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Ar inductively coupled plasma
Microelectronic Engineering 71 (2004) 54–62 www.elsevier.com/locate/mee
Etching mechanisms of (Ba,Sr)TiO3 thin films in CF4/Ar inductively coupled plasma q A.M. Efremov 1, Dong-Pyo Kim, Kyoung-Tae Kim, Chang-Il Kim
*
School of Electrical and Electronic Engineering, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Gu, Seoul 156-756, South Korea Received 3 July 2003; received in revised form 3 July 2003; accepted 5 September 2003
Abstract This work was devoted to an investigation of etching mechanisms for (Ba,Sr)TiO3 (BST) thin films in inductively coupled CF4 /Ar plasma. We have found that an increase of the Ar content in CF4 /Ar plasma causes non-monotonic behavior of BST etch rate, which reaches a maximum value of 40 nm/min at 80% Ar. The X-ray photoelectron spectroscopy (XPS) analysis indicated the accumulation of reaction products on the BST film surface in CF4 -rich plasma. Langmuir probe measurements show a weak sensitivity of both electron temperature and electron density to the change of CF4 /Ar mixing ratio. 0-D model for plasma chemistry gave monotonic changes of both volume densities and fluxes for active species responsible for the etching process. The analysis of surface kinetics confirms the possibility of non-monotonic etch rate behavior due to the concurrence of physical and chemical pathways in ion-assisted chemical reaction. Ó 2003 Elsevier B.V. All rights reserved. Keywords: BST; Etch rate; Electron temperature; Ion-assisted etching
1. Introduction With increasing density of memory devices, high-k ferroelectric thin films attract a great attention to substitute for conventional dielectrics in dynamic random access memories (DRAMs). q
This work was supported by Institute of Information Technology Assessment (IITA). * Corresponding author. Tel.: +8228205334; fax: +82281 29651. E-mail address: [email protected] (C.-I. Kim). 1 A.M. Efremov is an invited professor from Department of Microelectronic Devices and Materials Technology at Ivanovo State University of Chemistry and Technology in Ivanovo, Russia.
Among numerous ferroelectrics have been studied for DRAM device applications, (Ba,Sr)TiO3 (BST) thin films are known as one of the leading candidates due to high dielectric constant, low leakage current, small dielectric loss, lack of fatigue and low crystallization temperature [1,2]. Therefore the development of anisotropic etching process for BST thin films is an important task to provide a small feature size and an accurate pattern transfer. Until now, there are several works devoted to an investigation of etching characteristics of BST thin films using both chlorine-containing and fluorine-containing plasmas [3–9], including our earlier works [3,4,9]. Summarizing published data,
0167-9317/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.09.001
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it is possible to underline several common features characterized BST etch process. First is low volatility of both metal-chlorides and metal-fluorides, especially for Ba and Sr. Choi et al. [3], Shibano et al. [5] and Kang et al. [9] reported about the accumulation of reaction products on the etched surfaces using Cl2 -based as well as CF4 -based etching chemistries. As a result, etching products form a residue layer, which obstructs the access of active species and decreases the etch rate [3,7–9]. Accordingly, any changes of process parameters caused higher intensity of ion bombardment (i.e. increase in input power or in negative dc bias) increase the BST etch rate. Secondly, when a binary mixture of chemical active gas and noble gas is used for the etching, BST etch rate shows nonmonotonic dependence on gas mixing ratio. This effect was repeatedly reported in literature, for example, in [3,6,8] for Cl2 /Ar plasma as well as in [5,9] for CF4 /Ar gas mixture. In all the cases, it was found that BST etch rate has a maximum at 70– 80% Ar while the etch rate in pure Ar plasma exceeds etch rate in pure Cl2 or CF4 . Unfortunately, the reason of this effect is not defined and thus, BST etch mechanism is not still clear. As an explanation, the works mentioned above give only a qualitative suggestions about the concurrence of chemical and physical etch mechanisms. Another problem is that BST thin films are relatively new material involved onto microelectronic technology. That is why the majority of researches were focused in technological aspects while the problems of relationships between process parameters, plasma chemistry and surface kinetics have not been studied. This misunderstanding of the basic kinetic effects obstructs the development and optimization for BST etching process. In this work, we investigated etching characteristics and mechanism of BST thin films using CF4 /Ar gas mixtures in an inductive coupled plasma (ICP) system. Etching characteristics were investigated in the terms of BST etch rate and selectivity over photoresist (PR) mask as a function of CF4 /Ar mixing ratio. Plasma diagnostics were performed by Langmuir probe measurements. To understand the etching mechanism, the models of plasma chemistry and surface kinetics were developed.
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2. Experimental details (Ba,Sr)TiO3 thin films were prepared according to a formula of Ba0:6 Sr0:4 TiO3 using sol-gel method. Precursors were barium acetate and strontium acetate dissolved in acetic acid as well as Ti-isopropoxide dissolved in 2-methoxyethanol under N2 atmosphere. For thin film deposition, the stoichiometric mixture of precursors was syringed through a 0.2 lm syringe filter on the Pt/Ti/SiO2 /Si substrate and then spin-coated at 4000 rpm for 30 s. After spin-coating, BST films were kept on hot plate at 400 °C for 10 min aimed at removing organic contaminations. The pre-baked films were annealed at 700 °C for 60 min under O2 atmosphere for crystallization. The final thickness of BST films was about 300 nm. Experiments were carried out in a planar ICP reactor, which is described in details in our earlier works [9,10] Cylindrical working chamber (Ø 26 cm) was made from aluminum with Al2 O3 coating (anodizing) inside. On the topside, horizontal quartz window separates the chamber and 3.5-turn copper coil, connected to 13.56 MHz power generator. On the bottom, an electrode used as substrate holder was connected to another 13.56 MHz asymmetric rf generator to control dc bias voltage. The height of the working zone, i.e. the distance between quartz window and bottom electrode, was 9 cm. All the experiments were carried out under fixed input parameters: total pressure of CF4 /Ar mixture of 15 mTorr, total gas flow rate of 20 sccm, input power of 700 W, and dc bias voltage of )200 V while only the CF4 /Ar mixing ratio was varied. Temperature of the sample was stabilized at 30 °C. The etch rates of BST and PR (AZ1512, positive) were measured using the ellipsometry (L116B-85B, Gaertner Scientific Corp.) for the processing time of 1 min providing the stationary etching conditions. The samples size was about 2 cm2 . To measure etch rate, we developed the line striping of the PR with the line width/spacing ratio of 2 lm/2 lm. The initial thickness of the PR layer was about 1.5 lm. The etch rate of the PR was also controlled in the independent measurements using the satellite sample. Plasma diagnostics was represented by Langmuir probe (LP) measurements. For this purpose,
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we used a single cylindrical, and rf-compensated probe (ESPION, Hiden Analytical), which was installed through vertical view port on the chamber wall-side and placed in the center of the reactor working zone both in axial and radial directions. For the treatment of ‘‘voltage–current’’ traces aimed at obtaining electron temperature and electron density, we used software supplied by the equipment manufacturer. Compositional changes of the etched BST surfaces were investigated using X-ray photoelectron spectroscopy (XPS) (ESCALAB 220-IXL) with Al ka source (1486.6 eV).
3. Results and discussion For any plasma etch process with using a chemical active gas, there are two general factors affected the behavior of etch rate. The first is the fluxes of active species on the etched surface. The fluxes depend on stationary mass composition of gas phase resulted from the balance between formation and decay processes. Second factor works through the reaction probability and sputtering yields for main material as well as for low-volatile reaction products. Therefore, the investigations of etch mechanism is a complex task, which includes the simultaneous analysis of both volume and surface kinetics.
melting points (Tmp ) for the corresponding compounds [3,11]. From [11], it can be seen that Tmp (BaF2 ) ¼ 1368 °C, Tmp (SrF2 ) ¼ 1477 °C, Tmp (TiF3 ) ¼ 1200 °C and Tmp (TiF4 ) ¼ 284 °C. In this situation, we assume the BST etch mechanism to be represented by the combination of ion-assisted etching and physical sputtering while the contribution of spontaneous etching supported by thermal desorption of reaction products may be neglected. Fig. 1 illustrates the effect of CF4 /Ar mixing ratio on the etch rate of BST thin films as well as on the etch selectivity of BST over PR. Data show that the BST etch rate is non-monotonic and exhibits a maximum at 80% Ar. The absolute value of the etch rate at the maximum is about 40 nm/ min. The lowest etch rate was obtained in our experiments corresponds to a pure CF4 plasma (22 nm/min) while the etching in pure Ar plasma is about 1.5 times faster (32 nm/min). Experiments show also that any variations of input power and negative dc bias voltage in the range of 600–800 W and 150–250 V do not influence the shape of the curve shown in Fig. 1, but result in changes of absolute value for BST etch rate as well as in weak deviations of the position of etch rate maximum along the x-axis. For the PR, an increase of Ar content in CF4 /Ar mixture leads to monotonic decrease in the PR etch rate in the range of 0.96– 0.74 lm/min. As a result, the etch selectivity of
3.1. Etch rate and plasma parameters Before analyzing the etching results, it will be reasonable to overview the peculiarities of the etching behavior for BST films, which were found in earlier works. Shibano et al. [5] and Kang et al. [9] have discussed low volatility of metal-fluorides for BST components to be a main problem for the etching in fluorine-containing plasmas. The reason is that chemical reaction leads to formation of a residue layer obstructing the further access of active species to the etched surface. Generally, to characterize the volatility, we need the data on the saturated vapor pressures for the compounds of our interest. Unfortunately, for BaFx , SrFx and TiFx these data are absent and we can refer only to the simple correlation between volatilities and
Fig. 1. BST etch rate and etch selectivity over PR as a function of CF4 /Ar mixing ratio.
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BST over PR follows the behavior of BST etch and enriches a maximum of 0.049 for 80% Ar. Fig. 2 shows F 1s XPS narrow scan spectra for the samples etched using various CF4 /Ar mixing ratios as well as for the as-deposited BST film. After the etching in pure CF4 plasma, the XPS spectrum shows a wide peak in the region of 682– 687 eV with a maximum corresponding to a binding energy of 684.5 eV. Generally, fluorinecontaining compounds presented on the surface may belong not only to reaction products, but also to CFx -based polymer layer deposited from plasma volume. However, the contribution of the last factor seems to be negligible. There are two reasons for this conclusion. The first is that the XPS spectrum of C(1s) does not show the peaks of 291.2 and 291.9 eV for C(1s)–F bonds in CF2 and CF2 –CF3 groups [12], respectively. The second is the absence of the signal from F(1s)–C bonds at 687.5 eV [13] in the spectra shown in Fig. 2. In our opinion, the peak observed in Fig. 2 represents a sum of non-resolved and overlapped peaks for F(1s)–Ba in BaF2 (683.7 and 684.3 eV) and F(1s)– Sr in SrF2 (684.5 and 685.0 eV) [14]. Kang et al. [9] have made the same conclusion based on the results of XPS and SIMS analysis. The XPS data show also that the decrease of CF4 content in CF4 / Ar mixture leads to the rapid decrease of the peak intensity while the spectra for as-deposited and Ar-etched samples show the absence of fluorine-
containing compounds on the surface. Therefore, assuming the intensity of XPS signal to be proportional to surface density of corresponding compound, our XPS data confirm the accumulation of reaction products on the surfaces etched in CF4 -rich plasmas. Fig. 3 illustrates the results of plasma diagnostics using Langmuir probes. It can be seen that the influence of CF4 /Ar mixing ratio both on electron temperature and electron density is not very significant. Actually, as the Ar content in CF4 /Ar plasma increases from 0 to 100%, electron temperature drops down from 6.5 to 5.9 eV while electron density increases in the range of 5.35 1010 to 8.80 1010 cm3 . Anyway, the results of Fig. 3 seem to be reasonable. An only weak change of electron temperature mentioned in experiments is caused by rather close values of ionization potentials for CF4 and Ar: 15.9 and 15.8 eV, respectively. In this situation, as the gas composition varies from pure CF4 to pure Ar, sufficient deformations of electron energy distribution function (EEDF) are not expected. In our opinion, the behavior of electron temperature may be accepted as the indirect proof that under the conditions were investigated CF4 dissociation degree is not too high. The reason is that ionization potential for F atoms (17.42 eV) sufficiently exceeds ionization potential for Ar. Accordingly, it is possible to expect that high dissociation degree of
Fig. 2. F (1p) XPS narrow scan spectra for the samples etched using various CF4 /Ar mixing ratios.
Fig. 3. Electron temperature and electron density determined by Langmuir probe measurements as a function of CF4 /Ar mixing ratio.
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CF4 molecules and thus high volume density of fluorine atoms will provide more sufficient deviations of electron temperature with the change of CF4 /Ar mixing ratio than it was found in our experiments. As for the electron density, the behavior of this parameter may be explained by the changes of total ionization rate as well as electron diffusion coefficient due to the corresponding changes of electron temperature. Choi et al. [15] reported similar experimental results for CF4 /Ar plasma in ICP system. Analyzing the results discussed above, it is possible to consider for two general explanations for a non-monotonic etch rate of BST films as a function of CF4 /Ar mixing ratio. The first is the non-monotonic changes of both volume densities and fluxes of active species resulted from the influence of plasma parameters on volume kinetics. The second is the simultaneous action of two etching mechanisms with monotonic, but opposite tendencies to change with increasing Ar mixing ratio. To check the first assumption, we used plasma modeling.
of F atoms due to a low neutral–neutral collision frequency under low-pressure conditions. The rate coefficient of heterogeneous decay krec was determined considering first order kinetics for the recombination and diffusion transport of atoms to reactor walls [10,21]: DF ; ð2Þ k2 where cF is the probability of heterogeneous recombination for fluorine atoms (cF 0:05 from [22]), DF the effective diffusion coefficient and k is the effective diffusion length. Effective diffusion coefficients are represented by the combination of free diffusion coefficient and inter-diffusion coefficient, calculated using the Chapman–Enscog equation [10,21] while the effective diffusion length is determined by the given reactor axial and radial sizes [16]. To estimate total volume density of positive and negative ions, we used a combination of balance kinetic equation for negative ions with plasma quasi-neutrality equation: krec ¼ cF
CF4 kda ne n0 ð1 dÞ kii nþ nF ;
ð3Þ
ne þ nF nþ ;
ð4Þ
3.2. Gas phase composition To analyze the influence of gas mixing ratios on volume densities and fluxes of plasma active species, we applied 0-dimensional (0-D) plasma modeling assuming the Maxwellian EEDF and quasi-stationary approximation for volume kinetics [10,16–18]. Considering [19,20], we also assume CF4 molecules to be a main source of fluorine atoms in plasma volume while the densities of unsaturated CFx ðx < 4Þ radicals are sufficiently lower than CF4 density. Accordingly, a balance equation of chemical kinetics determining volume density of fluorine atoms may be written as follows: CF4 kdis þ kdiCF4 ne n0 ð1 dÞ krec nF þ ð1=sres ÞnF ; ð1Þ where k is the rate coefficients for the processes specified in Table 1, ne the electron density, n0 the total density of neutral particles, d the fraction of Ar in gas mixture, sres is the residence time. Eq. (1) does not take into account volume recombination
where nþ is the total density of positive ions, kii the average rate coefficient of ion-ion recombination assuming close partial rate coefficients for each kind of positive ion (kii 1 107 cm3 /s from [23]). Eq. (3) assumes F to be a dominant type among negative ions [19] while the decay of negative ions is limited only by volume reactions of ion-ion recombination [10]. The last assumption is connected with the presence of a double electric layer and negative charges on the reactor walls covered by dielectric materials. Volume density of the Arþ ions inside nþ value was estimated as follows [10]: nArþ
Ar kion ne n0 d ; ðS=V ÞUB þ kii nF
ð5Þ
Ar where kion is the ionization rate coefficient for Ar atoms, S and UB the effective ion collection area and ion Bohm velocity for Arþ ions, V is the plasma volume. The peculiarities of the determination of both S and UB parameters for the elec-
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Table 1 Reaction set for simulation of volume kinetics in CF4 /Ar plasma Process
Eth (eV)
Rate coefficient
CF4 + e ! CF3 + F + e CF4 + e ! CFþ 3 + F + 2e CF4 + e ! CF3 + F Ar + e ! Arþ + 2e þ þ F + nþ (CFþ x , F , Ar ) ! n + F Arþ ! wall F ! wall
5.6 15.9 3.0 15.76 – – –
CF4 kdis ¼ 1.190 1016 Te1:309 exp()1.446 105 /Te )a kdiCF4 ¼ 1.159 1011 Te0:765 exp()1.993 105 /Te )a CF4 kda ¼ 2.369 108 Te0:489 exp() 5.876 104 /Te )a Ar kion ¼ 1.23 107 exp() 18.68/Te )b kii ¼ 1.0 107 (cm3 /s) ðS=V ÞUB (s1 ) cD=k2 (s1 )
a b
cm3 /s, Te in K. cm3 /s, Te in eV.
tronegative plasmas were described in details by Ashida and Lieberman [16] and by Malyshev and Donnelly [24]. In simplest case, assuming ion collection areas to be equal for all kinds of positive ions, the parameter ðS=V Þ may be approximated as plasma surface to volume ratio [25]. Fig. 4 illustrate the influence of gas mixing ratio on volume densities of neutral and charged particles in CF4 /Ar plasma. Calculations show that the increase of Ar mixing ratio causes a monotonic decrease of CF4 dissociation rate. The reason is that total dissociation rate coefficient (as the sum of partial coefficients for each process producing F atoms) and electron density have an opposite tendencies to change. That is why the multiplicaCF4 tion of ðkdis þ kdiCF4 Þne remains practically a constant (240–280 s1 ) while the dissociation rate changes proportionally to fraction of the Ar in gas
Fig. 4. Volume densities on neutral and charged particles evaluated from 0-D plasma model.
mixtures. Although the effective diffusion coefficient and thus a recombination rate coefficient for F atoms are sensitive to the change of mixture composition (krec ¼ 177–472 s1 for 2–98% Ar), both the dependences are monotonic. As a result, volume density of F atoms follows the behavior of CF4 dissociation rate. Olthoff and Wang [26] have reported similar results for CF4 /Ar plasma. As an indirect proof for the monotonic behavior of F atoms volume density, it is possible to involve the dependence of the PR etch rate on CF4 /Ar mixing ratio. It is well known that in fluorine-containing plasmas PR is dominantly etched chemically by fluorine atoms [27]. Accordingly, PR etch rate decreases monotonically during addition of Ar and follows the fluorine atoms volume density. For the charged particles, we have found that, even in CF4 -rich plasmas, total density of positive ions is close to electron density. Relative density of negative ions b ¼ n =ne characterizing plasma electronegativity does not exceed 2 for pure CF4 and decreases with increasing Ar mixing ratio. This result is in the frameworks of general tendency repeatedly mentioned in literature: at low pressures electronegative plasmas transform to moderate or low electronegative form [16,17]. Fig. 4 shows also total density of fluorine-conþ taining positive ions (i.e. CFþ x , F ) calculated as þ the difference between n and nArþ . Considering [26], we assume that a major component inside this value is CFþ 3 . The reasons are that CF3 molecules have higher volume density among CFx radicals (lower recombination and sticking probabilities) [23], lower ionization potential and higher ionization cross-section.
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The results on gas phase composition represented in Fig. 4 show that the etching behavior of BST thin films cannot be explained directly by variations of volume densities of active species. In other words, no single active species can provide a maximum on the etch rate as a function of the CF4 /Ar mixing ratio. It means that the reason may be connected with the surface kinetics through the simultaneous action of several kinds of active species.
To calculate the fluxes of neutral and charged particles to the surface, we used the methods described in [16–18]. The probability of chemical reaction cch may be approximated by the upper limit followed from the stoichiometry of reaction products (for example, cch ¼ 0:5 for Me–F2 ) [31]. Similar to [32,33], we assume that Ys and Yd are a function of square root of ion energy, based on the collision cascade approximation for sputtering process: 1=2
Ys ¼ AðE1=2 E0;s Þ; 3.3. Surface kinetics To investigate the relationships between composition of gas phase and surface kinetics, we used the phenomenological model based on theory of active surface sites [28–31]. The model was based on such assumptions as: (1) only F atoms are effective in chemical reaction; (2) only Arþ ions are effective in the sputtering process; (3) sputtering of the substrate is possible only when the incident ion impacts the clean surface; (4) all kinds of positive ions are effective for the ion-stimulated desorption of reaction products. Total etching rate obtained in experiments may be represented as the sum of partial rates of chemical reaction and physical sputtering: ER ¼ ð1 HÞcch SF CF þ ð1 HÞYs CArþ ;
ð6Þ
where C is the fluxes of species to the etched surface, Ys the sputtering yield, cch the probability of chemical interaction, SF the sticking probability of F atoms, H fraction of fluorinated surface. Assuming the contribution of spontaneous chemical etching (i.e. the contribution of thermal desorption of reaction products) to be negligible, stationary balance equation for active sites on the surface may be written as follows: X ð1 HÞcch SF CF ¼ H Yd;j Cþ;j ; ð7Þ where Yd;j and Cþ;j is the partial yields of ionstimulated desorption and partial fluxes for all kinds of positive ions existed in plasma. Combining Eqs. (6) and (7), the equation for etch rate may be obtained: P Yd;j Cþ;j ðcch SF CF þ Ys CArþ Þ P ER ¼ : ð8Þ cch SF CF þ Yd;j Cþ;j
1=2
Yd ¼ BðE1=2 E0;d Þ;
ð9Þ
where A and B are parameters, which depend on type of ion and sputtered material, E is the incident ion energy, which is the sum of ion acceleration energy in plasma sheath (approximately 6.2Te assuming CFþ 3 to be a dominant positive ion in CF4 -rich plasma) and the negative DC bias voltage, applied to the substrate while E0;s and E0;d are threshold energies for sputtering and ionstimulated desorption, respectively. The parameters A and E0;s for BST thin films sputtered by Arþ ions may be extracted from [34] (A ¼ 0:13, E0;s ¼ 30 eV). Parameters SF , B and E0;d are not known exactly for BST, but the reasonable ranges for their deviation may be evaluated using an indirect literature data for well-studied systems, for example for F–SiO2 and F–Si [29,31]. These ranges are 0.3–0.5, 0.1–1.0 and 4–10 eV for SF , B and E0;d , respectively. Additionally, it is possible to expect that Yd;Arþ > Yd;CFþx i.e. Arþ ions play a dominant role in ion-stimulated desorption. The reason is high sticking coefficients of CFþ x ions for metalcontaining surfaces. Then, these ions can be easily neutralized on the surface either forming polymer layer [23] or returning back to gas phase as neutral reactants. Although the assumptions mentioned above seem to be reasonable, we expect that the Eq. (8) works only in qualitative scale and thus, may be applied only for the analyses of relative etch rate behavior. It is evidently that SF and Yd depend on a large number of factors such as temperature of the surface, stoichiometry of the reaction products, type of incident ion and surface atom etc., which cannot be taken into account accurately. That is why we can use SF and Yd (i.e. the coefficient B and E0;d in Eq. (9)) only as the model parameters.
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Fig. 5 shows the behaviors of both chemical ð1 HÞcch SF CF and physical channels as a function of CF4 /Ar mixing ratio. As the Ar mixing ratio increases, the rate of physical sputtering increases monotonically and follows the behavior of Arþ volume density. The reason is that a small change in electron temperature escorted the transition from CF4 -rich to Ar-rich plasma does not influence sufficiently on both ion Bohm velocity and sputtering yield. At the same time, the rate of ion-assisted chemical reaction shows a maximum in the range of 45–55% Ar due to the competition between two processes: the decreasing both volume density and flux of chemically active species to the etched surface and the increasing fraction of free surface acceptable for chemical reaction. We have found also that the behavior of fraction of fluorinated surface H calculated using Eq. (7) is in good agreement with the change in F 1s XPS intensity. Finally, Fig. 6 demonstrates that total etch rate determined by Eqs. (6) or (8) keeps nonmonotonic behavior while the location of maximum depends also on quantitative correlation between chemical and physical pathways. It can be seen that the increase in efficiency of ion-stimulated desorption increases the rate of chemical reaction in CF4 -rich plasma, decreases the contribution of sputter etching and shifts maximum etch rate toward lower Ar mixing ratios.
Fig. 5. Influence of CF4 /Ar mixing ratio on partial rates of ion assisted chemical reaction and physical sputtering as predicted by the model of surface kinetics. Model parameters: (1) BArþ ¼ 0.1; (2) BArþ ¼ 0.2; (3) BArþ ¼ 0.3; (4) BArþ ¼ 0.5 while SF ¼ 0.3, E0;d ¼ 7 eV, BArþ =BCFþx ¼ 5.
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Fig. 6. Influence of CF4 /Ar mixing ratio on total etch rate as predicted by the model of surface kinetics. Model parameters are the same with Fig. 5.
It is important to note once more that the model were used cannot provide an exact quantitative agreement between measured and calculated etch rats in absolute scale due to simplifications in primary assumptions. Nevertheless, we can obtain a quantitative agreement in relative scale. Fig. 7 shows the comparison for experimental and modeling data with a normalization point corresponding to pure Ar plasma. Calculations show that, in best case (i.e. within any reasonable variations of all coefficients employed in Eq. (8)), the model gives an outstanding description for relative
Fig. 7. Comparison of relative behavior of BST etch rate obtained by experiment and modeling.
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behavior of BST etch rate in Ar-rich plasma, but systematically underestimates the etch rate in CF4 rich plasma. One of the reasons may be connected with a chemical activity of CFx radicals, which were not taken into account as reactants.
4. Conclusion In present work, we carried out an investigation of etching mechanisms for BST thin films in inductively coupled CF4 /Ar plasma. We have found that an increase of the Ar content in CF4 /Ar plasma leads to an increase in BST etch rate, which reaches a maximum value of 40 nm/min at 80% Ar. The XPS analysis indicated the accumulation of reaction products on the BST film surface in CF4 rich plasma. Langmuir probe measurements indicated weak influence of CF4 /Ar mixing ratio on both electron temperature and electron density. Calculations of gas phase composition using 0-D plasma model gave monotonic changes of both volume densities and fluxes for fluorine atoms and positive ions. The analysis of surface kinetics demonstrated the possibility of non-monotonic etch rate behavior in the system with monotonic changes of fluxes of both chemically and energetically active species. It was found that the reason for etch rate maximum is the concurrence of physical and chemical pathways in ion-assisted chemical reaction.
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[7] H.M. Lee, D.C. Kim, W. Jo, K.Y. Kim, J. Vac. Sci. Technol. A 16 (1998) 1891. [8] D.S. Wuu, C.C. Lin, R.H. Horng, F.C. Liao, Y.H. Liu, J. Vac. Sci. Technol. A 19 (2001) 2231. [9] P.S. Kang, K.T. Kim, D.P. Kim, C.I. Kim, A.M. Efremov, Surf. Coat. Technol. 171 (2003) 273. [10] A.M. Efremov, D.P. Kim, C.I. Kim, J. Vac. Sci. Technol. A 21 (2003) 1568. [11] D.R. Lide, Handbook of Chemistry and Physics, CRC Press, New York, 1998–1999. [12] J.E. Chase, F.J. Boerio, J. Vac. Sci. Technol. A 21 (2003) 607. [13] M. Matsui, T. Tatsumi, M. Sekine, J. Vac. Sci. Technol. A 19 (2001) 2089. [14] J. Chastain (Ed.), Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Corp., Minnesota, 1992. [15] C.J. Choi, O.S. Kwon, Y.S. Seol, Y.W. Kim, I.H. Choi, J. Vac. Sci. Technol. B 18 (2000) 811. [16] S. Ashida, M.A. Lieberman, Jpn. J. Appl. Phys. 36 (1997) 854. [17] M.A. Lieberman, S. Ashida, Plasma Sources Sci. Technol. 5 (1996) 145. [18] C. Lee, M.A. Lieberman, J. Vac. Sci. Technol. A 13 (1995) 368. [19] M.V.V.S. Rao, S.P. Sharma, B.A. Cruden, M. Meyyappan, Plasma Sources Sci. Technol. 11 (2002) 69. [20] K. Knizikevicius, Appl. Surf. Sci. 201 (2002) 96. [21] M.V. Malyshev, V.M. Donnelly, J. Appl. Phys. 87 (2000) 1642. [22] G.P. Kota, J.W. Coburn, D.B. Graves, J. Vac. Sci. Technol. A 17 (1999) 282. [23] D. Zhang, M.J. Kushner, J. Vac. Sci. Technol. A 18 (2000) 2661. [24] M.V. Malyshev, V.M. Donnelly, J. Appl. Phys. 90 (2001) 1130. [25] M.V. Malyshev, V.M. Donelly, A. Kornblit, N.A. Ciampa, J. Appl. Phys. 84 (1998) 137. [26] J.K. Olthoff, Y. Wang, J. Vac. Sci. Technol. A 17 (1999) 1552. [27] R.J. Shul, S.J. Pearton (Eds.), Handbook of Advanced Plasma Processing Technique, Springer, Berlin, 2000. [28] U. Gerlach-Meyer, Surf. Sci. 103 (1981) 524. [29] D.C. Gray, I. Tepermeister, H.H. Sawin, J. Vac. Sci. Technol. A 11 (1993) 1243. [30] H.W. Winters, J.W. Coburn, Surf. Sci. Rep. 14 (1992) 162. [31] D.I. Slovetsky, Plasma Chem. 15 (1989) 208 (in Russian). [32] C. Lee, D.B. Graves, M.A. Lieberman, Plasma Chem. Plasma Proc. 16 (1996) 99. [33] W. Jin, S.A. Vitale, H.H. Sawin, J. Vac. Sci. Technol. A 20 (2002) 2106. [34] L. Stafford, J. Margot, S. Delprat, M. Chaker, D. Queney, J. Vac. Sci. Technol. A 20 (2002) 530.
Etching mechanisms of (Ba,Sr)TiO3 thin films in CF4/Ar inductively coupled plasma q A.M. Efremov 1, Dong-Pyo Kim, Kyoung-Tae Kim, Chang-Il Kim
*
School of Electrical and Electronic Engineering, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Gu, Seoul 156-756, South Korea Received 3 July 2003; received in revised form 3 July 2003; accepted 5 September 2003
Abstract This work was devoted to an investigation of etching mechanisms for (Ba,Sr)TiO3 (BST) thin films in inductively coupled CF4 /Ar plasma. We have found that an increase of the Ar content in CF4 /Ar plasma causes non-monotonic behavior of BST etch rate, which reaches a maximum value of 40 nm/min at 80% Ar. The X-ray photoelectron spectroscopy (XPS) analysis indicated the accumulation of reaction products on the BST film surface in CF4 -rich plasma. Langmuir probe measurements show a weak sensitivity of both electron temperature and electron density to the change of CF4 /Ar mixing ratio. 0-D model for plasma chemistry gave monotonic changes of both volume densities and fluxes for active species responsible for the etching process. The analysis of surface kinetics confirms the possibility of non-monotonic etch rate behavior due to the concurrence of physical and chemical pathways in ion-assisted chemical reaction. Ó 2003 Elsevier B.V. All rights reserved. Keywords: BST; Etch rate; Electron temperature; Ion-assisted etching
1. Introduction With increasing density of memory devices, high-k ferroelectric thin films attract a great attention to substitute for conventional dielectrics in dynamic random access memories (DRAMs). q
This work was supported by Institute of Information Technology Assessment (IITA). * Corresponding author. Tel.: +8228205334; fax: +82281 29651. E-mail address: [email protected] (C.-I. Kim). 1 A.M. Efremov is an invited professor from Department of Microelectronic Devices and Materials Technology at Ivanovo State University of Chemistry and Technology in Ivanovo, Russia.
Among numerous ferroelectrics have been studied for DRAM device applications, (Ba,Sr)TiO3 (BST) thin films are known as one of the leading candidates due to high dielectric constant, low leakage current, small dielectric loss, lack of fatigue and low crystallization temperature [1,2]. Therefore the development of anisotropic etching process for BST thin films is an important task to provide a small feature size and an accurate pattern transfer. Until now, there are several works devoted to an investigation of etching characteristics of BST thin films using both chlorine-containing and fluorine-containing plasmas [3–9], including our earlier works [3,4,9]. Summarizing published data,
0167-9317/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.09.001
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it is possible to underline several common features characterized BST etch process. First is low volatility of both metal-chlorides and metal-fluorides, especially for Ba and Sr. Choi et al. [3], Shibano et al. [5] and Kang et al. [9] reported about the accumulation of reaction products on the etched surfaces using Cl2 -based as well as CF4 -based etching chemistries. As a result, etching products form a residue layer, which obstructs the access of active species and decreases the etch rate [3,7–9]. Accordingly, any changes of process parameters caused higher intensity of ion bombardment (i.e. increase in input power or in negative dc bias) increase the BST etch rate. Secondly, when a binary mixture of chemical active gas and noble gas is used for the etching, BST etch rate shows nonmonotonic dependence on gas mixing ratio. This effect was repeatedly reported in literature, for example, in [3,6,8] for Cl2 /Ar plasma as well as in [5,9] for CF4 /Ar gas mixture. In all the cases, it was found that BST etch rate has a maximum at 70– 80% Ar while the etch rate in pure Ar plasma exceeds etch rate in pure Cl2 or CF4 . Unfortunately, the reason of this effect is not defined and thus, BST etch mechanism is not still clear. As an explanation, the works mentioned above give only a qualitative suggestions about the concurrence of chemical and physical etch mechanisms. Another problem is that BST thin films are relatively new material involved onto microelectronic technology. That is why the majority of researches were focused in technological aspects while the problems of relationships between process parameters, plasma chemistry and surface kinetics have not been studied. This misunderstanding of the basic kinetic effects obstructs the development and optimization for BST etching process. In this work, we investigated etching characteristics and mechanism of BST thin films using CF4 /Ar gas mixtures in an inductive coupled plasma (ICP) system. Etching characteristics were investigated in the terms of BST etch rate and selectivity over photoresist (PR) mask as a function of CF4 /Ar mixing ratio. Plasma diagnostics were performed by Langmuir probe measurements. To understand the etching mechanism, the models of plasma chemistry and surface kinetics were developed.
55
2. Experimental details (Ba,Sr)TiO3 thin films were prepared according to a formula of Ba0:6 Sr0:4 TiO3 using sol-gel method. Precursors were barium acetate and strontium acetate dissolved in acetic acid as well as Ti-isopropoxide dissolved in 2-methoxyethanol under N2 atmosphere. For thin film deposition, the stoichiometric mixture of precursors was syringed through a 0.2 lm syringe filter on the Pt/Ti/SiO2 /Si substrate and then spin-coated at 4000 rpm for 30 s. After spin-coating, BST films were kept on hot plate at 400 °C for 10 min aimed at removing organic contaminations. The pre-baked films were annealed at 700 °C for 60 min under O2 atmosphere for crystallization. The final thickness of BST films was about 300 nm. Experiments were carried out in a planar ICP reactor, which is described in details in our earlier works [9,10] Cylindrical working chamber (Ø 26 cm) was made from aluminum with Al2 O3 coating (anodizing) inside. On the topside, horizontal quartz window separates the chamber and 3.5-turn copper coil, connected to 13.56 MHz power generator. On the bottom, an electrode used as substrate holder was connected to another 13.56 MHz asymmetric rf generator to control dc bias voltage. The height of the working zone, i.e. the distance between quartz window and bottom electrode, was 9 cm. All the experiments were carried out under fixed input parameters: total pressure of CF4 /Ar mixture of 15 mTorr, total gas flow rate of 20 sccm, input power of 700 W, and dc bias voltage of )200 V while only the CF4 /Ar mixing ratio was varied. Temperature of the sample was stabilized at 30 °C. The etch rates of BST and PR (AZ1512, positive) were measured using the ellipsometry (L116B-85B, Gaertner Scientific Corp.) for the processing time of 1 min providing the stationary etching conditions. The samples size was about 2 cm2 . To measure etch rate, we developed the line striping of the PR with the line width/spacing ratio of 2 lm/2 lm. The initial thickness of the PR layer was about 1.5 lm. The etch rate of the PR was also controlled in the independent measurements using the satellite sample. Plasma diagnostics was represented by Langmuir probe (LP) measurements. For this purpose,
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we used a single cylindrical, and rf-compensated probe (ESPION, Hiden Analytical), which was installed through vertical view port on the chamber wall-side and placed in the center of the reactor working zone both in axial and radial directions. For the treatment of ‘‘voltage–current’’ traces aimed at obtaining electron temperature and electron density, we used software supplied by the equipment manufacturer. Compositional changes of the etched BST surfaces were investigated using X-ray photoelectron spectroscopy (XPS) (ESCALAB 220-IXL) with Al ka source (1486.6 eV).
3. Results and discussion For any plasma etch process with using a chemical active gas, there are two general factors affected the behavior of etch rate. The first is the fluxes of active species on the etched surface. The fluxes depend on stationary mass composition of gas phase resulted from the balance between formation and decay processes. Second factor works through the reaction probability and sputtering yields for main material as well as for low-volatile reaction products. Therefore, the investigations of etch mechanism is a complex task, which includes the simultaneous analysis of both volume and surface kinetics.
melting points (Tmp ) for the corresponding compounds [3,11]. From [11], it can be seen that Tmp (BaF2 ) ¼ 1368 °C, Tmp (SrF2 ) ¼ 1477 °C, Tmp (TiF3 ) ¼ 1200 °C and Tmp (TiF4 ) ¼ 284 °C. In this situation, we assume the BST etch mechanism to be represented by the combination of ion-assisted etching and physical sputtering while the contribution of spontaneous etching supported by thermal desorption of reaction products may be neglected. Fig. 1 illustrates the effect of CF4 /Ar mixing ratio on the etch rate of BST thin films as well as on the etch selectivity of BST over PR. Data show that the BST etch rate is non-monotonic and exhibits a maximum at 80% Ar. The absolute value of the etch rate at the maximum is about 40 nm/ min. The lowest etch rate was obtained in our experiments corresponds to a pure CF4 plasma (22 nm/min) while the etching in pure Ar plasma is about 1.5 times faster (32 nm/min). Experiments show also that any variations of input power and negative dc bias voltage in the range of 600–800 W and 150–250 V do not influence the shape of the curve shown in Fig. 1, but result in changes of absolute value for BST etch rate as well as in weak deviations of the position of etch rate maximum along the x-axis. For the PR, an increase of Ar content in CF4 /Ar mixture leads to monotonic decrease in the PR etch rate in the range of 0.96– 0.74 lm/min. As a result, the etch selectivity of
3.1. Etch rate and plasma parameters Before analyzing the etching results, it will be reasonable to overview the peculiarities of the etching behavior for BST films, which were found in earlier works. Shibano et al. [5] and Kang et al. [9] have discussed low volatility of metal-fluorides for BST components to be a main problem for the etching in fluorine-containing plasmas. The reason is that chemical reaction leads to formation of a residue layer obstructing the further access of active species to the etched surface. Generally, to characterize the volatility, we need the data on the saturated vapor pressures for the compounds of our interest. Unfortunately, for BaFx , SrFx and TiFx these data are absent and we can refer only to the simple correlation between volatilities and
Fig. 1. BST etch rate and etch selectivity over PR as a function of CF4 /Ar mixing ratio.
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57
BST over PR follows the behavior of BST etch and enriches a maximum of 0.049 for 80% Ar. Fig. 2 shows F 1s XPS narrow scan spectra for the samples etched using various CF4 /Ar mixing ratios as well as for the as-deposited BST film. After the etching in pure CF4 plasma, the XPS spectrum shows a wide peak in the region of 682– 687 eV with a maximum corresponding to a binding energy of 684.5 eV. Generally, fluorinecontaining compounds presented on the surface may belong not only to reaction products, but also to CFx -based polymer layer deposited from plasma volume. However, the contribution of the last factor seems to be negligible. There are two reasons for this conclusion. The first is that the XPS spectrum of C(1s) does not show the peaks of 291.2 and 291.9 eV for C(1s)–F bonds in CF2 and CF2 –CF3 groups [12], respectively. The second is the absence of the signal from F(1s)–C bonds at 687.5 eV [13] in the spectra shown in Fig. 2. In our opinion, the peak observed in Fig. 2 represents a sum of non-resolved and overlapped peaks for F(1s)–Ba in BaF2 (683.7 and 684.3 eV) and F(1s)– Sr in SrF2 (684.5 and 685.0 eV) [14]. Kang et al. [9] have made the same conclusion based on the results of XPS and SIMS analysis. The XPS data show also that the decrease of CF4 content in CF4 / Ar mixture leads to the rapid decrease of the peak intensity while the spectra for as-deposited and Ar-etched samples show the absence of fluorine-
containing compounds on the surface. Therefore, assuming the intensity of XPS signal to be proportional to surface density of corresponding compound, our XPS data confirm the accumulation of reaction products on the surfaces etched in CF4 -rich plasmas. Fig. 3 illustrates the results of plasma diagnostics using Langmuir probes. It can be seen that the influence of CF4 /Ar mixing ratio both on electron temperature and electron density is not very significant. Actually, as the Ar content in CF4 /Ar plasma increases from 0 to 100%, electron temperature drops down from 6.5 to 5.9 eV while electron density increases in the range of 5.35 1010 to 8.80 1010 cm3 . Anyway, the results of Fig. 3 seem to be reasonable. An only weak change of electron temperature mentioned in experiments is caused by rather close values of ionization potentials for CF4 and Ar: 15.9 and 15.8 eV, respectively. In this situation, as the gas composition varies from pure CF4 to pure Ar, sufficient deformations of electron energy distribution function (EEDF) are not expected. In our opinion, the behavior of electron temperature may be accepted as the indirect proof that under the conditions were investigated CF4 dissociation degree is not too high. The reason is that ionization potential for F atoms (17.42 eV) sufficiently exceeds ionization potential for Ar. Accordingly, it is possible to expect that high dissociation degree of
Fig. 2. F (1p) XPS narrow scan spectra for the samples etched using various CF4 /Ar mixing ratios.
Fig. 3. Electron temperature and electron density determined by Langmuir probe measurements as a function of CF4 /Ar mixing ratio.
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CF4 molecules and thus high volume density of fluorine atoms will provide more sufficient deviations of electron temperature with the change of CF4 /Ar mixing ratio than it was found in our experiments. As for the electron density, the behavior of this parameter may be explained by the changes of total ionization rate as well as electron diffusion coefficient due to the corresponding changes of electron temperature. Choi et al. [15] reported similar experimental results for CF4 /Ar plasma in ICP system. Analyzing the results discussed above, it is possible to consider for two general explanations for a non-monotonic etch rate of BST films as a function of CF4 /Ar mixing ratio. The first is the non-monotonic changes of both volume densities and fluxes of active species resulted from the influence of plasma parameters on volume kinetics. The second is the simultaneous action of two etching mechanisms with monotonic, but opposite tendencies to change with increasing Ar mixing ratio. To check the first assumption, we used plasma modeling.
of F atoms due to a low neutral–neutral collision frequency under low-pressure conditions. The rate coefficient of heterogeneous decay krec was determined considering first order kinetics for the recombination and diffusion transport of atoms to reactor walls [10,21]: DF ; ð2Þ k2 where cF is the probability of heterogeneous recombination for fluorine atoms (cF 0:05 from [22]), DF the effective diffusion coefficient and k is the effective diffusion length. Effective diffusion coefficients are represented by the combination of free diffusion coefficient and inter-diffusion coefficient, calculated using the Chapman–Enscog equation [10,21] while the effective diffusion length is determined by the given reactor axial and radial sizes [16]. To estimate total volume density of positive and negative ions, we used a combination of balance kinetic equation for negative ions with plasma quasi-neutrality equation: krec ¼ cF
CF4 kda ne n0 ð1 dÞ kii nþ nF ;
ð3Þ
ne þ nF nþ ;
ð4Þ
3.2. Gas phase composition To analyze the influence of gas mixing ratios on volume densities and fluxes of plasma active species, we applied 0-dimensional (0-D) plasma modeling assuming the Maxwellian EEDF and quasi-stationary approximation for volume kinetics [10,16–18]. Considering [19,20], we also assume CF4 molecules to be a main source of fluorine atoms in plasma volume while the densities of unsaturated CFx ðx < 4Þ radicals are sufficiently lower than CF4 density. Accordingly, a balance equation of chemical kinetics determining volume density of fluorine atoms may be written as follows: CF4 kdis þ kdiCF4 ne n0 ð1 dÞ krec nF þ ð1=sres ÞnF ; ð1Þ where k is the rate coefficients for the processes specified in Table 1, ne the electron density, n0 the total density of neutral particles, d the fraction of Ar in gas mixture, sres is the residence time. Eq. (1) does not take into account volume recombination
where nþ is the total density of positive ions, kii the average rate coefficient of ion-ion recombination assuming close partial rate coefficients for each kind of positive ion (kii 1 107 cm3 /s from [23]). Eq. (3) assumes F to be a dominant type among negative ions [19] while the decay of negative ions is limited only by volume reactions of ion-ion recombination [10]. The last assumption is connected with the presence of a double electric layer and negative charges on the reactor walls covered by dielectric materials. Volume density of the Arþ ions inside nþ value was estimated as follows [10]: nArþ
Ar kion ne n0 d ; ðS=V ÞUB þ kii nF
ð5Þ
Ar where kion is the ionization rate coefficient for Ar atoms, S and UB the effective ion collection area and ion Bohm velocity for Arþ ions, V is the plasma volume. The peculiarities of the determination of both S and UB parameters for the elec-
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Table 1 Reaction set for simulation of volume kinetics in CF4 /Ar plasma Process
Eth (eV)
Rate coefficient
CF4 + e ! CF3 + F + e CF4 + e ! CFþ 3 + F + 2e CF4 + e ! CF3 + F Ar + e ! Arþ + 2e þ þ F + nþ (CFþ x , F , Ar ) ! n + F Arþ ! wall F ! wall
5.6 15.9 3.0 15.76 – – –
CF4 kdis ¼ 1.190 1016 Te1:309 exp()1.446 105 /Te )a kdiCF4 ¼ 1.159 1011 Te0:765 exp()1.993 105 /Te )a CF4 kda ¼ 2.369 108 Te0:489 exp() 5.876 104 /Te )a Ar kion ¼ 1.23 107 exp() 18.68/Te )b kii ¼ 1.0 107 (cm3 /s) ðS=V ÞUB (s1 ) cD=k2 (s1 )
a b
cm3 /s, Te in K. cm3 /s, Te in eV.
tronegative plasmas were described in details by Ashida and Lieberman [16] and by Malyshev and Donnelly [24]. In simplest case, assuming ion collection areas to be equal for all kinds of positive ions, the parameter ðS=V Þ may be approximated as plasma surface to volume ratio [25]. Fig. 4 illustrate the influence of gas mixing ratio on volume densities of neutral and charged particles in CF4 /Ar plasma. Calculations show that the increase of Ar mixing ratio causes a monotonic decrease of CF4 dissociation rate. The reason is that total dissociation rate coefficient (as the sum of partial coefficients for each process producing F atoms) and electron density have an opposite tendencies to change. That is why the multiplicaCF4 tion of ðkdis þ kdiCF4 Þne remains practically a constant (240–280 s1 ) while the dissociation rate changes proportionally to fraction of the Ar in gas
Fig. 4. Volume densities on neutral and charged particles evaluated from 0-D plasma model.
mixtures. Although the effective diffusion coefficient and thus a recombination rate coefficient for F atoms are sensitive to the change of mixture composition (krec ¼ 177–472 s1 for 2–98% Ar), both the dependences are monotonic. As a result, volume density of F atoms follows the behavior of CF4 dissociation rate. Olthoff and Wang [26] have reported similar results for CF4 /Ar plasma. As an indirect proof for the monotonic behavior of F atoms volume density, it is possible to involve the dependence of the PR etch rate on CF4 /Ar mixing ratio. It is well known that in fluorine-containing plasmas PR is dominantly etched chemically by fluorine atoms [27]. Accordingly, PR etch rate decreases monotonically during addition of Ar and follows the fluorine atoms volume density. For the charged particles, we have found that, even in CF4 -rich plasmas, total density of positive ions is close to electron density. Relative density of negative ions b ¼ n =ne characterizing plasma electronegativity does not exceed 2 for pure CF4 and decreases with increasing Ar mixing ratio. This result is in the frameworks of general tendency repeatedly mentioned in literature: at low pressures electronegative plasmas transform to moderate or low electronegative form [16,17]. Fig. 4 shows also total density of fluorine-conþ taining positive ions (i.e. CFþ x , F ) calculated as þ the difference between n and nArþ . Considering [26], we assume that a major component inside this value is CFþ 3 . The reasons are that CF3 molecules have higher volume density among CFx radicals (lower recombination and sticking probabilities) [23], lower ionization potential and higher ionization cross-section.
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The results on gas phase composition represented in Fig. 4 show that the etching behavior of BST thin films cannot be explained directly by variations of volume densities of active species. In other words, no single active species can provide a maximum on the etch rate as a function of the CF4 /Ar mixing ratio. It means that the reason may be connected with the surface kinetics through the simultaneous action of several kinds of active species.
To calculate the fluxes of neutral and charged particles to the surface, we used the methods described in [16–18]. The probability of chemical reaction cch may be approximated by the upper limit followed from the stoichiometry of reaction products (for example, cch ¼ 0:5 for Me–F2 ) [31]. Similar to [32,33], we assume that Ys and Yd are a function of square root of ion energy, based on the collision cascade approximation for sputtering process: 1=2
Ys ¼ AðE1=2 E0;s Þ; 3.3. Surface kinetics To investigate the relationships between composition of gas phase and surface kinetics, we used the phenomenological model based on theory of active surface sites [28–31]. The model was based on such assumptions as: (1) only F atoms are effective in chemical reaction; (2) only Arþ ions are effective in the sputtering process; (3) sputtering of the substrate is possible only when the incident ion impacts the clean surface; (4) all kinds of positive ions are effective for the ion-stimulated desorption of reaction products. Total etching rate obtained in experiments may be represented as the sum of partial rates of chemical reaction and physical sputtering: ER ¼ ð1 HÞcch SF CF þ ð1 HÞYs CArþ ;
ð6Þ
where C is the fluxes of species to the etched surface, Ys the sputtering yield, cch the probability of chemical interaction, SF the sticking probability of F atoms, H fraction of fluorinated surface. Assuming the contribution of spontaneous chemical etching (i.e. the contribution of thermal desorption of reaction products) to be negligible, stationary balance equation for active sites on the surface may be written as follows: X ð1 HÞcch SF CF ¼ H Yd;j Cþ;j ; ð7Þ where Yd;j and Cþ;j is the partial yields of ionstimulated desorption and partial fluxes for all kinds of positive ions existed in plasma. Combining Eqs. (6) and (7), the equation for etch rate may be obtained: P Yd;j Cþ;j ðcch SF CF þ Ys CArþ Þ P ER ¼ : ð8Þ cch SF CF þ Yd;j Cþ;j
1=2
Yd ¼ BðE1=2 E0;d Þ;
ð9Þ
where A and B are parameters, which depend on type of ion and sputtered material, E is the incident ion energy, which is the sum of ion acceleration energy in plasma sheath (approximately 6.2Te assuming CFþ 3 to be a dominant positive ion in CF4 -rich plasma) and the negative DC bias voltage, applied to the substrate while E0;s and E0;d are threshold energies for sputtering and ionstimulated desorption, respectively. The parameters A and E0;s for BST thin films sputtered by Arþ ions may be extracted from [34] (A ¼ 0:13, E0;s ¼ 30 eV). Parameters SF , B and E0;d are not known exactly for BST, but the reasonable ranges for their deviation may be evaluated using an indirect literature data for well-studied systems, for example for F–SiO2 and F–Si [29,31]. These ranges are 0.3–0.5, 0.1–1.0 and 4–10 eV for SF , B and E0;d , respectively. Additionally, it is possible to expect that Yd;Arþ > Yd;CFþx i.e. Arþ ions play a dominant role in ion-stimulated desorption. The reason is high sticking coefficients of CFþ x ions for metalcontaining surfaces. Then, these ions can be easily neutralized on the surface either forming polymer layer [23] or returning back to gas phase as neutral reactants. Although the assumptions mentioned above seem to be reasonable, we expect that the Eq. (8) works only in qualitative scale and thus, may be applied only for the analyses of relative etch rate behavior. It is evidently that SF and Yd depend on a large number of factors such as temperature of the surface, stoichiometry of the reaction products, type of incident ion and surface atom etc., which cannot be taken into account accurately. That is why we can use SF and Yd (i.e. the coefficient B and E0;d in Eq. (9)) only as the model parameters.
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Fig. 5 shows the behaviors of both chemical ð1 HÞcch SF CF and physical channels as a function of CF4 /Ar mixing ratio. As the Ar mixing ratio increases, the rate of physical sputtering increases monotonically and follows the behavior of Arþ volume density. The reason is that a small change in electron temperature escorted the transition from CF4 -rich to Ar-rich plasma does not influence sufficiently on both ion Bohm velocity and sputtering yield. At the same time, the rate of ion-assisted chemical reaction shows a maximum in the range of 45–55% Ar due to the competition between two processes: the decreasing both volume density and flux of chemically active species to the etched surface and the increasing fraction of free surface acceptable for chemical reaction. We have found also that the behavior of fraction of fluorinated surface H calculated using Eq. (7) is in good agreement with the change in F 1s XPS intensity. Finally, Fig. 6 demonstrates that total etch rate determined by Eqs. (6) or (8) keeps nonmonotonic behavior while the location of maximum depends also on quantitative correlation between chemical and physical pathways. It can be seen that the increase in efficiency of ion-stimulated desorption increases the rate of chemical reaction in CF4 -rich plasma, decreases the contribution of sputter etching and shifts maximum etch rate toward lower Ar mixing ratios.
Fig. 5. Influence of CF4 /Ar mixing ratio on partial rates of ion assisted chemical reaction and physical sputtering as predicted by the model of surface kinetics. Model parameters: (1) BArþ ¼ 0.1; (2) BArþ ¼ 0.2; (3) BArþ ¼ 0.3; (4) BArþ ¼ 0.5 while SF ¼ 0.3, E0;d ¼ 7 eV, BArþ =BCFþx ¼ 5.
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Fig. 6. Influence of CF4 /Ar mixing ratio on total etch rate as predicted by the model of surface kinetics. Model parameters are the same with Fig. 5.
It is important to note once more that the model were used cannot provide an exact quantitative agreement between measured and calculated etch rats in absolute scale due to simplifications in primary assumptions. Nevertheless, we can obtain a quantitative agreement in relative scale. Fig. 7 shows the comparison for experimental and modeling data with a normalization point corresponding to pure Ar plasma. Calculations show that, in best case (i.e. within any reasonable variations of all coefficients employed in Eq. (8)), the model gives an outstanding description for relative
Fig. 7. Comparison of relative behavior of BST etch rate obtained by experiment and modeling.
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behavior of BST etch rate in Ar-rich plasma, but systematically underestimates the etch rate in CF4 rich plasma. One of the reasons may be connected with a chemical activity of CFx radicals, which were not taken into account as reactants.
4. Conclusion In present work, we carried out an investigation of etching mechanisms for BST thin films in inductively coupled CF4 /Ar plasma. We have found that an increase of the Ar content in CF4 /Ar plasma leads to an increase in BST etch rate, which reaches a maximum value of 40 nm/min at 80% Ar. The XPS analysis indicated the accumulation of reaction products on the BST film surface in CF4 rich plasma. Langmuir probe measurements indicated weak influence of CF4 /Ar mixing ratio on both electron temperature and electron density. Calculations of gas phase composition using 0-D plasma model gave monotonic changes of both volume densities and fluxes for fluorine atoms and positive ions. The analysis of surface kinetics demonstrated the possibility of non-monotonic etch rate behavior in the system with monotonic changes of fluxes of both chemically and energetically active species. It was found that the reason for etch rate maximum is the concurrence of physical and chemical pathways in ion-assisted chemical reaction.
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