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In Situ Spectroscopic Ellipsometry Monitoring of Multilayer Growth Dynamics via Molecular Layer Epitaxy Vladimir Burtman, Yuval Ofir, and Shlomo Yitzchaik* Inorganic and Analytical Chemistry Department, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel Received July 17, 2000. In Final Form: December 29, 2000 Real time monitoring of organic monolayer self-assembly by molecular layer epitaxy (MLE) processes was studied by in situ spectroscopic ellipsometry techniques. For the MLE of imide-based organic heterostructures using chemisorption of 3,4,7,8-naphthalenetetracarboxylic dianhydride (NTCDA) and 1,6-diamino-n-hexane (DAH) on prefunctionalized surfaces, in situ ellipsometry reveals that the reaction kinetics can be best fitted to an S-shaped deposition curve with saturated coverage of about 20 min by the Langmuir-Hinshelwood model, with a slow initial phase, followed by a faster second phase. The rate of deposition at each moment is proportional to the number of empty sites multiplied by the number of occupied sites. Calculated deposition rate constants for every pulse are kT ) 5.6 × 10-5 s-1 for first deposition of NTCDA on a template (T-layer), decreasing to kA ) 1.5 × 10-5 s-1 for NTCDA and to kB ) 7.2 × 10-6 s-1 for DAH assembly pulses correspondingly. A modified Rudzinski-Aharoni kinetic model for adsorption that correlates adsorption energy with valid numbers of reactive sites was used to estimate an equilibrium surface absorption energy of 16 kcal for a NTCDA layer and 29 kcal for a DAH layer.
Introduction Development and understanding of the surface processes involved in the growth of organic solid-state materials are of widespread interest given the considerable technological importance of processing nanoscale films having well-defined structure and composition.1 For the development of novel fabrication methods2,3 of ultrathin organic films, real-time monitoring4 for the perfection of the molecular assembly process is needed. Recently we developed a new self-assembly route, molecular layer epitaxy (MLE),5 for vapor phase assembly of organic hetetrostructures that provides epitaxial growth via covalent bonding as shown in Figure 1. First a template layer is deposited on an oxide surface, such as Si/SiO2 (Figure 1, step i), exposing the propylamine functionality toward the interface, which in turn dictates epitaxial growth. Then discrete pulses of reactants, liquids or solids that undergo self-limiting reactions, are carried to the surface by an inert carrier gas in an MLE deposition reactor. An alkylamine-containing surface is hit with a pulse of 3,4,7,8-naphthalenetetracarboxylic dianhydride (NTCDA) precursor (Figure 1, step ii), forming imide linkages. Then a pulse of a vaporized aromatic or aliphatic diamine spacer (Figure 1, step iii) regenerates the amine functionality on the surface, which can again react with a dianhydride. Repeatedly cycling through these steps (1) Greenham, N. L.; Friend, R. F. Solid State Physics; Ehrenreich, H., F. Spaepen, F., Eds.; Academic Press: San Diego, CA, 1995; Vol. 49. (2) Cai, C.; Busch, M. B.; Tao, Y.; Muller, B.; Gan, Z.; Kundig, A.; Bosshard, C.; Liakatas, I.; Juger, M.; Gunter, P. J. Am. Chem. Soc. 1998, 120, 8563. (3) Rosnik, J. J. W. M.; Blauw, M. A.; Geerligs, L. G.; van der Drift, E.; Rousseeuw, B. A. C.; Radelaar, S. Opt. Mater. 1998, 9, 416. (4) (a) Yitzchaik, S.; Roscoe, S. B.; Kakkar, A. K.; Allan, D. S.; Marks, T. J.; Xu, Z.; Zhang, T.; Lin, W.; Wong, G. K. J. Phys. Chem. 1993, 97, 6958. (b) Richter, A. G.; Durbin, M. K.; Yu, C.-J.; Dutta, P. Langmuir 1998, 14, 5980. (5) (a) Burtman, V.; Zelichenok, A.; Yitzchaik, S. Angew. Chem., Int. Ed. 1999, 38, 2041. (b) Burtman, V.; Zelichenok, A.; Yakimov A.; Yitzchaik, S. In Semiconductive Polymers: Applications, Properties, and Synthesis; Hsieh, B. R., Ed.; ACS Symposium Series 735; American Chemical Society: Washington, DC, 1999; p 399.
(Figure 1, steps ii-iii) leads to the formation of 3,4,7,8naphthalenetetracarboxylic diimide (NTCDI)-based organic superlattices. Different from most ordered organic self-assembled thin films formed in solution by Langmuir-Blodgett techniques,6 self-assembled multilayers (SAMs),7 electrostatic polymer assembly8 or physisorbed on the substrates in ultrahigh vacuum (UHV)9 (>10-8 mbar) by organic molecular beam deposition (OMBD)10 and molecular layer deposition,11 the MLE approach employs a low-pressure vapor-phase monolayer (ML) by monolayer epitaxial growth via covalent bonding between interfacing layers. While the various solution-derived deposition methods are limited, in the case of conjugated heteroaromatic precursors due to their poor solubility in common organic solvents, the MLE route is a solvent-free process for volatile and thermally stable compounds. As compared with UHV deposition methods that are mass-flow limited, the work under low-pressure conditions in the MLE allows higher precursor concentrations in the vapor phase and thus faster deposition kinetics. Understanding the nature and time scale of monomolecular film formation processes is of fundamental importance to optimizing layer growth conditions and adapting deposition conditions to new building blocks. Several approaches have already been suggested for the study of surface phenomena in self-assembled films, to give a better understanding to surface reactions as compared with the solution counterparts. Examples are the quartz crystal microbalance12 for monitoring a gas/ (6) Donovan, K. J.; Elliot, J. L.; Scott, E. G.; Wilson, D. A.; Batzel, D. A.; Clark, T. R.; Kenney, M. E. Thin Solid Films 1996, 273, 229. (7) Yitzchaik, S.; Marks, T. J. Acc. Chem. Res. 1996, 29, 197. (8) Esker, A. R.; Mengel, C.; Wegner, G. Science 1998, 280, 892. (9) Tsuzuki, T.; Hirota, N.; Noma, N.; Shirota, Y. Thin Solid Film 1996, 273, 177. (10) Haskal, E. I.; Zhang, Y.; Burrows, P. E.; Forrest, S. R. Chem. Phys. Lett. 1994, 219, 325. (11) Yoshimura, T.; Tastuura, S.; Sotoyama, W.; Matsuura, A.; Hayano, T. Appl. Phys. Lett. 1991, 59, 482. (12) Kurth, D. G.; Bein, T. Angew. Chem., Int. Ed. Engl. 1992, 31 (3), 336.
10.1021/la0010065 CCC: $20.00 © 2001 American Chemical Society Published on Web 03/02/2001
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Figure 1. Surface chemistry of the molecular layer epitaxy (MLE) method, formation of organic heterostructures through vaporphase self-assembly.
solid interfacial reaction, sum-frequency generation,13 and FTIR in the attenuated total reflection mode14 for probing the reaction of octadecyltrichlorosilane (OTS) at the liquid/ solid interface. In situ second harmonic generation (SHG) measurements were reported for probing polymer grafting from solution onto mica surfaces15 and for studying the interaction of silanized surfaces with liquid crystal layer16 and also to probe electrode surface dynamics.17 In situ SHG monitoring of SAMs of hyperpolarizable chromophores proved to be a highly efficient method for probing in real time surface-reaction kinetics and packing dynamics.4 In the case of centrosymmetric precursors, the SHG tool is less sensitive, while spectroscopic ellipsometry does not decrease its sensitivity. On the basis of the ratio of two reflectance coefficients, ellipsometry is insensitive to the ambient conditions and, thus, ideally suited for real time surface-process monitoring. We studied MLE assembling and growth dynamic using data of an in situ multiwavelength ellipsometery technique that, aside from process monitoring, provides a tool to explore, in real time, the kinetics of the process with an insight to the growth mechanism of self-assembled heterostructures. Experimental Section The monitoring system was attached to a low-pressure MLE laminar flow (Re < 250) reactor with a base pressure of 10-5 Torr and molecular gas pressure of 10-3 Torr (Figure 2). The carrier (13) Guyot-Sionnest, P.; Superfine, R.; Hunt, J. H.; Shen, Y. R. Chem. Phys. Lett. 1988, 144, 1. (14) Cheng, S. S.; Scherson, D. A.; Sukenik, C. H., J. Am. Chem. Soc. 1992, 114, 5436. (15) Yerushalmi-Rozen, R.; Klein, J.; Berkovic, G., Langmuir 1992, 8, 1392. (16) Barmentlo, F.; Hoekstra, F. R.; Willard, N. P.; Hollering, R. W. J. Phys. Rev. A: At., Mol., Opt. Phys. 1991, 43, 5740. (17) Richmond, G. L. Electronal. Chem. 1991 17, 87.
Figure 2. In situ spectroscopic ellipsometry setup for realtime process monitoring, reflecting the periodical change of surface polarizability by detecting changes in light polarization. gas (Ar) assisted MLE setup enables the use of solid, liquid, and gas precursors in sublimers, bubblers, and gas lines, respectively, in a pulsed mode. Pulses of Ar gas were used for the cleaning steps between pulses of reactive precursors. The temperature controlling setup was divided for the various precursor reservoirs, feedthrough lines into the reactor, three major zones in the laminar flow reactor, the susceptor zone, and the lines getting out of the reactor. Float silicon wafers (Virginia Semiconductors) or glass/quartz windows (ChemGlass) were cleaned according to literature procedures.18 A propylamine-coated surface was achieved by self-assembly of aminopropyltrimetoxysilane (APTMS) in toluene.5 Molecules NTCDA (A) and DAH (B) were evaporated from separate sources. The reactor temperature (18) Decher, G.; Hong, J.-D. Makromol. Chem. Macromol. Symp. 1991, 46, 321.
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Figure 3. Example of 3D ellipsometry monitoring of MLE process: polarization coefficient ψ changes as a function of deposition time at different wavelengths. profile was 190, 220, and 190 °C for the three zones, the sample holder was held at 195 °C, and the source temperatures were held at 200 and 24 °C for NTCDA and DAH, respectively. A M44 spectroscopic ellipsometer (Woollam Co.) with 44 wavelengths in the spectral range 400-700 nm was used for in situ process monitoring at a fixed angle of incidence φ ) 75° to the reactor axis; see Figure 2. Optical windows of the ellipsometer were distant from the reactor body in a perpendicular direction to precursor flow and heated to avoid intensive precursor physisorption by condensation.19 Quartz optical windows and optical input/output tube connections were preclean in AcOH before every deposition experiment. Input/output tube connections of the ellipsometer were 2 cm in diameter. This diameter leaves enough space to focus the 1 cm light beam on the substrate without touching the walls and thus without polarization change, although the optical tube zone was relatively small in comparison with the reactor aspect section (5 × 10 cm2) to keep the laminar flow during the MLE process. The measured values are expressed as ψ and ∆. These values are related to the ratio of the Fresnel reflection coefficients Rp and Rs for p- and s-polarized light respectively
F ) Rp/Rs ) ei∆ tan ψ
(?)
The output data of in situ spectroscopic ellipsometry measurements is a 3D matrix, Figure 3, containing pairs of ψij and ∆ij values as a function of the different 44 wavelengths λi (400-700 nm) and also as a function of deposition time/operation mode tjAB, where j is the time index that runs from 0 until j0AB (j0AB indicates the final time slide of the A(B) pulse).
Results A detailed experimental MLE procedure for the buildup of the organic heterostructures is given in ref 5. A stepby-step buildup of the layers is also characterized by contact angle (CA) changes and IR functional group analysis. The following are the MLE steps given in Figure 1: Step i, the clean substrates were allowed to react with 3 mM APTMS in dry toluene at 90 °C for 8 h under N2 in a Schlenk line. CA changes from 17° to 45°, and the appearance of the 3200 cm-1 alkylamine IR peak was observed. All of the following steps were carried out in the MLE reactor: Step ii, 20 min of an NTCDA pulse at P ) 50 mTorr, and the susceptor temperature (Ts) was held at 195 °C; CA changes from 45° to 92°, and the appearance of the 1655 cm-1 IR peak of the imide bond formation was detected. An Ar purge pulse was given while changing (19) Procedure for determining if window effects are necessary. We take ex situ data on the calibration wafer. Then we fit data using model SiO2 layer on Si substrate with SiO2 thickness and the angle of incidence as fitting parameters. Then the piece of the calibration wafer was put in the MLE chamber and the data were recorded. If the thickness values are not the same, the internal procedure for determining windows effects of in situ M-44 software should be applied.
Figure 4. Change in polarization parameter (ψ) vs deposition time taken at 417 nm. The source precursors (A ) NTCDA and B ) DAH) operation during the assembly of (NTCDI-HM)4 heterostructure. Gray straight lines correspond to the cleaning Ar pulses.
precursors. Step iii, a 20 min DAH pulse at P ) 50 mTorr and Ts ) 195 °C was used. CA changes from 92° to 60°, and the appearance of 2930 cm-1 IR methylene stretching peak was observed. Figure 4 shows an example of MLE process monitoring for continued growth of the naphthalenetetracarboxyldiimide hexamethylene (NTCDI-HM)n structure, n ) 4, assembling from A and B type precursors in a single wavelength representation. The change in surface polarization parameters ψ, detected by in situ ellipsometry versus deposition time and source operation at input 417 nm wavelength. (For representation reasons only one of the 44 wavelengths and one measured ψ values are shown.) The temporal evolution of the monolayer by in situ ellipsometry (Figures 3 and 4) provides several interesting observations. The ellipsometry parameters pair, ψ and ∆, is very sensitive to the surface-bound monolayer buildup as can be seen in the raw data periodical growth and decay of surface polarizability at different steps of the ML assembling process. Figures 3 and 4 also provide information on the kinetic behavior of the self-assembly process since ψ and ∆ can be converted to surface chromophore or spacer relative coverage.20 The following considerations were taken into account to build the fitting model. (1) Due to the self-limited nature of the MLE growth, the ML thickness dA,B was considered to be the same, since no more than one ML can be grown at each assembly step. Data on dA,B and optical constants nA,B and A,B were available from our previous research.5 (2) The optical constants were slightly changed from one A(B) layer to the next A(B) layer due to quantum confinement effects5 and were corrected in the calculation at every deposition A(B) cycle. (3) For model consideration we determined that optical constants do not change a lot within the same deposition pulse.5 Generally the last assumption can limit the method applicability; however our preliminary study of the optical constant temperature dependence for solid-state MLE films does not revel essential changes, at least for the (NTCDI-HM)n system. The general strategy for spectroscopic ellipsometry raw data conversion is detailed in ref 21. First we separate data of different deposition steps in so-called “time-slide mode” (TSM). By the TSM method (20) The Savitzky-Golay filter method (SGFM) of Origin 5 was used for data smoothing. The SGFM essentially performs a local polynomial regression to determine the smoothed value for each data point. This method is superior to adjacent averaging, where the smoothed value at index i is the average of the data points in the interval [i - (n - 1)/2, i + (n -1)/2], inclusive, because SGFM tends to preserve features of the data such as peak height and width, which are usually “washed out” by adjacent averaging.
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we are fixing tj and studying the data in the spectroscopic mode: the change of ψi and ∆i pair as a function of λi wavelength (ψi and ∆i) ) f(λi). In addition the fitted model includes two known parameters: wavelength-dependent optical constants (based on absorption spectra) and oneby-one variable parameter surface coverage θj (thickness dA,B considered to be constant). ψi and ∆i (i is the wavelength index) can be converted by a fit procedure of experimental data to surface coverage θj by the following relationship
ei∆ tan ψ ) Rp/Rs ) f(nk,θj,λi,φ)
(2)
where the Rp and Rs ratio is a function of nk, and θj, which are refractive indices and surface coverage TSM mode; λi is one of 44 wavelengths, and φ ) 75° is the incident angle. The experimental matrix of ∆ and ψ allows a fit of the surface coverage by evaluation of one unknown parameter.22 The outcome of this elemental fitting step is an θj coverage at the tj moment. Cycling through those deposition A(B) cycles results in a θj(tj) pair. The last step is the assembly of these pairs to time-dependent coverage θ(t). This fitting strategy was used to build and adjust the calculation program. The next step in the fitting strategy was a model that made the θj calculation through a deposition A(B) cycle, considering all tjAB time slides.21 Figure 5 shows examples of ML growth of NTCDA (A type) with a total ML deposition time of about 18 min (Figure 5a) and DAH (B type) ML growth within 20 min (Figure 5b). First the monolayer density increases slowly and then rapidly and saturates at a full coverage of a single monolayer. Similar kinetic behavior was observed for a number of atomic layer epitaxys (ALEs),23 organic depositions,24 and also by ex situ UV absorption monitoring for the same (NTCDI-HM)n structure (see Figure 6). The case can be treated as generic type of LangmuirHinshelwood (LH) processes,25 where the deposition rate at each moment is proportional to the number of empty sites multiplied by the number of occupied sites. For (21) For example we select the time slice that represents the growth of the first A layer. Then the “A-layer”, containing the optical constant of A was added on the top of the model SiO2/Si (measured and fitted by ex situ ellipsometry) and the known thickness (9.6 Å) was set. Then we select only the optical constants (n and k) of the “A-layer” as a fitting parameters, proceed with a normal fit, and save them. If the optical parameters are not nearly the same as in the “A-layer” file (as a result of temperature dependence), one should replace the “A-layer” with the optical constants that one obtained from the model. Next we select a time slice that represents the growth of the B layer. We add the “Blayer”, containing the optical constant of B on top of the existing model, A-layer/SiO2/Si, and set the thickness of the B-layer (6.9 Å). Again we select only the optical constants of the “B-layer”, proceed with a normal fit, and save optical constants. In the case where the optical constants are not nearly the same as those in the “B-layer” file (as a result of temperature dependence), one should replace the “B-layer” with the optical constants that one got from the model. One should repeat this procedure on the next layers until the assurance that the optical constants of the A and B layers stop changing. Moving from one TS to another within the same A(B) pulse one can get the surface coverage within pulse (debugging mode). Once this point is reached, one can setup a multisample fit. To do so one needs to take data time slices representing the end of layer growth and save them as individual files. Then we load data and build models in the 10 spaces that WVASE software has for multiple models. Activating the fit window, we select edit parameters from the menu. In this dialogue box we couple all of the A and B layers coverage. Once this is done, one can perform the general fit. (22) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland Publication: Amsterdam, The Netherlands, 1987. (23) Voigtander, B. T.; Weber, P.; Smilauer, D.; Wolf, E. Phys. Rev. Lett. 1997, 78, 2164. (b) Ares, R.; Watkins, S. P.; Yeo, P.; Horley, G. A.; O’Brien, P.; Jones, A. C. J. Appl. Phys. 1998, 83, 3390. (24) Jones, R. C.; Clifford, C. A. Phys. Chem. Chem. Phys. 1999, 1, 5223. (25) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; John Wiley & Sons: New York, 1994.
Figure 5. Kinetic of MLE assembly during NTCDA (a) and DAH (b) ML growth. The solid gray line is a fit to eq 4 with marked characteristic A-C and D-F growth periods.
Figure 6. Ex situ UV-vis spectroscopy monitoring the deposition of NTCDA (step ii, Figure 1) at 381 nm (the line is only a guide for the eye).
randomly distributed adsorbents on surface in the absence of adsorbate-adsorbate interactions, the rate of surface reaction is given by
r ) kθaθb
(3)
where k is the rate coefficient, θa is the surface coverage of species a, and θb is the fraction of vacant sites. The analytic expression of (3) is
θ ) A2 + A1/(1 + exp((t - t0)/k))
(4)
where A1 and A2 are dimension parameters. Fitting our experimental data with the LH kinetic model is shown as a gray line in Figure 5a. Calculated k values for every pulse are 5.6 × 10-5 s-1 for the first deposition of NTCDA on a T-layer, decreasing then to 1.5 × 10-5 ((10%) for NTCDA and to 7.2 × 10-6 s-1 ((10%) for DAH assembly pulses correspondingly.
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Differences in k values for NTCDA on the T-layer pulse and other NTCDA pulses should be attributed to the high surface number density of amines on the T-layer and the decrease in the number of reactive sites on the B-layer interfaces. Amine surface number density was derived by the surface titration method26 to be about 20 Å2/NH2 on the T-layer (neglecting surface roughness). The NTCDI surface number density was determined by making use of the solution molar absorptivity of N,N′-dihexylNTCDI5 as a measure of the two-dimensional absorption coefficient. NTCDI molar absorptivity at 381 nm is 2.6 × 107 cm2 mol-1. The absorbance of the NTCDI monolayer is 0.015, yielding a coverage of approximately 5.7 × 10-10 mol/cm2. This coverage (3.4 × 1014 molecules/cm2) indicates the surface area occupied per molecule to be ca. 29 Å2. The projection of the crystal structure27 in two dimensions yields a molecular “footprint” of ca. 25 Å2. The implication is that, neglecting surface roughness, the coverage achieved by the MLE procedure is about 86% of the packing density of the single crystal. This also means that only 69% of the amines in the T-layer have reacted with the first NTCDI monolayer. All of the following A and B layers kept approximately the same coverage ca. 29-31 Å2/molecule.5 The step behavior of the θ function can be treated as a modified Rudzinski-Aharoni (RA) model28
θ(F,TF) ) (ξπ(F/TF))/(1 + ξπ(F/TF))
(5)
where F ) ( - χ)/κT0; is absorption energy on solid surface, χ is equilibrium energy, and TF is dimensionless temperature: TF ) T/T0. For the reduced temperature TF )1 (since deposition temperature does not change within deposition pulse), the function 4 is very close to the step function
{
0, for < lim Θi ) 1, for < c Tf0 c where i ) e, n for equilibrium and nonequilibrium state. Assuming that the absorption energies of reactive sites on the solid surface depend directly on deposition time within A(B) deposition cycles, we can study the surface coverage θ vs dimensionless time: t ) t/∆t (∆t is the total time of A(B) pulse). Fitting kinetic data through absorption energies, one can estimate an equilibrium surface absorption energy ((10%) that is 16 kcal for the NTCDA layer and 29 kcal for DAH layer. The S-shaped kinetic behavior can be rationalized in terms of the chemisorption process. At the beginning (stages A and D, Figures 5 and 7) the chemisorption process is slow since the number of fruitful collisions with surface molecules is small due to re-evaporation from the surface (a small sticking coefficient). However when a certain number of molecules attached covalently to the surface, the sticking probability sharply increased due to in-plane π-staking (stage B) and van der Waals (stage E) interactions, creating new adsorption centers on the substrate (stages B and E, Figures 5 and 7). This autocatalytic kinetic of the MLE process can be regarded as a classical type of Polani process, where every adsorbed molecule forms a new adsorption center for precursor molecules.29 Finally (26) (a) Moon, J. H.; Shin, J. W.; Kim, S. Y.; Park, J. W. Langmuir 1996, 12, 4621. (b) Moon, J. H.; Kim, J. H.; Kim, K.-j; Kanh, T.-H.; Kim, B.; Kim, C.-H.; Hahn, J. H.; Park, J. W. Langmuir 1997, 13, 4305. (27) Burtman, V.; Zelichenok, A.; Ofir, Y.; Nehama, M.; Yitzchaik, S., In preparation. (28) Rudzinski, W.; Aharoni, C. Langmuir 1997, 13, 1089. (29) Horiuti, J.; Polanyi, M. Acta Physicochim. 1935, 2, 505.
Figure 7. Animated scheme of autocatalytic and coveragedependent assembly for A-F growth modes.
the completion of the ML assembling process is shifting in the saturation regime (stages C and F, Figures 5 and 7) due to the restricted number of reactive sites. This slow adsorption regime is governed by steric and electrostatic repulsion of the precursor molecules from empty reactive sites that are surrounded by NTCDI or hexylamineoccupied sites. Discussion The important role of the overlayer configuration of reactant molecules on a catalytic surface has been established by many experimental investigations.30 Similarly, the influence of the overlayer structure on the kinetics of thermal desorption has been also demonstrated.31 The surface kinetic simulations32,33 allow the correlation between sites occupied by pairs of molecules and the magnitude of those pair correlations for a random distribution of molecules on the surface to be obtained. Such effects arising from lateral interaction have been referred to as “topological” effects.32 The energy barriers to reaction for each pair of reactant molecules depend on the configuration of their neighboring sites, since each of the molecules in the reacting pair experiences lateral interactions with molecules in the neighboring sites. The energy of the transition state for the reaction may be also affected by the conformation of the neighboring sites. However the change in energy levels of the reactant molecules and the transition state are, in general, different because the lateral interactions experienced by the reactant molecules are different from those experienced by the transition state. Hence, the energy barrier to (30) (a) Bonzel, H. P.; Ku, R. Surf. Sci. 1973, 40, 85. (b) Barteau, M. A.; Ko, E. I. Madix, R. J. Surf. Sci. 1981, 104, 161. (c) Bechthold, G. E. Surf. Sci. 1983, 115, L125. (d) Akhter, S.; White, J. M. Surf. Sci. 1986, 171, 527. (e) Engel, T.; Ertl, G. J. Chem. Phys. 1978, 69, 1267. (f) Gland, J. L.; Kollin, E. B. J. Chem. Phys. 1983, 78, 963. (g) Stuve, E. M.; Madix, R. J.; Brundle, C. Surf. Sci. 1984, 146, 155. (31) (a) Tracy, J. C. J. Chem. Phys. 1972, 56, 2736. (b) Tailor, J. L.; Ibbotson; Weinberg, W. H. J. Chem. Phys. 1978, 69, 4298. (c) Pfnur, H.; Feulner, P.; Engelhardt, H. A.; Menzel, D. Chem. Phys. Lett. 1978, 59, 481. (d) Ibach, H.; Erley, W.; Wagner, H. Surf. Sci. 1980, 92, 29. (e) Mesters, C. M. A. M.; Wielers, H.; Gijzeman, O. L. J.; Geus, J. W.; Boostsma, G. A Surf. Sci. 1982, 115, 237. (g) Papp, H. Surf. Sci. 1983, 129, 205. (32) (a) Silverberg, M.; Ben-Shaul, A. J. Chem. Phys. 1985, 83, 6501. (b) Silverberg, M.; Ben-Shaul, J. Chem. Phys. 1987, 87, 3187. (33) (a) Silverberg, M.; Ben-Shaul, A. Chem. Phys. Lett. 1987, 134, 491. (b) Silverberg, M.; Ben-Shaul, J. Stat. Phys. 1988, 52, 1179. (c) Gupta, D.; Hirtzel, C. S. Surf. Sci. 1989, 210, 322.
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reaction depends on the number of occupied neighboring sites. This has been referred to as an “energetic” effect.32 Moreover it was shown that correlation between nearestneighbor molecules affects the reaction rate coefficient significantly.34 We consider that variation in the distribution of local configurations of a pair of reactant molecules as a function of deposition time (eq 3) and fractional energy site dependent surface coverage (eq 5) can be responsible for experimentally observed autocatalytic effects in the MLE process. In an LH type surface reaction desorption has a barrier associated with bringing the reacting species from their equilibrium binding sites to the transition state, where they start to bond and desorb from the surface. For atomic recombination, conceptually the simplest bond formation process, the activation barriers to desorption are often substantial, ranging from 0.28 eV for D2 on Ag(111)35 to 0.7 eV for Cu(111),36 while N recombination has an activation energy of 1.5 eV even on Cu(111)37,38 where the metal-nitrogen bond is relatively weak. Desorption occurs when thermal excitation of the adsorbate by the heat bath of the metal lattice is sufficient to overcome the barrier. If we consider two atoms bound in local adsorption sites, each of these has a collision frequency of ca. 1013 s-1 with the surface and desorption can only occur when sufficient energy is transferred into the local metal/adsorbate system for the atoms to recombine and desorb. Since typical thermal desorption rates in these experiments are ca. 1010-3 ML/s, the success rate is extremely low. Recombinative desorption is therefore a highly improbable event, with a very low cross section compared to apparently comparable processes studied in the gas phase. This makes it extremely difficult to include both the excitation and reaction steps on an equal basis in any theoretical model. Taking the usual definitions for the sticking probability S and the desorption flux distribution P, then at equilibrium the energy distributions in desorption are related to the sticking probability by39,40,41
P(E,θ,ν,J;T,Θ) ∝ (E exp-E/kT) × (exp-ν,J/kT)S(E,θ,ν,J;T,Θ) (7) where P(E,θ,ν,J;T,Θ) is the translational energy (E) distribution for products desorbing at an angle θ to the surface normal, in quantum state (ν, J) with an internal energy ν, J, from a surface with a coverage Θ and (34) Kang, H. C.; Jachimowski, T. A.; Weinberg, W. H. J. Chem. Phys. 1990, 93, 1418. (35) Healey, F. R.; Carter, N.; Hodgson, A. Surf. Sci. 1995, 328, 67. (36) Anger, G.;. Winkler, A.; Rendulic, K. D. Surf. Sci. 1989, 220, 1. (37) Berko, A.; Solymosi. F. Appl. Surf. Sci. 1992, 55, 193. (38) Skelly, J. F.; Munz, A. W.; Bertrams, T.; Murphy, M. J.; Hodgson, A. Surf. Sci. 1998, 415, 48. (39) Rettner, C. T.; Michelsen, H. A.; Auerbach, D. J. J. Chem. Phys. 1995, 102, 4625. (40) Comsa, G.; David. R. Surf. Sci. Rep. 1985, 5, 145. (41) Cardillo M. J.; Balooch M.; Stickney, R. E. Surf. Sci. 1975, 50, 263.
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temperature T. S(E,θ,ν,J;T,Θ) is the sticking coefficient under the same conditions of surface temperature T and coverage Θ. If the energy dependence for dissociative chemisorption is known, the translational energy distribution in desorption, P(E), can be predicted directly. Assuming that S(E) is measured for a beam incident along the surface normal, i ) 0, then the translational energy release in this direction is determined by the product of the thermal distribution function (E exp-E/kT) with the sticking probability
P(E) ∝ (E exp-E/kT)S(E,θ,ν,J;T)
(8)
If sticking is nonactivated and the sticking function S(E) does not vary severely with energy, we would expect the translational energy distribution to be approximately thermal. Since the first term (E exp-E/kT) falls exponentially at high energies (E . kT), this will dominate and result in a thermal, exponential tail to P(E) unless S(E) increases very rapidly in this region. MLE behavior is best described by the case of activated dissociation, where S increases very rapidly around some threshold Eo, such as observed for H2 on Cu and Ag surfaces. The dissociation threshold is abrupt, the energy release may be peaked at E . kT, and S is represented by (9)
S(v,J,E) ) 1/2A(ν,J)(1 + erf[(E - E0(ν,J)/w(ν,J)]) (9) The thermal distribution in this case is known as “situation of activated sticking”. The translational energy release does not peak near kT as in case of statistical distribution but instead shows a peak around the threshold for sticking. At higher energy the tail to the P(E) distribution shows the same exponential tail {P(E) ∝ exp(-E/kT)} as seen in all other classical statistic distributions. Conclusions Here we showed an example of MLE process monitoring that utilizes the adsorption kinetic of source precursors for external control on the film growth process. We demonstrated that similar to ALE, MLE takes advantage of the self-limiting nature of the chemisorption process for achieving layer-by-layer growth with uniform coverage of ideally one ML per adsorption cycle.5 The results of in situ ML monitoring illustrate the heretofore unexplored potential of in situ ellipsometry for elucidating selfassembly from the vapor phase. Acknowledgment. S.Y. acknowledges support for this research by the Israel Science Foundation (ISF) under Grant (225/99-1) and the Israel Academy of Science and Humanitarians. V.B. thanks the Berg Foundation for a Post Doc fellowship; Y.O. thanks the Israel Ministry of Science for an Eshkol scholarship. We thank Dr. A. Zelichenok, J. Hale, and Professor C. Aharoni for helpful discussions. LA0010065
