Kinetics of Plasmon-Driven Hydrosilylation of Silicon Surfaces: Photogenerated Charges Drive Silicon- Carbon Bond Formation

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Kinetics of Plasmon-driven Hydrosilylation of Silicon Surfaces: Photogenerated Charges Drive Silicon- Carbon Bond Formation

Chengcheng Rao, Brian C. Olsen, Erik J. Luber,＊ Jillian M. Buriak＊

Department of Chemistry, University of Alberta, 11227–Saskatchewan Drive, Edmonton, AB T6G 2G2, Canada.

*E-mail: [email protected], [email protected]

ABSTRACT

Optically transparent PDMS stamps coated with a layer of gold nanoparticles were employed as plasmonic stamps to drive surface chemistry on silicon surfaces. Illumination of a sandwich of plasmonic stamps, an alkene ink, and hydride-terminated silicon with green light of moderate intensity drives hydrosilylation on the surface. The key to the mechanism of the hydrosilylation is the presence of holes at the Si-H-terminated interface, which is followed by attack by a proximal alkene and formation of the silicon-carbon bond. In this work, detailed kinetic studies of the hydrosilylation on silicon with different doping levels, n++, p++, n, p, and intrinsic were carried out to provide further insight into the role of the metal-insulator-semiconductor (MIS) junction that is set up during the stamping. Moderately doped n-type and p-type silicon are found to have the fastest rate of hydrosilylation, approximately 10 times faster than that of highly doped n++ and p++ silicon, and about 20 times faster than intrinsic silicon. The kinetic studies were correlated with the properties of the moderately doped silicon substrates, and point to the near- optimal convergence of factors in moderately doped silicon that result in the fastest observed rates of hydrosilylation. Moderately doped silicon has a sufficiently large depletion width and built-in field that results in most photogenerated holes in the bulk being swept to the surface while also being able to separate electron-hole pairs generated by the intense E-field of the gold nanoparticle LSPR. These conditions lead to the highest concentration of holes at the silicon surface, and highest rates of hydrosilylation.

Keywords: Hydrosilylation, plasmon, LSPR, stamping, silicon, surface, metal-insulator-semiconductor, junction

Graphical Abstract

INTRODUCTION

Light energy can be converted to chemical energy by plasmonic nanostructures to drive chemical reactions.1–4 The combination of plasmonics and surface chemistry is an emerging research area, with a wide range of promising applications that includes sensing, photovoltaics, catalysis, imaging, and nanomedicine, among others.5–9 Localized surface plasmon resonance (LSPR) in metallic nanostructures is a well established as the platform for surface enhanced Raman spectroscopy (SERS), and has seen increasing interest as a driver of highly localized surface chemistry, as described beautifully in a recent review.10 Depending on the size and other properties of the metallic nanostructures, illumination with the resonant optical wavelength to excite LSPR modes can be used to drive surface chemical reactions. Published examples include silicon-carbon bond formation on silicon surfaces via hydrosilylation of alkenes and alkynes,11–13 aryl monolayer formation on gold through organic iodide cleavage,14 thiol-ene Click chemistry on gold surfaces ,15 several examples of localized polymerization ,16–21 and spatially selective activation of light-sensitive monolayers in close proximity to gold colloids,22 among others. The mechanisms for the plasmon-driven surface chemistry appear to vary, and have been proposed to result from the strong and confined electromagnetic field, local generation of heat, or hot carriers, although it is very challenging to parse out the precise roles of the LSPR.10 Previously, our group has demonstrated the use of ‘plasmonic stamps’ comprising arrays of either ordered and disordered gold nanoparticles integrated with flexible and optically transparent PDMS.11–13 Upon illumination with visible light that corresponds with the maximum of the LSPR-based absorption of the gold nanoparticles, these stamps drive the patterned hydrosilylation of alkene and alkyne “inks” on Si-H-terminated surfaces in ~1 h at room temperature. Mechanistic work points to the central involvement of charge carriers generated in the proximal silicon, induced by the intense electric fields of the LSPRs of the gold nanoparticles. Surface coverage is dependent upon doping levels of the silicon, which when combined with other observations, seems to favour a mechanism based upon a metal-insulator-semiconductor junction while at the same discounting others, such as localized heating.11–13 In this work, we carry out detailed kinetic studies to further delve into the mechanism of LSPR-driven surface chemistry on silicon surfaces. With the kinetics data, a physical model was built to show the relationship between reaction rate and doping density, optical absorption coefficients, depletion width, and the plasmonic electric field.

EXPERIMENTAL METHODS

Materials Si wafers (111-oriented, prime grade, p-type, B-doped, ρ = 1–10 Ω cm, thickness of 600–650 μm; 111-oriented, prime grade, n-type, P-doped, ρ = 1–10 Ω cm, thickness of 600–650 μm; 111- oriented, prime grade, n-type, As-doped, ρ = 0.001–0.004 Ω cm, thickness of 500–550 μm; 111- oriented, prime grade, p-type, B-doped, ρ = 0.001–0.005 Ω cm, thickness of 400–450 μm) were purchased from WRS Materials Inc. Millipore water (resistivity of 18.2 MΩ•cm) was used for the preparation of all aqueous solutions. The precursors for Sylgard 184 PDMS were purchased from

Dow Corning. NH4OH (aqueous, 30%) and HCl (aqueous, 37%) were purchased from Caledon

Laboratories, Ltd. H2O2 (aqueous, 30%) was obtained from Sigma-Aldrich. NH4F (aqueous, 40%, semiconductor grade) was purchased from Transene Company, Inc. 1H,1H,2H-perfluoro-1- decene (99.0%) from Sigma-Aldrich was passed through a short column of hot alumina (dried at 100 °C for over 24 h and used while still hot), in a nitrogen-filled glove box, to remove water residues and peroxides, and then further deoxygenated with nitrogen gas via a brief sparge. The optical filter [CW526 (center band wavelength) of 526 nm; full width at half-maximum (fwhm) of 180 nm, Figure S4] was purchased from Edmund Optics Inc.

Characterization SEM images were obtained using a field emission scanning electron microscope (S-4800, Hitachi); the working pressure for imaging was <10-8 Torr with a 30 kV accelerating voltage. UV-vis absorption spectroscopy measurements were carried out in air using an Agilent UV-8453 spectrophotometer at 1 nm resolution. Prior to measurement, a baseline correction procedure (through a blank PDMS stamp) was implemented. Tapping mode atomic force microscopy (AFM) micrographs were captured using a Digital Instruments/Veeco Nanoscope IV with silicon PPP-NCHR cantilevers purchased from Nanosensors (thickness 4 μm, length 125 μm, width 30 μm, n-type Si with an Al coating, resonance frequency of 330 kHz, force constant of 10–130 N/m, tip height of 10 μm, and tip radius of <10 nm.). Sessile drop contact angles of the functionalized silicon surfaces were measured using 3 μL of water on a Rame-Hart Model 100-00 contact-angle goniometer after the droplet on the sample surface reached a static state. The resistivity of silicon wafers were measured by a Lucus Pro4 4000 sheet and bulk resistivity measurement system with Keithley 2601A sourcemeter. X-ray photoelectron spectroscopy (XPS) spectra were taken on a Kratos Axis Ultra X-ray photoelectron spectroscopy system using an Al source with an energy of 1487 eV, in the University of Alberta Centre for Nanofabrication, with binding energies calibrated to C(1s, 285.0 eV).

Blank PDMS Stamp Preparation Polydimethylsiloxane (PDMS) prepolymer and the curing agent (Sylgard 184, Dow Corning) were mixed in a 10:1 ratio and degassed by applying a vacuum three times to the prepolymer at room temperature. Then, 10 mL of the mixtures were added to a 100 mm polystyrene petri dish, with a PDMS layer thickness of ~3 mm, and cured at 65 °C in an oven for over 6 h. The cured PDMS was removed slowly and carefully from the petri dish, cleaned with Soxhlet extraction in hexane for 6 h in order to remove low molecular weight PDMS, and rinsed with ethanol and water. The blank PDMS was cut into 1 × 1 cm2 squares and stored under vacuum.

Silicon Wafer Cleaning and Preparation By using a Disco DAD 321 dicing saw, Si(111) wafers were cut into 1 × 1 cm2 squares. After being sonicated in 2-propanol for 15 min and dried with a nitrogen gas stream, each chip underwent a standard RCA cleaning procedure: the chips were immersed in a base solution

[H2O/30% NH4OH (aq)/30% H2O2 (aq) (6:1:1)] at 80 °C for 15 min, rinsed with water, and then immersed in an acid solution [H2O/37% HCl (aq)/30% H2O2 (aq) (5:1:1)] at 80 °C for another 15 min. The chips were rinsed with water and dried in a stream of nitrogen gas.

Gold Dewetting on Si and PDMS Surfaces The sputtering system, ATC Orion 8 (AJA International Inc.) was used to deposit the gold films onto Si wafers (111-oriented, prime grade, p-type, B-doped, ρ = 1–10 Ω cm, thickness of 600– 650 μm）or the blank PDMS at room temperature. The working argon gas (99.99% purity) pressure was 4 mTorr. The sputtering powers were fixed to 100 W and 150 W, and the deposition rates were 0.16 and 0.22 nm/s, respectively. Afterwards, thermal treatment at 150 °C for 20 h of the deposited thin gold films on silicon wafers or PDMS substrates was carried out in an oven to induce dewetting, and then allowed to cool to room temperature.

Plasmonic Stamping on Hydride-Terminated Silicon Surfaces

The cleaned silicon chips were immersed in degassed 40% NH4F for 5 min and deoxygenated water for 10 s, respectively. After being dried with an argon stream, each chip was transferred immediately into an argon-filled glovebox (O2 and H2O < 1 ppm) and placed into a customized sample holder, as shown in the SI of previous work.13 Typically, neat 1H,1H,2H-perfluoro-1- decene (30 μL) was dropped onto the hydride-terminated Si(111) surface and covered by the plasmonic stamp with the side containing the gold nanoparticles facing the Si surface. A quartz slip was then placed onto the top of the plasmonic stamp. Two bulldog clamps were applied on both sides to hold the sandwich structure together and apply reproducible and even pressure. White light (150 W bulb) was focused through a periscope convex lens, filtered through a

bandpass filter (CW526), and shone onto the sandwiched sample for the required length of time, with an incident intensity of 50 mW/cm2. Upon completion of the reaction, the wafer was rinsed with dichloromethane three times and dried with a stream of argon gas. The wafers were immediately subjected to water contact angle measurements or XPS analyses.

RESULTS AND DISCUSSION

Kinetic Studies of Plasmon-induced Hydrosilylation on Si Surfaces

Figure 1. Preparation of the PDMS-based plasmonic stamps. (a) Sputtered film of gold on PDMS is thermally dewetted, leading to isolated film of gold nanoparticles. (b) AFM micrograph of the surface of a plasmonic stamp. (c) Visible wavelength transmission spectra of 5 different plasmonic stamps to show reproducibility. Inset shows an optical image (photograph) of a plasmonic stamp.

Plasmonic PDMS stamps with gold nanoparticle elements were prepared as shown in Figure 1, and then applied to drive surface hydrosilylation reactions, Figure 2. The stamps were prepared as described previously (additional details in the Supplementary Information).13 Briefly, a film of gold was sputtered onto a freshly prepared square of PDMS, followed by thermal dewetting of the gold to form a film of 30-40 nm diameter gold nanoparticles on the surface of the stamps. The visible spectrum of the stamp shows a maximum at 546 ± 3 nm that corresponds to the LSPR of the gold nanoparticles. As a starting point, stamps were pressed on a freshly prepared Si(111)–H surface, sandwiching a thin layer of the reactive “ink” molecule, in this work 1H,1H,2H-perfluoro-1-decene, and illuminated through the PDMS stamp with 50 mW/cm2 green

light for 60 minutes, as shown in Figure 2a. After the reaction, the silicon substrate was rinsed thoroughly with dichloromethane, dried with a stream of nitrogen, and the water contact angle measured. For 60 minutes of illumination, the observed static water contact angle increased from ~83° for the Si-H-terminated silicon, to ~105°. The contact angle of a smooth monolayer of this perfluorinated alkene on silicon with maximum substitution would be expected to be 115–119°,23 but due the patchy nature of the resulting monolayer that mirrors that of the gold nanoparticles of the stamp, it is lower. Control experiments showed that both illumination and the gold nanoparticles are necessary to induce hydrosilylation and the resulting increase in static water contact angle. The net difference of 22° for the static water contact angle provides a wide window for carrying out kinetic studies, during which the illumination time is varied, to further investigate the proposed mechanism, Figure 2b.

Figure 2. Outline of plasmonic stamp-assisted hydrosilylation on a Si(111)–H surface. (a) The PDMS-based plasmonic stamp with gold nanoparticles is pressed onto the surface of Si(111)-H with a thin layer of the perfluorinated alkene ‘ink.’ Optical photographs show the water contact angles on the silicon surfaces before (left) and after (right) hydrosilylation.

Kinetic studies were performed using 5 different doped Si(111) wafers, ranging from highly doped n-type (n++), to n-type (n), to intrinsic (i), to p-type (p), to highly doped p-type (p++). Figure 3 shows the change of static water contact angles on Si(111)-H using the plasmonic stamps and 1H,1H,2H-perfluoro-1-decene as the ink for up to 9 h of illumination. As can be seen, the water contact angles for plasmon-induced hydrosilylation with 1H,1H,2H-perfluoro-1-decene will all eventually surpass 100°, given sufficient time (over 9 h). Despite all the substrates reaching the same terminal contact angle, there are clearly significant differences in

hydrosilylation kinetics for different doping densities. The moderately doped p-type and n-type silicon substrates show the fastest hydrosilylation kinetics, followed by the n++ and p++ substrates, with the intrinsic undoped silicon the slowest by far. The rates of the reactions were calculated, as will be described later. To first substantiate the data derived from the goniometry (water contact angle) measurements, X-ray photoemission spectroscopy (XPS) was carried out, as shown in Figure 4 to monitor the change of the fluorine signal. The F(1s) spectrum was used to compare the yield of hydrosilylation reactions at 1 h for the five differently doped silicon wafers, all plotted on the same scale. Hydrosilylation on lightly doped n- and p-type silicon (Figure 4 a,b) shows the highest F 1s signal intensity, followed by n++ and p++ type silicon (Figure 4c and d), while intrinsic silicon (Figure 4e) has the lowest intensity. The Si(2p) spectra of all silicon samples reveal no oxidation to the detection limits of the instrument, which would appear as higher energy features above 102 eV, and would complicate quantitative analyses.24,25

Figure 3. Kinetic profile of plasmonic stamp-assisted hydrosilylation on a hydrogen-terminated Si(111) surface of various doping densities and types. Data is fit to aFigure 1. Preparation of the PDMS-based plasmonic stamps. (a) Sputtered film of gold on PDMS is thermally dewetted, leading to isolated gold nanoparticles. (b) AFM micrograph of the surface of a plasmonic stamp. (c) Visible wavelength transmission spectra of 5 plasmonic stamps showing reproducibility. Inset shows an optical image (photograph) of a completed plasmonic stamp. classic Langmuir kinetics model (Equation 1). Each black dot represents a unique sample that had been illuminated for the indicated time. The error bars represent the standard deviation of five measurements on the same sample.

Figure 4. F(1s) and Si(2p) regions of X-ray photoelectron spectra (XPS) following 1 h of hydrosilylation of 1H,1H,2H-perfluoro-1-decene on Si(111)–H with illumination through a plasmonic stamp. (a) n-type silicon, (b) p-type silicon, (c) n++-type silicon, (d) p++-type silicon, and (e) intrinsic silicon.

Analyses of Reaction Rates The kinetic data obtained and shown in Figure 3 were analyzed to calculate reaction rates in order to shed light on the mechanism of hydrosilylation. Similar to previous work by Huck et al., which examined UV-mediated hydrosilylation on Si,26 the water contact angle increases with time of

illumination until the terminal contact angle is reached (~105°), corresponding to maximum substitution of Si-H groups by Si-R groups on the silicon surface under these conditions. A mathematical description of the hydrosilylation kinetics is straightforward to derive, and follows first-order adsorption kinetics. If there are a total of �, the number of available surface sites for grafting on the silicon surface, then the rate of change in the number of grafted sites, �, is assumed to be proportional to the number of available surface sites d� = �� d� (1) = �(� − �� − �) where � is the total number of surface sites of H-terminated silicon and � is the number of Si sites that have become oxidized. The prefactor � is a steric parameter, and accounts for the average number of silicon sites that become unavailable after a molecule is grafted to the silicon surface. For planar aromatic molecules, the value of � can be quite large (� ≈ 7), while linear molecules are expected to have � values in the range of 1 to 3.27 Lastly, the proportionality factor, �, which is known as the first-order rate constant or kinetic constant, quantifies the rate of the hydrosilylation reaction. If it is assumed that oxidation of the silicon surface is negligible — which is substantiated by XPS measurements shown in Figure 4 — Equation 1 can be converted to substitution level, � = �/�, and subsequently solved d� = �(1 − ��) d� d�′ = � ��′ 1 − ��′ (2) 1 − ln|1 − ��| = �� 1 − exp(−��) ∴ � = �

If we take the limit as the time approaches infinity, the substitution level equals 1/�, which gives the physically intuitive situation where the maximum substitution level, �, is equal to 1/�. It is also noted that we can write �obs = ��, which yields the following equation for the relative substitution level, �,

� = �/� = 1 − exp(−�obs�) (3) Finally, the relative substitution level can be related to the experimentally measured water contact angle by assuming that they are linearly related via a simple rule of mixtures � = � + (� − � )� w M (4) �w = � + (�M − �)(1 − exp(−�obs�))

where � is the water contact angle for H-terminated silicon (~82 ± 2°) and �M is the maximum contact angle for a terminally/maximally substituted surface. The data in Figure 3 are fit to Equation 4 by implementing a non-linear least squares 28 algorithm from SciPy (a Python library). The value of � is constrained to the range of 80–84° -7 -1 -1 and �obs is constrained to the range of 10 –10 sec , while the value of �M is fixed at 105°. The maximum contact angle is constrained to be the same for all silicon substrates, independent of the doping level as there is no thermodynamic or chemical reason to believe that the terminal/maximal substitution would differ, as even in the most heavily doped case (� = 1.8×1019 cm-3), where there is only ~1 dopant atom per 3000 silicon atoms on the surface. This assumption is substantiated by the data in Figure 3 where it appears that all silicon substrates eventually approach the same terminal/maximal contact angle. The fixed terminal contact angle of 105° is chosen by taking the average value of the contact angles of the n and n++ substrates measured after 9 hours of reaction. Lastly, when fitting these data, the uncertainty in each measured data point is accounted for by minimizing the following objective function

(�(� , � , � ) − � ) min obs (5) � where � are the standard deviations of the contact angles on the same sample from five measurements. The results of these fittings are shown in Figure 3, and the values of rate constants are tabulated in Table 1, where the uncertainty of the rate constant is computed from the covariance matrix of the fitting procedure.

Table 1. Important parameters of Schottky junction parameters between gold and silicon of various doping types and levels. ��: doping density; ��: Fermi level; �bi: built-in potential; a �: depletion width; �/��: illumination length. The uncertainty given is the standard deviation of these measurements, and at least 10 measurements were collected.

a -3 -1 Si type Resistivity (Ω cm) �obs/10 s n 15.1 ± 0.2 1.0 ± 0.1 p 6.5 ± 0.5 1.6 ± 0.1 n++ 0.0036 ± 0.0002 0.13 ± 0.01 p++ 0.0067 ± 0.0008 0.14 ± 0.04 Intrinsic 1.52×104 ± 0.09×104 0.057 ± 0.005

The following important observations from these data are made: the rate constant of moderately n-type doped silicon is ~10x larger than degenerately doped n++ silicon, and ~20x

larger than intrinsic silicon. The rate constants of p-type silicon with similar doping to the n-type silicon are within the same order of magnitude, but are slightly higher.

From Kinetics to Mechanism In previous work exploring plasmonic stamping of hydrosilylation on H-terminated silicon, the following mechanisms were considered: resonant photon scattering, nanoparticle plasmonic heating, hot carrier injection, and near-field electromagnetic electron-hole pair generation (EHP).11,12 The observations summarized in these two papers concluded that near-field electromagnetic electron-hole pair generation from the plasmonic field into the silicon was the most likely driving force that led to localized hydrosilylation on the surface. The Schottky, or metal-insulator-semiconductor (MIS) junction, comprising the gold nanoparticles, the alkene ink, and the silicon substrate, rendered the key step of the mechanism more probable, as will be described.12 The proposed mechanism of this hydrosilylation reaction, under these conditions, is reliant on holes generated at, or migrating to, the hydride-terminated silicon surface, as outlined in Figure 5.11–13,26,29–33 Nucleophilic attack of the hole by the alkene results in formation of the silicon-carbon bond and a β-silyl-substituted carbocation that can then abstract a nearby hydride to neutralize the alkyl termination.

Figure 5. Schematic that highlights the key step of the mechanism of hydrosilylation, the nucleophilic attack of the surface silicon atom by an alkene to form a silicon-carbon bond. Note, the all-trans packing configuration of the perfluoroalkyl chains on the functionalized surface is unlikely, and would be expected to have some degree of disorder.

The concentration of holes at the Si-H surface is deemed to be the limiting reagent with respect to the kinetics as the alkene ink is neat (not diluted). The role of doping levels of the silicon with respect to affecting the surface concentration of holes, in the presence of the electric field of a nearby LSPR is attributed to the much deeper depletion regions of the moderately doped n- and p-type silicon (~300–2000 nm), compared to the much shorter depletion width of the intrinsic undoped silicon (~1–5 nm); the photogenerated holes are expected to be swept to the silicon surface via the action of the built-in electric field of the depletion region. The deeper depletion region would therefore result in generation of many more holes, leading to a higher yield of the hydrosilylated alkyl product on the silicon surface. This mechanistic hypothesis was largely qualitative, as it was difficult to connect a handful of contact angle measurements to theoretical predictions. Now that we have, in hand, the kinetic rate constants, it should be possible to bridge these experimentally measured constants to theoretical predictions. The important observation is that the rate of the reaction should be directly proportional to the density of holes at the surface,34 which is further proportional to the short-circuit current density, �, or photoinduced current density, �, of the Schottky junction under illumination. To estimate the �, it is first necessary to calculate the values of key parameters of these junctions for the different types of silicon substrates used, which are shown in [tbl:junction_params] below.

Table 2. Important parameters of Schottky junction parameters between gold and silicon of various doping types and levels. ��: doping density; ��: Fermi level; �bi: built-in potential; �: depletion width; �/��: illumination length. -3 Si type � (cm ) � (eV) �bi (eV) � (nm) 1/� (nm) n 2.97×1014 4.35 0.80 1.9×103 250 n++ 1.81×1019 4.06 1.09 8.9 125 p 2.10×1015 4.93 0.22 3.7×102 250 p++ 1.53×1019 5.16 0.01 1.1 200 Intrinsic 8.30×109 4.61 0.54 2.92×105 250

In Table 2 the doping density, �, is determined experimentally from four-point probe resistivity measurements listed in Table 1. The Fermi level, �, is determined from the following equations.

� � � = � + ln(� /� ) � (6) � � � = � − ln(� /� ) + � � where � is the electron affinity of silicon (4.05 eV), ��/� is the thermal energy of the charge carriers at a temperature � (25.9 meV), � is the indirect bandgap of silicon (1.12 eV), while � 19 and � are the density of states at the conduction and valence band edges, which are 2.81×10 19 -3 and 1.88×10 cm respectively. The built-in potential, �bi, is estimated using the Mott-Schottky rule,35

� = �Au − � (7) where �Au is the work function of gold, which is assumed to be 5.15 eV. The depletion width, �, is given by,

2� � � = Si bi (8) ��

-12 where �Si is the permittivity of silicon (1.05×10 F/cm). Finally, � is the optical absorption coefficient of silicon at 526 nm.12 Using this data regarding the properties of the Schottky junction, we can begin to formulate a more detailed mechanistic understanding of the plasmonic stamping hydrosilylation reaction kinetics. For the sake of simplicity, we shall restrict ourselves to n-type substrates. When the plasmonic stamp is placed in contact with the substrate, there is a net flow of majority carriers (electrons) towards the interface in order to equilibrate the Fermi levels between the n-type silicon and the gold nanoparticles. This results in a built-in field, and over the depletion width (Equation 8) photogenerated holes would be swept toward the junction, with electrons being swept in the opposite direction. The generation rate of electron-hole pairs in the silicon at depth, �, from the surface will be proportional to the electromagnetic field strength of the incident illumination, which can be approximated by Beer’s Law

�(�, �) = �exp(−�(�)�) (9) where � is the electron-hole pair generation rate at the surface and �(�) is the absorption coefficient, as a function of the incident illumination wavelength. For the purposes of this analysis, we assume a constant absorption coefficient, which is a reasonable approximation, since the incident white light is filtered over a narrow wavelength range. As such, the absorption coefficient is taken at the center wavelength of the filter of 526 nm, which is listed in Table 2.

The total rate of carrier absorption, �, can be determined by integrating Equation 9

� = � (�) �� = �/� (10) Using this result we can make the simplifying assumption that there is uniform illumination over a distance of 1/�, with a constant generation rate �, which will result in the same total carrier generation rate. Using this model of carrier generation we can approximate the photogenerated current density of holes of these illuminated Schottky junctions.

The current density needs to be broken up into two parts: the drift current �, and the diffusion current �. The drift current is the current from electron-hole pairs generated within the depletion region, and the diffusion current results from electron-hole pairs generated outside the depletion region. Furthermore, the photocurrent density needs to be separated into the current from the electron-hole pairs generated from the intense E-field of the plasmons and the continuous wave (CW) illumination of the incident light source. For the moderately doped n-type silicon used in this work, the depletion width is ~1900 nm, which is much larger than the illumination length, �= 1/� = 250 nm. As such, the diffusion current is zero, as all EHPs are generated within the depletion region,

CW � = ��/� (11) In the case of degenerately doped n++ silicon, the depletion width (~9 nm) is much less than the illumination length (125 nm), as such, electron hole pairs will be generated outside of the built-in field and holes will isotropically diffuse a distance �, before they recombine (on average), which 35 is known as the diffusion length. It is straightforward to show that if �� holes are generated at a depth, �, from the surface, the diffusion current density contribution from these holes will be

��(1 − �/�)/2��, which is integrated to give the final result / �� CW = (1 − �/� ) �� 2 (12) �� 1 = 1 − 2� 2��

The diffusion length of n++ silicon is ~2 μm and the value of 1/2�� = 0.03 << 1, which gives the simple result of �� CW = (13) 2� For intrinsic silicon the depletion width is very large, but due to the extremely low density of majority carriers (~8.3×109 cm-3), the built-in field strength is very weak and the average kinetic energy imparted by the built-in field is less than the thermal energy at room temperature (25.9

meV). As such, the current density from the continuous wave illumination is identical to the n++ substrate, being purely diffusional (the diffusion length of intrinsic silicon is even larger than n++) �� CW = (14) 2� Next, we need to consider the additional charge carriers generated by the plasmonic field. The plasmonic electric field can be very intense, generating a very high density of charge carriers 10,36 within the effective spatial extent of the plasmonic field, �SPR. The generation rate due to the plasmonic field is

�SPR = �� (15) where � is the enhancement factor of the plasmonic field. For n-type silicon, the depletion width is definitely larger than the spatial extent of the plasmonic field, as such it is assumed that all of the plasmonically generated carriers will be swept towards the junction,

SPR � = ��SPR (16) If we now combine Equation 11 and Equation 16, the total photocurrent density is given by

� = �CW + �SPR (17) � = ��(1/� + ��SPR) For degenerately doped silicon the depletion width is very small (~9 nm) is likely less than the effective spatial extent of the plasmonic field. Therefore, it is assumed that any charge carriers generated outside of the depletion region will recombine rapidly, due to the extremely high density of electron-hole pairs generated by the plasmonic field. The photocurrent density due to the plasmonic field is thus

SPR � = �� (18) where the final expression for the total photocurrent density of n++ silicon is

CW SPR � = � + � 1 (19) � = �� + �� 2� For intrinsic silicon, we assume that none of the plasmonically generated charge carriers are captured, due to the weak built-in field, and the total photogenerated current is simply given by Equation 14. Given that the kinetic rate constant will be proportional to the photocurrent densities, the ratio of rate constants should equal the corresponding ratio of photocurrent densities. For the ratio between n++ and intrinsic silicon,

1 � � 2� + ��++ ++ = ++ = ++ � � 1 2� (20) 1 � 1 ⇒ � = ++ − 2�++ �� ++ It is worth noting at this point that the depletion widths listed in Table 2 are what would be expected without illumination. However, under illumination the bands will move towards flat band conditions, and as such when calculating the value of �, a reduced depletion width of 4.5 nm (instead of 8.9 nm) is used. Using the values in Table 2 and the experimentally determined ratio of rate constants (�++/� ~2.3), then the enhancement factor is estimated to be ~50. Next, we take the ratio of n-type and intrinsic, giving the expression � � 1/� + �� = = SPR � � 1/(2� ) (21) 1 � 1 ⇒ �SPR = − � 2�� Again, if we use the values in Table 2, the experimentally determined ratio of rate constants

(�/� ~ 17.5) and value of � = 49, the value of �SPR comes to 39 nm, which is physically reasonable. Finally, the expression for the ratio of rate constants for n-type to n++ is given by � � 1/� + �� = = SPR (22) �++ �++ 1/(2�) + ��++

Utilizing the derived values of �=50, �SPR=39 nm, and the absorption coefficients from Table 2, the predicted value of the rate constant ratio is 9.2. This predicted ratio of 9.2 agrees remarkably well with the experimental value of �/� ~ 7.7, especially considering the large number of simplifying assumptions that went into this model. It is believed that in the case of p-type silicon, a similar analysis can be applied, despite the majority carriers being holes. The very deep work function of Au would still result in holes being swept towards the silicon surface. The slightly higher experimentally observed rate constants for p-type silicon (compared to n-type) are not entirely clear at this point, but it may be due to the additional holes that accumulate at the silicon surface from the Schottky junction.

Figure 6. Schematic of charge generation and collection in intrinsic, n- and n++- type silicon, as indicated. The arrows in the charges indicate the drift/diffusion direction of holes. The shading in the silicon represents the depletion region near the interface.

The results of the model based upon the kinetic data and these calculations are summarized in Figure 6. As mentioned earlier, the key step of the mechanism of hydrosilylation is the generation of holes that accumulate at the interface of the hydride-terminated silicon, that then react with a nearby alkene. As described in earlier papers,11–13 nucleophilic attack by the alkene results in silicon-carbon bond formation and formation of a β-silyl-substituted carbocation that is neutralized by a combination of the electron and a hydrogen atom from the surface. The kinetic studies and calculations in this work further hone this mechanism by elucidating the non- linear combination of 3 different effects at play: doping, the thickness of depletion regions in this architecture, and charge carrier diffusion. As shown in Figure 6, the built-in field of intrinsic silicon is so weak that it does not sweep charge carriers towards the interface and thus relies entirely on random diffusion of photogenerated holes towards the silicon surface to drive the hydrosilylation reaction. High doping, on the other hand, will have a higher concentration of holes at the interface, as it will capture an equal amount of photogenerated holes as intrinsic silicon via diffusion, as well as a fraction of the holes generated from the intense electric field of the LSPR. The highly doped silicon only captures a fraction of the LSPR generated holes, as the depletion width is very small (a few nanometers) relative to the spatial extent of the LSPR electric field. The moderately doped n-type silicon, on the other hand, has the optimum level of doping (a Goldilocks scenario). As outlined in Figure 6, the depletion width with n-type silicon is greater

than the optical absorption depth and will sweep all of the photogenerated holes to the interface, as it has a sufficiently strong built-in field (compared to intrinsic silicon). Moreover, it will also capture all of the plasmonically generated holes. The result for the moderately doped silicon is an optimum of these factors at which the fastest observed rates of alkene hydrosilylation are observed.

SUMMARY

While experimentally simple to execute, the mechanism of plasmonic stamp-driven surface chemistry on silicon is challenging to elucidate. The sandwich architecture formed upon stamping the plasmonic stamp on the alkene ink on the silicon surface results in a metal-insulator- semiconductor (MIS) junction. Upon illumination, the high electric field of the LSPR generates electron-hole pairs in the silicon, which is the key to the mechanism of hydrosilylation. The localization of holes at the interface results in nucleophilic attack by a nearby alkene, leading to the silicon-carbon bond forming event of hydrosilylation. The concentration of holes is thus the limiting reagent and plays a critical role in the rate of the LSPR-driven reaction. Moderately doped silicon shows the fastest rates as it represents the optimum of the width of depletion and charge carrier diffusion, compared to more highly doped and intrinsic silicon.

ASSOCIATED CONTENT

Supporting Information. Additional experimental details regarding the sputtering deposition of gold, and SEM and AFM characterization of gold films before thermal annealing on native oxide- capped silicon surfaces.

AUTHOR INFORMATION

Corresponding Authors *E-mail: [email protected] *E-mail; [email protected]

ORCID Chengcheng Rao: 0000-0002-4308-7201 Erik J. Luber: 0000-0003-1623-0102 Brian C. Olsen: 0000-0001-9758-3641 Jillian M. Buriak: 0000-0002-9567-4328

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This work was supported by a grant from the Natural Sciences and Engineering Research Council (NSERC, RGPIN-283291-09), Alberta Innovates Technology Futures (iCORE IC50-T1 G2013000198), and the Canada Research Chairs Program (CRC 207142).

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