Modeling of Perpendicularly Driven Dual-Frequency Capacitively Coupled Plasma
aa r X i v : . [ phy s i c s . p l a s m - ph ] D ec APL/By H. Y. Wang
Modeling of Perpendicularly Driven Dual-Frequency Capacitively Coupled Plasma
Hong-Yu Wang , (), Wei Jiang (), Zhen-Hua Bi (), and You-Nian Wang () ∗ School of Physics and Optoelectronic Technology,Dalian University of Technology, Dalian, 116024, P.R.China Department of Physics, Anshan Normal University, Anshan, 114007, P.R.China (Dated: November 13, 2018)We proposed an altered configuration for dual-frequency (DF) capacitively coupled plasmas(CCP). In this configuration, two pairs of electrodes are arranged oppositely, and the discharg-ing is perpendicularly driven by two rf sources. With Particle-in-cell/Monte Carlo method, we havedemonstrated this configuration can remove the harmful electromagnetic and DF coupling effectsin conventional DF-CCP.
PACS numbers: 52.80.Pi , 52.27.Aj, 52.65.Rr
Dual-frequency (DF) capacitively coupled plasmas(CCP) are commonly used as etching and deposition de-vices in the microelectronics, flat panel display and solarcells industries [1, 2]. Compare to the other two sources,inductive coupled plasma (ICP) and electron cyclotronresonance (ECR) discharges, CCP can produce uniformplasma over larger areas. In typical DF-CCP [3, 4], thetwo rf source with different frequencies are applied to thesame electrode or the opposite two electrodes. The highfrequencies (hf) source controls the plasma density whilethe low frequency (lf) source controls the ion flux andion energy and angular distribution (IEDs and IADs).Quasi-independent control of plasma density and IEDFsis the main merit of DF-CCP over single-frequency CCP.Therefore DF-CCP has been widely used in state-of-artindustry reactors. To achieve more flexibilities, somevariants of DF-CCP, such as adopting very high fre-quency (VHF)[5], applying additional dc source [6] andseries resonance CCP [7], have received intense investi-gation recently.High etching rates, uniformity, anisotropy, selectivityand low dielectric damage are the essential requirementsof the CCP etching devices. There is no perfect solutionsto satisfy all the requirements above simultaneously, onemust make tradeoffs. Although successful in practice,DF-CCP still expose some problems. The first one isthe electromagnetic (EM) effect[8, 9, 10], which will oc-cur when very high frequency (VHF) sources (typically > λ is comparable to the reactor radius. Due tothe standing wave effect [11], the merit of plasma unifor-mities over large areas will be broken. The second oneis hf-lf source coupling effects [12]. When only increas-ing the hf voltage, the density increases and the sheaththickness decreases, thus more ions will appear in thehigh energy end of IEDs. This is not desired becausedielectric damage may be introduced. But when only in-creasing the lf voltage, the sheath thickness increases andthe bulk plasma lengths decrease and thus the density de- ∗ Electronic address: [email protected]
LF RFHF RF (+) HF RF (-)
Plasma
FIG. 1: Schematic of the perpendicularly driven DF-CCP. creases. This is also not desired because of the reducedetching rate. Some configurations, like shaped electrodes[13] and asymmetrical discharges [14], are proposes tomitigate above harmful effects.In this letter, we propose an altered configuration forDF-CCP. Not like the conventions disk-like cylindricalconfiguration [1], here the discharge chamber is a three-dimensional (3D) flat regular hexahedron, whose cross-sectional schematic is shown in Fig.1. Two pairs ofrectangular electrodes are arranged oppositely, in theleft/right surface and the top/bottom surface, respec-tively. In the front/back surface (not shown in the figure)and in the gaps between the electrode, thick dielectricinsulators are placed to confine the plasmas. The dis-charging is perpendicularly driven by two rf sources. Thesmaller pairs (left and right) electrodes (LE and RE) arepowered by the same hf sources, but with the phase dif-ference of π . This can be realized with a opposite phasepower divider, for example, a balun [15] applied betweenthe rf source and the devices. The bottom electrode (BE)is powered by the lf source and the top electrode (TE)is grounded. The wafer is placed on the BE. We willdemonstrate that this configuration can remove aboveproblems.In order to study such a configuration, we have adopteddirect implicit Particle-in-cell/Monte Carlo (PIC/MC)algorithms [16] in 2D planar geometry. Although thisconfiguration is inherently 3D, due to the confinementby the insulators, the plasma is uniform between theside-wall insulators and thus 2D model is sufficient, ifthe front/back spacing is large. The details of the algo-rithms are described elsewhere [17], therefore we will onlypresent the simulation parameters here. The BE and TElengths are X = 8cm, and the LE and RE lengths are Y = 1 . . ω hf = 60MHz and V hf = 50V or 100Vare applied to LE and RE, with the phase difference of π . The lf sources of ω lf = 2MHz and V lf = 50V or 100Vare applied to BE. In the gaps, the instant potentials arelinearly interpolated. Argon gas is used with the pres-sure of 10mTorr and temperature of 300 K . We considerelastic, excitation and ionization collisions for electronsand elastic and charge transfer collisions for Ar + ions,respectively. Square cells are used, thus X direction isuniformly divided to 256 cells and Y direction dividedto 64 cells. The space and time steps are fixed to allsimulations, ∆ x = 0 . / t e = ∆ t i = 0 . × − s.All results are given by averaging over one lf period af-ter reaching equilibrium of 1000 rf periods. Because thediodes areas are equal for X / Y separately and only theideal voltage sources in the external circuit, we did notconsider the external circuit and the self-biasing for sim-pleness.The average potential, electron and ion density for thecase of V hf = 100V and V lf = 50V are shown in Fig.2.Near each electrode, there is a sheath, therefore the den-sities are in an elliptical profile and the maximum valueis in the center. The sheathes are symmetric in bothdirections, but the average sheath thicknesses are largerfor TE and BE than that for LE and RE. This is a nat-ural result, since when the density is fixed, the sheaththickness inversely scales with the frequency[1].We plotted the cross-sectional profiles of n e for differ-ent voltages in Fig.3. The plasma density is mainly de-termined by the hf source. When increasing the V hf bytwo times, the electron densities also increase by a factorof larger than 2. While when increasing V lf , the elec-tron densities are nearly unchanged. The cross-sectionalprofiles are flat in the center. As we have mentioned,in conventional DF-CCP, when increasing the lf voltage,the bulk plasma length will decrease and thus the densitywill decrease[12]. In this present configuration, there isno such a effect, since the sheath thicknesses are decou-pled.The ion flux to BE is presented in Fig.4. Similar to thedensity, the flux is mainly determined by the hf source.When increasing the V hf by two times, the flux also in-crease by a factor of larger than 2. While V lf has nosignificant effects on the flux. Compare the conventionCCP driven by 13 . (c)(b)(a) Y ( c m ) n e,Max = 8.3 x m -3 X (cm) Y ( c m ) Max = 114.5 V Y ( c m ) n i,Max = 8.3 x m -3 FIG. 2: Average (a)electron density n e , (b)ion density n i and(c) potential Φ for the case of V hf = 100V and V lf = 50V. E l e c t r on D en s i t y ( m - ) X (cm)
FIG. 3: Cross-sectional profiles of electron density n e at Y =1cm for different voltages. as we have mentioned, the plasma density and ion fluxwill not be uniform over the wafer. In this configuration,the wafer can be placed on X plate while the hf sourcesare in Y direction, therefore the harmful EM effects arenaturally removed.In industry devices, it is also highly desired that theions are anisotropic. The ion angle distributions (IADs)for different voltages are depicted in Fig.5. Whateverthe rf voltage is, most ions has the angle of several de-grees. This means the ions still keep anisotropic in thisconfiguration.The last issue in this configuration is IEDs. The IEDsis influenced not only by rf frequency and voltage, butalso by the ion transit time τ i . In conventional DF-CCP,if one increases V hf while keeping the V lf constant, theplasma density will increases and the sheath thicknesswill decrease. Therefore τ i will decreases and the profiles
50V - 50V 50V -100V 100V - 50V 100V -100V 100V - 50V (Y Electrode Flux) I on F l u x ( m - s - ) X (cm)
FIG. 4: Ion flux onto the BE for different voltages. We alsoplotted the flux to LE for comparison -2 -1 I A D F s ( a . u . ) Degree
FIG. 5: Ion angle distributions (IADs) for different voltages. of the IEDFs will correspondingly shift to the higher en-ergy tails in some cases. This will result dielectric damageas we have mentioned. Furthermore, the etching unifor-mity also requires the IEDs being unchanged at differentposition on the electrodes.We plotted unnormalized IEDs for different positionsfor the case of V hf = 100V and V lf = 50V in Fig.6(a).Here the IEDs are sampled over four 1cm segments be-ginning at the center of the BE. It can be seen that theshape of IEDs is nearly unchanged over 3cm. Note herethe slight amplitude difference is from the flux difference(Fig.4). Only in the electrode edge, the shape is differ-ent. The reason is the ions always response to the averageelectric field. In the sheath near the X electrode, the ionsare mainly accelerated by the field E y produced by thelf source.We showed the IEDs over entire BE for different volt-ages in Fig.6(b), since the IEDs are similar at differentposition. There are clearly four peaks in all the IEDs,and the peaks can be divided in to two pairs. Each pairof the peaks seems to be produced by the hf or lf sourcesolely, namely, the lower peaks pair are produced by the lf source and the high peak are produced by the hf source.For we still have ω rf > ω i , the center energy of IEDs V i U nno r m a li z ed I E D F s ( a . u . ) (a) (b) I E D F s ( a . u . ) Energy (eV)
FIG. 6: (a)Ion energy distributions (IEDs) for different po-sitions for the case of V hf = 100V and V lf = 50V; (b)Ionenergy distributions (IEDs) for different rf voltages. still obey the simple estimation of 0 . V lf + 2 V hf ), where2 denote the two hf sources. Unlike the conventional DF-CCP, the IEDs do not shift to the higher energy tail. If V lf >> V hf , the IEDs will be solely determined by the lfsource.In summary, we have proposed an altered configura-tion of DF-CCP, which is in 3D flat regular hexahedronshape and is perpendicularly driven by two rf sources.The plasma density and ion flux are solely determinedby the hf source, and are uniform over larger area, with-out the harmful EM and DF coupling effect. At the sametime, the IEDs are mainly determined by the lf source,there are no excessive high energy ions in the tail of theIEDs, which will avoid the dielectric damage. In practi-cal devices, the geometry is 3D, but the qualitative re-sults here will not change and one may even adopted atriple frequency configuration. If X length is very large,rf breakdown laws by Lisovskiy [18] should be consideredfor the reactors design.This work was supported by the National Natural Sci-ence Foundation of China (No.10635010). [1] Lieberman M A and Lichtenberg A J Principles ofPlasma Discharges and Materials Processing 2nd edn2005. (New York: Wiley)[2] T. Makabe and Z. L. Petrovic Plasma Electronics: Appli-cations in Microelectronic Device Fabrication 2006. (NewYork: Taylor and Francis Group)[3] G. Wakayama and K. Nanbu, IEEE Trans. Plasma Sci.
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