Effect of gas mixing ratio on etch behavior

Effect of gas mixing ratio on etch behavior of ZrO2thinfilms in Cl2-based inductively coupled plasmasAlexander EfremovDepartment of Electronic Devices and Materials Technology,State University of Chemistry and Technology,7F.Engels St.,153000Ivanovo,RussiaNam-Ki MinDepartment of Control and Instrumentation Engineering,Korea University,Jochiwon,Chungnam339-700,South KoreaSun Jin YunElectronics and Telecommunications Research Institute,161Gajung-dong,Yusong-gu,Daejeon305-350,KoreaKwang-Ho Kwon a͒Department of Control and Instrumentation Engineering,Korea University,Jochiwon,Chungnam339-700,South Korea͑Received14July2008;accepted15September2008;published30October2008͒The analysis of the ZrO2thinfilm etch mechanism in the Cl2/Ar,Cl2/He,and Cl2/N2inductivelycoupled plasmas was carried out.It was found that an increase in additive gas fraction atfixed gaspressure and input power results in increasing ZrO2etch rate,which changes from1.2nm/min forpure Cl2plasma up to3.15,2.40,and2.31nm/min for80%Ar,N2,and He,ngmuirprobe diagnostics and zero-dimensional plasma modeling indicated that both plasma parameters andactive species kinetics are noticeably influenced by the initial composition of the gas mixture.Fromthe model-based analysis of etch kinetics,it was shown that,similarly to the case of BCl3-basedplasmas,the behavior of the ZrO2etch rate corresponds to the ion-flux-limited etch regime.©2008American Vacuum Society.͓DOI:10.1116/1.2998806͔I.INTRODUCTIONRecently,a range of high dielectric constant͑high-k͒ma-terials,namely,ZrO2,Ta2O5,HfO2,and TiO2,were inten-sively investigated as the gate dielectrics to substitute forSiO2in the complementary metal-oxide-semiconductortechnology.1–3Among these materials,the ZrO2combinessuch favorable properties as a high dielectric constant͑20–25͒,a wide band gap͑5–7eV͒,and a close thermal expan-sion coefficient with Si that results in good thermal stabilityof ZrO2/Si interfaces.Accordingly,the development of an anisotropic dry etch process for ZrO2thinfilms is an impor-tant task to be solved for obtaining an accurate pattern trans-fer as well as stable device parameters.The most of existing works reported on the ZrO2“dry”etching process were focused on the BCl3-based gas chem-istries.Particularly,Pelhos et al.4investigated the etch be-havior of Zr1−x Al x O y thinfilm in Cl2/BCl3plasma.Chang and co-workers5–7reported on the etch process of ZrO2thin film in both Cl2and Cl2/BCl3plasmas and provided the experimental data on the dependences of the etch rate on main operating conditions.Finally,in our previous works, the ZrO2etch process was analyzed by both experiments and modeling using BCl3/Ar,8BCl3/CHF3/Ar,9and BCl3/He ͑Ref.10͒chemistries.The results reported in Refs.4–10can be summarized as follows:͑1͒In both Cl2-and BCl3-based plasmas,the ZrO2etch rate is limited by the low volatility of Zr chlorides͑the melting points are772°C for ZrCl2and 437°C for ZrCl4͒.11The addition of BCl3to Cl2increases the ZrO2etch rate due to the extraction of oxygen from the oxide through the spontaneous reaction2BCl x+ZrO2→Zr +2BOCl x͑Refs.6and7͒.͑2͒The etch thresholds determined from the dependence of etch rate from the square root of ion energy in Cl2and BCl3plasmas are very close.5,7This prob-ably means that the BCl x radicals do work as a catalyst but not as the main chemically active species.͑3͒The main en-chants are the Cl atoms while the behavior of the ZrO2etch rate corresponds to the ion-flux-limited etch regime of ion-assisted chemical reaction.8–10The mixtures of Cl2with Ar,He,or N2are the frequently used as plasma-forming gases for dry patterning some metals and metal oxides.12An important feature of such systems is that the etch result can be optimized not only by varying the operating conditions,but also by adjusting the gas mixing ratio,which directly influences the balance between chemi-cal and physical etch pathways.Also,there are some works that reported an increase in the etch rates of Au,13MgO,14 Pt,15and many other materials with increasing fraction of additive gases.The objective of this study was to investigate the effects of Ar,He,or N2on the ZrO2etch behavior in the Cl2-based plasmas as well as to understand how the additive gas influences the ZrO2etch rate through the changes of plasma parameters,plasma compositions,and surface kinet-ics.a͒Electronic mail:kwonkh@korea.ac.kr14801480 J.Vac.Sci.Technol.A26…6…,Nov/Dec20080734-2101/2008/26…6…/1480/7/$23.00©2008American Vacuum SocietyII.EXPERIMENTAL AND MODELING DETAILSA.Experimental setupThe130-nm-thick ZrO2films were deposited on Si͑100͒substrates at150°C using a plasma-enhanced atomic layer deposition method.A detailed description on the deposition method and operating conditions is given in Ref.16.The experiments were performed in a planar inductively coupled plasma͑ICP͒reactor.8–10The reactor consisted of a cylindrical quartz chamber with a radius͑r͒of16cm and a five-turn copper coil located on a10-mm-thick horizontal quartz window.The coil was connected to a13.56MHz power supply via the matching network.The distance be-tween the quartz window and the bottom electrode͑l͒was 12.8cm.The bottom electrode was made from the anodized aluminum and was also connected to a13.56MHz power supply in order to control the dc bias voltage on the sub-strate.During the etching process,the temperature of the bottom electrode was stabilized at17°C by the circulation of de-ionized water.The experiments were performed under such operating parameters as total gas pressure͑p͒of 6mTorr,input ICP power͑W͒of600W,bias power͑W dc͒of50W,and total gasflow rate͑q͒of70SCCM͑SCCMdenotes cubic centimeter per minute at STP͒.The Cl2/Ar, Cl2/He,and Cl2/N2mixing ratios were set in the range of 0%–80%Ar,He,or N2by adjusting the partial gasflow rate of the components.The ZrO2samples were placed in the center of the bottom electrode and had the size of about2ϫ2cm2,which is much smaller than the area of the bottom electrode.In fact,this allows neglecting both loading effect and disturbance of plasma parameters by the etch products.In order to deter-mine the etch rates,the etched depths were measured using a surface profiler͑Alpha-step500,Tencor͒.For this purpose, we developed the line striping of the photoresist͑PR͒͑AZ1512,positive͒with the linewidth/spacing ratio of 2␮m/2␮m.The initial thickness of the PR layer was about 1.5␮m.Plasma diagnostics was performed by Langmuir probe ͑LP͒measurements and quadrupole mass spectrometry ͑QMS͒.The LP diagnostics was realized with a double probe ͑DLP2000,Plasmart Inc.͒.The probe was installed through the chamber wall-side view port,placed at4cm above the bottom electrode and centered in the radial direction.For the treatment of I-V curves in order to obtain electron tempera-ture͑T e͒and total positive ion density͑n+͒,we used the software supplied by the equipment manufacturer.The cal-culations were based on the double probe theory developed by Johnson and Malter,17and the Allen–Boyd–Reynolds ap-proximation for the ion saturation current density was used.18 The QMS measurements͑HPR-30,Hiden Analytical͒were realized in RGA mode delivering the data on neutral species only.B.Plasma modelingTo obtain the data on the steady-state densities of plasma active species,we used a simplified zero-dimensional model with a Maxwellian electron energy distribution function ͑EEDF͒͑Refs.19and20͒and with the experimental data on T e and n+as input parameters.Though in the nonequilibrium systems the real EEDFs are not exactly Maxwellian,the ap-plicability of such a simplification for the modeling of the Cl2-based low-pressure͑pϽ50mTorr͒inductive discharges was shown in many published works.For example,Refs.21 and22demonstrate an acceptable agreement between mea-sured and model-predicted plasma parameters for both Cl2 and Cl2/Ar plasmas obtained with the Maxwellian approxi-mation for EEDF in the close range of experimental condi-tions as used in this study.The modeling algorithm was based on the simultaneous solution of following equations.͑1͒The kinetic equations for both neutral ground-state and charged species in a steady-state͑dn/dt=0͒approxima-tion R F=͑␯B+␯G+1/␶R͒n,where R F is the average forma-tion rate for the given type of species,n is their volume-average density,␯B is the loss frequency in bulk plasma,␯G is the frequency of the heterogeneous loss,and␶R is the residence time.The set of reactions taken into account by the model is given in Table I.The rate coefficients for electron impact reactions͑R1–R13͒were calculated as k=ͩ2e m eͪ1/2͵␧thϱf M͑␧͒␴͑␧͒ͱ␧d␧,͑1͒where f M͑␧͒is the Maxwellian EEDF,␧th is the threshold energy,and␴͑␧͒is the process cross section.23For the N2 molecules,we neglected the dissociation.24For the Cl at-oms,we assumed␯BӶ␯G=͓͑⌳2/D͒+͑2r/0.25␥Cl␷T͔͒−1,25 where␥ClϷ0.05͑Ref.26͒is the recombination probabil-ity,⌳−2=͑2.405/r͒2+͑␲/l͒2is the effective diffusion length,19and␷T=͑8k B T/␲m Cl͒1/2.The effective diffusion coefficient was calculated as D−1=D f−1+D in−1,where D f is the free diffusion coefficient,and D in is the interdiffusion coefficient given by the Chapman–Enskog equation to-T ABLE I.Simplified reaction set for the modeling of Cl2/Ar,Cl2/He,and Cl2/N2plasmas.No.SchemeRate coefficient,thresholdenergyR1Cl2+e→Cl2++2e11.5eVR2Cl2+e→Cl−+Cl++e12.0eVR3Cl2+e→Cl+Cl++2e12.6eVR4Cl2+e→Cl2−→Cl+Cl−¯R5Cl2+e→Cl2*͑B3⌸͒→Cl+Cl+e 3.0eVR6Cl+e→Cl++2e13.5eVR7Cl−+e→Cl+2e 3.4eVR8Ar+e→Ar++2e15.8eVR9Ar+e→Ar m͑3P0,3P1,3P2͒+e11.55eVR10He+e→He++2e24.6eVR11He+e→He m͑1S0,3S1͒+e19.8eVR12N2+e→N2++2e15.6eVR13N2+e→N2͑A3⌺u+͒+e 6.17eVR14Cl−+n+͑Cl2+,Cl+,Ar+,He+,N2+→n+Cl͒ 5.0ϫ10−8cm3/sR15n+͑Cl2+,Cl+,Ar+,He+,N2+͒→wall␷/d cR16Cl͑g͒+Cl͑s͒→Cl2͑s͒→Cl2͑g͒r Clϳ0.05JVST A-Vacuum,Surfaces,and Filmsgether with Blanc’s law.21,22For simplicity,we assumed the temperature of the neutral particles ͑T ͒to be indepen-dent of gas mixing ratio and to be equal to 700K.19,21For negative ions,we applied ␯G =0.19For positive ions,we used ␯G Ϸ␷/d c with d c =0.5rl /͑rh l +lh r ͒.22The ion Bohmvelocities␷were calculated as ␷=ͱeT e ͑1+␤s ͒/m i ͑1+␤s ␥T ͒,where ␤s =␤͓exp ͑͑1+␤s ͒͑␥T −1͒/2͑1+␤s ␥T ͔͒͒−1͑Refs.19and 27͒is the relative den-sity of negative ions at the plasma sheath edge,␥T =T e /T i ,and ␤=n Cl −/n e is the bulk electronegativity.Simi-larly with Refs.20and 21,we assumed equal tempera-tures for all kinds of ions T i ϷT +͑0.5−T ͒/p ,where T is the gas temperature in eV and p is in mTorr.The correc-tion factors h l and h r for the radial and axial sheath sizes are given by the low-pressure ␭ഛ͑T i /T e ͒͑R ,L ͒diffusion theory.27͑2͒The quasineutrality conditions for volume densities of charged species ͑n e +n Cl −=n +,where n +=n Cl 2++n Cl ++n X +and n X +=n Ar +,n He +,or n N 2+͒,as well as for their fluxes tothe reactor walls ͑⌫e =⌫Cl 2++⌫Cl ++⌫X +,where ⌫X +=⌫Ar +,⌫He +,or ⌫N 2+͒.III.RESULTS AND DISCUSSIONFrom several published works,28–31it can be understood that,for the given combination of plasma-forming gas and etched material,the variations of etch rate versus main oper-ating parameters ͑gas pressure,gas flow rate,source power,and gas mixing ratios ͒depend on the volatility of reaction products ͑in fact,on the desorption mechanism for reaction products ͒and fluxes of active species on the etched surface.The low volatility of ZrCl x ͑Refs.5and 11͒allows one to neglect their spontaneous ͑thermally activated ͒desorption as well as to assume the ion-assisted chemical reaction to be the main etch mechanism,at least in the Cl 2-rich plasmas.Also,the direct chlorination of the ZrO 2surface at nearly room temperature seems to be impossible because the Zr–O bond is much stronger than the Zr–Cl one ͑8.06eV versus 5.11eV,respectively ͒.11That is why the role of ion bom-bardment includes,at least,͑1͒the destruction of the Zr–O bonds to support the formation of ZrCl x ,and ͑2͒the sputter-ing of the ZrCl x layer to provide the access of Cl atoms to the etched surface.In such a situation,the ion-flux-limited etch regime for the ZrO 2looks to be predetermined.For further investigations,we selected the gas mixing ratio as the main parameter and kept other parameters fixed.The reason is that the mixing ratio of Cl 2with Ar,He,or N 2directly reflects the transition between chemical and physical etch pathways and,thus,allows an accurate understanding of the etch mecha-nism.A.ZrO 2etch rateFrom Fig.1,it can be seen that an increase in fraction of any additive gas up to 80%results in the monotonic increase in the ZrO 2etch rate,which rises by a factor of 2.63in Cl 2/Ar plasma ͑1.20–3.15nm /min for 0%–80%Ar ͒,by a factor of 2.0in Cl 2/N 2plasma ͑1.20–2.40nm /min for 0%–80%N 2͒,and by a factor of 1.93in Cl 2/He plasma ͑1.20–2.31nm /min for 0%–80%He ͒.These situations are different compared with,for instance,the BCl 3/Ar plasma,where the addition of Ar resulted only in an insufficient change in the ZrO 2etch rate ͑35.8–31.4nm /min for 0%–83%Ar with a maximum of 41nm /min at 30%–35%Ar ͒.8For the BCl 3/He plasma,Ref.10reported an increase in the ZrO 2etch rate by a factor of 1.56͑36.2–56.7nm /min for 0%–83%He ͒,which is also lower than the results of the present work.Therefore,though Ar,He,and N 2are the inert gases with no direct chemical effects on the etch kinetics,their addition to Cl 2provides an evident acceleration of the ZrO 2etch process.From Fig.1͑b ͒,it can be seen that an increase in the ZrO 2etch rate is accompanied by a relatively weak decrease in the negative dc bias on the etched sample ͑−U dc =125–61,125–99,and 125–117for 0%–80%Ar,He,and N 2,respectively ͒.Considering that the sputtering yields Y for both native material and low volatile reactionproductsF IG .1.Measured ZrO 2etch rate ͑a ͒and negative dc bias ͑b ͒as functions of the additive gas fraction in the Cl 2/Ar,Cl 2/He,and Cl 2/N 2plasmas.The lines are to guide the eyes only.J.Vac.Sci.Technol.A,Vol.26,No.6,Nov/Dec 2008are proportional to the square root of ion bombardment en-ergy␧͑Refs.29and30͒͑and␧ϷeU dc for the collisionlessplasma sheath͒,the changes in sputtering yields with increas-ing fraction of any additive gas can be assumed to be insuf-ficient.In pure Ar,the ZrO2etch rate͑in fact,the pure physi-cal sputtering rate͒is more than two times lower than that forpure Cl2plasma͑ϳ0.4nm/min͒while for pure N2and Hegases it is about0.2nm/min.Taking into account the in-creasing ion current densities for all three systems with in-creasing fractions of additive gases͑the corresponding datawill be discussed later͒,one can assume that a growth of theZrO2etch rate with additions of Ar,He,or N2up to80%israther connected with an acceleration of ion-assisted chemi-cal reaction than with increasing rate of physical sputteringof the native oxide surface.B.Plasma parameters and compositionFigure2illustrated the results of the LP plasma diagnos-tics.From Fig.2͑a͒,it can be seen that an increase in addi-tive gas fraction results in increasing electron temperatures inthe ranges2.16–2.67,2.16–7.46,and2.16–2.52eV for0%–80%Ar,He,and N2,respectively͓Fig.2͑a͔͒.The effect ofgas mixing ratio on T e results from the differences in thresh-old energies and cross sections for plasma components.Among Cl2,Cl,and additive gas species,the electron impactreactions for Ar,He,or N2have higher thresholds with closervalues of excitation and ionization potentials͑see Table I andRefs.10,22,and24͒,but lower cross sections at the EEDFmaximum.That is why the dilution of Cl2by the above-mentioned additive gas lowers the energy loss in the mediumpart of the EEDF,increases the fraction of“fast”electrons,and shifts T e toward higher values.22,24Figure2͑b͒showsthat an increase in the fraction of any additive gas from0%–80%causes a monotonic increase in measured n+,which arein the ranges8.82ϫ1010–3.71ϫ1011cm−3for Cl2/Ar, 8.82ϫ1010–1.18ϫ1011cm−3for Cl2/He,and8.82ϫ1010–9.64ϫ1010cm−3for Cl2/N2plasmas.This can be caused by an increase in total ionization rate as well as by thechange of total charge balance determining plasma quasineu-trality.Since the threshold energies for most of electron-impactprocesses exceed͑3/2͒T e,their rate coefficients are sensitiveto the change in gas mixing ratios and follow the behavior ofT e.In pure Cl2plasma,the effective rate coefficient for theformation of Cl atoms22,24͓k dis=͑k3+k4+2k5͒,where the low-case indices at k correspond to the reaction number inTable I͔is mainly contributed by R5͑Refs.21and22͒͑k5=6.47ϫ10−9–8.48ϫ10−9cm3/s for0%–80%Ar, 6.47ϫ10−9–1.57ϫ10−8cm3/s for0%–80%He,and 6.47ϫ10−9–8.18ϫ10−9cm3/s for0%–80%N2͒.Such a situa-tion is due to lower threshold of R5compared with R3and higher cross section compared with R3and R4providing k5/k3=2.18ϫ103,k5/k4=29,and k disϷ2k5.The dilution of Cl2by Ar,He,or N2does not change the situation except a bit decreasing k5/k3as well as increasing k5/k4.As the frac-tion of additive gas increases from0%–80%,an increase in the dissociation frequency␯dis=k dis n e͑1.76ϫ102–3.20ϫ103s−1for Cl2/Ar,1.76ϫ102–1.77ϫ103s−1for Cl2/He, and1.76ϫ102–6.67ϫ102s−1for Cl2/N2͒partially compen-sates a decrease in the Cl2density,so that the Cl atom for-mation rate falls slower than is predetermined by the change of the initial mixture composition.Accordingly,both density of Cl atoms n Cl and theirflux⌫ClϷ0.25n Cl͑8k B T/␲n Cl͒1/2 decrease only by factors of1.46,1.55,and1.71at60%Ar, He,and N2,respectively͓Fig.3͑a͔͒.An increase in the Cl2 dissociation degree͑n Cl/n Cl2=2.12–38.7, 2.12–21.3,and 2.12–8.05for0%–80%Ar,He,and N2,respectively͒is as-sociated with increasing␯dis.This result is in good agreement with published data.22,32,33Also,we obtain a not bad agree-ment in the relative behaviors of the model-predicted and measured by QMS Cl atom densities.The model-predicted electron density shows the same be-havior with n+and occupies the ranges2.63ϫ1010–3.67ϫ1011, 2.63ϫ1010–1.10ϫ1011,and 2.63ϫ1010–7.92 F IG. 2.Measured electron temperatures͑a͒and measured and model-predicted densities of charged species͑b͒as functions of the additive gas fraction in the Cl2/Ar,Cl2/He,and Cl2/N2plasmas.In͑a͒,the lines are to guide the eyes only.In͑b͒,the symbols are the measured n+,and the lines are the model predicted n e.JVST A-Vacuum,Surfaces,and Filmsϫ1010cm −3for 0%–80%Ar,He,and N 2,respectively ͓Fig.2͑b ͔͒.These correlate with a behavior of total ionization rates ͑5.53ϫ1014–6.63ϫ1015,5.53ϫ1014–1.34ϫ1016,and 5.53ϫ1014–8.72ϫ1014cm −3s −1for 0%–80%Ar,He,or N 2͒.The density of Cl −decreases from 6.19ϫ1010to 4.36ϫ109,from 7.2ϫ1010to 8.27ϫ109,and from 7.2ϫ1010to 1.49ϫ1010cm −3for 0%–80%Ar,He,or N 2,respectively ͑fol-lowing the rate of dissociative attachment R4͒,which corre-spond to n Cl −/n e =2.36–0.01, 2.36–0.08,and 2.36–0.19.These values are in good agreement with published data for low-pressure Cl 2and Cl 2/Ar ICPs.19–22In pure Cl 2plasma,the densities of Cl 2+and Cl +are quite close with n Cl +/n Cl 2+=0.85.The dilution of Cl 2by any additive gas increases the n Cl /n Cl 2ratio and causes the domination of Cl +over the Cl 2+providing n Cl +/n Cl 2+=1.40–13.4, 1.50–13.4,and 1.13–2.81for 20%–80%of Ar,He,or N 2,respectively.The density of Cl +was found to be higher than those for Ar +,He +,or N 2+even at 80%additive gas ͑n Cl +/n Ar +=1.6,n Cl +/n He +=220,and n Cl +/n N 2+=6.3͒.This is because of low ionization rates͑high threshold and low cross sections ͒for additive gas spe-cies.The flux of positive ions ⌫+͑which is mainly composed from Cl +͒,as well as the ion current density j is Х0.61e ͚n +,i ␷i ,shows an increase with increasing additivegas fraction ͓Fig.3͑b ͔͒due to both n +and ion Bohm veloc-ity.An acceptable agreement between measured and model-predicted ion current densities allows one to assume that the models provide an adequate description of the steady-state gas phase composition and plasma parameters.C.Etch mechanism analysisFrom the above data,it can be understood that the behav-ior of the ZrO 2etch rate with increasing fractions of Ar,He,or N 2contradicts the behavior of ⌫Cl but follows the behav-ior of ⌫+.Such a situation is quite typical for the ion-flux-limited etch regime,which can be realized through both physical sputtering of the ZrO 2surface as well as through the ion-assisted chemical reaction with the ion-stimulated de-sorption of reaction products as the rate-limiting stage.Tak-ing into account the much lower ZrO 2etch rates in pure additive gases compared with those in pure Cl 2plasma,one can accept the last variant as the main reaction mechanism,at least under the given set of experimental conditions.To investigate the situation in detail,we applied the simplified model of etch kinetics for the ion-assisted chemical reaction,which is based on the theory of active surface sites.28–31Similarly to Refs.8–10,the assumptions were formulated as follows:͑1͒The Cl atoms are the main chemically active species,͑2͒the formation of low volatile Zr chlorides is the main channel for the loss of active surface sites,͑3͒the con-tribution of physical sputtering of ZrO 2can be neglected,and ͑4͒all types of positive ions are effective for the ion-stimulated desorption of reaction products.In such a situa-tion,the total etch rate is R Ϸ␦s 0⌫Cl ͑1−␪͒,where ␦is the stoichiometric coefficient for reaction products ͑for example,␦=0.25for ZrCl 4͒,s 0=0.3–0.5͑Refs.32–34͒is the sticking coefficient for etchant species,and ␪is the fraction of chlo-rinated surface.When neglecting the spontaneous desorption of reaction products,the steady-state balance for free surfacesites ͑1−␪͒is ␦s 0⌫Cl ͑1−␪͒=␪Y d ⌫+,where Y d =A ͑␧1/2−␧01/2͒͑Refs.31and 32͒is the ion-type-averaged yield of ion-stimulated desorption,A is the constant,and ␧0is the desorp-tion threshold.The parameters A and ␧0for BCl 3plasma can be derived from the experimental dependence of ZrO 2etch rate on the incident ion energy as A =0.04–0.06and ␧0ϳ21eV ͑Y d ϳ0.5atom/ion for ␧ϳ100eV ͒.5–7Considering that in our systems the dominant ion is Cl +instead of BCl 2+in the BCl 3plasma,the parameter A should be corrected pro-portionally to the momentum transferred to the surface in a single collision ͑i.e.,proportionally to ͱm i ͒.Finally,the rate of ion-assisted chemical reaction can be expressed as R =␦s 0⌫Cl ͩ1−␦s 0⌫Cl ␦s 0⌫Cl +Y d ⌫+ͪ.͑2͒For the given set of input parameters,and independently of the type of additive gas,one can obtain Y d ϳ0.5–0.4and ␦s 0⌫Cl /Y d ⌫+=70–5ӷ1for 0%–80%Ar,He,or N 2.This means that the efficiency of chlorination is higher than the efficiency of ion-stimulated desorption,the etched surface is highly chlorinated ͑␪=0.98–0.49͒,and a pure ion-flux-limited etch regime takes place,at least for 0%–50%additiveF IG parison of measured ͑symbols ͒and model-predicted ͑lines ͒Cl atom densities ͑a ͒and ion current densities ͑b ͒as functions of the additive gas fraction in the Cl 2/Ar,Cl 2/He,and Cl 2/N 2plasmas.J.Vac.Sci.Technol.A,Vol.26,No.6,Nov/Dec 2008gas.In such a situation,Eq.͑2͒can be simplified in a form of R Ϸ␪Y d ⌫+showing that the etch is mostly sensitive to the change of Y d ⌫+and is weakly sensitive to the variations of ⌫Cl .The fact that the model-predicted etch rates ͑Fig.4͒do not reproduce the exponentlike increase of j is mentioned by Fig.3͑b ͒results from a decrease in the fraction of chlori-nated surface due to a decrease in ⌫Cl .Nevertheless,one can assume that the differences in the etch rates for various ad-ditive gases are mainly connected with the differences in charged species kinetics and transport.When the fraction of Cl 2in any gas mixtures reaches zero,we obtain ␪,R →0,and the etch rate is only the rate of physical sputtering,which is Y s ⌫+.The well known fact is that the sputtering yields Y s are normally much lower than the yields of ion-stimulated de-sorption ͑Y s ϳ0.05atom/ion for Ar +at ␧ϳ100eV ͒.35This explains why the etch rate in pure Ar,He,or N 2gases is much lower compared with the Cl 2-containing mixtures.Also,the relative behaviors of the etch rates calculated using Eq.͑2͒are in not bad agreement with the experimental data.This allows one to assume that the model provides the ad-equate description of the main kinetic effects determining the behavior of the ZrO 2etch rate.Finally,we would like to note that the models of plasma chemistry and etch kinetics used in this work do not provide an exact quantitative analysis of the ZrO 2etching mechanism due to simplifications and some uncertainties in primary as-sumptions.However,the model-based analysis allows one to see the basic relationships between input process parameters and the etch rate,illustrates the relative contributions of both chemical and physical etch pathways,and determines the factors of primary influence on the process characteristics.IV.CONCLUSIONIn this work,we attempted the analysis of the ZrO 2etch kinetics and mechanisms using the Cl 2/Ar,Cl 2/He,andCl 2/N 2inductively coupled plasmas.It was found that an increase in any additive gas fraction causes an increase in the ZrO 2etch rate,which changes from 1.2nm /min for pure Cl 2plasma up to 3.15,2.40,and 2.31nm /min for 80%Ar,N 2,and He,ngmuir probe diagnostics and zero-dimensional plasma modeling showed that plasma param-eters,densities of active species,and their fluxes are sensi-tive to the fraction of additive gas,but the trends are the same for all three gas mixtures.It was found that,under the given set of experimental conditions,the ZrO 2etch rate is very low sensitive to the behavior of Cl atom flux and gen-erally follows the behavior of ion flux that corresponds to the ion-flux-limited etch regime of ion-assisted chemical reac-tion.In such a situation,the differences in the etch rates for various additive gases are mainly connected with the differ-ences in charged species kinetics and transport.1Ultrathin SiO 2and High-K Materials for ULSI Gate Dielectrics ,edited by H.R.Huff,C.A.Richter,M.L.Green,G.Lucovsky,and T.Hattori ͑Materials Research Society,Warrendale,PA,1999͒,V 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