters. Because of the drift of the plasma potential in time, these measurements were performed starting in Ar plasma with the same value of the plasma potential. Then, every point was measured after the same interval of time.

At plasma densities below 10 16 m -3 one expects low etching rates for both positive and negative ions.

Etching rates by negative ions have been previously reported in ICP [26] or after glow discharges [8].

However, since the current setup was improved to provide a negligible V pl drift during 1 hour of operation for x >100 we could also confirm the etching rates and the resulted surface morphology. The etching rates on silicon corresponding to both positive and negative ions for two values of the discharge current (150 and 500 mA) as a function of ion energy are presented in figure 11, where Ar=2 sccm, SF 6 =0.5 sccm, x =206 for I d =500 mA and x =301 for I d =150 mA. For all measured points, the etching rate by negative ions was slightly below of than that by positive ions with a value of 45 nm/min measured for 500 mA and 250 eV.

Etching with 13 nm/min was also observed for 500 mA and 0 eV (the sample was kept at plasma potential) by plasma radicals. A high electron fraction present for low x can bring a large thermal flux when biasing the substrate at 250 V. However, it has been shown that for x >100 the heat flux is reduced to values comparable to those resulted by positive ion [44]. For example, monitoring the substrate temperature at 500 mA and 250 eV we could see an increase of only 10 ∞ C during negative ion etching comparative with positive ion etching. Not only low charging, but also less damage is targeted by negative ion etching. Thus, it is important to check on the resulted surface morphology by the two types of ions. The AFM measurements presented in figure 12 for Ar=2 sccm, SF 6 =0.5 sccm, 500 mA discharge current, 50 eV and

x =206 show that the negative ion etching resulted in a surface characterized by a root mean square (RMS) of 12.6 nm while for positive ions the RMS was 34.9 nm.

IV. Summary and conclusions

Highly electronegative plasmas with a density ratio of the negative ion to electron larger than a few hundreds were investigated in Ar/SF 6 gas mixtures in DC plasma with multipolar magnetic confinement and transversal magnetic filter. The main negative ion species were F -, 5 SF -and 6 SF -. The drift of the plasma potential in time was compensated with proper wall cleaning and temperature enhanced gas desorption. The effect of large or small electrodes biased positively with respect to V pl on electronegative plasma parameters was investigated and the results prove the possibility to create centimetre-size sheaths dominated by negative ions without igniting anodic glows, elevating plasma potential or bringing high thermal fluxes to the substrate as long as the density ratio of negative ion to electron exceeds 50. For similar electronegativities the etching rates by negative ions is very close to that by positive ions. These results suggest that a low density plasma (10 14 -10 16 m -3 ) is transiting from a distinct behaviour associated to discharges with low and medium values for electronegativity to a negative ion dominated regime (ion-ion plasmas) when the electron fraction is less than 2% of the negative ion density. This value for electronegativity can be regarded as a requested parameter for applications that involves negative sheaths and negative ion etching at heat fluxes comparable to those by positive ions.

Figure 1 .

 1 Figure 1. (a) Experimental setup: PM-permanent magnets; C 1 ,C 2 -metallic cylinders; H-heater; PP-planar probe; LP1, LP2-Langmuir probes; I-insulators; (b) Detail of the magnetic filter.

Figure 2 .

 2 Figure 2. (a) The ratio of the negative ion density to electrons for 150 mA and 500 mA in SP (continuous line) and TP (dashed line) for a constant Ar flow of 2 sccm; (b) the corresponding positive ion densities; (c) the corresponding electron temperatures.

Figure 3 .

 3 Figure 3. Negative ion species as a function of the SF 6 flow (a) I d =150 mA and (b) I d =500 mA, for a constant Ar flow of 2 sccm.

Figure 4 .

 4 Figure 4. (a) Plasma potential drift in time for different flow rates of Ar/SF 6 at constant ratio 8; (b) the electronegativity corresponding to the same flow rates of Ar/SF 6 from (a); (c) plasma potential drift after cleaning the reactor chamber. The discharge current is 150 mA for all curves.

Figure 5 .

 5 Figure 5. Plasma potential relaxation after it was brought down to -20 V for two different temperatures of the inner metallic cylinders.

Figure 6 .

 6 Figure 6. (a) Plasma potential as a function of U W for different SF 6 flow rates; (b) corresponding ion densities. For all curves Ar flow is 2 sccm, I d =150 mA and the values in parentheses correspond to x .

Figure 7 .

 7 Figure 7. Radial profile of the plasma potential and electron temperature before (U W = 10 V) and after the jump (U W = 25 V) corresponding to curve SF 6 = 0 from figure 6, for Ar= 2 sccm and I d =150 mA.

Figure 8 .

 8 Figure 8. Current-voltage characteristics recorded by planar probe for different discharge currents in Ar plasma for a constant flow of 2 sccm (SF 6 = 0 sccm).

Figure 9 .

 9 Figure 9. Current-voltage characteristics recorded by planar probe for a discharge current I d =500 mA for different SF 6 flow rates at a constant Ar flow of 2 sccm.

Figure 10 .

 10 Figure10. The plasma potential and x dependence on the SF 6 flow for a discharge current of 500 mA for V pp =0 V with filled squares and V pp =200 V with filled circles.

Figure 11 .

 11 Figure 11. Etching rates for positive and negative ions for discharge currents of 150 and 500 mA (Ar= 2 sccm, SF 6 = 0.5 sccm).

Figure 12 .

 12 Figure 12. AFM measurements for (a) positive ions and (b) negative ions after etching in Ar/SF 6 plasma (x =206) with 2 sccm Ar flow, 0.5 sccm SF 6 flow, I d =500 mA and 50 eV ion energy.

Figure 1 .

 1 Figure 1. (a) Experimental setup: PM-permanent magnets; C 1 ,C 2 -metallic cylinders; H-heater; PP-planar probe; LP1, LP2-Langmuir probes; I-insulators; (b) Detail of the magnetic filter.

Figure 2 .

 2 Figure 2. (a) The ratio of the negative ion density to electrons for 150 mA and 500 mA in SP (continuous line) and TP (dashed line) for a constant Ar flow of 2 sccm; (b) the corresponding positive ion densities; (c) the corresponding electron temperatures.

Figure 3 .

 3 Figure 3. Negative ion species as a function of the SF 6 flow (a) I d =150 mA and (b) I d =500 mA, for a constant Ar flow of 2 sccm.

Figure 4 .

 4 Figure 4. (a) Plasma potential drift in time for different flow rates of Ar/SF 6 at constant ratio 8; (b) the electronegativity corresponding to the same flow rates of Ar/SF 6 from (a); (c) plasma potential drift after cleaning the reactor chamber. The discharge current is 150 mA for all curves.

Figure 5 .

 5 Figure 5. Plasma potential relaxation after it was brought down to -20 V for two different temperatures of the inner metallic cylinders.

Figure 6 .

 6 Figure 6. (a) Plasma potential as a function of U W for different SF 6 flow rates; (b) corresponding ion densities. For all curves Ar flow is 2 sccm, I d =150 mA and the values in parentheses correspond to x .

Figure 7 .

 7 Figure 7. Radial profile of the plasma potential and electron temperature before (U W = 10 V) and after the jump (U W = 25 V) corresponding to curve SF 6 = 0 from figure 6, for Ar= 2 sccm and I d =150 mA.

Figure 8 .

 8 Figure 8. Current-voltage characteristics recorded by planar probe for different discharge currents in Ar plasma for a constant flow of 2 sccm (SF 6 = 0 sccm).

Figure 9 .

 9 Figure 9. Current-voltage characteristics recorded by planar probe for a discharge current I d =500 mA for different SF 6 flow rates at a constant Ar flow of 2 sccm.

Figure 10 .

 10 Figure10. The plasma potential and x dependence on the SF 6 flow for a discharge current of 500 mA for V pp =0 V with filled squares and V pp =200 V with filled circles.

Figure 11 .

 11 Figure 11. Etching rates for positive and negative ions for discharge currents of 150 and 500 mA (Ar= 2 sccm, SF 6 = 0.5 sccm).

Figure 12 .

 12 Figure 12. AFM measurements for (a) positive ions and (b) negative ions after etching in Ar/SF 6 plasma (x =206) with 2 sccm Ar flow, 0.5 sccm SF 6 flow, I d =500 mA and 50 eV ion energy.

V. Acknowledgments

This work was partially supported by the Marie Curie International Reintegration Grant, project No. 46409.