H2 Mixtures

Jun 24, 2014 - Production of B Atoms and BH Radicals from B2H6/He/H2 Mixtures Activated on Heated W Wires. Hironobu Umemoto*†‡, Taijiro Kanemitsuâ...
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Production of B Atoms and BH Radicals from B2H6/He/H2 Mixtures Activated on Heated W Wires Hironobu Umemoto,*,†,‡ Taijiro Kanemitsu,†,‡ and Akihito Tanaka§ †

Graduate School of Engineering and §Faculty of Engineering, Shizuoka University, Johoku, Naka, Hamamatsu, Shizuoka 432-8561, Japan ‡ Japan Science and Technology Agency, CREST, Sanbancho, Chiyoda, Tokyo 102-0075, Japan ABSTRACT: B atoms and BH radicals could be identified by laser-induced fluorescence when B2H6/He/H2 mixtures were activated on heated tungsten wires. The densities of these radical species increased not only with the wire temperature but also with the partial pressure of H2. The densities in the presence of 0.026 Pa of B2H6 and 2.6 Pa of H2 were on the order of 1011 cm−3 both for B and BH when the wire temperature was 2000 K. Densities in the absence of a H2 flow were much smaller, suggesting that the direct production of these species on wire surfaces is minor. B and BH must be produced in the H atom shifting reactions, BHx + H → BHx−1 + H2 (x = 1−3), in the gas phase, while H atoms are produced from H2 on wire surfaces. The B atom density increased monotonously with the H atom density, while the BH density showed saturation. These tendencies could be reproduced by simple modeling based on ab initio potential energy calculations and the transition-state theoretical calculations of the rate constants. The absolute densities could also be reproduced within a factor of 2.5. Mankelevich et al.11 However, neither of these studies detected B atoms in the absence of a H2 flow. It is important to examine if B atoms are produced in the absence of a H2 flow and also to measure the absolute densities of these species. In the present study, the absolute densities of B and H atoms as well as BH radicals were measured by laser spectroscopic techniques, in both B2H6/He and B2H6/He/H2 systems. A mass spectrometer was used to measure the decomposition efficiencies of B2H6 under various conditions. The production mechanisms of B and BH are discussed on the basis of the energetics evaluated by ab initio calculations. The rate constants for the H atom shifting reactions were calculated by conventional transition-state theory. Some experiments also were carried out in the B2H6/He/D2 system.

1. INTRODUCTION Recently, we have reported on the decomposition mechanism of PH3, one of the most widely used dopant gases in the semiconductor industry, on heated metal wire surfaces.1−3 It has been shown that PH3 can be decomposed efficiently and that the major products on the wire surfaces are P and H atoms. PH and PH2 radicals also could be identified, but their densities in the absence of a H2 flow were much smaller than that of P atoms. These species are produced in secondary processes in the gas phase. Similar results have been reported in the decomposition of SiH4, and it has been shown that Si is one of the major species produced directly on wire sufaces.4−8 In contrast, the main products in the decomposition of NH3 are NH2 and H, and the production of N atoms is minor.9 If these differences can be ascribed to the difference in bond energies, because the bond energy of H−BH2 is comparable to that of H−NH2, the direct production of B atoms and BH radicals from B2H6, another typical dopant material, on hot wire surfaces should be minor. On the other hand, if B atoms are produced efficiently on wire surfaces, we may conclude that bond energies are not important in the decomposition kinetics of hydride species on hot metal surfaces. The gas-phase chemistry occurring in hot-wire-activated B2H6/H2 and B2H6/CH4/H2 mixtures has been studied by Comerford et al.10 They measured the spatial distributions of B and H atoms using a resonance-enhanced multiphoton ionization technique and concluded that H atom shifting reactions, BHx + H ↔ BHx−1 + H2 (x = 1−3), play key roles. This conclusion has been supported by the modeling studies of © 2014 American Chemical Society

2. EXPERIMENTAL METHODS The experimental procedure and apparatus were similar to those described elsewhere.1−3,12−15 Because B2H6 is toxic and explosive, a safe gas handling system supplied by Tomoe Shokai Co. Ltd. was employed. B2H6 diluted with He (or a mixture with H2) was decomposed in a cylindrical chamber evacuated by a turbomolecular pump (Osaka Vacuum, TG220FCAB). Gas flow rates were controlled by mass flow controllers (Horiba STEC, SEC-40M). A coiled tungsten wire (Nilaco, 30 cm in length and 0.39 mm in diameter, 99.95%) was resistively heated Received: May 10, 2014 Revised: June 23, 2014 Published: June 24, 2014 5156

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indirect nature of this procedure, uncertainty by a factor of 2 may not be avoidable in the present absolute density evaluation. In the detection of H atoms, vacuum-ultraviolet (VUV) laser absorption, VUV-LIF, and two-photon LIF techniques were employed.18 With VUV laser absorption, it is possible to determine the absolute densities, while VUV-LIF is more sensitive. Two-photon LIF is useful when the H atom density is more than 1012 cm−3. In VUV absorption and VUV-LIF, the laser wavelength was tuned to that of Lyman-α, 121.6 nm. A dye laser (Sirah, CSTR-LG-18) was pumped with a Nd:YAG laser (Quanta-Ray, LAB-170). The output at 729.6 nm was doubled in frequency by a BBO crystal and then tripled by a mixture of Kr and Ar. The resulting VUV light was collimated with a 100 mm focal length MgF2 lens. In the absorption measurements, the intensity after passing through the chamber was measured by monitoring the NO+ ion current. In the VUVLIF measurements, the induced fluorescence was detected with a solar-blind photomultiplier tube (Hamamatsu Photonics, R6835) through a MgF2 collimating lens and an interference filter. In two-photon LIF, the frequency of the dye laser output at 615.3 nm was tripled using two BBO crystals and a polarizer. The resulting radiation at 205.1 nm was focused with a 150 mm focal length lens. Balmer-α fluorescence at 656.3 nm was detected with a photomultiplier tube through an interference filter. To detect BH radicals, we employed a LIF technique at around 433 nm, which corresponds to the diagonal bands of the A 1Π−X 1Σ+ transition. A Nd:YAG laser-pumped dye laser (Sirah, CBST-LG-24) was used as a light source. The induced fluorescence was detected with a photomultiplier tube through dichroic filters (Sigma Koki, DIF-BLE) and recorded with a digital oscilloscope. A boxcar averager-gated integrator system was used when the spectra were recorded. The absolute density of BH(X 1Σ+, ν″ = 0, J″ = 2) was evaluated with a procedure similar to that for B atoms. This density can be converted to total density using the rotational temperature evaluated from the LIF spectrum. H2 (Japan Air Gases, 99.999%), D2 (Sumitomo Seika, isotopic purity 99.5%), B2H6 (Takachiho Kako, diluted with He to 2.0%), He (Japan Air Gases, 99.999%), Kr (Nihon Sanso, 99.995%), Ar (Japan Air Gases, 99.999%), and NO (Nihon Sanso, 99%) were used from cylinders without further purification. Boron, used in the mass spectrometric measurements, was obtained from Aldrich, and the purity was 99.7%.

using a DC power supply (Takasago, EX-1125H2). The wire temperature was measured with a two-wavelength thermometer (LumaSense Technologies, ISR 12-LO). The wire temperature could not be evaluated from the electric resistivity because the W wires were borodized when heated in the presence of B2H6 and their resistivity increased with borodization. The following measurements were carried out using borodized wires unless otherwise stated. Borodization was carried out by heating the wires in the presence of a B2H6/He/H2 flow at least for 1 h. Mass spectrometric analyses were carried out to measure the B2H6 and H2 densities. A quadrupole mass spectrometer (Anelva, M-QA200TS) was attached to the chamber through a sampling hole. The electron impact energy was 70 eV. The mass spectrometer was differentially pumped down to 5 × 10−4 Pa with another turbo molecular pump (Osaka Vacuum, TG350FCWB). It is possible to evaluate the decomposition efficiencies of B2H6 at various wire temperatures by measuring the peak heights of B2H2+ fragment ions. The absolute densities of H2 were evaluated by comparing the H2+ mass signal with that when a known amount of H2/He was flown. B atom densities were evaluated using a laser-induced fluorescence (LIF) technique. The distance between the wire and the laser beam detection zone was 9 cm. Laser absorption was also tried, but the B atom density was too low to be measured. B atoms can be detected at 249.677 and 249.773 nm, which correspond to the transitions between 2s23s 2S1/2 and the two spin−orbit ground states, 2s22p 2P1/2 and 2P3/2. The latter state was mainly monitored because the signal was more intense. The light source was a dye laser (Sirah, CBST-LG-24) pumped with a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser (Quanta-Ray, PRO-190). The output was doubled in frequency with a β-BaB2O4 (BBO) crystal. The induced fluorescence was detected with a photomultiplier tube (Hamamatsu Photonics, R212UH) through a collimating lens and an interference filter. The photomultiplier signals were processed with a boxcar averager-gated integrator system (Stanford Research Systems, SR240/SR250/SR280) or a digital oscilloscope (LeCroy, HDO4032 or 6051A). The absolute density was estimated by comparing the LIF intensity under saturated conditions with the intensity of Rayleigh scattering caused by Ar. This procedure was similar to those employed for the absolute density measurements of other radical species, such as Si atoms.1,5,9,12,13 The differential cross section for Rayleigh scattering by Ar was calculated to be 1.31 × 10−26 cm2 from the wavelength, 249.8 nm, and the refractive index, 1.00031. Under saturated conditions, the population ratio of the upper 2s23s 2S1/2 state to that of the lower 2s22p 2P3/2 state is 1/4 when the excitation laser is linearly polarized.16 When the 2s22p 2P3/2 → 2s23s 2S1/2 → 2s22p 2P3/2 transition cycle is considered, the emission from the 2s23s 2S1/2 state is isotropic because the corresponding depolarization coefficient is zero.16 Correction for the quenching of the upper 2s23s 2S1/2 state was not necessary because of its short radiative lifetime, 4.0 ns.17 The [2P1/2]/[2P3/2] population ratio evaluated from the LIF spectrum agreed with that of the statistical weight, 1/2. This is reasonable because the energy splitting is only 15.3 cm−1. Unfortunately, in contrast to the situation in the detection of Si atoms,5 the present system cannot be regarded as an ideal twolevel one. The spontaneous radiation to 2s22p 2P1/2 during the laser pulse may overpopulate the 2s22p 2P1/2 state and lead to an underestimation of the absolute density of 2s22p 2P3/2. This effect was not taken into account. Besides this, because of the

3. EXPERIMENTAL RESULTS 3.1. Mass Spectrometric Determination of Decomposition Efficiency. Figure 1 shows the wire temperature dependence of the B2H6 and H2 densities measured in the presence and in the absence of a H2 flow. The B2H6 density begins to decrease when the W wire temperature is higher than 1000 K, but the temperature dependence is less remarkable over 1800 K. When the flow rate and the total pressure of B2H6/He are 10 sccm (1 sccm = 6.9 × 10−7 mol s−1) and 1.9 Pa, the decomposition efficiency of B2H6 over 2000 K is 72%. This decomposition efficiency, in the absence of a H2 flow, depends little on the flow rate as long as the residence time of gas molecules in the chamber is kept constant. The H2 density at high wire temperatures in the B2H6/He system is consistent with the complete decomposition mechanism, B2H6 → 2B + 3H2. However, the deposition of BHx (x ≥ 1) besides B atoms on chamber walls may not be excluded because the evacuation rate of H2 is slower than that of B2H6 at low pressures. 5157

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In Figure 3, the B atom density is plotted against the reciprocal of the W wire temperature. The B2H6/He flow rate

Figure 1. Dependence of B2H6 and H2 densities on the W wire temperature. Closed circles and triangles represent the B2H6 and H2 densities, respectively, in the absence of a H2 flow. The B2H6/He flow rate was 10 sccm, and the total pressure was 1.9 Pa. Open squares represent the B2H6 density in the presence of a H2 flow at 20 sccm. The B2H6/He flow rate was 10 sccm, and the total pressure was 3.9 Pa.

Figure 3. B atom densities as a function of the reciprocal of the W wire temperature. The B2H6/He flow rate was 10 sccm. The H2 flow rates were 30, 20, and 10 sccm from top to bottom. The total pressures were 4.7, 3.9, and 2.7 Pa.

The decrease in the B2H6 density could also be observed in the presence of a H2 flow. The efficiency over 2000 K was 55% when the H2 flow rate was 20 sccm and the total pressure was 3.9 Pa. This decrease in the B2H6 density is in contrast to the decomposition of PH3. In PH3 systems, the decomposition efficiency is large in the absence of a H2 flow but very small when it is present. This difference between B2H6 and PH3 can be explained by the small reactivity of H atoms with B compounds deposited on chamber walls. PH3 can be reproduced on chamber walls from H atoms and the deposited compounds. It has been shown that PH3 is produced efficiently in the reactions between H atoms and red phosphorus.15 On the other hand, no B2H6 signal could be observed mass spectrometrically when H2 was decomposed in the presence of solid boron. B2H5D and other D-substituted isotopologues were not identified in the B2H6/He/D2 system either. This is again in contrast to the PH3/He/D2 system, where PH2D and other isotopologues could be identified, suggesting the absence of a reaction between H atoms and the deposited B compounds. The minor change observed in the decomposition efficiency of B2H6 when H2 was introduced can be ascribed to the difference in the residence time of the material gas. 3.2. Detection of B Atoms. In B2H6/He/H2 systems, it was easy to detect B atoms when the W wire temperature was higher than 1900 K. On the other hand, in the absence of a H2 flow, the B atom density was very small. Figure 2 illustrates the LIF spectrum observed in the presence of a H2 flow.

was fixed at 10 sccm, while the H2 flow rate was changed between 10 and 30 sccm. Comerford et al. have reported that the B atom density decreases against the Ta or Re wire temperature over 2400 K and discussed the possibility of B atom accommodation into the wire.10 No such decrease was observed in the present W systems, but the B atom density saturated at high wire temperatures, which can also be explained by accommodation. It was possible to observe B atom signals even in the absence of a B2H6/He flow, that is, in pure He or H2 systems, when aged wires were used. This can be explained by the ejection of accommodated B atoms in the wires. Similar phenomena were reported by Comerford et al.10 In their systems, the B atom signal decreased rapidly with time when the B2H6 flow was switched off. In our systems, the decrease after the flow was broken was rather slow. It was possible to detect B atoms even after 1 h. In Figure 3, we plot the differences in B atom densities measured in the presence and in the absence of a B2H6/He flow. In the measurements without a B2H6/He flow, the total pressure was kept the same as that in the presence by introducing He. Similar results were obtained when the B2H6/He flow rate was 5 sccm. The apparent activation energy showed minor dependence on the flow rates of B2H6/He or H2; below 2050 K, it was calculated to be ∼450 kJ mol−1. This value is much larger than that observed in the production of P atoms from PH3 in the similar temperature range, ∼220 kJ mol−1,1 or for H atoms in the B2H6/He/H2 systems, ∼200 kJ mol−1, but it is comparable to that obtained by Comerford et al. for the production of B atoms from B2H6 on borodized Ta below 2150 K, 405 kJ mol−1.10 It should be noted that B atoms could not be detected when a new wire was heated in the presence of H2. This shows that the B compounds deposited on chamber walls have a minor effect on the production of B atoms. This is consistent with the result of mass spectrometric measurements that the B2H6 density decreases with wire temperature in the presence of a H2 flow. The B atom density increased almost linearly against the B2H6/He flow rate in the presence of an excess amount of H2, as is shown in Figure 4. This result is similar to that obtained by Comerford et al. for Ta.10 In such flow rate dependence measurements, the total pressure was kept constant by

Figure 2. LIF spectrum of B atoms. The flow rates of B2H6/He and H2 were 5 and 20 sccm, respectively. The W wire temperature was 2050 K, while the total pressure was 3.1 Pa. 5158

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Figure 4. B atom density as a function of B2H6/He flow rate. The H2 flow rate was 20 sccm, while total pressure was kept at 3.9 Pa by introducing He. The W wire temperature was 2050 K.

Figure 6. H atom density as a function of the reciprocal of the W wire temperature measured by VUV laser absorption (open circle) and twophoton LIF (closed circle). The flow rates of B2H6/He and H2 were 5 and 20 sccm, respectively. The total pressure was 3.1 Pa.

introducing He to keep the diffusion rate constant. Because the evacuation rate was fixed, the B2H6 partial pressure must almost be proportional to the flow rate. Figure 5 shows the H2 flow

mol−1.14,18−20 The dissociation of H2 on borodized W may be different from that on clean surfaces. The minor B2H6/He flow rate dependence of the H atom density in the presence of a H2 flow is in contrast to the results observed in PH3/He/H2 and SiH4/H2 systems. In these systems, the H atom density decreases with an increase in the flow rate of PH3/He or SiH4.1,5 These decreases have been attributed to the consumption of H atoms in the etching processes of deposited species on chamber walls. In B2H6/He/ H2 systems, such etching processes must be minor, as discussed in sections 3.1 and 3.2. As will be discussed in section 4.1, H atoms must be consumed in the gas-phase reactions with BHx, but H atoms may also be reproduced from H2 formed in these reactions. In B2H6/He/H2 systems, the H atom density increased with an increase in the H2 flow rate. Figure 7

Figure 5. B atom density as a function of H2 flow rate. The B2H6/He flow rate was 10 sccm, while total pressure was kept at 3.9 Pa by introducing He. The W wire temperature was 2050 K. The dashed line represents the calculated value.

rate dependence at 2050 K. The B atom density increased with the increase in the H2 flow rate, which should be proportional to the partial pressure, but the dependence was not linear. This nonlinear dependence will be discussed in section 4.3. As has been mentioned, the B atom density in the absence of a H2 flow is very small. 3.3. Detection of H Atoms. The H atom density increased with increases in the wire temperature and the H2 flow rate but showed minor dependence on the B2H6/He flow rate in the presence of an excess amount of H2. H atoms also could be detected, with a VUV-LIF technique, in the absence of a H2 flow, but the density was 1 order of magnitude smaller than the one in its presence. Although minor, H atoms may be produced directly on wire surfaces by reactions such as B2H6 → B2H5 + H and B2H6 → 2BH3 followed by BH3 → BH2 + H. Once H atoms are produced, H2 may be produced in H shifting reactions, BHx + H → BHx−1 + H2, which will be discussed in section 4.1. H atoms may also be reproduced from H2 thus produced. In Figure 6, the H atom density in a B2H6/He/H2 system is plotted against the reciprocal of the W wire temperature. This plot is almost linear, and the activation energy for the production of H atoms is calculated to be 200 ± 3 kJ mol−1. The error limit is the standard deviation. This activation energy is a little smaller than that in pure H2 systems, 210−239 kJ

Figure 7. H atom density as a function of H2 flow rate. The B2H6/He flow rate was 10 sccm, while the total pressure was kept at 3.9 Pa by introducing He. The W wire temperature was 2050 K.

shows the results obtained with a two-photon LIF technique at 2050 K. This dependence is not linear and resembles that of the B atom density shown in Figure 5. Similar results were obtained at 1600 K when an absorption technique was employed. 3.4. Detection of BH Radicals. Figure 8 shows the LIF spectrum of the A 1Π−X 1Σ+ transition of BH recorded in the presence of 10 sccm of B2H6/He and 20 sccm of H2, under the conditions in which the signal intensity was proportional to laser intensity. The total pressure was 3.9 Pa, and the wire temperature was 2050 K. The wavelength dependence of the laser intensity is corrected in this figure. Besides the (0,0) band, the (1,1) band could be observed between 434 and 436 nm. 5159

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Figure 8. LIF spectrum of BH(X 1Σ+, ν″=0,1). The flow rates of B2H6/He and H2 were 10 and 20 sccm, respectively. The W wire temperature was 2050 K, while the total pressure was 3.9 Pa.

Figure 10. BH radical density as a function of H2 flow rate. The B2H6/ He flow rate was 10 sccm, while the total pressure was kept at 3.9 Pa by introducing He. The W wire temperature was 2050 K. The dashed line represents the calculated value.

Taking into account the small difference in the Franck− Condon factors,21 the density of BH(ν = 1) is estimated to be ∼15% of BH(ν = 0). The (0,0) band spectrum can be reproduced by assuming a rotational temperature of 340 K. This temperature is similar to those obtained for other hydride radicals produced in similar procedures, between 300 and 500 K.1,5,9,12,22 The rotational assignments for BH radicals were given by Fernando and Bernath.23 Hönl−London formulas can be used for the line strengths.24 Emission via off-diagonal transitions can be ignored because the Franck−Condon factors are fairly small.21 In the B2H6/He/D2 system, the BD signal was much more intense than the BH signal. Not only BH2 + D → BD + H2 addition−elimination reactions, which will be discussed in section 4.2, but also BH + D → BD + H exchange reactions may take place. The rotational assignments for BD also were given by Fernando and Bernath.23 Figure 9 shows the wire temperature dependence of the BH density. Because BH radicals could be detected even in the

removal process, BH + H → B + H2. The absolute densities were estimated by a procedure similar to that employed for B atoms. In such measurements, as for the density evaluation of B atoms, uncertainty by a factor of 2 may be unavoidable. The lifetime of BH(A 1Π, ν′=0) was measured to be 138 ± 2 ns, independent of the H2 partial pressure, showing that the quenching processes of BH(A 1Π) can be ignored. This observed lifetime is in fair agreement with the radiative lifetimes reported by other investigators.25−27

4. DISCUSSION 4.1. Production Mechanism of B Atoms and BH Radicals. Results of the present experiment show that B atoms and BH radicals are not produced directly on the wire surfaces but are produced in the reactions with H atoms in the gas phase. BH3 is the strongest candidate as the direct decomposition product of B2H6 because the dimerization energy of BH3 is only 134 kJ mol−1. The inefficient production of B and BH in the absence of a H2 flow may be related to the large B−H(HB−H) bond energy, 322(323) kJ mol−1, as was discussed in the Introduction. The direct production of BH2 on wire surfaces cannot be excluded, but because the bond energy of H2B−H, 421 kJ mol−1, is larger than those of B−H and HB− H, the direct production of BH2 may also be minor. The above bond energies, as well as the exothermicities and the endothermicities in the following reactions, are calculated values in the present study. Details of the computational procedure will be given in section 4.2. The following reaction mechanism may be assumed B2H6 flow in k in H 2 flow in

Figure 9. BH radical density as a function of the reciprocal of the W wire temperature. The flow rates of B2H6/He and H2 were 10 and 20 sccm, respectively. The total pressure was 3.9 Pa.

absence of B2H6 when aged wires were used, the background signals in He/H2 systems were subtracted. This plot is not Arrhenius-type either, but it is possible to evaluate the apparent activation energy below 2050 K. It was ∼245 kJ mol−1, which is much smaller than that for the production of B atoms, ∼450 kJ mol−1. The BH density increased almost linearly against the B2H6/He flow rate, while it showed saturation against the H2 flow rate, as shown in Figure 10, suggesting the presence of not only a production process, BH2 + H → BH + H2, but also a

k in′

B2H6 → 2BH3 − 134 kJ

(1)

H 2 → 2H − 416 kJ

(2)

BH3 + H ↔ BH 2 + H 2 − 6 kJ

5160

(3/−3)

BH3 → deposit/flow out

(4)

BH 2 + H → BH + H 2 + 93 kJ

(5)

BH 2 → deposit/flow out

(6)

BH + H → B + H 2 + 93 kJ

(7)

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BH → deposit/flow out

(8)

B → deposit/flow out

(9)

B2H6 flow out H 2 flow out

quadratic configuration interaction calculation including single and double substitution and second-order Møller−Plesset perturbation theory, respectively. The present values are in fair agreement with those reported by other investigators.31,32 No experimental information is available for the rate constants for the H shifting reactions, reactions 3, 5, and 7, but Harris and co-workers have evaluated these rate constants based on the ab initio potential energy calculations and the transition-state theoretical calculations.32,33 They found no potential barrier in reaction 5, while addition−elimination processes are possible for reactions 3 and 7. The barriers for these processes are much lower than those for the direct abstractive paths. Similar results were obtained in our present calculations. The present QCISD calculations show that reactions 3 and 7 have barriers, while no barrier is present in reaction 5. As for reaction 3, the potential barrier for the abstractive path via a transition state in a C2v symmetry was calculated to be 63 kJ mol−1. This barrier height is in fair agreement with that calculated by Schlegel et al., 52 kJ mol−1.32 This transition state is second-order and has two imaginary frequencies. The presence of another lower-barrier path via BH4 in a Td symmetry, an addition−elimination path, was also confirmed in the present calculations, but the positions and the energies of the transition states were a little different from those reported by Schlegel et al.32 Such difference may be ascribed to the difference in the level of theory. The potential energy of the transition state to produce BH4 from BH3 and H was calculated to be 26 kJ mol−1 higher than that of the reactants, while that for the decomposition to BH2 and H2 is 18 kJ mol−1 higher. Both transition states have Cs symmetries. Schlegel et al. have reported that the latter is 5 kJ mol−1 higher compared to the energy of BH3 + H.32 Similar addition−elimination processes via stable BH3 or BH2 intermediate states are possible for reactions 5 and 7. No barrier could be found for the formation of BH3 from BH2 + H. The potential energy of the transition state for the decomposition of BH3 to produce BH + H2 is lower than the energy of the reactants, BH2 + H. These results are consistent with the results of other investigators,31,32,34 and we may conclude that there is practically no barrier for reaction 5. As for reaction 7, a nonlinear transition state, with an energy 17 kJ mol−1 higher than the reactants, was found between BH + H and BH2. This transition-state geometry was confirmed with intrinsic reaction coordinate (IRC) calculations. No barrier was found between BH2 and B + H2. 4.3. Calculation of the B Atom and BH Radical Densities. We tried to reproduce the dependence of the B atom density on the H2 flow rate, shown in Figure 5, using the experimentally obtained H atom densities and the rate constants obtained by conventional transition-state theory.35 The calculated potential barriers and the rate constants for reactions 3 and 7 at 500 K were 25.9 and 17.4 kJ mol−1 and 1.6 × 10−13 and 2.8 × 10−12 cm3 s−1, respectively. As for the rate constant for reaction 5, the geometric average of the preexponential factors for reactions 3 and 7, 1.2 × 10−10 cm3 s−1, was employed because no barrier was found. The rate constant for reaction −3 was calculated from the principle of detailed balance. No quantum effect, such as tunneling, was included. Strictly speaking, the evacuation rate, kout, increases with the H2 flow rate even when the total pressure is kept constant. When the total pressure was 3.9 Pa, in the presence of a H2 flow at 20 sccm, [B2H6] was 84% of that found in its absence. According to the mass spectrometric measurements, on the other hand,

kout kout

Reaction 1 may take place not only on wire surfaces but also in the gas phase. This point will be discussed in section 4.4. The reverse processes of reactions 5 and 7 were not included because they are fairly endothermic. These reverse processes may take place in the hot region near the filament but may not take place in the cool or warm region whose volume is much larger. The reaction between BH and H2 can be ignored at low pressures.28 The reproduction of B2H6 on chamber walls was not included because B2H6 was not detected when H2 was decomposed on wire surfaces. The contributions of the bimolecular reactions, 2B2H6 → B3H9 + BH3 and B2H6 + H → B2H5 + H2, must be minor because of their large activation energies. The activation energy for the former reaction has been reported to be 120 kJ mol−1,29 while the barrier height for the latter reaction is 61 kJ mol−1 according to our calculation. The unimportance of the latter reaction is also supported by the mass spectrometric observation that the decomposition efficiency of B2H6 is decreased by the addition of H2. The reaction of 2BH3 → BH4 + BH2 is 379 kJ mol−1 endothermic. In other words, the decomposition of B2H6 to produce BH2 + BH4 is more endothermic than that to produce 2BH3. The accommodation of BHx into the wire was not included just for simplicity. Under steady-state conditions, it is easy to derive the following equations for the densities of B2H6 and the intermediates. [B2H6] =

k in k1 + kout

[BH3] =

2k1(k5[H] + k6 + k −3[H 2])[B2H6] k 3[H](k5[H] + k6) + k4(k5[H] + k6 + k −3[H 2])

[BH 2] =

2k1k 3[H][B2H6] k 3[H](k5[H] + k6) + k4(k5[H] + k6 + k −3[H 2])

[BH] =

[B] =

2k1k 3k5[H]2 [B2H6] {k 3[H](k5[H] + k6) + k4(k5[H] + k6 + k −3[H 2])}(k 7[H] + k 8)

2k1k 3k5k 7[H]3 [B2H6] {k 3[H](k5[H] + k6) + k4(k5[H] + k6 + k −3[H 2])}(k 7[H] + k 8)k 9

The rate constant for reaction (i) is represented by ki. The spatial distributions of gaseous species are assumed to be uniform, and rate constants for surface reactions include the surface/volume ratio. The validity of the above mechanism will be discussed in the following sections based on the rate constants calculated by transition-state theory. The present model may be too simple but can be a starting point of discussion. 4.2. Theoretical Calculations of the Energetics. The exothermicities/endothermicities listed in reactions 1, 2, 3, 5, and 7, as well as the bond energies shown above, are the results of Gaussian 09 calculations.30 The geometry optimization as well as the potential energy and the zero-point-energy calculations were carried out at the QCISD/6-31G(d,p) level of theory. Similar results were obtained at the MP2/6-31G(d,p) and QCISD/6-31+G(d,p) levels, although the results for MP2 were less quantitative. Here, QCISD and MP2 represent 5161

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that for B and that for H, (450 − 200) = 250 kJ mol−1. This agrees well with the observed energy, ∼245 kJ mol−1. 4.4. Production Mechanism of BH3. The production mechanism of BH3 from B2H6, reaction 1, is not clear. Both thermal decomposition in the gas phase29,36−41 and catalytic decomposition on the wire surfaces are possible. Mankelevich and co-workers suggested the importance of gas-phase decomposition rather than the catalytic decomposition,10,11 although the contribution of catalytic decomposition was also mentioned.11 This is partly because they carried out their experiments under rather high pressure conditions, such as 2.7 kPa. Under such conditions, the number of collisions between gas molecules in the hot region near the filament may be comparable to or larger than the collision numbers with wire surfaces. On the other hand, under the low-pressure conditions of the present study, below 5 Pa, decomposition in the gas phase may be rather minor. One way to ascertain the importance of wire surface reactions is to examine the dependence of the radical densities on wire material. It should be remembered that wire material dependences have been observed in the decomposition of SiH4, PH3, and P4.2,3,42 This point will be discussed in future publications.

the decomposition efficiency of B2H6 decreases with the H2 flow rate. In the B2H6/He system, the efficiency at 2050 K was 67% at 3.9 Pa, while it was 55% in the presence of a H2 flow, suggesting that k1 decreases with the addition of H2. Fortunately, these effects compensate, and the value of k1[B2H6] at 2050 K in the presence of a H2 flow at 20 sccm is just 14% larger than that in its absence. Thus, the H2 flow rate dependence of k1[B2H6] was ignored in the present analysis. [H2] may be assumed to be independent of the wire temperature. The rate constants for reactions 4, 6, 8, and 9 as well as k1[B2H6] were adjusted to reproduce the experimental results. Here, to simplify the procedure, the same values were assumed for k4, k6, k8, and k9. This is reasonable if these removal processes are diffusion-rate-controlled. Using the gas-phase rate constants at 500 K, the best agreement was obtained when these rate constants were assumed to be 14 s−1. These values may be larger at lower total pressure conditions. The best value for k1[B2H6] was 4.1 × 1013 cm−3 s−1. The dashed line illustrated in Figure 5 represents the calculated result. The agreement is excellent. We also tried to reproduce the present results using the rate constants at 1000 K, but the agreement was not as good as that at 500 K. It was possible to reproduce the present experimental results using rate constants at 300 K, but in this case, the values of k4 − k9 became too small. These must be larger than kout, which is estimated to be 2.5 s−1 from the chamber volume, flow rate, and pressure. The gas temperature must decrease with the distance from the wire. H atom shifting reactions can take place only in the hot or warm region. Unfortunately, it was impossible to reproduce the absolute densities of BH with the above parameters. The calculated BH density was 40% of that observed, although the tendency in the H2 flow rate dependence could be reproduced, as shown in Figure 10. Of course, a better agreement could be obtained by using other parameters, but in that case, the calculated B atom density becomes larger than the observed one. This discrepancy may be, in part, ascribed to the simplicity of the present model. The spatial distribution of the intermediate species as well as the gas temperature is not taken into account. There could be problems in the transition-state-theoretical calculation of the rate constants for the H shifting reactions. The uncertainty in the absolute density estimation could also be a cause of this disagreement. Accommodation of BHx (x = 0−3) into the wire as well as etching of a borodized filament by H2 to produce BHx (x = 1−3) may also be the cause of this discrepancy. It should be emphasized, however, that the tendency in the H2 flow rate dependence could be reproduced well both for B atoms and BH radicals. As for the wire temperature dependence of the B atom density, if we ignore the temperature dependence of all of the rate constants and substitute the measured H atom densities at various temperatures, the apparent activation energy between 1800 and 2050 K is calculated to be 319 kJ mol−1. This is much smaller than the observed value, ∼450 kJ mol−1. This difference can be ascribed to the temperature dependence of the rate constants. It is hard to imagine that k1 is independent of wire temperature, and this may be the main cause of the larger activation energy for B atoms compared to H atoms. The activation energy required for the production of BH is much smaller than that for B atoms. Under steady-state conditions, [BH] is given by k9[B]/k7[H]. If k7 and k9 are wiretemperature-independent, the activation energy for the production of BH should be given by the difference between

5. CONCLUSIONS B2H6 can be decomposed easily when activated on heated W wire surfaces, but the production of B atoms and BH radicals is inefficient unless H2 is introduced. This suggests that B and BH are produced in the H atom shifting reactions, BHx + H → BHx−1 + H2 (x = 1−3), in the gas phase because H atoms can easily be produced from H2 on hot wire surfaces. The inefficient direct production of B and BH on wire surfaces may be ascribed to the large bond energies of H−BHx. This mechanism was further confirmed by the H2 flow rate dependence of the densities of B atoms and BH radicals as well as by simple model calculations based on the rate constants obtained by conventional transition-state theory.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: **-81-53-4781275. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially funded by a Grant-in-Aid for Science Research (No. 26410010) from the Japan Society for the Promotion of Science.

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REFERENCES

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