Plasma density enhancement in radiofrequency hollow electrode discharge

Liuliang HE (賀柳良),Feng HE (何鋒) and Jiting OUYANG (歐陽吉庭)

1 College of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,People’s Republic of China

2 School of Physics,Beijing Institute of Technology,Beijing 100081,People’s Republic of China

Abstract The plasma density enhancement outside hollow electrodes in capacitively coupled radiofrequency (RF) discharges is investigated by a two-dimensional (2D) particle-in-cell/Monte-Carlo collision (PIC/MCC) model.Results show that plasma exists inside the cavity when the sheath inside the hollow electrode hole is fully collapsed,which is an essential condition for the plasma density enhancement outside hollow electrodes.In addition,the existence of the electron density peak at the orifice is generated via the hollow cathode effect (HCE),which plays an important role in the density enhancement.It is also found that the radial width of bulk plasma at the orifice affects the magnitude of the density enhancement,and narrow radial plasma bulk width at the orifice is not beneficial to obtain high-density plasma outside hollow electrodes.Higher electron density at the orifice,combined with larger radial plasma bulk width at the orifice,causes higher electron density outside hollow electrodes.The results also imply that the HCE strength inside the cavity cannot be determined by the magnitude of the electron density outside hollow electrodes.

Keywords: RF capacitively coupled plasma sources,plasma density enhancement,hollow cathode effect,hollow electrode

1.Introduction

Radio-frequency capacitively coupled plasma sources (RFCCPs) are widely utilized in the microelectronics industry[1,2].Two plate electrodes are usually utilized in typical RFCCPs,and the electron density is often lower than 1015m-3.Hence the etching and deposition rates are very low [3–5].Raising the driving frequency [2,6] or utilizing the magnetic field [7–10] can increase the electron density.However,the standing wave effect [11–14] and the skin effect [15,16]may appear with a high driving frequency,and plasma nonuniformity occurs,which is not conducive to large-area plasma treatment.However,the standing wave effect and skin effect will not appear with a low driving frequency.Therefore,it is preferable for the microelectronics industry if plasma with high density can be obtained at a low driving frequency.

In addition to parallel-plate electrodes [17–19],hollow electrodes [20–25] are also frequently applied in RF and direct current (DC) discharges.With a hollow electrode,RFCCPs can produce higher plasma density outside the cavity when a low frequency is utilized,which implies that plasma density enhancement effect exists in RF discharges with hollow electrodes [20–22,26–28].Moreover,utilizing hollow electrodes with different shapes,uniform plasma density can be obtained and the film deposition quality can be improved [29–31].

Due to the cavity structures,electrons are confined inside the hollow electrode [32] and oscillate between the side walls,forming the hollow cathode effect (HCE) [25,33,34].Via the HCE,inelastic collisions increase [33],which cause higher ionization and plasma density inside the cavity[3,4,26].Electron density up to (2–3)×1017m-3was obtained with a ring-shaped hollow electrode,which is ten times that of the density when parallel-plate electrodes are utilized [3].In addition,RF-CCPs with multi-hole electrodes were also reported to enhance thin-film deposition rates [35] and increase the electron density [26,36,37] over large pressure ranges.

Although previous investigations have shown that RFCCPs with hollow electrodes can enhance the electron density outside the cavity,the mechanism of density enhancement is still unclear.Previous studies have also found that discharge conditions affect the magnitude of electron density outside the cavity [21,28,38,39].For instance,electron density outside the cavity can be influenced by the pressure,magnetic field and electrode gap [28,38,40].Furthermore,the shape,depth and diameter of the hollow electrode can also affect the magnitude of electron density outside the cavity [22,26,36].However,the effect of these factors on the magnitude of electron density outside the cavity is not clear,which is important for the design of hollow electrodes and the modification of discharge conditions to improve plasma properties.In addition,in experimental studies,researchers often determine the strength of the HCE based on the magnitude of electron density outside the cavity [20,21,36],and they consider that the higher the electron density outside the cavity,the stronger the HCE inside the cavity.Hence,further investigation is needed to ascertain whether the above method to determine the HCE strength is suitable.

The purpose of this study is to investigate the plasma density enhancement mechanism and influence factors of the plasma density enhancement magnitude in RF-CCPs with hollow electrodes.This article is elaborated in the following sequence.The 2D PIC/MCC simulation is described in section 2.The results are shown in section 3.Section 4 provides a summary.

2.Simulation model

The reactor geometry studied here can be found in figure 1 of our previous work [41].An RF source and a DC bias voltageVDC=-30 V are both applied on the hollow electrode,and the frequency of the RF source is 13.56 MHz,while radiirof the powered hollow electrode and the grounded plate electrode are both 1.6 cm.The distancedbetween the two electrodes is set to be 1 cm.The pressurepof the working gas argon is 1 Torr.A cylindrical coordinate is adopted for the axis-symmetric discharge device,and the simulation area is that enclosed by the red dashed line.The origin of the coordinates (Z=0 cm,R=0 cm) is located at the center of the orifice,withZ＞ 0 cm andZ＜ 0 cm denoting the axial positions inside and outside the hollow electrode,respectively.

An electrostatic 2D PIC-MCC code (the XOOPIC code)is adopted in this study [42–45].A detailed model description is included in our previous study [40].Therefore,only a brief description of this model is included here.The initial temperatures of electrons and argon ions are 2 eV and 0.04 eV,with the same density.The temperature of the working gas argon is also set to be 0.04 eV,with an invariant density.The time step of electrons is set to be 3×10-13s,and the time step of ions is set to be 3×10-12s.The spatial grids are set at 256 (R)×192 (Z).

In RF-CCPs with hollow electrodes,the ionization degree is low and collisions occur mainly between neutral and charged particles.Collisions between electrons and neutral particles are elastic,excitation and ionization collisions,and the collision cross-sections are taken from [46].Charge-exchange collisions and elastic collisions are considered between ions and neutral particles,and the collision cross-sections are cited from [47].The same collision types were considered in other RF hollow electrode discharges[33,48–50].

3.Results

3.1.Effect of discharge parameters on plasma characteristics

3.1.1.Depth of the cavityFigure 1 depicts the electron density profiles with different cavity depthshof 0–1.5 cm when the sheath inside the hole is fully collapsed or expanded,with the cavity diameterD=1 cm,RF voltage amplitudeV0=210 V and secondary electron emission coefficientγAr+=0.1.As can be seen from figure 1,withh=0.5–1.5 cm,an electron density peak exists at theZaxis inside the cavity,manifesting the existence of the HCE in the cavity [49].Due to the HCE,withh=0.5–1.5 cm,the electron density inside the cavity is higher than that with the parallel-plate configuration (h=0 cm).To do a comparison,two vertical dashed lines are presented at the hollow electrode sheath fully collapsed and expanded phases of each cavity depth.As shown in figure 1,with different cavity depths ofh=0.2–1.5 cm,when the sheath inside the hole expands,electrons inside the hole move towards the grounded electrode,causing a decrease in the volume of electrons inside the hole.

Figure 1.Electron density profiles at different cavity depths h when the sheath inside the hole is fully collapsed or expanded,with the cavity diameter D=1 cm,RF voltage amplitude V0=210 V and secondary electron emission coefficient γAr+=0.1.

Time-averaged electron density profiles along theZaxis with differenthare shown in figure 2(a).As can be seen from figure 2(a),from inside to outside the hole,the electron density increases with the depth of the cavity,and the electron density outside the cavity is higher than that with the parallel-plate electrodes (h=0 cm).Figure 2(b) shows the time-averaged radial sheath thickness along the side wall of the hollow electrode at different cavity depthshof 0.5–1.5 cm.The radial sheath thickness is the width between the radial sheath edge and the side wall of the hollow electrode,while the position of the radial sheath edge is obtained by finding where ?2φ/?R2becomes zero for the first time(hereφis the potential) [33].As can be seen from figure 2(b),from the orifice to the cavity bottom,the radial sheath thickness at the side wall increases,which means that the sheath at the side wall of the hollow electrode is tilted.Figure 2(c) shows the variation of the time-averaged radial plasma bulk width at the orifice with the cavity depthh,while the radial plasma bulk width is equal to the value of the cavity diameterDsubtract twice the radial sheath thickness.As shown in figure 2(c),with the cavity depthhincreasing from 0.5 to 1.5 cm,the radial width of bulk plasma at the orifice increases.

Figure 2.(a) Time-averaged electron density profiles inside and outside the cavity with different cavity depths h (at R=0 cm).(b) Timeaveraged radial sheath thickness at the side wall of the cavity with different cavity depths h of 0.5,1 and 1.5 cm.(c) Variation of the timeaveraged radial width of bulk plasma at the orifice with the cavity depth h.

3.1.2.RF voltageFigure 3 shows the electron density profiles with different RF voltagesV0of 150–210 V when the sheath inside the hole is fully collapsed or expanded,with the cavity diameterD=1 cm,cavity depthh=1.5 cm andγAr+=0.1.With differentV0of 150–210 V,an electron density peak exists at theZaxis inside the hole,manifesting the existence of the HCE in the hole.Due to the HCE,withV0of 150–210 V,the electron density inside the cavity is higher than that with the parallel-plate configuration withV0=210 V (h=0 cm).However,withV0=150 V,in the yellow dashed rectangular area,the electron density is lower than the initial electron density,which implies that discharges can only occur in the area between the hollow electrode hole and the grounded electrode whenV0is low anddis narrow.As also shown in figure 3,with differentV0,when the sheath inside the hole expands,electrons inside the hole move towards the grounded electrode,causing a decrease in the volume of electrons inside the hole.

Figure 3.Electron density profiles at different RF voltages V0 when the sheath inside the hole is fully collapsed or expanded,with the cavity diameter D=1 cm,cavity depth h=1.5 cm and γAr+=0.1.

Time-averaged electron density profiles along theZaxis with differentV0are shown in figure 4(a).As can be seen from figure 4(a),from inside to outside the hole,the electron density increases with the RF voltageV0.Figure 4(b)shows the variation of the time-averaged radial plasma bulk width at the orifice with the RF voltageV0.The curve in figure 4(b) shows that the time-averaged radial plasma bulk width at the orifice increases with the RF voltageV0.

Figure 4.(a) Time-averaged electron density profiles inside and outside the cavity with different RF voltages V0 (at R=0 cm).(b)Variation of the time-averaged radial width of bulk plasma at the orifice with the RF voltage.

3.1.3.Diameter of the cavityFigure 5 shows the electron density profiles with differentDof 0–2 cm when the sheath inside the hole is fully collapsed or expanded,with the cavity depthh=1.5 cm,RF voltageV0=210 V andγAr+=0.1.With the small cavity diameterD=0.4 cm,even the sheath inside the hole is fully collapsed,there is no plasma inside the hole,and the electron density outside the hole is almost equal to that with the parallel-plate configuration (D=0 cm).WithD=0.7 cm,an electron density peak with density up to 2.6×1016m-3exists at theZaxis inside the cavity,and the peak value is higher than that withD=1–2 cm.The results indicate that the strongest HCE is obtained withD=0.7 cm.WithDincreasing from 0.7 to 2 cm,the density of electrons inside the hole reduces,which means that the HCE intensity inside the cavity is gradually attenuated.

Figure 5.Electron density profiles at different cavity diameters D of 0–2 cm when the sheath inside the hole is fully collapsed or expanded,with the cavity depth h=1.5 cm,RF voltage V0=210 V and γAr+=0.1.

Time-averaged electron density profiles along theZaxis with differentDare shown in figure 6(a).As can be seen from figure 6(a),at different axial positions,the electron densityneoutside the cavity withD=0.7–2 cm is higher than that with the parallel-plate configuration (D=0 cm).However,withD=0.7 cm,the electron density decreases dramatically along theZaxis,and afterZ＜ -0.28 cm,the electron density withD=0.7 cm is lower than that withD=1–2 cm.Furthermore,it can be seen from figure 6(b) that the radial width of bulk plasma at the orifice withD=0.7 cm is smaller than that withD=1–2 cm.

3.1.4.Secondary electron emission coefficientFigure 7 shows the electron density profiles with different secondary electron emission coefficientsγAr+when the sheath inside the hole is fully collapsed or expanded,with the cavity diameterD=1 cm,cavity depthh=0.5 cm and RF voltageV0=210 V.As can be seen from figure 7,with differentγAr+of 0–0.2,an electron density peak exists at theZaxis inside the hole,manifesting the existence of the HCE in the hole,and the electron density inside the hole increases withγAr+.However,withγAr+=0.2,despite the sheath inside the hole is fully expanded,the electron density peak is located completely inside the cavity.

Figure 7.Electron density profiles at different γAr+ of 0,0.1 and 0.2 when the sheath inside the hole is fully collapsed or expanded,with the cavity diameter D=1 cm,cavity depth h=0.5 cm and RF voltage V0=210 V.

Figure 8.(a) Time-averaged electron density profiles inside and outside the cavity with different γAr+ of 0,0.1 and 0.2 (at R=0 cm).(b) Variation of the time-averaged radial width of bulk plasma at the orifice with γAr+.

Figure 9.Radial profiles of the time-averaged electron density ne with different h at different axial positions of (a) Z=-0.3 cm,(b) Z=-0.45 cm and (c) Z=-0.6 cm.

Time-averaged electron density profiles along theZaxis with differentγAr+are shown in figure 8(a),and the electron density with the parallel-plate configuration (h=0 cm) withγAr+=0.1 is also shown for comparison.WithγAr+=0.2,from inside to outside the cavity,the electron density decreases dramatically.OnceZ＜ -0.15 cm,the electron density withγAr+=0.2 is lower than that withγAr+=0 and 0.1,and onceZ＜ -0.3 cm,the electron density withγAr+=0.2 is almost equal to that with the parallel-plate configuration withγAr+=0.1.WithγAr+increasing from 0 to 0.2,the time-averaged radial width of bulk plasma at the orifice increases,as shown in figure 8(b).

3.1.5.The synergistic effect of the cavity depth and diameterThe radial profiles of the time-averaged electron densitynewith differenthare shown in figure 9,and the parameters are the same as those used in section 3.1.1.As can be seen from figure 9,at different axial positions ofZ=-0.3,-0.45 and -0.6 cm outside the cavity,the radial distributions of the electron density are not uniform,presenting a mountain-like distribution,with the electron density peak at theZaxis.In addition,the closer to the orifice,the higher the electron density outside the hole,and the worse the plasma uniformity.At different axial positions outside the cavity,withh=0.2–1.5 cm,the electron density increases with the cavity depthh.However,withhincreasing from 1.5 to 3 cm,the electron density decreases.Although the plasma uniformity needs to be improved,the maximum electron density can always be obtained outside the cavity withh=1.5 cm.Therefore,with the parameter settings shown in section 3.1.1,the optimum cavity depth for the plasma density enhancement ish=1.5 cm.

Figure 10 shows the radial profiles of the time-averaged electron densitynewith differentD,and the other parameters are the same as those shown in section 3.1.3.It can be seen from figure 10 that the radial distributions of the electron density with different cavity diameters are not uniform,with electron density peaks at theZaxis.With different cavity diameters,the closer to the orifice,the higher the electron density outside the cavity.At axial positionsZ=-0.3 and -0.45 cm,the electron density at theZaxis has the maximum value withD=1 cm.However,atZ=-0.6 cm,the electron density at theZaxis has the maximum value withD=1.5 cm.With the cavity diameterDincreasing from 1 to 2 cm,the plasma uniformity is gradually improved.

Figure 10.Radial profiles of the time-averaged electron density ne with different D at different axial positions of (a) Z=-0.3 cm,(b) Z=-0.45 cm and (c) Z=-0.6 cm.

Figure 11.EEDF at the orifice and the central region of two electrodes at ωt/2π=0.41 when the sheath inside the hole expands,with V0=210 V,D=1 cm,h=1.5 cm and γAr+=0.1.

Figure 12. Variations of the EEDF with D at the orifice region at ωt/2π=0.41 when the sheath inside the hole expands.

Figure 13. EEDF of γAr+=0.1 and 0.2 at the orifice region at ωt/2π=0.41 when the sheath inside the hole expands.

As shown in figures 6(a) and 10,ifZ＞ -0.5 cm,the maximum electron density outside the cavity is obtained withD=1 cm,and high electron density plays a crucial role in the enhancement of the plasma etching rate.Therefore,if other parameters remain constant,as shown in sections 3.1.1 and 3.1.3,atZ＞ -0.5 cm,the optimum cavity depth and diameter for the plasma density enhancement areh=1.5 cm andD=1 cm,respectively,while the plasma uniformity can be improved by utilizing a multi-ring electrode [51].

3.2.Plasma density enhancement mechanism and influence factors

According to the above simulation results,the enhancement mechanism of plasma density and influence factors of the plasma density enhancement magnitude outside hollow electrodes are analyzed.

The variations of the electron density withhandV0are analyzed as follows.With different cavity depthshor RF voltagesV0,an electron density peak exists at the orifice (see figures 1 and 3),which is generated via the HCE and contains numerous energetic electrons [4,51].When the sheath inside the hole expands,some energetic electrons in the electron density peak are pushed out of the cavity by the tilted sheath at the side wall and the expanding sheath at the cavity bottom [4,51].The electrons with high energy pushed out of the hole will cause high ionization and hence enhanced plasma density outside the hole [4,51].The electron energy distribution function (EEDF) at the orifice region and at the central region of two electrodes atωt/2π=0.41 is shown in figure 11,withV0=210 V,D=1 cm,h=1.5 cm andγAr+=0.1.Phaseωt/2π=0.41 is close to phaseωt/2π=0.5 when the sheath inside the hole is completely expanded.The EEDF is obtained by calculating the electron energy in a local area over 20 RF cycles after the discharge is stable.As shown in figure 11,at the orifice region,the probability of electrons with energy exceeding 15.76 eV (the first ionization energy of argon atom) is much higher than that at the central region of the two electrodes,which indicates that more energetic electrons are generated at the orifice region via the HCE.

In addition,with the cavity depth or the RF voltage increasing,both the radial plasma bulk width and the electron density at the orifice increase,and the electron density at the orifice with the cavity depthh=1.5 cm or the RF voltageV0=210 V even reaches 1.3 ×1016cm-3.This indicates that more energetic electrons can be pushed out of the hole through the expanding sheath of the hollow electrode and cause higher plasma density outside the hole.Therefore,with the depth of the hole or the RF voltage increasing,the electron density outside the hole also increases.

SinceDvaries from 0.4 to 2 cm,withD=0.7 cm,the electron density has the maximum value at the orifice.However,outside the cavity,the electron density withD=0.7 cm is lower than that withD=1–2 cm after a certain axial distance from the orifice (see figure 6(a)).The reason is analyzed as follows.WithD=0.7 cm,the HCE in the cavity is the strongest and the electron density at the orifice is the highest (see figure 5).Hence,in the same orifice region,the probability of electrons with energy exceeding 15.76 eV has the maximum value withD=0.7 cm,as shown in figure 12,and some electrons even reach an energy of 30 eV.Highenergy electrons pushed out of the hole with the highest density cause the maximum electron density near the orifice.However,due to the minimum radial plasma bulk width withD=0.7 cm (compared withD=1–2 cm),the number of high-energy electrons pushed out of the hole is also the smallest,resulting in the sharp decrease in the plasma density along the axial distance.The results above also indicate that it is not suitable to determine the strength of the HCE through the magnitude of the electron density outside hollow electrodes.

Electron density profiles at shallowhor smallDare analyzed as follows.With the shallow cavity depthh=0.2 cm,a small amount of plasma exists inside the hole when the sheath inside the hole is completely collapsed (see figure 1).Bulk plasma electrons inside the hole gain high energy via repeated interactions with the expanding side wall sheath[51] and are all pushed out of the hole by the expanding sheath of the hollow electrode (see figure 1),hence the plasma density outside the hole is enhanced slightly (see figure 2(a)).However,with the small cavity diameterD=0.4 cm,there is no plasma inside the cavity even at the hollow electrode sheath fully collapsed phase (see figure 5),hence the electron density outside the cavity is not enhanced(see figure 6(a)).Therefore,an essential condition for the plasma density enhancement outside the hole is that plasma exists inside the hole when the sheath inside the hole is fully collapsed.

The variations of the electron density withγAr+are analyzed as follows.WithγAr+=0.2,even the sheath inside the hole is fully expanded,and the electron density peak is completely located inside the cavity (see figure 7),which means that energetic electrons in the electron density peak can hardly be pushed out of the hole when the sheath inside the hole expands.Therefore,withγAr+=0.2,although the highest electron density is inside the cavity and the largest radial width of bulk plasma at the orifice (see figures 8(a)and (b)),the electron density outside the hole still decreases sharply with the axial distance (see figure 8(a)).However,due to the largest secondary electron emission coefficient,more secondary electrons will be emitted from the plane part of the hollow electrode.Therefore,compared with that ofγAr+=0 and 0.1,the electron density has the maximum value above the plane part of the hollow electrode withγAr+=0.2(see figure 7).To further illustrate the importance of the existence of the electron density peak at the orifice for the plasma density enhancement outside hollow electrodes,the EEDF at the orifice region withγAr+=0.1 and 0.2 atωt/2π=0.41 is presented in figure 13.Since the electron density peak generated via the HCE is not located at the orifice withγAr+=0.2,there are few energetic electrons with energy exceeding 15.76 eV located at the orifice region atωt/2π=0.41.However,withγAr+=0.1,an electron density peak exists at the orifice.Hence more energetic electrons with energy exceeding 15.76 eV are located at the orifice region.When the sheath inside the hole expands,more electrons with high energy are pushed out of the hole and cause higher ionization and plasma density.Therefore,the electron density withγAr+=0.1 is higher than that withγAr+=0.2 outside the cavity (see figure 8(a)).

Through investigation into the electron density distributions inside and outside the hollow electrode hole with different hole depths,voltages,cavity diameters andγAr+,it is found that an electron density peak exists at the orifice generated via the HCE,which plays an important role in the density enhancement outside hollow electrodes.

4. Conclusion

The plasma density enhancement mechanism and influence factors of the density enhancement magnitude in RF-CCPs with hollow electrodes are investigated via a 2D PIC/MCC model.Results show that plasma exists inside the cavity when the sheath inside the hole is fully collapsed,which is an essential condition for the plasma density enhancement outside hollow electrodes.In addition,an electron density peak exists at the orifice generated via the HCE,which also plays a crucial role in the density enhancement.It is also found that the radial width of bulk plasma at the orifice significantly affects the plasma density enhancement magnitude outside hollow electrodes.If the radial width of bulk plasma at the orifice is the narrowest,even though the HCE is the strongest and the electron density at the orifice is the highest,the plasma density outside the cavity may also be low.Therefore,it is not suitable to determine the HCE strength through the magnitude of the electron density outside the hollow electrode hole.Higher electron density at the orifice,combined with larger radial plasma bulk width at the orifice,helps to obtain higher density enhancement magnitude outside hollow electrodes.