J. Phys. Chem. B 2000, 104, 3327-3336
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Controlling Surface Chemistry with Light: Spatially Resolved Deposition of Rovibrational-State-Selected Molecules† L. B. F. Juurlink, R. R. Smith, and A. L. Utz* Department of Chemistry and W. M. Keck Foundation Laboratory for Materials Chemistry, Tufts UniVersity, Medford, Massachusetts 02155 ReceiVed: September 27, 1999; In Final Form: January 25, 2000
We report the spatially resolved deposition of infrared laser excited methane molecules onto a Ni(100) substrate. A narrow bandwidth infrared laser excites methane molecules in a supersonic molecular beam to V ) 1 of the ν3 C-H stretching vibration. Tuning the laser to the center of the Doppler-broadened absorption profile selectively excites only those molecules whose transverse velocity is nearly zero. The molecular beam impinges on a Ni(100) substrate where laser-excited molecules dissociate with up to 1600 times the probability of molecules that do not absorb infrared light. Despite the fact that the entire Ni(100) surface is exposed to the molecular beam, only a narrow region of laser-enhanced carbon deposition appears on the substrate. We can control excitation conditions to deposit a single stripe, or a set of equally spaced parallel stripes of carbon on the surface. A model of the deposition process based on optical broadening mechanisms in our experiment quantitatively predicts deposition area dimensions without any adjustable parameters. Extension of the model to other feasible experimental conditions points to the possibility of achieving submicrometer resolution. These results demonstrate a new means of exerting spatial control over deposition processes and highlight an important experimental consideration for future eigenstate-resolved gas-surface reactivity studies employing narrow-bandwidth optical pumping.
I. Introduction Gas-surface reactions are multistep processes that involve complex interactions between the solid substrate and the gasphase reactants.1 The nature of these interactions can vary with the system studied. While many reactions depend sensitively on the geometric and electronic structure of the substrate, others appear to depend more strongly on the extent of excitation in the gas-phase reagent.2 The direct dissociative chemisorption of methane, which is rate limiting in the industrial steam reforming reaction, is an example of the latter case and the subject of this work.3 The potential energy surface governing dissociative chemisorption is a function of many degrees of freedom that complicate experimental efforts to unravel the reaction mechanism. Translational, vibrational, and rotational energy in the gas-phase reagent, surface temperature, surface structure, and the orientation and impact parameter of the incident gas-phase molecule can all have profound effects on the outcome of the gas-surface encounter. The situation is even more complex for polyatomic reagents, where the presence of many vibrational modes further increases the problem’s dimensionality. Studies that quantify the reactivity of incident molecules in selected rotational and vibrational states offer a unique opportunity to probe the potential energy surface along specific coordinates. Identifying the most reactive degrees of freedom reveals the nature of the reaction coordinate. Such state-resolved data also test theory more stringently than do dissociation probabilities averaged over many internal states of the incident molecule. Despite these strong motivations for performing stateresolved experiments, experimental progress has been hampered †
Part of the special issue “Gabor Somorjai Festschrift”. * To whom correspondence should be addressed. E-mail:
[email protected].
by the difficulty of preparing a sufficiently high flux of stateselected molecules and then quantifying their reactivity. During the past 8 years, several groups have succeeded in quantifying the dissociative chemisorption probability for neutral gas-phase molecules in selected quantum states. Three general approaches have emerged for performing these state-resolved measurements. Michelson et al.4-6 reported vibrational-stateresolved reaction probabilities for hydrogen dissociation on copper single crystal surfaces. Since vibrations are not efficiently cooled in most supersonic expansions, they modeled the vibrational state population present in supersonic expansions from a range of nozzle source temperatures. The unusually sparse vibrational structure of H2 and D2 allowed them to extract vibrational-state-resolved dissociation probabilities from measurements on thermally averaged vibrational state distributions. While this approach yielded a wealth of insight into the hydrogen/copper system, its utility is limited to systems in which the reagent has a single, very high frequency vibrational mode. In an alternative approach, a pulsed laser source optically excites a temporally resolved ensemble of state-selected molecules. Time- and state-resolved detection of the scattered products reveals details of nonreactive scattering channels, while the absence of scattered flux signals dissociative chemisorption. This approach probes the nonreactive scattering channel directly, but the relatively low duty cycle for excitation makes direct detection of the reactive channel extremely difficult or impossible. Several groups have successfully applied this technique to study dissociative chemisorption. Sitz and co-workers studied hydrogen dissociation on Pd(111) with rovibrational state resolution,7 and Auerbach, Wodtke, and co-workers have recently reported similar studies on very highly vibrationally excited NO scattering from oxygen-covered Cu(111).8 The two groups relied on stimulated Raman scattering and stimulated
10.1021/jp993454v CCC: $19.00 © 2000 American Chemical Society Published on Web 03/21/2000
3328 J. Phys. Chem. B, Vol. 104, No. 14, 2000 emission pumping, respectively, to prepare the reagents in the selected initial quantum state. State-resolved resonance-enhanced multiphoton ionization (REMPI) detection probed the flux and internal state of scattered molecules in both studies. Our recent eigenstate-resolved study of methane dissociation on Ni(100) was the first to probe the reaction dynamics of a vibrationally excited polyatomic molecule, and it illustrated a third approach to studying state-resolved gas-surface reaction dynamics.9 We found that infrared laser excitation of the antisymmetric C-H stretching normal mode in CH4 resulted in a dramatic enhancement of the molecules’ dissociative chemisorption probability. In that study, a single mode continuous wave (CW) infrared laser with an optical bandwidth less than 1 MHz crossed a supersonic molecular beam containing methane. Laser-excited methane molecules promoted to V ) 1, J ) 2 of the ν3 antisymmetric C-H stretching vibration dissociated with a probability up to 1600 times greater than those molecules that do not absorb infrared light. In contrast to the previously mentioned studies, we detected the surface-bound products of the reactive channel to quantify dissociative chemisorption probability. Our use of a single mode infrared laser raises new issues and presents opportunities that are unique to optical pumping experiments using very narrow bandwidth laser sources. The bandwidth of our color center laser is at least 2 orders of magnitude less than the bandwidth of the pulsed lasers used in previous studies of gas-surface reactivity. Here, we show that the details of our excitation scheme result in a striking spatial distribution of the dissociated molecules on the Ni(100) substrate, and that the deposition pattern arises from relative magnitudes of the homogeneous and inhomogeneous broadening mechanisms that govern our optical pumping scheme. The data presented demonstrate a novel means of improving spatial resolution in molecular beam epitaxy, and also highlight an important experimental consideration that impacts our own and future studies of eigenstate-resolved surface chemistry that use narrow-bandwidth optical pumping.
Juurlink et al.
Figure 1. Schematic illustration of the supersonic molecular beam chamber.
II. Experimental Approach A detailed description of our triply differentially pumped supersonic molecular beam surface analysis chamber appears elsewhere, and we only summarize key features here.10 A supersonic molecular beam of methane, typically seeded in hydrogen, expands from a heated nozzle source and is triply differentially pumped prior to entering an ultrahigh vacuum (UHV) surface analysis chamber. The UHV chamber houses a 1 cm diameter Ni(100) single crystal oriented to within 0.1° of the (100) plane, an electron gun and hemispherical electron energy analyzer for Auger electron spectroscopy measurements, a sputter gun for crystal cleaning, and a quadrupole mass spectrometer located on the molecular beam axis for time-offlight analysis of the molecular beam. A schematic illustration of the apparatus appears in Figure 1. A unique feature of our apparatus is its ability to excite a significant fraction of the incident molecular beam into a single rovibrational eigenstate using infrared laser radiation. We then quantify the enhanced dissociative chemisorption probability of these state-selected molecules. Infrared light from a CW, single mode color center laser enters a four-mirror multipass cell housed in the first differential pumping chamber and makes up to 16 orthogonal passes through the molecular beam.11 The orthogonal excitation geometry prevents the velocity spread along the molecular beam flight axis from projecting onto the laser’s propagation direction. Such a projection would Doppler
Figure 2. Infrared absorption spectrum of methane in the supersonic molecular beam. Trace a shows infrared absorption as measured by the pyroelectric bolometer. Trace b is the derivative signal for light transmitted through the Fabry-Perot e´talon. Locking the laser frequency to the zero crossing of the derivative signal centered on the CH4 absorption feature keeps the infrared light in resonance with the methane transition.
shift most molecules in the molecular beam out of resonance with the infrared light. A room-temperature pyroelectric bolometer housed in the second differential pumping stage provides a direct measure of infrared absorption.12 The detector is mounted on a linear motion feedthrough. It can be moved into the molecular beam path for absorption measurements or retracted to allow the beam to pass freely into the surface analysis chamber. The 2 mm diameter bolometer intercepts a solid angle of the molecular beam that is centered on the Ni(100) crystal, but the detector’s solid angle is much smaller than that subtended by the crystal. Therefore, observation of laserexcited molecules impinging on the bolometer guarantees that laser-excited molecules will fall on the Ni(100) surface when the bolometer is retracted from the beam path. Figure 2 shows the absorption signal we measure with the bolometer while scanning the infrared laser over the R(1) transition to the ν3, V ) 1, J ) 2 eigenstate. Under favorable conditions, we excite up to 16% of all methane molecules in the incident beam.10
Controlling Surface Chemistry with Light We ensure that the infrared light remains in resonance with the methane absorption throughout the experiment by locking the laser frequency to the transmission fringe of a temperaturestabilized, vacuum-jacketed Fabry-Perot e´talon with a computercontrolled servo loop. Characterization of our frequency stabilization scheme demonstrates that the laser frequency drifts by no more than 1 MHz during an experiment.10 The width of the transmission fringe and our estimate of the Fabry-Perot cavity’s resolution places an upper limit on the laser bandwidth of 1 MHz, which is consistent with the manufacturer’s specifications. We note that the instantaneous line width of the color center laser is typically much less than 1 MHz, but high-frequency acoustic modes of the laser cavity introduce frequency jitter that increases the laser’s effective bandwidth. We quantify the dissociative chemisorption of CH4 by detecting carbon deposition on the surface with Auger electron spectroscopy. Methane physisorbed on the surface desorbs promptly from our 475 K Ni(100) surface, and carbon dissolution into the bulk does not occur with a significant rate until higher temperatures.13 We integrate the Auger electron peaks for carbon (272 eV) and Ni (848 eV) and take the ratio of peak integrals as a measure of relative carbon coverage. The known 0.50 ML carbon coverage resulting from the self-limiting saturation coverage of C2H4 on Ni(100) calibrates our carbon measurements. An extended exposure of a clean surface to the electron beam verifies that the 20 nA electron beam does not result in additional carbon deposition during our measurement. We adjust the focal properties of the electron gun and hemispherical analyzer so the imaging area of the hemispherical analyzer defines the spatial resolution of the spectrometer. We measure the spatial resolution of the Auger electron spectrometer by exposing the surface to a high kinetic energy beam of methane while positioning the Ni surface so the edge of the molecular beam image falls near the crystal center. This procedure results in an abrupt boundary where surface carbon coverage changes from 0.00 ML to 0.15 ML. We measure carbon coverage as a function of crystal position relative to the hemispherical analyzer focal point, and deduce that the hemisphere images a 1.0 mm diameter spot on the surface. Monitoring the Ni Auger signal as the Ni(100) crystal edge passes through the detection area confirms this measure of spatial resolution. The measurements described in this study are maps of carbon deposition collected following methane doses with and without laser excitation. Varying the position of the crystal during the dose allows us to characterize the full image of the molecular beam when it passes through the largest aperture in our sliding beam valve. Under those conditions, we calculate the molecular beam diameter at the position of the crystal to be 1.1 cm. We generate the carbon deposition maps by making individual measurements of carbon coverage at a series of points on the crystal surface. We translate the crystal in front of the hemispherical analyzer to vary the point characterized, and we ensure that the sample-to-spectrometer working distance remains fixed for all measurements. III. Results and Analysis Figure 3 illustrates the striking localization of laser-enhanced deposition that we observe in our experiments. The open symbols show the location of carbon deposition without laser excitation and indicate the spatial extent of the molecular beam. The solid symbols show the spatial distribution of laserenhanced deposition. When we deconvolute the spot size of our Auger electron spectrometer, the region of laser-enhanced
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Figure 3. Carbon coverage as a function of horizontal displacement from crystal center. Open symbols are for a methane dose without laser excitation, and the solid symbols are for a dose in which infrared light excites a portion of the beam to the ν3 V ) 1, J ) 2 eigenstate. The solid lines passing through the data are from models described in the text.
deposition is nearly a factor of 5 narrower than the molecular beam image. The data in Figure 3 were collected under the following conditions. A supersonic molecular beam of 2% CH4 in H2 expands from a 295 K nozzle source and impinges on a clean Ni(100) crystal. Time-of-flight measurements reveal the beam’s translational energy (44.0 kJ/mol) and energy width (∆E/E e 5%). In the optical pumping experiment, infrared light from a single-mode, CW color center laser intersects the molecular beam at 90° to the flow axis and 30 cm upstream from the surface. The infrared light is tuned into resonance with a methane absorption feature and excites 12% of all methane molecules in the beam to the J ) 2 rotational level of the ν3 antisymmetric C-H stretching eigenstate via the R(1) transition at 3038.4985 cm-1. To ensure that dissociative chemisorption probability remains constant during the exposure, dose times for the laser-enhanced deposition are adjusted to result in carbon coverage of e0.14 ML. The spatial distribution of carbon deposition for the laseroff dose agrees quantitatively with our predictions of molecular beam diameter and our measurement of Auger electron sampling area. Since the Ni(100) crystal intercepts a very small solid angle centered on the molecular beam flight axis, methane flux is constant over the crystal face. The relatively constant carbon coverage measured for the laser-off experiment is consistent with that expectation and indicates that our technique for quantifying carbon coverage as a function of position on the crystal does not exhibit a significant bias. Collimating apertures along the molecular beam path define the molecular beam’s size (1.1 cm diameter) at the crystal surface. A convolution of this beam diameter with the 1.0 mm Auger electron spectrometer spot size appears as a solid line passing through the laser-off data in Figure 3. III.a. Optical Broadening Mechanisms. To model the spatial distribution of carbon in the laser-on dose, we must examine details of the laser excitation process. We identify six factors that contribute to the observed line width of the methane absorption transition in Figure 2. These same factors determine the dimensions of the laser-enhanced deposition region in Figure
3330 J. Phys. Chem. B, Vol. 104, No. 14, 2000
Juurlink et al.
TABLE 1: Transit-Time Broadening for Three Different Molecular Beams
TABLE 2: Transverse Velocities and Doppler Frequency Shifts for Three Different Molecular Beams
beam
V||, m/s
Ekin, kJ/mol
∆νtt, MHz
100% CH4 22% CH4/H2 2% CH4/H2
1000 1729 2345
8.0 23.9 44.0
1.1 1.9 2.5
beam
3. We examine these factors in detail in the following paragraphs. These factors can be divided into broadening mechanisms that arise from the details of the infrared excitation process, and the laser bandwidth, which is an inherent property of our color center laser light source. The principle effect of the broadening mechanisms is to increase the range of frequencies that can be resonant with the optical transition. If the broadened absorption profile is identical for all molecules in the sample, the broadening is homogeneous. When light overlaps with any portion of a homogeneously broadened absorption profile, all molecules in the beam have an equal probability for excitation. Lifetime (natural), transit-time, saturation (power), and collisional broadening are all homogeneous broadening mechanisms. If the broadened profile arises from an ensemble average, i.e., different subsets of molecules in the sample absorb different frequencies of light, then the broadening is inhomogeneous. When narrow bandwidth light excites different parts of an inhomogeneously broadened absorption feature, distinct subsets of molecules in the sample are excited. Doppler broadening is an inhomogeneous broadening mechanism. Our ability to excite a portion of the inhomogeneously broadened Doppler profile of CH4 in the molecular beam is the basis for the localized deposition we observe. While inhomogeneous broadening makes spatially resolved deposition possible, laser bandwidth and homogeneous broadening mechanisms determine the ultimate dimensions of the localized deposition region. Demtro¨der provides an excellent overview of these broadening mechanisms.14 In our experiments, transit-time broadening is the dominant homogeneous broadening mechanism for methane molecules in the molecular beam. The radiative lifetime of methane in the ν3 vibrational state is very long,15 so the natural line width for transitions from V ) 0 to ν3 is about 16 Hz. In strong optical fields, saturation broadening decreases the excited-state lifetime and results in further broadening.14 We have quantified the extent of saturation in our optical pumping experiments10 and calculate that saturation broadening increases the natural line width by less than a factor of 2. Methane molecules in the seeded supersonic molecular beam travel at velocities up to 2800 m/s. Our orthogonal excitation geometry coupled with methane’s high speed limits the laser-molecule interaction time. Table 1 summarizes transit times for three different molecular beams passing through our 1.4 mm diameter laser spot. For molecules passing through plane wave radiation, the molecules’ flight time alone determines the transit-time broadened line width. When the laser is not perfectly collimated, the constant-phase fronts of the radiation field are no longer planar, and it is the molecule’s flight time through a constant-phase region of space that becomes important. Following Demtro¨der,14 we have
∆νtt ≈
[ ( )]
0.4V πw2 1+ w Rλ
2
(1)
where ∆νtt is the full-width at half peak maximum (fwhm) due to transit-time broadening, V is the molecular speed, w is the laser beam waist (as a half-width), λ is the radiation wavelength, and R is the radius of curvature of the constant-phase fronts in
V||, m/s
Ekin, kJ/mol
l, m
t, µs
∆rmax, m
V⊥,max, ∆νmax, m/s MHz
100% CH4 1000 22% CH4/H2 1729 2% CH4/H2 2345
@ Pyroelectric Detector 8.0 0.2141 214 0.0010 23.9 0.2141 124 0.0010 44.0 0.2141 91 0.0010
4.7 8.1 10.9
1.4 2.4 3.3
100% CH4 1000 22% CH4/H2 1729 2% CH4/H2 2345
@ Ni(100) Surface 8.0 0.4039 404 0.0050 23.9 0.4039 234 0.0050 44.0 0.4039 172 0.0050
12.4 21 29
3.8 6.5 8.8
the laser-molecule interaction volume. We gently focus the laser light, and its focal point is located approximately 0.5 m before the multipass cell. Therefore, for our excitation geometry, a beam waist of 0.7 mm, a wavelength of λ ≈ 3.3 µm, and a molecular speed of 2345 m/s, we calculate a homogeneous line width (fwhm) of 2.5 MHz. Demtro¨der points out that for molecules flying through a laser field with a Gaussian intensity profile, transit-time broadening leads to a Gaussian absorption profile with fwhm ) ∆νtt. Table 1 summarizes calculated values of ∆νtt for the three molecular beams used in this study. While elastic and inelastic collisions during optical excitation can broaden an absorption feature, we do not expect collisional broadening to be important in our experiments. The collision frequency in a supersonic expansion drops rapidly with distance from the nozzle source. For expansion conditions similar to ours, Miller shows that over 99% of the collisions in the supersonic expansion occur within the first 20 nozzle diameters downstream from the nozzle source. Beyond that distance, no more than one additional collision remains for the average molecule.16 Since our multipass cell is located more than 1200 nozzle diameters downstream, we do not expect collisions during optical excitation to be a significant source of line broadening. Doppler broadening is the most important inhomogeneous broadening mechanism in our laser excitation step. Molecules in the molecular beam have a range of transverse velocities due to their divergence from a 25 µm nozzle orifice to a 1.1 cm diameter image at the Ni(100) crystal. Those molecules traveling along the beam axis have zero transverse velocity, while those traveling toward the edge of the beam image have a maximum transverse speed. The maximum transverse velocity component of a particular molecular beam, V⊥,max, depends on a molecule’s maximum displacement from the beam axis upon impact with the surface, ∆rmax, and the flight time from nozzle to surface, t. Flight time is the quotient of the velocity component parallel to the flight axis divided by the nozzle-surface distance, l. Therefore,
V⊥,max )
∆rmax V|∆rmax ) t l
(2)
Table 2 lists ∆rmax and the maximum transverse speeds for beams impinging on both the 2 mm diameter pyroelectric bolometer absorption detector and the 10 mm diameter Ni(100) crystal. The range of transverse speeds present in each beam leads to Doppler broadening. Since the bolometer intercepts a smaller solid angle of the beam than does the Ni(100) crystal, molecules impinging on the edge of the detector have a smaller transverse velocity component than do those molecules impinging on the edge of the Ni(100) substrate. Examining the basis for Doppler broadening reveals the origin of the spatially resolved deposition we observe. Infrared light and the molecular beam propagate in the horizontal plane and are mutually orthogonal, so transverse velocity components in
Controlling Surface Chemistry with Light
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the horizontal plane project onto the laser’s propagation axis. The resulting Doppler shift in absorption frequency is given by eq 3.14
∆ν ) ν0
V⊥ c
(3)
Here, ∆ν is the Doppler shift associated with molecules moving with transverse velocity V⊥ in the horizontal plane, ν0 is the unperturbed peak absorption frequency for the transition, and c is the speed of light. Equation 3 clearly shows that molecules with different velocity components in the horizontal plane have different Doppler frequency shifts. Table 2 shows the maximum Doppler shift expected for the ν3 R(1) fundamental transition at 3038 cm-1. Since both parallel and antiparallel transverse velocities are possible in the multipass cell, the fwhm for the Doppler broadened profile is twice the maximum frequency shift. Table 2 shows that the Doppler shift for molecules impinging on the Ni sample is much greater than the laser line width or the homogeneous line width of molecules in the molecular beam. The role of laser bandwidth in our experiments depends on its magnitude relative to the homogeneous absorption line width. Two limiting cases illustrate this point. In the first, the molecules’ homogeneous absorption line width is very narrow relative to the 1 MHz laser bandwidth. When the laser frequency, with its instantaneous line width of ∼100 kHz, jitters within the 1 MHz frequency envelope, different transverse velocity subgroups of molecules will be excited in the beam, each for a fraction of the total irradiation time. This situation results in the time-averaged dissociation probability at a particular point on the substrate differing significantly from the true laser-enhanced dissociation probability. In contrast, if the homogeneous absorption profile is broader than the laser bandwidth, frequency jitter does not alter the identity of the molecules excited. All molecules whose Doppler shifted absorption profile is resonant with the 1 MHz laser bandwidth envelope will be resonant with the instantaneous frequency of the laser radiation for the full irradiation time. Since the transit-time broadened homogeneous line width of all beams in our study exceeds the laser bandwidth of 1 MHz, the latter case holds. This point is crucial to both our calculations of infrared excitation efficiency outlined in ref 10 and of absolute reaction probability for state-selected molecules impinging on the surface. III.b. Predicted Deposition Pattern. In our state-resolved dissociative chemisorption experiments, we adjust the FabryPerot reference e´talon cavity length so that its transmission maximum coincides with ν0, the unperturbed absorption frequency for methane molecules traveling along the center of the molecular beam flight axis (V⊥ ) 0). When we lock our laser frequency to the Fabry-Perot transmission fringe, only those molecules whose homogeneously broadened absorption profile overlaps with the laser frequency can absorb light. Those molecules whose absorption peak is Doppler shifted by significantly more than the half-width of the homogeneous absorption profile will not be excited. Thus, infrared excitation selects a subset of CH4 molecules whose transverse velocity along the laser propagation direction is nearly zero. Since there are essentially no direction-changing collisions in the molecular beam following infrared absorption, selective excitation of molecules with a specific transverse velocity component maps onto a specific region of laser-enhanced deposition on the surface. Figure 4 depicts the situation. We can quantitatively predict the width of the enhanced deposition region we observe. Figure 4 shows that those
Figure 4. Excitation of an inhomogeneous absorption profile with narrow bandwidth radiation. Three different subsets of molecules in the molecular beam each have the same homogeneous line width, ∆ν. Their peak absorption frequency is Doppler shifted due to their differing transverse velocities relative to the laser propagation direction, V⊥. For the situation illustrated, laser light at frequency ν0 and bandwidth ∆νL is resonant only with those molecules whose transverse velocity component is nearly zero. As a result, laser-enhanced carbon deposition on the Ni(100) surface is localized on the crystal center.
molecules whose Doppler-shifted homogeneous absorption profiles overlap with the laser line width can absorb light and react with enhanced probability on the Ni(100) surface. Since the transit-time broadened absorption profile for reactive molecules significantly exceeds the laser line width in our experiments, the homogeneous line width, coupled with the transverse speed and nozzle-surface flight time for molecules in the molecular beam determines the physical dimensions of the enhanced deposition region. We begin our quantitative analysis by focusing on the data in Figure 3, for which the molecular speed along the flow axis is 2345 m/s. The transit-time broadened homogeneous line width for the CH4 in the beam is 2.5 MHz (fwhm). Methane molecules whose absorption profile is Doppler shifted by half this line width would still absorb light from a laser fixed at frequency ν0, albeit with about half the probability. We substitute a 1.3 MHz half-width into eq 3 and solve for V⊥ ) 4.3 m/s. (Molecules traveling with a transverse velocity of (4.3 m/s along the laser’s propagation direction would have their peak absorption frequency shifted by 1.3 MHz from ν0.) The flight time for molecules to travel from the nozzle to the surface determines how far a molecule with a given transverse velocity moves away from the molecular beam axis. Table 2 shows that the flight time for CH4 in the 2345 m/s beam is 172 µs. We calculate a transverse displacement from the beam center of 0.7 mm for CH4 molecules with V⊥ ) 4.3 m/s. The optical path for infrared light in our multipass cell simultaneously excites molecules moving to the right and left of the crystal center. Thus, we predict a laser enhanced deposition region (0.7 mm from crystal center for a fwhm of 1.4 mm. Qualitative inspection of Figure
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Juurlink et al. closed symbols show carbon deposition for a 1730 m/s CH4 beam. The two regions have identical widths. Offsetting contributions from the transit-time broadened homogeneous line width and the molecular time-of-flight time account for the two molecular beams producing laser-enhanced deposition areas with the same dimensions. Equation 1 shows that the transit-time broadened line width depends linearly on molecular beam speed along the flight axis. Since transit-time broadening dominates all other homogeneous broadening mechanisms by several orders of magnitude in our experiment, the homogeneous line width of methane molecules in the beam is directly proportional to molecular beam speed. Molecules whose transverse velocity exceeds some critical value are Doppler shifted out of resonance with the laser frequency at ν0 and absorb significantly less or no infrared light. We rearrange eq 3 to calculate the transverse velocity needed to Doppler shift the homogeneous line width by half its fwhm.
Figure 5. Carbon coverage versus horizontal displacement from crystal center for laser-excited molecular beams with two different incident velocities. Open symbols result from a 2345 m/s CH4 molecular beam, while the solid symbols result from a 1730 m/s CH4 beam.
3 shows that this estimate is consistent with the experimental data. We improve our modeling of the laser-enhanced deposition area by properly accounting for the various line shapes in our experiment. Transit-time broadening leads to a Gaussian absorption profile.14 We therefore treat each CH4 molecule in the molecular beam as having a homogeneous Gaussian absorption profile with fwhm ) 2.5 MHz. The infrared laser light has a bandwidth of 1 MHz, fwhm. We calculate the transversevelocity-dependent absorption of light at frequency ν0 by convoluting the laser bandwidth with the Doppler-shifted homogeneous line width for all molecules impinging on the crystal face. We multiply this transverse-velocity-dependent profile by the nozzle-to-surface flight time results to predict the spatial distribution of carbon deposition. We then convolute this spatial distribution with the 1 mm diameter circular spot size of our Auger electron spectrometer to reproduce the experimentally measured carbon deposition map. Finally, we add the known dissociation probability9 resulting from the molecules in the molecular beam that are not excited by the laser. These molecules result in a small, but measurable deposition of 0.005 ML of carbon across the entire face of the crystal. The results of this convolution appear as the solid line passing through the laser-on data in Figure 3. The prediction is in excellent agreement with the data. We note that our predictions of deposition region widths for both laser-on and laser-off experiments contain no adjustable parameters. Molecular motion in the vertical direction is not subject to the same limitations. Since transverse velocity components in the vertical plane do not project on the laser’s propagation axis, molecular motion in the vertical direction does not result in Doppler detuning. We have mapped carbon deposition in the vertical direction, and find uniform laser-enhanced deposition over the entire 1.0 cm diameter crystal. III.c. Role of Molecular Beam Speed. A cursory inspection of eq 2 might suggest that the width of the laser-enhanced deposition area should depend on molecular beam speed, but that is not the case. Figure 5 shows carbon deposition maps for two laser-enhanced deposition experiments performed at different molecular beam speeds. The open symbols show carbon deposition from a 2345 m/s CH4 molecular beam, while the
V⊥ )
[ ( )]
c∆νtt 0.2Vc πw2 ≈ 1+ 2ν0 ν0w Rλ
2
(4)
The full-width of the laser-enhanced desorption region, ∆x, is twice the product of V⊥ and the nozzle-surface flight time, t ) l/V, where l is the nozzle-surface distance.
∆x ≈
[ ( )]
πw2 0.4Vc 1+ ν0w Rλ
2
[ ( )]
1 0.41c πw2 1+ ) V ν0w Rλ
2
(5)
Equation 5 shows that the horizontal dimension of the laserenhanced deposition region is independent of molecular beam velocity, within the limit where the homogeneous line width is a linear function of molecular beam speed. This independence arises from the offsetting effects of a greater transverse velocity but shorter flight time for molecules in the faster molecular beam. III.d. Role of Excitation Geometry. The results presented in Figure 3 depend sensitively on the alignment of our optical multipass cell and on the alignment of the laser with the molecular beam. In this section, we begin by examining the effect of laser alignment with the molecular beam, then consider multipass cell alignment, and conclude with an experimental measurement that confirms our model of the process. When the infrared laser is tuned near ν0, only those molecules moving along paths that are very nearly orthogonal to the laser absorb infrared light. Figure 6 shows the laser-molecular beam interaction region. The angular divergence of the molecular beam is exaggerated to highlight geometric effects. In Figure 6a, the laser propagation direction is orthogonal to the molecular beam axis. Molecules traveling along that axis (path A) have a zero component of velocity along the laser’s propagation direction, so they absorb light and react with higher probability on the Ni(100) substrate. Molecules traveling along path B are not resonant with the laser because the projection of their flow velocity onto the laser propagation direction Doppler shifts their absorption peak out of resonance with the laser frequency ν0. Figure 6b shows the situation when the laser is not aligned perpendicularly to the molecular beam axis. Now molecules traveling along path B are moving orthogonally to the laser propagation direction and can absorb light; molecules traveling along path A have a nonzero projection of their velocity along the laser propagation direction and are Doppler shifted out of resonance. Subtle changes in the direction of laser propagation alter the path of laser-excited molecules and affect their point of impact on the Ni(100) surface. The small displacement of
Controlling Surface Chemistry with Light
Figure 6. Detailed view of the laser-molecular beam interaction region. In part a, the laser is orthogonal to molecular path A, and only molecules traveling on or very near the center axis of the molecular beam absorb light and react with higher probability on the Ni(100) surface. In part b, the laser is no longer orthogonal to the molecular beam flow axis, but it is orthogonal to molecules moving along path B. Molecules moving along path A have a nonzero velocity component along the laser propagation direction and are Doppler shifted out of resonance with the laser light. Molecules moving along path B absorb light and react with enhanced probability.
Figure 7. Detailed view of the multipass cell, in which mirror 3 is slightly misaligned. The misalignment results in three distinct beamlaser intersection angles. Since only molecules moving orthogonally to the laser absorb light, the three beam crossings result in three distinct molecular paths, A, B, and C for laser-excited molecules.
the laser-enhanced deposition region in Figure 3 from the crystal center is a manifestation of this effect. The homogeneous line width of molecules in the beam does allow molecules with small transverse velocities to remain in resonance with infrared light at ν0, and molecules traveling toward or away from the incident laser’s propagation direction are equally likely to be excited by light in the multipass cell. A well-aligned multipass cell results in up to 16 parallel crossings of infrared light through the molecular beam. Half of the passes are parallel with the laser’s propagation direction upon entering the chamber, while the other half are exactly antiparallel. Misalignment of one mirror in the multipass cell can result in two or more laser-enhanced deposition areas appearing on the Ni(100) substrate. In Figure 7, molecules emerge from the molecular beam nozzle and pass through the multipass cell on their way to the Ni(100) substrate. Mirror three in the multipass cell is mounted on a kinematic mount and was tilted 0.40° from its optimal position to illustrate the effect of multipass cell misalignment. We recorded the extent of rotation of the adjustment screw on the mount and used the pitch of the screw and the pivot distance on the optical mount to calculate the 0.40° tilt angle. Light enters the multipass cell and reflects specularly from each of the four mirrors. The first two passes (incident
J. Phys. Chem. B, Vol. 104, No. 14, 2000 3333
Figure 8. Carbon deposition resulting from a misaligned multipass cell. The symbols are the measured carbon coverages and the solid line is the model described in the text.
light plus first reflection from mirror 2) are orthogonal to the molecular beam flow axis. They selectively excite molecules moving along path A. The misalignment of mirror 3 rotates the next two parallel laser-beam crossings into an orientation that is orthogonal to path B. The fifth pass is further rotated in the same direction by mirror 3 and is orthogonal to path C. Enhanced deposition on the Ni(100) surface occurs where molecular paths A, B, and C impinge on the substrate. For such a misalignment, paths A, B, and C differ by a constant angular displacement. Therefore, a set of discrete laser-molecular beam intersection angles gives rise to an equal number of discrete propagation directions for the laser excited molecules. We find that alignment errors of 0.1° or less can affect the geometry of the deposition area. We have experimentally verified the effects of a misaligned multipass cell, and the resulting carbon deposition map appears in Figure 8. The data were collected with a 2% CH4/H2 mixture expanding from a 400 K nozzle source. The higher nozzle temperature increases the speed of the beam, and we calculate a transit-time broadened homogeneous line width of 3 MHz. Since laser excitation occurs only for those molecules traveling perpendicularly to the laser direction, we infer that the four paths leading to laser-enhanced deposition on the surface differ by the measured 0.40° angular offset of the laser passes in the multipass cell. We calculate the spatial distribution for a single pass, as detailed in section III.b, and then sum spatial distributions for four molecular paths separated by 0.40° to obtain the solid line passing through the data in Figure 8. Once again, our model, with no adjustable parameters, is an accurate predictor of the spatial distribution of carbon deposited on the surface. The data in Figure 8 serve as useful diagnostics for our excitation scheme. The model described in the preceding paragraph assumes that peak carbon coverage is identical in all four regions. Since the total flux of methane is constant across the surface, the excellent agreement of the model and the data in Figure 8 suggests that infrared laser excitation efficiency remains constant for at least eight sequential laser-molecular beam crossings. This finding confirms our expectation that in a large excess of photons relative to absorbers in the beam that photon number does not decrease significantly with increasing molecular beam crossings. It also indicates that our focal conditions for the infrared light keep the light well collimated during its travel through the multipass cell.
3334 J. Phys. Chem. B, Vol. 104, No. 14, 2000 IV. Discussion The localized deposition we observe impacts future studies of state-resolved gas-surface chemistry as well as applications of laser enhanced chemistry to deposition processes. In this section, we explore the implications of localized deposition on fundamental studies of gas-surface reactivity and on its potential application to vibrationally enhanced chemical vapor deposition. The broadening mechanisms affecting our CH4/Ni(100) studies are typical of those for a wide range of small molecules seeded in supersonic molecular beams. Transit times are largely determined by the speed of the light carrier gases used in the molecular beam, and the radiative lifetimes for vibrationally excited states are similar to, or longer than, that of the ν3 state in methane. Therefore, homogeneous line widths for CW-excited infrared transitions of many small molecules in collision-free molecular beams will be similar to those of CH4. Molecular beam divergence and speed in combination with the transition frequency and excitation geometry determine the Doppler shift for molecules impinging on the surface. Since these factors do not differ appreciably among small molecules, the magnitude of the Doppler shifts for infrared absorption by other small molecules in a supersonic beam gas-surface experiment will also be similar to that of methane. Our own studies illustrate how narrow-bandwidth excitation of an inhomogeneously broadened absorption profile affects state-resolved studies of gas-surface reactivity. A number of issues involving experimental alignment and stability determine whether absolute sticking probabilities can be obtained from a particular set of experimental data. The narrow region of laser-enhanced deposition that we report in Figure 3 results in one set of issues. In experiments that quantify reactivity with a spatially resolved probe, the probe must coincide with not only the portion of the substrate imaged by the molecular beam but also with the region exposed to the flux of laser excited molecules. Under the experimental conditions of Figure 3, the total molecular beam flux is constant across the entire crystal face and laser excitation enhances average reactivity of the beam 30-fold. Despite this, if our 1 mm diameter AES probe were centered 2 mm to the left of crystal center, we would detect little or no reactivity enhancement. Probes that sample an area much larger than the region of enhanced deposition will systematically underestimate the extent of laser enhancement and be less sensitive to enhancement. We estimate that in Figure 3, the average carbon coverage over the entire 1 cm diameter Ni(100) crystal is only one-fourth of that at the peak of the laser-enhanced deposition region. A second set of issues arises from the correlation between excitation geometry and frequency with the spatial location of laser-enhanced deposition on the substrate. Our experiments measure carbon coverage at a point on the surface averaged over the dose time. This average only reflects the state-resolved probability we seek if the point of measurement was exposed to laser excited molecules for the entire dose time. Laser frequency drift and pointing instability both move the location of the laser-excited flux across the surface and reduce the average sticking probability measured at a single point on the surface. Our laser frequency stabilization system provides excellent long-term stability of the excitation frequency and ensures that laser-excited flux at the point of measurement remains constant for the entire dose time. Day-to-day variations in laser-molecular beam alignment can also cause the laser excited region to move across the surface. We collect a carbon deposition map across the crystal face each day to verify that
Juurlink et al. we measure carbon deposition at the point where laser excited molecules impact the surface. The localization of laser-enhanced deposition provides a convenient means of quantifying the reactivity enhancement of state-selected molecules. Our data analysis procedure relies on a measure of the difference in average reaction probability for the molecular beam with and without laser excitation.9 We exploit the spatial mapping described here to obtain both quantities in a single experiment. Using Figure 3 as an example, we measure carbon deposition at the peak of the laser-enhanced deposition region (x ) 1.2 mm) for our laser-on coverage and take carbon coverage at a point well removed from the peak (e.g., x ) -4.0 mm) as a measure of laser-off coverage. In state-resolved studies involving a pulsed laser excitation source, the duration of the laser pulse truncates the lasermolecule interaction time and broadens the homogeneous line width further. Experimental details determine the role of broadening mechanisms in such studies. Because of the potential for broadening mechanisms to have a significant impact on the acquisition and interpretation of experimental results, we suggest that such factors must be considered in any state-resolved gassurface reactivity study involving optical pumping of gas-phase reagents in a supersonic molecular beam. Several groups have used lasers producing 6 ns pulses of light to pump selected vibrational states of molecules in a supersonic molecular beam. In those experiments, the laser pulse duration replaces transit time as the factor limiting laser-molecule interaction time. A transform-limited 6 ns Gaussian light pulse leads to a homogeneous line width of about 100 MHz. Hou et al. achieve this theoretical limit for the injection seeded tunable dye laser system they use as a “dump” laser in their stimulated emission pumping studies of NO reactivity on an oxidized copper surface.8 For experiments using a pulsed source of infrared light for excitation in the beam, Doppler shifts will be similar to those we observe in our experiments. Thus, the 100 MHz bandwidth of a 6 ns pulse of infrared light would contain frequencies capable of exciting the entire Doppler profile of molecules incident on the surface. Doppler shift is proportional to excitation frequency, so vibrational excitation schemes using visible or ultraviolet photons will be subject to much larger Doppler shifts for molecules impinging on the surface. We note that transitions stimulated by a 330 nm photon have a Doppler shift 10-fold greater than that reported in Table 2 for absorption of our 3.3 µm infrared photon. In the case of vibrational excitation using a 330 nm photon, molecules impinging near the crystal edge would be Doppler shifted by 88 MHz, which is significant relative to the ∼100 MHz fwhm of the laser light. In that case, laser-enhanced deposition across the entire surface may not be uniform. Our color center laser and the injection-seeded laser used by Hou et al. both operate on a single longitudinal mode. The longitudinal mode spacing of these lasers significantly exceeds the spread of Doppler-shifted absorption frequencies that can be absorbed by molecules impinging on the surface. Thus, only light from one longitudinal mode of the laser will be resonant with molecules impinging on the substrate. This factor may complicate efforts to reproducibly measure absolute reaction probabilities for state-selected molecules, as the vibrational excitation efficiency, and thus the fractional extent of excitation in the beam, will vary with the time-averaged fraction of light present in the correct longitudinal laser mode. Although the number of examples of gas-surface reactions that are activated by vibrational pumping of the gas-phase reagent is currently small, vibrational excitation is an effective
Controlling Surface Chemistry with Light means of depositing a chemically significant quantity of energy into a degree of freedom that may be well-coupled to the reaction coordinate. It is likely that other systems will also exhibit a significant reactivity enhancement upon vibrational excitation. Such excitation creates nonequilibrium distributions of energy in the system that may lead to deposition products or structures differing from those that dominate thermally activated reactions. We conclude with a brief discussion of how the factors presented here may impact attempts to apply optical pumping to control or enhance deposition on a substrate. Attempts to use optical excitation of gas-phase reagents to promote or control gas-surface reactivity will first need to overcome the collisional deactivation of the optically excited molecules prior to their impact with the surface. This means that the mean free path for the molecules must be equal to or greater than the laser-substrate distance. Such conditions are readily met in molecular beam epitaxy systems. The requirement for low-collision conditions will also prevent collisional (pressure) broadening from becoming a dominant broadening mechanism. In an excitation geometry similar to that depicted in Figure 1, Doppler shifts in the absorption frequency place restrictions on the range of incident angles molecules may have with respect to the substrate. This restriction has two consequences. To expose large area substrates, an array of dosers may be required to provide a uniform flux of molecules impinging on the surface at near normal incidence and with a sufficiently small transverse velocity component as to permit their absorption of light. The angular spread of molecular paths from a single doser may be too great to permit uniform excitation across the entire substrate. At the same time, this restriction offers the opportunity to prepare a highly reactive flux of molecules impinging on the surface with a well-defined incident angle. Such considerations may be of value to etching processes. It is instructive to examine factors limiting the spatial resolution of this technique. The range of transverse velocities that may be excited by a narrow-bandwidth laser source is limited by the homogeneous line width of the molecular absorption feature, the Doppler shift associated with each transverse velocity, and the laser line width. Color center lasers have been stabilized to better than 100 kHz line width, and by better collimating the laser and expanding the excitation volume with a cylindrical lens, it is feasible to reduce the limiting homogeneous line width by an order of magnitude to about 100 kHz. Following the procedure outlined in section III, we estimate the maximum transverse velocity that might be excited in our methane experiments to be 16 cm/s. The horizontal displacement that would result from this velocity component depends on the flight time from nozzle to surface. If the nozzle surface distance were reduced to 10 cm and the flight velocity remained constant at 2345 m/s, the half-width for the laser-enhanced deposition area would be 7 µm. Timp et al.17 point out a different strategy for obtaining spatial resolution in deposition processes, and other groups have subsequently confirmed the feasibility of their approach.18-20 They create a standing wave optical field and rely on the spatial focusing that occurs when atoms pass through the field. The periodicity they report is half the wavelength of the light used, with the feature size being still smaller. We suggest that a variation of that approach may permit submicrometer lithography using molecular precursors. Boraas et al. report the use of an optical buildup cavity for excitation of molecules in a molecular beam.21 Such a cavity also creates a standing wave. For our experiments, the periodicity of the
J. Phys. Chem. B, Vol. 104, No. 14, 2000 3335 wave would be half the wavelength of the infrared light, or about 1.6 µm. When a collimated molecular beam passes through the buildup cavity, those molecules passing through the nodes in the standing wave field would not be excited, while those passing through the peak intensity areas would be excited and react with enhanced probability on the substrate. In contrast to the situation for an expanding molecular beam, where the nozzle location and Doppler shifts alone define the spatial distribution of excited molecules impinging on the surface, the standing wave field places an additional constraint on the spatial distribution of molecules that may be excited. Molecules must not only have a small transverse velocity component in order to be resonant with the excitation light source; they must pass through a portion of the standing wave where the optical field is large. The spatial patterning imprinted on the methane sample by standing wave excitation will only be degraded by transverse flight between the buildup cavity and the surface. If the optical buildup cavity is located close to the surface (e.g., 1 cm), we predict that broadening due to transverse flight out off the flight axis will result in a half-width of less than 700 nm. Since this source of broadening is less than the periodicity of the standing wave pattern in the buildup cavity, it should be possible to obtain spatial resolution dominated by the dimensions of the standing wave in the cavity. V. Conclusions We report experimental measurements that reflect and highlight the role of homogeneous and inhomogeneous broadening mechanisms in optical pumping studies of gas-surface reactivity. Infrared laser excitation of methane in a supersonic molecular beam creates vibrationally excited molecules with a significantly enhanced probability for dissociative chemisorption on a clean Ni(100) surface. The inhomogeneous nature of Doppler broadening allows us to excite a subset of molecules in the molecular beam whose transverse velocity component is well defined. The lack of collisions between the optical pumping region and the surface results in a coherence between a molecule’s transverse velocity component and its location of impact on the Ni(100) substrate. Spatially resolved Auger electron spectroscopy maps the surface-bound reaction products and quantifies this effect. A model based on the known broadening mechanisms affecting our experiment reproduces the data well without any adjustable parameters and supports our interpretation of the data. The model we develop allows us to examine how spatial mapping may or may not affect studies of gas-surface reactivity using pulsed laser sources. We find that the manifestation of spatially resolved deposition depends on the balance of a number of factors including the frequency of the exciting radiation, the laser pulse width, and the speed of the molecular beam under study. We also point out several considerations that affect one’s ability to observe or quantify laser-enhanced reactivity in these experiments. We suggest that it is prudent to consider the role of these processes in any study of gas-surface reactivity involving the optical excitation of molecules in a supersonic molecular beam. There is considerable interest in developing spatially resolved deposition processes, and we note that the combination of narrow bandwidth laser excitation with supersonic molecular beams offers a means of using light to control the spatial distribution of reaction products on the surface. We point out several key considerations that would affect the implementation of our approach to a deposition process. We also use the model developed to explain our experimental results to predict the
3336 J. Phys. Chem. B, Vol. 104, No. 14, 2000 ultimate spatial resolution that may be possible using a feasible set of experimental conditions. Improved laser stabilization and shortening the nozzle-surface distance could improve spatial resolution to about a 15 µm full width. Finally, we suggest a new approach to controlling the spatial deposition of molecules on a surface. The approach exploits the spatial distribution of the electric field in a standing wave optical buildup cavity and the transverse velocity selectivity of our narrow-bandwidth optical pumping scheme. Using a set of feasible estimates for laser bandwidth and excitation geometry, we show that it may be possible to deposit submicrometer features by controlling the excitation of gas-phase molecular precursors. Acknowledgment. We thank the National Science Foundation for supporting this work through Award CHE-9703392. References and Notes (1) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; Wiley-Interscience: New York, 1994. (2) Jacobs, D. C. J. Phys. Condens. Matter 1995, 7, 1023-1045. (3) Rostrup-Nielsen, J. R. Catalytic Steam Reforming; Springer: Berlin, 1984. (4) Rettner, C. T.; Michelsen, H. A.; Auerbach, D. J. Chem. Phys. 1993, 175, 157-169. (5) Michelsen, H. A.; Rettner, C. T.; Auerbach, D. J.; Zare, R. N. J. Chem. Phys. 1993, 98, 8294-8307.
Juurlink et al. (6) Rettner, C. T.; Auerbach, D. J.; Michelsen, H. A. Phys. ReV. Lett. 1992, 68, 1164-1167. (7) Gostein, M.; Sitz, G. O. J. Chem. Phys. 1997, 106, 7378-7390. (8) Hou, H.; Huang, Y.; Guiding, S. J.; Rettner, C. T.; Auerbach, D. J.; Wodtke, A. M. Science 1999, 284, 1647-1650. (9) Juurlink, L. B. F.; McCabe, P. R.; Smith, R. R.; DiCologero, C. L.; Utz, A. L. Phys. ReV. Lett. 1999, 83, 868-871. (10) McCabe, P. R.; Juurlink, L. B. F.; Utz, A. L. ReV. Sci. Instrum. 2000, 71, 42. (11) Gough, T. E.; Gravel, D.; Miller, R. E. ReV. Sci. Instrum. 1981, 52, 802-803. (12) Miller, R. E. ReV. Sci. Instrum. 1982, 53, 1719-1723. (13) Schouten, F. C.; Gijzeman, O. L. J.; Bootsma, G. A. Surf. Sci. 1979, 87, 1-12. (14) Demtro¨der, W. Laser Spectroscopy Basic Concepts and Instrumentation, 2nd ed.; Springer-Verlag: Berlin, 1996. (15) Hess, P.; Moore, C. B. J. Chem. Phys. 1976, 65, 2339. (16) Miller, D. R. Free Jet Sources. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press: New York, 1988; Vol. 1; pp 14-53. (17) Timp, G.; Behringer, R. E.; Tennant, D. M.; Cunningham, J. E. Phys. ReV. Lett. 1992, 69, 1636-1639. (18) McClelland, J. J.; Scholten, R. E.; Palm, E. C.; Celotta, R. J. Science 1993, 262, 877-880. (19) Johnson, K. S.; Thywissen, J. H.; Dekker: N. H.; Berggren, K. K.; Chu, A. P.; Younkin, R.; Prentiss, M. Science 1998, 280, 1583-1586. (20) Anderson, W. R.; Bradley, C. C.; McClelland, J. J.; Celotta, R. J. Phys. ReV. A 1999, 59, 276-2485. (21) Boraas, K.; Anex, D.; Ewing, G.; Reilly, J. P. J. Phys. Chem. 1985, 89, 4174.
