Chemical modeling of a high-density inductively-coupled plasma reactor containing silane

Surface & Coatings Technology 201 (2007) 8849 – 8853 www.elsevier.com/locate/surfcoat

Chemical modeling of a high-density inductively-coupled plasma reactor containing silane A.Y. Kovalgin ⁎, A. Boogaard, I. Brunets, J. Holleman, J. Schmitz MESA + Institute for Nanotechnology, Chair of Semiconductor Components, University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands Available online 1 May 2007

Abstract We carried out the modeling of chemical reactions in a silane-containing remote Inductively Coupled Plasma Enhanced Chemical Vapor Deposition (ICPECVD) system, intended for deposition of silicon, silicon oxide, and silicon nitride layers. The required electron densities and Electron Energy Distribution Functions (EEDF) were taken from our earlier Langmuir-probe measurements. The EEDF exhibited a fraction (0.5%) of fast electrons in the energy range between 20 and 40 eV, strongly deviating from Maxwell–Boltzmann (MB) distribution. We considered 16 electron impact dissociation/ionization reactions and 26 secondary reactions for homogeneous propagation of plasma species. We noticed a significant difference (orders of magnitude) between the concentrations of the species obtained using experimental EEDFs and MB energy distributions, pointing to the importance of the fast electron tail. For silicon oxide films, a qualitative agreement between the radical densities in plasma at different total pressures and the deposition rate was observed. © 2007 Elsevier B.V. All rights reserved. Keywords: ICP; Modeling; PECVD; Plasma; Silane

1. Introduction High-density inductively-coupled plasma enhanced chemical vapor deposition (HD ICPECVD) reactors are used nowadays for a variety of low-temperature materials processing applications [1– 3], including deposition of thin dielectric and semiconductor films, film etching and surface and materials modification. ICP reactors utilizing mixtures of silane with argon or hydrogen are used for deposition of amorphous or polycrystalline silicon. A low-temperature deposition of silicon oxide is often done from a SiH4–N2O mixture, whereas silicon (oxy)nitride is commonly deposited using SiH4–NH3, SiH4–N2, or (N2O)–SiH4–N2 gas sources. Modeling of ICP reactors is mainly done to obtain densities of certain particles, gas-distribution properties, and spatial plasma non-uniformities [4,5]. These are important parameters in process control and optimization. The experimental characterization of plasmas mostly involves mass-spectrometry, optical emission spectroscopy (OES), and Langmuir-probe measurements [6–11]. Literature also reports on modeling of chemical processes occurring in ⁎ Corresponding author. Tel.: +31 53 4892841. E-mail address: [email protected] (A.Y. Kovalgin). 0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2007.04.086

etching ICP reactors [12,13] as well as in IC depositing plasmas [14,15]. Chemical modeling will add to the understanding of physics and chemistry of deposition processes. In ICP deposition systems with silane (SiH4), both primary (i.e., electron-impact) and secondary (i.e., homogeneous) reactions in the plasma play an important role. Due to the complexity of chemical reactions both in the plasma and at the surface, the mechanisms underlying the film deposition are not yet fully understood and further knowledge is still required. Focusing on ICP reactors, in this work we will model chemical reactions in Ar–SiH4 plasmas. This is a first step towards the modeling of near-room temperature ICP-deposition processes of thin films in silane-containing systems (e.g., amorphous silicon, silicon oxide and silicon nitride films). 2. Model approach It is well-known that plasma chemistry depends to a large extent on the electron density and EEDF. The design-related features of a plasma reactor together with the plasma excitation method can make each type of a plasma reactor rather unique. This can lead to strong deviations of the EEDF from the widely used Maxwell–Boltzmann (MB) or Druyvesteyn distributions.

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Fig. 1. EEDFs obtained by Langmuir probe method for Ar plasma at several vertical probe positions [16]. The probe position is measured in mm from reactor top: 80 mm corresponds to the RF coil position and 240 mm to the wafer holder (chuck) position. Other conditions: ICP power of 300 W, total pressure of 1 Pa, 500 sccm of Ar flow. The symbols represent the measurements and the dotted line shows the Maxwell–Boltzmann distribution fitted to those measurements for kTe = 1.8 eV. EEDFs measured at different total pressures can be found in ref. [16] and [45].

In this work, we show the influence of the EEDF on the plasma chemistry. We demonstrate that the use of an inappropriate EEDF can cause strong disagreements between the measured kinetic behavior and the modeling. In our approach to modeling we used the experimentally measured EEDFs. As a first step, we carried out detailed measurements of EEDF in our ICP reactor for non-depositing sources such as pure Ar and N2 plasmas, as well as Ar–N2 and Ar–N2O mixtures with a Langmuir probe. As a second step, we verified the EEDFs for depositing plasmas with small additions of SiH4, using optical emission spectroscopy. Finally, we carried out chemical modeling of Ar-SiH4 plasmas using the experimentally obtained and verified EEDFs. A detailed description of the remote ICP reactor used in this study is given in [16]. Briefly, the ICP source (supplied by Alcatel Micro Machining Systems; 13.56 MHz, max. electric power of 2 kW) is placed on top of the diffusion chamber (also supplied by Alcatel). An extensive gas distribution system can supply gases to the deposition system. Argon was used as a carrier gas, the process pressure ranged from 0.68 to 12 Pa, while the argon flow was between 100 and 500 sccm. A flow of 10–100 sccm of nitrogen (N2), nitrous oxide (N2O) and Ar–SiH4 (2% SiH4 in argon) were added to the argon carrier gas to study their effect on the electron energy distribution and electron density of the plasma. For non-depositing plasmas, we measured electron densities and EEDFs by means of a Langmuir probe [16]. The Langmuir probe was introduced vertically from the top of the reactor. The EEDF of Ar plasmas could largely be described by the MB distribution function. However, it also contained a fraction (∼ 0.5%) of fast electrons in the energy range between 20 and 40 eV, strongly deviating from the MB distribution. It was noticed that the tail of fast electrons moved to higher energies as we measured more towards the chuck (see Fig. 1). This tail of fast electrons could be shifted to lower energies (Emax ∼ 20– 30 eV) when the pressure was increased up to 6 Pa. As to further

be shown in Sections 3 and 4, such fast electrons can strongly influence the plasma composition. As it is not possible to carry out Langmuir-probe measurements for plasmas with silane due to the formation of deposits on the probe, we performed OES measurements in plasmas with silane in order to monitor certain particles (e.g., Si and SiH radicals) and obtain relative mean electron temperatures (kTe) [17]. Combining both methods, we demonstrated that EEDFs, as measured by the Langmuir probe in Ar/N2 and Ar/N2O plasmas, resemble EEDFs in plasmas with small additions of silane, provided that (a) precursor fractions are low (SiH4 ≤ 0.8% and N2O ≤ 15% of total pressure), and (b) total pressure does not exceed 8 Pa. As such, the measured EEDFs without silane were used as input for chemical modeling and optimization of deposition processes in plasmas containing silane. To model electron impact reactions, one should know the reaction rate constants. The rate constants ki were calculated from the corresponding electron impact cross sections σi (E) using the relationship rffiffiffiffiffiffi Z l pffiffiffiffi 2 E d f ð E Þd ri ð E ÞdE d ki ¼ me 0 where me is the electron mass and f(E) is the electron energy distribution function [18]. 3. Primary and secondary reactions As a first approach to modeling, we considered 7 electron impact dissociation-, 13 electron impact ionization-, and 22 homogeneous secondary reactions listed in Tables 1 and 2. We omitted the high-pressure regime (normally not suitable for deposition of high-quality materials for microelectronics applications) and the gas-phase nucleation resulting in formation of polysilanes. We calculated the radical densities in plasma as a function of the reaction time, assuming a certain EEDF. The initial concentration of SiH4 in the volume was given by the gas flows and total pressure. The initial density of electrons was assumed equal to that without silane (as measured by the Langmuir probe). The initial concentrations of the other species listed in Tables 1 and 2 were zero. The system of non-linear differential equations, dCi/dt, deduced from the reactions listed in Tables 1 and 2, has been resolved as a function of the reaction time. The densities of silane, free radical species, ions, electrons, atomic and molecular hydrogen, and disilane were obtained. As a second approach to modeling, we will consider fluid dynamics and calculate all the local densities in the given ICP reactor. However, in this paper we only focus on the influence of EEDF on plasma chemistry (expressed in terms of different reaction rate constants for a given electron-impact reaction) and demonstrate the influence of the secondary reactions on actual radical densities in plasma. 4. Radical and ion concentration Analyzing the reaction rate constants shown in Tables 1 and 2, three important conclusions can be made. First, the rate

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Table 1 Calculated rates for primary electron-impact dissociation and ionization reactions at room temperature. Experimental EEDF is measured at 500 sccm of Ar flow, 1 Pa of total pressure, and electric power of 300 W No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Reaction e + SiH4 → SiH2 + H2 + e →SiH3 + H + e →Si + 2H2 + e →SiH + H2 + H + e →Si⁎ + 2H2 + e →SiH⁎ + H2 + H + e e + H2 → 2H + e e + SiH4 → SiH+2 + H2 + 2e →SiH+3 + H + 2e →Si+ + 2H2 + 2e →SiH+ + H2 + H + 2e →SiH2 + H+2 + 2e →SiH3 + H+ + 2e e + H2 → H+2 + 2e e + H2 → H+ + H+ 2e e + H → H+ + 2e

E1) a eV

Ref.2)

2.2 4.0 4.2 5.7 9.5 8.9 4.5 11.6 12.2 13.6 15.1 24.3 ∼ 24 15.4 ∼ 24 13.6

[19–21] [19–21] [19–21] [19–21] [19–21] [19–21] [19–21] [22] [22] [22] [22] [22] [22] [23] [23] [24]

Rate constants for different EEDFs3),cm3/s 240 mm

80 mm

1.8 eV

1.9 × 10− 8 1.2 × 10− 8 1.8 × 10− 9 2.5 × 10− 9 1.4 × 10− 9 2.2 × 10− 9 3.3 × 10− 9 1.3 × 10− 8 9.1 × 10− 9 2.5 × 10− 9 3.2 × 10− 9 8.7 × 10− 11 9.9 × 10− 10 4.3 × 10− 9 1.5 × 10− 10 2.6 × 10− 9

1.5 × 10− 9 6.6 × 10− 10 8.1 × 10− 11 1.1 × 10− 10 5.6 × 10− 11 9.4 × 10− 10 1.4 × 10− 10 5.5 × 10− 10 4.0 × 10− 10 9.2 × 10− 11 1.3 × 10− 10 1.8 × 10− 12 2.4 × 10− 11 1.7 × 10− 10 2.8 × 10− 12 9.7 × 10− 11

4.0 × 10− 9 1.5 × 10− 9 6.6 × 10− 11 4.3 × 10− 11 7.1 × 10− 12 1.0 × 10− 11 8.9 × 10− 11 9.2 × 10− 11 5.9 × 10− 11 3.9 × 10− 12 3.4 × 10− 12 2.1 × 10− 15 1.9 × 10− 14 4.1 × 10− 12 3.9 × 10− 15 8.4 × 10− 12

1)

Ea is the appearance energy. References contain the appearance energies and reaction cross sections σ(E) at room temperature. 3) Column “240 mm” corresponds to the reaction rate constant calculated using the experimental EEDF measured at 240 mm (see Fig. 1 and ref. [16]); column “80 mm” corresponds to the rate constant calculated using the experimental EEDF measured at 80 mm; the “1.8-eV” column shows the rate constants calculated assuming Maxwell–Boltzmann distribution for kTe = 1.8 eV. 2)

constants of the electron-impact reactions increase with increasing electron energy. The highest fraction of high-energy electrons corresponds to the column in Table 1 marked as “240 mm” [16], whereas the lowest fraction is given by the MB distribution (see the “1.8 eV” column). Second, the rate constants of the homogeneous reactions listed in Table 2 are comparable to those of the electron-impact reactions (Table 1). From this, one can already expect a significant influence of the homogeneous secondary reactions on plasma chemistry. Third, the rate constants of the homogeneous reactions involving SiHx radicals are rather high. From this, a depletion of the plasma from SiHx radicals due to the secondary reactions can be expected. Although some reactions involving SiHx radicals result in a formation of disilane (Si2H6), the electron-impact dissociation of Si2H6 leads to a large extent to the appearance of Si2Hy (y = 5–1) species [14]. The possible homogeneous formation of particles (to be considered in our future approach to modeling) can further increase the plasma depletion from SiHx radicals. For plasmas with silane, silicon- or hydrogen-containing species play an important role for the deposition process. It is generally accepted that for PECVD of high-quality a-Si:H films, SiH3 radicals formed in plasma are needed for growing smooth films [33–36]. These radicals are desired as the species with longest lifetime providing high surface migration. SiH3 radicals have a smaller sticking probability (0.28 below 400 °C according to [37]) and can therefore experience several surface sites before reacting [38,39]. This would result in a conformal coverage associated with chemical vapor deposition regime [40]. In contrast to this, any SiH2 species, arriving at the a-Si:H surface, have a sticking coefficient near 1 and can react on contact. Similar to that, the coefficients of SiH and Si radicals

are close to unity on an a-Si:H surface even at room temperature [41,42]. The dominance of SiH2, SiH, and Si species in plasma under certain conditions would result in a columnar microstructure associated with physical vapor deposition [40]. Table 2 Summary on secondary (homogeneous) gas-phase reactions at room temperature No. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 a

Reaction SiH + H2 → SiH3 SiH2 + SiH4 → Si2H6 SiH2 + H2 → SiH4 SiH2 + H → SiH3 SiH2 + H → SiH + H2 SiH3 + SiH3 → SiH2 + SiH4 SiH3 + H → SiH4 SiH3 + H → SiH2 + H2 SiH3 + SiH3 → Si2H6 SiH4 + H → SiH3 + H2 SiH4 + Si → SiH2 + SiH2 SiH4 + SiH → Si2H5 SiH4 + SiH2 → Si2H6 Si2H6 + H → SiH4 + SiH3 Si2H6 + H → Si2H5 + H2 Si2H6 + SiH3 → Si2H5 + SiH4 Si2H5 + H → Si2H6 Si2H5 + SiH3 → Si2H6 + SiH2 SiH+ + e → Si + H SiH+2 + e → SiH + H SiH+3 + e → Si + H2 + H H+2 + e → H + H SiH2 + e → SiH+2 + 2e SiH3 + e → SiH+3 + 2e SiH + e → SiH+ + 2e Si + e → Si+ + 2e Evaluated at 3 Torr.

Rate constant, cm3/s − 12

2.0 × 10 1.1 × 10− 10 2.5 × 10− 13 1.1 × 10− 12 2.0 × 10− 13 1.5 × 10− 10 5.0 × 10− 10 2.0 × 10− 11 3.0 × 10− 10 4.3 × 10− 13 5.3 × 10− 13 3.4 × 10− 10 1.1 × 10− 10 1.2 × 10− 12 1.2 × 10− 12 9.6 × 10− 14 5.0 × 10− 10 1.5 × 10− 10 1.7 × 10− 7 1.7 × 10− 7 1.7 × 10− 7 9.2 × 10− 7 1.2 × 10− 8 7.0 × 10− 9 3.2 × 10− 8 1.1 × 10− 7

Ref. [25] [26] a [26] a [25] [26] [26,27] [27] [26] [27] [27] [25] [26] a [26] a [26] [26] [26] [27] [26] [25] [25] [25] [28] [29] [30] [31] [32]

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The favorable participation of SiH3 radicals in PECVD of silicon oxide, amorphous silicon and silicon nitride films is also reported in [8–11,43]. SiH3 radicals were detected by means of threshold ionization mass spectrometry [8,10] and cavity ring down spectroscopy [9]. A high density of SiH3 radicals was reported, whereas Si and SiH species had much lower density in plasma [10]. It was shown that in Ar–H2–SiH4 plasmas, highH2 flows resulted in a dominant formation of SiH3 radicals. At low-H2 flows, a significant amount of very reactive SiHx (x ≤ 2) radicals was detected [8]. The latter could indicate the importance of the secondary reactions in plasma between hydrogen and the other reactive species (see Table 2). By cavity ring down spectroscopy, it was shown that Si and SiH species had a much lower density in the downstream plasma and that those radicals were therefore of minor importance for the aSiNx:H deposition process. Modeling Ar–SiH4 plasmas by only assuming reactions 1– 16 (see Table 1, rate constants for the EEDF at 240 mm) and reactions 18, 25, 26, 30 and 31, involving the formation of disilane (Table 2), results in a saturated concentration of SiH2 radicals around 3 × 1010 cm−3, for the reaction time of 5 ms and plasma conditions indicated in the caption to Fig. 2. This is higher compared to the density of SiH3 species, and 4–5 times higher with respect to SiH and Si species. The assumption of a MB distribution with kTe of 1.8 eV, for the same 21 reactions, reaction time, and plasma conditions, would result in a decreased density of SiH2 radicals down to ∼ 1 × 1010 cm−3 and a decreased density of SiH and Si species in the order of 10 9 cm −3 . The relative radical densities (for both the experimental and MB distributions) were in a qualitative agreement with [44], where a photolysis of SiH4 molecules was studied. It was measured that silane mainly dissociated on SiH2 (83%) and SiH3 (17%) radicals, whereas the concentrations of SiH and Si radicals were about 3%. However, as the experimental plasma monitoring carried out in [8–10] showed a dominance of SiH3 radicals instead of SiH2 species, a strong influence of secondary gas-phase reactions on

Fig. 3. Modeled radical densities (reaction time of 1.5 ms) versus total pressure. Input data for modeling: experimental EEDFs were measured at 240 mm under 500 sccm of Ar flow and electric power of 300 W, and at all the total pressures indicated in this figure; initial electron concentration was 6.3 × 109, 2.2 × 1010, or 2.6 × 1010 cm− 3 for a total pressure of 1, 2, or 6 Pa, respectively; SiH4–Ar mass flow (2% SiH4 in Ar) was 10 sccm. It is important to note that the use of the MB distribution for modeling did not show the relative increase of SiH3 radicals at 6 Pa.

plasma composition should be assumed. Taking the rest of the reactions from Table 2 into account (42 reactions in total) caused a tremendous change of the plasma composition. The results depicted in Fig. 2 clearly indicate that SiH3 radicals can have the highest density in plasma, exceeding the densities of the other SiHx (x ≤ 2) species after already a few milliseconds of the reaction time. It is calculated that already after 4 ms of the reaction time, the difference between the radical concentrations, obtained using the experimental and MB distributions, is more than one order of magnitude. In Fig. 3, one can see that the radical concentrations decrease with increasing total pressure. In principle, the opposite behavior can be expected because the electron and silane concentrations both increase. However, due to the secondary reactions, the actual radical densities appear to be lower at a higher pressure. We deposited silicon dioxide to verify this theoretical result [45]. The measured deposition rate of SiO2 layers, obtained in our ICP reactor using a mixture of SiH4, Ar, and N2O, indeed decreased from 4.7 nm/min at a pressure of 2 Pa down to 3.5 nm/min at a pressure of 6 Pa. The mentioned in [45] influence of total pressure on the electrical properties of SiO2 layers (i.e., better properties at 6 Pa compared to those at 1 and 2 Pa) can be explained by the increased relative fraction of SiH3 radicals at 6 Pa (see Fig. 3; it is important to note that the use of the MB distribution for modeling does not show this increase). This results in a higher impact of SiH3 radicals on the film formation at 6 Pa and in a better electrical quality of the layers. 5. Conclusions

Fig. 2. Modeled radical densities versus reaction time. Input data for modeling: experimental EEDF was measured at 240 mm under 500 sccm of Ar flow, 1 Pa of total pressure, and electric power of 300 W (see Fig. 1); initial electron concentration was 6.3 × 109 cm−3 (Langmuir probe measurements); SiH4–Ar mass flow (2% SiH4 in Ar) was 10 sccm.

In this paper, we presented our first results on modeling of chemical reactions in our ICP reactor. We demonstrated the influence of electron energy distribution function on electronimpact reactions occurring in Ar–SiH4 plasma. The use of an

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inappropriate EEDF (e.g., MB) caused significant disagreements between measured kinetic behavior and modeling. We showed the importance of the secondary homogeneous reactions in such plasmas. For an insufficient number of the secondary reactions, the radical densities strongly deviating from the expected values can be calculated. As an example, the modeled radical densities decreased with increasing the total pressure. This was in agreement with the deposition rate measured for SiO2 films. Acknowledgments The authors would like to thank Alcatel for supplying the ICP source, deposition chamber and Langmuir probe. This work (project number STW-TEL 6358) is supported by the Dutch Technology Foundation (STW). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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