Kinetics of Electrochemical Derivatization of the Silicon Surface by

Universite´ de Versailles-St-Quentin en Yvelines, 78000 Versailles, France. Received April 17, 2002. The hydrogenated silicon surface can be derivati...
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Langmuir 2002, 18, 5851-5860

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Kinetics of Electrochemical Derivatization of the Silicon Surface by Grignards Samira Fellah,† Anna Teyssot,† Franc¸ ois Ozanam,† Jean-Noe¨l Chazalviel,*,† Jacky Vigneron,‡ and Arnaud Etcheberry‡ Laboratoire de Physique de la Matie` re Condense´ e, CNRS-E Ä cole Polytechnique, 91128 Palaiseau, France, and Institut Lavoisier, Universite´ de Versailles-St-Quentin en Yvelines, 78000 Versailles, France Received April 17, 2002 The hydrogenated silicon surface can be derivatized with alkyl groups using anodization in a Grignard reagent. The derivatized surfaces have been characterized using infrared spectroscopy and X-ray photoelectron spectroscopy, and the kinetics of the reaction have been investigated using in situ infrared spectroscopy. The initial reaction rate is found to be on the order of one grafted alkyl group per two elementary charges passed through the interface, corresponding to a faradaic efficiency on the order of unity. The kinetics are modeled assuming that the derivatization proceeds through electrochemically generated alkyl radicals. For the case of a flat (111) Si surface, the results are accounted for by a reaction rate proportional to current density and to radical concentration at the surface, leading to a fast reaction up to completion of monolayer coverage. The detailed shapes of the kinetic curves, and their variations with experimental conditions, are well reproduced by the model. At an atomically rough surface, the kinetics exhibit a power-law behavior. These nonexponential kinetics can be ascribed to a distribution of rate constants associated with steric-hindrance effects, as quantitatively confirmed by numerical simulations. In practice, these results show that the maximum theoretical coverage may be hard to reach. They also indicate that the electrochemical techniques are intrinsically much faster than the available chemical techniques, which is probably favorable for reaching this maximum coverage. In the case of a Grignard from bromide and iodide, the role of the halogen in improving the electronic passivation of the surface is also demonstrated. This indicates that halogenation of the surface can be a side reaction in the derivatization process. However, the dominant reaction pathway appears to be abstraction of surface hydrogen by an electrochemically generated alkyl radical and reaction of the resulting Si dangling bond with the Grignard or another alkyl radical.

Introduction There has been a lot of recent interest in the organic derivatization of the silicon surface, in view of potential applications such as the realization of ultrathin dielectric films or sensor applications.1 Most often, the functional organic groups are attached to a native silicon oxide film present at the silicon surface. However, for electronic applications or the passivation of luminescent porous silicon, it is now recognized that derivatization of the surface with formation of a direct Si-C bond results in a surface with good electronic properties and better chemical stability than those obtained through the classical Si-O-C bridging.2-4 The starting point is a hydrogenated silicon surface, obtained upon dissolution of a SiO2 layer in fluoride medium. Several routes have been explored, among which the most popular ones are halogenation5,6 or addition of a double bond on the SiH group.6-11 The latter reaction may start from an alkene and is achieved thermally,7 photochemically,6,8,11 or in the presence of a catalyst9,11 or may be initiated by the † ‡

CNRS-E Ä cole Polytechnique. Universite´ de Versailles-St-Quentin en Yvelines.

(1) Ulman, A. Adv. Mater. 1990, 2, 573. (2) Kar, S.; Miramond, C.; Vuillaume, D. Appl. Phys. Lett. 2001, 78, 1288. (3) Buriak, J. M. Chem. Commun. 1999, 1051 and references therein. (4) Chazalviel, J.-N.; Ozanam, F. Mater. Res. Soc. Symp. Proc. 1999, 536, 155. (5) Bansal, A.; Li, X.; Lauermann, I.; Lewis, N. S.; Yi, S. I.; Weinberg, W. H. J. Am. Chem. Soc. 1996, 118, 7225. (6) Terry, J.; Linford, M. R.; Wigren, C.; Cao, R.; Pianetta, P.; Chidsey, C. E. D. Appl. Phys. Lett. 1997, 71, 1056.

formation of radicals.10 Thermal reaction with Grignard reagents RMgX also leads to formation of SiR bonds.11,12 Alternately, electrochemical routes have been explored. Such is the cathodic reduction of diazo compounds13 or halogenoalkanes14 or the anodic decomposition of Grignards.15-17 The latter reaction plausibly involves radicals and is related to the thermal route. However, in either case the reaction mechanism is unclear. In the following we present an investigation of the kinetics of the anodic derivatization reaction with Grignards. The reaction has been monitored in real time using in situ (7) (a) Sung, M. M.; Kluth, G. J.; Yauw, O. W.; Maboudian, R. Langmuir 1997, 13, 6164. (b) Sieval, A. B.; Vleeming, V.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 1999, 15, 8288. (c) Sieval, A. B.; Opitz, R.; Maas, H. P. A.; Schoeman, M. G.; Meijer, G.; Vergeldt, F. J.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 2000, 16, 10359. (8) (a) Cicero, R. L.; Linford, M. R.; Chidsey, C. E. D. Langmuir 2000, 16, 5688. (b) Boukherroub, R.; Wayner, D. D. M. J. Am. Chem. Soc. 1999, 121, 11513. (9) Buriak, J. M.; Stewart, M. P.; Geders, T. W.; Allen, M. J.; Choi, H. C.; Smith, J.; Raftery, D.; Canham, L. T. J. Am. Chem. Soc. 1999, 121, 11491. (10) Linford, M. R.; Fenter, P.; Eisenberg, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145. (11) Boukherroub, R.; Morin, S.; Bensebaa, F.; Wayner, D. D. M. Langmuir 1999, 15, 3831. (12) Kim, N. Y.; Laibinis, P. E. J. Am. Chem. Soc. 1998, 120, 4516. (13) Henry de Villeneuve, C.; Pinson, J.; Bernard, M. C.; Allongue, P. J. Phys. Chem. B 1997, 101, 2417. (14) Gurtner, C.; Wun, A. W.; Sailor, M. J. Angew. Chem., Int. Ed. 1999, 38, 1966. (15) Dubois, T.; Ozanam, F.; Chazalviel, J.-N. Proc. Electrochem. Soc. 1997, 97-7, 296. (16) Fide´lis, A.; Ozanam, F.; Chazalviel, J.-N. Surf. Sci. Lett. 2000, 444, L7. (17) Chazalviel, J.-N.; Fellah, S.; Ozanam, F. J. Electroanal. Chem., in press.

10.1021/la0203739 CCC: $22.00 © 2002 American Chemical Society Published on Web 06/19/2002

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Figure 1. Typical ex situ IR data: grafting of ethyl groups on an atomically flat (111) Si surface (diethyl ether + 3 M ethylmagnesium bromide, 0.5 mA/cm2, 300 s). p-polarized absorbance spectra of the modified surface (a) referred to the initial hydrogenated surface [see the sharp negative ν(SiH) peak] and (b) referred to the surface after thermal oxidation (600 °C, 1 min, corresponding to a ∼6 Å thick layer): see the negative oxide bands and the small broadened positive SiH band (see enhancement by a factor of 10), indicating that ∼50% of the hydrogen is left on the ethylated surface. Curve c shows the SiH band for the case of a methylated surface, on the same enhanced scale as for the ethylated surface. Notice that its intensity is much smaller, corresponding to less than 10% of the hydrogen initially present on the surface. The sloping baseline at low wavenumbers in (a) is partly due to a change in electronic absorption associated with a change in band bending.

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Figure 2. Wide-scan XPS spectra of atomically flat (111) Si surfaces using monochromatized Al KR radiation. (a) Hydrogenated surface compared with the surface after thermal oxidation (SiO2 thickness ∼2 nm). (b) Surface after grafting of methyl and decyl groups compared with the hydrogenated surface.

In this section we will successively present the ex situ IR and XPS results and then the in situ IR results. Ex Situ IR Measurements. Typical ex situ IR measurements are shown in Figure 1. The upper spectrum represents the absorbance of the derivatized surface referred to the hydrogenated surface. The absence of a significant signal in the region 1050-1250 cm-1 stands as evidence that little oxidation of the surface has taken place during the derivatization.18 The bands in the ν(CH) region provide direct evidence for the presence of alkyl chains on the surface. In the case of methyl groups, we have already published polarized-IR data indicating that the derivatized surface maintains its ordering, the methyl groups standing perpendicular to the surface.16 The loss of hydrogen is indicated by the sharp negative signal at 2083 cm-1. A reference sample with no hydrogen was obtained by thermal oxidation. For the case of methylation, comparison with this reference sample shows that less than 10% of the initial hydrogen is left on the surface after the modification, as shown in Figure 1c. This means that over 90% of the hydrogen has been removed from the Si surface. For longer alkyl chains, the magnitude of the ν(SiH) signal indicates that about 50% of the surface hydrogen has been removed, as shown in Figure 1b.

XPS Measurements. The XPS data provide an absolute test of the initial hydrogenated surface, as well as of the derivatized surface. This test is especially stringent since the surfaces have been exposed to air for a few hours before introduction into the XPS spectrometer. Therefore, the observed quantities of oxygen and carbon must be regarded as upper boundaries to the actual contamination of the freshly prepared surfaces. The atomically flat hydrogenated surface exhibits extremely reproducible results, namely, a surface with oxygen ( Q0); (c) simulation with two distinct site reactivities (A ) 1, p ) 1, initial θ1H ) 0.14, γ1 ) 0.057).

Long Alkyl Chains and Role of the Halogen. In the case of alkyl chains longer than methyl, steric hindrance prevents 100% substitution of the surface hydrogens by alkyl groups. In principle, a maximum substitution of ca. 50% may be expected. As a matter of fact, the infrared data indicate that the loss of hydrogen is typically 50% of that observed in the case of methyl. However, the XPS data indicate that the halogen initially present in the Grignard remains in a significant amount on the Si surface. This demonstrates that the fraction of the surface that is not accessible to alkyl groups is partly modified by substitution of hydrogen by the halogen. This implies that halogen radicals are generated in the electrochemical process and play a role similar to that of the alkyl radicals in reactions 2c and 3b, this role becoming significant when the reactivity of the alkyl radicals is limited by steric hindrance effects. The lower concentration of Cl on the surfaces, as compared to Br and I, is consistent with the lower generation rate of Cl•.22,25 Notice however that the halogen enters the reaction only as a minority pathway (not taken into account in our model). In the opposite case (halogenation followed by reaction of the Grignard with the halogenated surface), the amount of hydrogen left on the surface would be much lower than is actually observed. The role of halogen radicals is also apparent in the case of methylation. Though the XPS data show that the amounts of halogen on the methylated surfaces are very (24) See, e.g.: Venkateswara Rao, A.; Ozanam, F.; Chazalviel, J.-N. J. Electrochem. Soc. 1991, 138, 153. (25) The low generation rate of halogen radicals in the case of chlorine may also account for the significantly faster kinetics observed as compared to the case of bromine and iodine (see Table 1): an increased concentration of halogen radicals (the case of Br and I, especially for methyl Grignards) may lead to a parallel recombination pathway for the alkyl radicals, effectively increasing the value of K.

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weak, the infrared data indicate that there is a significant difference among the three halogens, with respect to the electronic quality of the derivatized surface. This piece of information can be obtained from an analysis of the baseline in the spectra. This baseline generally appears from the beginning of the anodic treatment. It is always negative and exhibits a spectral shape characteristic of free-hole absorption.24 It then indicates that a depletion layer appears during the derivatization; i.e., positively charged surface states are created. This effect, essentially absent for the case of CH3MgI, is measurable for CH3MgBr, and becomes very strong for CH3MgCl. Methylation of a (111) flat surface should encounter steric problems only at step sites. If dangling bonds are left at such sites, surface states and band bending are expected to appear. These states are cured out if the dangling bond is saturated by a halogen atom, a process which apparently takes place to a lesser extent for the case of chlorine. This again was to be expected indeed, since generation of Cl• radicals is far less efficient than that of I• and Br• radicals.22,25 Atomically Rough Surfaces and Steric Hindrance Effects. The kinetics observed at atomically rough surfaces are at variance with those discussed above. The initial evolution seems significantly faster than that at flat surfaces (lower Q0), but there is a long-term evolution, absent for flat surfaces, better fitted by a power law than by an exponential (see Figure 8a,b). It seems plausible that such a behavior is associated with a distribution of the reactivities of the different surface sites (i.e., a distribution of k). For testing such a possibility, the set of eqs 10 and 11 can be transposed to the case of several types of sites with respective rate constants k0, k1, ..., km. It then becomes

κ ) A(1 -

∑i γiκθiH)2/(p+1)

dθiH ) - γiκθiH dτ

(12)

(13)

where the θiH are the partial hydrogen coverages corresponding to type-i sites (∑iθiH ) θH), γi ) ki/k0, κ ) (2ek0NS/ J)c(0), and A ) k0NS[2p(p + 1)ep-1/KDJp-1]1/(p+1). As can be seen in Figure 8c, the experimental curves can be easily reproduced from such a model. It may be sufficient to take two or three types of sites (m ) 1 or 2), with γi in the range from 10-1 to 10-2, and initial values of the θiH of comparable magnitude. The origin of a distribution of site reactivities was to be expected at atomically rough surfaces, either due to distinct chemical environments (SiH, SiH2, SiH3) or because some sites are hardly accessible to the reactants, due to steric hindrance. However, a distinct problem of steric hindrance may also arise in the case of long alkyl chains. In that case, the reactivity of a given site is not fixed forever at the beginning of the experiment, but instead it decreases with time as the neighborhood of that site becomes occupied by attached alkyl chains (which may be termed a “dynamic” steric effect). Such a problem cannot be treated with time-independent reactivities ki, as was done above. To assess the consequences of such steric hindrance effects on the kinetics of derivatization, we have made a specific computer simulation. For the sake of simplicity, we have assumed that c(0) is set by the outdiffusion/recombination of the radicals, so that the kinetics at an ideal nonhindered surface would be exponential. We have modeled the Si surface by a triangular lattice of points, and have assumed that the

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sites, do also play a role, the model of a progressively decreasing p(nocc) being seemingly more appropriate than that of a steep drop for some critical value of nocc. Summary

Figure 9. Simulation of the dynamic steric hindrance effect associated with the grafting of large species: (a) sharp drop of the reactivity for a critical value of the number of occupied neighbors nocc (for nocc g 3); (b) progressive decrease in reactivity, according to the law exp(-nocc2). The charge Q is scaled to the characteristic charge 2eNS for modification in the unhindered case. Notice that the initial slope of the curves remains unity. The curves are the result of the simulation. The circles indicate a fit of the simulated curves: (a) with an exponential, 0.51[1 - exp(-q/0.45)], and (b) with a power law, 0.39[1 - (1 + q/0.36)-0.94].

probability of alkyl attachment at a given site is determined by the number of first neighbors nocc already occupied by alkyl groups (0 e nocc e 6). Alkyl groups were then attached at random, with due attention to the reaction probabilities of the various sites. The evolution of the hydrogen coverage of such a surface is shown in Figure 9, for two different cases: in the first case, the probability of reaction p was assumed to drop abruptly from its initial value to zero, when nocc reaches a critical value (here when nocc g 3). In the second case, a progressive variation of the reaction probability was assumed [namely, here we chose p(nocc) ∝ exp(-nocc2)]. It was further verified that the simulation correctly predicts an exponential behavior when the reaction probability is kept constant. The two assumptions on p(nocc) are seen to lead to very different results. In the case of an abrupt variation (site blocked if nocc g 3), the behavior remains nearly exponential, and the characteristic time of the exponential is decreased relative to that of the nonhindered case in the same proportion as the maximum achievable substitution (here by about a factor of 2). In the case of a progressive variation of p(nocc), the derivatization tails out to very long times, as for the case of a distribution of k: since the probability decreases with nocc but never vanishes, full derivatization remains possible, though reached in unphysically long times. The simulated curves are fairly fitted by power laws. It then appears that steric hindrance effects can give rise to various deviations of the kinetic curves from the ideal case represented by methylation of an atomically flat (111) surface. The experimental data indicate that the length of the alkyl chain has no strong effect at atomically flat surfaces, but pronounced deviations of the kinetic curves toward a power-law shape are observed on going from atomically flat to atomically rough surfaces. These observations tend to favor the idea of a “frozen” distribution of site reactivity; i.e., the reactivity of the sites is mainly due to the morphology of the initial surface. However, the experimental data also indicate that the power-law exponents at rough surfaces somewhat decrease on going from methyl to longer alkyl chains. This shows that the “dynamic” steric effects, that is, the decrease of site reactivity induced by occupancy of the neighboring

Anodic alkylation of the silicon surface in a Grignard reagent appears as a very efficient method for derivatizing the silicon surface. The reaction kinetics are quantitatively accounted for in the framework of a model assuming electrochemical generation of alkyl radicals, and reaction of these radicals with the hydrogenated silicon surface, in competition with outdiffusion/recombination of the radicals in the electrolyte. The initial reaction rate somewhat depends on the specific system (alkyl, halogen, solvent), but is generally close to the maximum expected rate of one modified site per two elementary charges. In the case of iodide and to some extent bromide Grignards, halogen radicals are involved as a secondary reaction pathway, which allows for attachment of the halogen and electronic passivation of the sites sterically inaccessible to the alkyl groups. Since the full derivatization just requires a few hundred microcoulombs per square centimeter, the reaction may be completed on the time scale of 1 s. This is especially noticeable since the concentration of radicals at the surface remains very low. This illustrates the advantage of electrochemistry as a means to generate the radicals at the right place, allowing for optimum efficiency. The advantage of intrinsically very fast kinetics may be especially useful for the case of surfaces with distributed reactivity, such as atomically rough surfaces, or for the attachment of long alkyl chains, where steric hindrance effects may decrease the kinetics of the last derivatizable sites by several orders of magnitude. Finally, the good understanding of this reaction, which was obtained through in situ infrared measurements, may be helpful for understanding the reaction of Grignards with the silicon surface by the thermal or the photochemical route, which may actually consist of zero-current electrochemical processes. Experimental Section The silicon substrates were cut from p-type (3-8 Ωcm resistivity), (111)-oriented, 0.5 mm thick, float-zone-purified, double-side-polished Si wafers. They were shaped as 20 × 15 mm2 platelets. The two longer edges were polished at 45° bevel for use as multiple-total-internal-reflection prisms. The sample surface was prepared by oxidation in a sulfochromic mixture or a hot H2O2/H2SO4 mixture and oxide dissolution by rinsing in electronic grade 50% HF or 40% NH4F. Both types of rinse lead to a hydrogenated surface, but rinsing in HF leads to an atomically rough surface (with SiHx groups, x ) 1-3),26 whereas rinsing in NH4F may lead to (111) surfaces atomically flat over distances of several micrometers (with SiH groups only, the SiH bonds standing normal to the surface).27 In the latter case, to avoid pitting of the surface, care was taken to bubble nitrogen into the NH4F solution and into the water used for the final rinse. Also, part of the 20 × 15 mm2 surface was roughened by sandblasting, to act as a sacrificial anode in the electrochemical process taking place during immersion in NH4F.28 For the in situ IR studies, a leak-proof polytrifluorochloroethylene (PTFCE) cell was designed. The sample was pressed against an aperture in the cell wall with an O-ring seal (10 mm inner diameter) made of silicone elastomer encapsulated in a thin (0.1 mm) polished PTFCE casing.17 On the opposite wall of the cell, a copper counter electrode was mounted in a similar (26) Burrows, V. A.; Chabal, Y. J.; Higashi, G. S.; Raghavachari, K.; Christman, S. B. Appl. Phys. Lett. 1988, 53, 998. (27) Higashi, G. S.; Chabal, Y. J.; Trucks, G. W.; Raghavachari, K. Appl. Phys. Lett. 1990, 56, 656. (28) Allongue, P.; Henry de Villeneuve, C.; Morin, S.; Boukherroub, R.; Wayner, D. D. M. Electrochim. Acta 2000, 45, 4591.

Electrochemical Derivatization of the Si Surface way. For filling the cell, its upper end was fitted to a glass tube ending with a ground stopper. After surface preparation, the Si sample was mounted onto the empty cell, and the assembly was introduced into a glovebox. After being filled with the electrolyte, the cell was closed, taken from the glovebox, and transferred to the IR spectrometer. The spectrometer was a Bomem MB100, used in the external mode with a liquid-nitrogen-cooled mercurycadmium telluride photovoltaic detector. The geometry of the samples and the cell led to 10 useful internal reflections taking place at the Si/electrolyte interface. The electrochemical cell was driven by a homemade galvanostat (10 mA, 100 V). The spectrometer and galvanostat were controlled by a PC equipped with an IEEE 488 card. For the XPS studies, one-side-polished samples were used. The modification was carried out in the glovebox, holding the sample from a corner in an open cell with a copper counter electrode. Transfer of the samples from the glovebox to the XPS spectrometer was made through air and required a time of a few hours. The XPS spectrometer was a VG Instruments ESCALAB 220i model. Data were taken using monochromatized Al KR1 excitation. The ultimate overall resolution of the instrument is ≈ 300 meV fwhm. Surface modifications with methyl, ethyl, pentyl, decyl, and octadecyl groups were investigated. The Grignard reagents were purchased from Aldrich and used as supplied. For the case of methyl, the iodide, bromide, and chloride Grignards were available. Depending on the Grignard, the solvent was either diethyl ether or tetrahydrofuran (THF). Systematic studies were made, with independent changes of the alkyl chain, the halogen, and the solvent, to investigate the effect of these parameters on the kinetics of the reaction.

Acknowledgment. The Laboratoire de Physique de la Matie`re Condense´e is UMR 7643 du Centre National de la Recherche Scientifique. This work was partly supported by the Programme Mate´riaux du CNRS and by CEC under Contract ICA3-CT-1999-00016. S.F. benefited from an Algerian-French cooperation grant and A.T. from an Erasmus scholarship. Appendix: Surface Reaction Kinetics The present reaction is regarded here as a two-step process, where an Si surface site evolves from tSiH to tSi• (eq 2c) and then from tSi• to tSiR (eq 3a or 3b). From the known average enthalpies of C-H, Si-H, and Si-C bonds,21 the enthalpy variations associated with reactions 2c and 3b can be roughly estimated as ∼-0.5 and ∼-4 eV, respectively (reaction 3a being thermodynamically equivalent to reaction 3b at the potentials of interest). However, the concentration of R• in solution is rather low (typically, for 100 µA/cm2, Ka ≈ 105 s-1, and even without any consumption of R• at the electrode, we calculate c(0) ≈ 10-6 M). The low concentration of R• reduces the free-enthalpy drop associated with both reactions by an amount of ∼0.35 eV. As a result, reaction 2c is much less off-equilibrium than is usually the case in solution chemistry. In a similar way, the radicals Solv•, created by hydrogen abstraction from the solvent, may be in near equilibrium with R• and tSi• (eq 3c). The experimental observation of a weak reincrease of the SiH signal after the current is turned off gives direct evidence that the concentration of tSi• is significant and that reaction 3c can operate backward (see Figure 10). These facts strongly suggest that there is a pool of radicals (R•, tSi•, Solv•) whose concentration ratios are fixed by the various hydrogentransfer reactions (e.g., reactions 2c and 3c and similar reactions), and the rate-limiting step of the grafting reaction is reaction 3a or 3b. This is the basic hypothesis of our kinetic model. To check its validity, we have tried to estimate the rates of the various reactions involved at the surface. Typical

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Figure 10. Experimental evidence for hydrogen transfer from the solvent to a surface tSi•. When the anodic current is turned off, there is a slight reincrease of the ν(SiH) absorption band, attributable to repair of the broken SiH surface bonds. 3 M CH3MgI in diethyl ether, J ) 300 µA/cm2, pulses at t ) 50, 450, and 850 s, pulse duration 0.3 s.

Figure 11. Schematics of the reactions taking place at the surface and in its vicinity, for an applied current density on the order of 100 µA/cm2 (associated flow of elementary charges ∼1015 cm-2 s-1). The numbers in brackets are estimated orders of magnitude for the concentrations. The numbers along the arrows are the surface reaction rates (cm-2 s-1). The reaction rates for the reactions taking place in the electrolyte have been converted into surface reaction rates upon multiplying by the diffusion length of the relevant species. The bold arrows represent the dominant pathway in typical conditions.

estimates are shown in Figure 11. In addition to R• and tSi•, two radical species, Solv•R and Solv•β, were taken into account (representing the radicals formed from the solvent by abstraction of a hydrogen in the R and β positions, respectively). The enthalpies relative to R• were taken as ∆H ) -0.5 eV (tSi•), -0.4 eV (Solv•R), and -0.1 eV (Solv•β). [The tSi• radical is probably less stable than its molecular counterparts, since bond-angle relaxation is impeded by the silicon crystal lattice. We have taken the SiH bond enthalpy of (CH3)3Si-H (90 kcal/mol) as a plausible estimate,21 whence ∆H ≈ -0.5 eV.] The rate constants for hydrogen transfer between two species in solution were taken as C exp(-Ea/kBT), with C ) 109 M-1 s-1 and Ea ) (∆H/2) + [(∆H/2)2 + 0.52]1/2, a form which reproduces the known trends (Ea ≈ 0 for ∆H , 0, Ea ≈ ∆H for ∆H . 0, Ea ≈ 0.5 eV for ∆H ≈ 0) and the correct orders of magnitude for the known rates (e.g., 103-104 M-1 s-1 for R• f Solv•R).21 The rate constants for hydrogen transfer between a surface species and a solution species have been taken of the same form. However, at the surface, the prefactor C is expected to be much larger than in solution, because the SiH bond is pointing normal to the surface, and a molecule incident on the surface will easily meet the linear tSi‚‚‚H‚‚‚R transition state. By analogy with the reactions of monatomic radicals, a value of C ) 1012 M-1 s-1 has been assumed.21 Finally, the grafting reaction has been assumed to proceed according to reaction 3b, with a rate constant of 109 M-1 s-1.

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With the above values, the dominant reactions are seen to be R• f tSi• f Solv•R. The concentration of tSi• is governed by the balance between R• f tSi (rate ∝ c(0)[tSiH]) and tSi• f Solv•R (rate ∝ [tSi•]). Hence, [tSi•]/[tSiH] is proportional to c(0), which is consistent with the two-step description of the main text. When the substitution of the tSiH groups by tSiR groups is nearly completed, the direct path R• f Solv•R must become dominant, which is not expected to affect the validity of the two-step description. The present estimates do not take charged species into account. As a matter of fact, surface dangling bonds may also appear in the charged states tSi- and Si+. At opencircuit potential, it is likely that the semiconductor will be in depletion, and most of the tSi• species will turn to tSi-, exhibiting lowered reactivity. Such may be the case in Figure 10, where recovery of the hydrogen is seen to take place with a characteristic time in the range 1-102 s, and nonexponential kinetics. Under polarization, tSimay be involved in the creation of R•

tSi• + RMgX f tSi- + R• + MgX+

(1a)

tSi- + h+ f tSi•

(1b)

which introduces a new proportionality link between [tSi•] and c(0). Conversely, it is plausible that tSi+ will be involved in reaction 3a:

tSi• + h+ f tSi+

(3a-1)

tSi+ + RMgX f tSiR + MgX+

(3a-2)

The rate of either step is hardly predictable, but we think that the global rate of reaction 3a must be larger than that of reaction 3b, because if reaction 3b were dominant, Solv• (as well as R•) could be grafted onto the silicon surface, which is clearly excluded by experiment. In conclusion, the two-step description of the main text is fairly supported by an examination of the various possible reaction paths. However, the large number of such paths and the lack of reliable data on the many rate constants would make any analysis beyond this simple two-parameter approach rather speculative. LA0203739