J. Phys. Chem. 1993,97, 2270-2274
2270
Surface Dynamics of Epitaxially Grown KBr Overlayers on a NaCl Substrate S. A. Safron,' G . G. Bishop, J. Duan, E. S. Gillman, and J. C . Skofronick Departments of Chemistry and Physics and MARTECH, The Florida State University, Tallahassee, Florida 32306
N. S. Luo and P. Ruggerone Max PIanck Institut f i r Strtimungsforschung, Bunsenstrasse 10, 3400 Gtittingen, Germany Received: August 4, 1992; In Final Form: November 9, I992
The results of high-resolution helium atom scattering experiments on the dynamics of thin epitaxially grown films of KBr on NaCl(001) are presented and interpreted with a simple force constant model. The measurements reported are for two, three, four, and seven monolayers. The model treats the KBr overlayer with force constants obtained by fitting the bulk dispersion curves, the NaCl surface as a rigid wall, and the coupling between the two by a second set of force constants. The latter are determined by the fit to these data and are softer than the KBr force constants.
Time of Flight
I. Introduction
I
, Detector
High-resolution helium atom scattering (HAS), originally developed as a spectroscopy for crystal surfaces, now appears to be the probe of choice for studies of the dynamical behavior of very thin epitaxially grown films on crystal substrate~.~-I3Even though HAS scattering cross sections may be small, the method has very large incident intensities and the favorable signal-tonoise makes measurements possible. Additionally, because the probe consists of neutral helium atoms at low thermal energies, the method does not damage or modify the surface under investigation in any wayIJ and it has been used successfully on all crystal surface types from metals to insulators. The surface dynamics of the latter is the topic of this paper. Surface dynamical information from very thin films can also be obtained by electron energy loss spectro~copy,'~ by optical methods,I5 and by neutron scattering.16 However, electron scattering is known to cause radiation damage to the alkali halides and thus has the potential to introduce uncertainties into inelastic scattering measurements." At the same time, optical methods for obtaining dynamical information are limited to the region at or near the Brillouin zone center and, further, by the fact that optical frequency radiation penetrates the material and is thus not a true surface probe.l5 Neutron scattering also suffers in that the neutrons readily penetrate both the overlayer and the substrate, and although they have been used in some special studies, they have not shown the promise of H A S i 6 Thus, at present HAS represents the most versatile method for studies of the surface dynamics of thin films, particularly for insulating overlayers. 11. Experimental Section
The HAS instrument employed in this work is shown schematically in Figure 1 and has been described previously in detail.I8 Briefly, it is formed by several, separately pumped, ultra-highvacuum (UHV) chambers connected together with a fixed angle of 90' between the beam source-to-target axis and the crystal target-to-detector axis. The main features are the nozzle beam source, which produces a nearly monoenergetic (Avlv= 1W )He beam; the manipulator in the scattering chamber, which allows orientation and temperature control (1 10-1000 K) of the crystal target; a time-of-flight(TOF) path (1040 mm) for energy analysis of the scattered He atoms, using a chopped (7 ps) He atom beam; and the electric quadrupole mass spectrometer detector coupled to a computer-controlled data acquisition system. 0022-3654/93/2097-2270%04.00/0
r" I
7 ;
Skimmer
Beamsource
Figure 1. Schematic view of the HAS instrument with the deposition source. For this instrument the sum of the incident and scattering angles ei er = 900.
+
The NaCl(001) target surface was prepared from a cleaved singlecrystal of NaCl as described e l ~ e w h e r e . 'The ~ - ~deposition ~ of KBr was carried out by sublimation from a piece of singlecrystal KBr arranged to provide a broad effusive source; it was controlled by a shutter as indicated in Figure 1. A thickness monitor, not shown in Figure 1, was used primarily to ensure that the deposition rate was uniform and that the number of monolayers deposited was the same as that determined by the oscillation period of the specular intensity (as in Figure 2) and the deposition time. Three types of measurements were made with this instrumental arrangement: (1) intensityvs deposition thickness for the specular beam, carried out under a variety of experimental conditions (e.g., as in Figure 2); (2) angular distributions of the scattered He atoms at different coverages and surface temperatures; and (3) TOF measurements at different coverages. The latter two were carried out after interrupting the deposition with the shutter. It was found that thegrowth could be turned on and off repeatably if the substrate temperature was not too high. It was also found that a clean NaCl(001) surface could be recovered by heating the target crystal to about 700 K for approximately an hour. From the arrival time spectra, incident angles,and the incident wave vector of the He atoms, one can calculate the energy and momentum transfer to the surface and thereby construct the surface phonon dispersion curves. For He atom scattering events involving single phonons, energy and crystal momentum con@ 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2271
Surface Dynamics of KBr Overlayers 120
100 h
N
4
3; 1 . c. .-
40
-r
R
""'I1
..
KBr/NaC1(001) T=223 K k , =?.22L' Rate=0.5 MUS
L
c
v) Q, c.
-c
20 "."
'.O
Phonon Wave Vector (oa QX )
00
0
5
0
10
Coverage (ML) Figure 2. Plot of the specularintensity versus the coverage in monolayers of the deposited KBr overlayers, adapted from ref 12. The labeled peaks correspond to the number of monolayers.
servation requirelJ8
ha = h2k:/2m - h2k?/2m
(1)
n 2
0.0
and
1 .o
zi
& = & - - Ri = + 0
(2)
Here &and Ri are the final and in_itialHe,atom wave vectors with projections onto the s;rface of Kr and Ki, respectively; m is the mass of the He atom; G is a surface reciprocal lattice vector; and w is the frequency of the created (e < 0) or annihilated (o> 0) phonon with surface momentum Q. The surface unit meshes of NaCl and KBr are rotated by 45' with respect to the bulk unit cell directions and have surface latticeconstants(a, = ab,1k/2~/~) of 3.99 and 4.661(, respectively.21 This translates to the fact that six KBr units (27.96 A) fit very nearly onto seven NaCl's (27.93 A) in each direction, a large mismatch of about 17%. III. Results The real-time behavior of the growth is monitored by observing the elasticspecular scattering intensityduring deposition as shown in Figure 2.12J3.22 This curve shows the intensity oscillations that correspond to layer-by-layer growth. One should note that the first oscillation maximum corresponds to a deposition time twice the period for the later ones. This suggests23that the first oscillation corresponds to the formation of a bilayer but that further growth consists of single layers. That is, the large lattice misfit forcesthe initiallydeposited KBr molecules to orient normal to the surface, but in subsequent layers they align parallel to the surface.12+23 The perpendicular orientation evidently allows a better energetic accommodation of the misfitting molecules. This behavior has also been observed in the NaCl/Ge(001) system.23 Thus the growth of the first new layer needs twice the number of molecules that each additional layer requires. Figure 3 shows a series of measured dispersion curves in the rM region of the surface Brillouin zone (Le., (100) crystal direction) for a cleaved NaCl(001) surface (a),19320 followed by results for KBr/NaC1(001) for layer thicknesses of NL = two (b), three (c), four (d), and seven (e) monolayers (ML)and finally for a cleaved KBr(OO1) surface (f).18 The first and the last of these panels are included for comparison. The TOF spectra for the overlayer results in Figure 3 were measured under different experimentalsignal-to-noise conditions as implied by the specular intensity vs thickness curve in Figure 2. In much of this work, accumulation times of the order of 90 min were needed to obtain adequate signals for the single phonon
PhononWave Vector (Oa Qn )
O'O
"."
1.o
Phonon Wave Vector (Oa /2n ) O'O
Figure 3. Experimental dispersion results for (a) a cleaved NaCl(001) surface,19(b) two monolayers,(c) three monolayers,(d) four monolayers, (e) seven monolayers, and (f) a cleaved KBr(OO1) surface.'* See the cited references for the model calculations that accompany the data in (a) and (f). For (b)-(e) the solid points are from strong TOF peaks, while the open points represent data that are only of moderate quality.
peak positions.12 As can be seen by the number of data points in Figure 3d, the NL = 4 case represents our most extensively examined system. For each overlayer system shown in Figure 3 there is found a well-defined, low-energyphonon dispersionbranch, which appears similar to the Rayleigh (or lowest energy sagittal plane acoustic) mode that was measured for the cleaved KBr in Figure 3f.1-2J8 It differs from that Rayleigh mode primarily in that it does not go to zero at the point but rather remains at a finite phonon energy, A more careful examination of panels (b)-(e) shows that the energy of this mode at the zone center decreases with increasing layer thickness, going very nearly as l / N ~ l / ~ . In addition to the Rayleigh-like mode, there are also higher energy modes that are observed. Some of the points appear to relate to the S2 surface optical mode of KBr(OOl), which lies in the gap between the acoustic and optical bulk bands,18 while the other experimental results scatter in between.
IV. Theoretical Calculations and Discussion A proper treatment of the vibrational behavior of the overlayer would employ the shell model in a slab dynamics calculation, as has been done for the cleaved alkali halide crystals.24 Recently, such a calculation has been carried out for a KBr overlayer on RbCl.2S However, unlike KBr/RbCl where the substrate and overlayer have nearly identical lattice constants, for KBr/NaCl one would have to consider a very large surface unit cell of dimensions =28 A X 28 A, since six KBr's fit onto seven NaCl's. Since a shell model calculation of this size presents formidable difficulties, we have sought here to present a simplified model that can still reproduce the essential character of the physical behavior. We find that the low-energy experimental features detected by HAS in this epitaxial growth work can be understood in terms of a simple force constant model that includes the forces in the
Safron et al.
2272 The Journal of Physical Chemistry, Vol. 97, No. IO, 1993
1.0 1.o 0.0 Reduced Wave Vector Coordinate ( 5 )
0.0
0
05
Figure 4. Comparison between the neutron scattering bulk dataz6 and the theoretical results of our model. The reduced wave-vector coordinate { = q a / 2 r , where a is the bulk lattice constant and q is the crystal momentum.
KBr overlayer,the effect of the NaCl substrate, and the coupling of the substrate to the overlayer.’ For thelayersof KBr we take intoaccount thenearest-neighbor interactions between the K+ ions, between the B r ions, and between K+and B r ions. We introduce six force constants: three radial force constants, &K, perer, and @ K B ~ ,and three tangential force constants CYKK, C Y B ~ B and ~, C Y K B ~ . For ionic crystals the dominant interaction is the Coulomb force, which depends on the distance between particles and on the ionic charges. Thus, we can take the coupling parameters between the K+ ions to be identical with those between the B r ions; Le., &K = flBrBr and CYKK = CYBrBr. In addition, the constraint represented by the equilibrium condition under rotation2 introduces the relationship between the tangential force constants that (YKBr = - ~ C Y K K . Therefore, the number of independent parameters is reduced to only three. We are then able to obtain a set of reliable KBr force constants, which can be used as a basis for the simulation of the surface dynamical properties by fitting to the measured bulk dispersion curves.2J6-28 It should be stressed that in this model we are neglecting the long-range interaction between the ions and are including only the short-range contribution. This means that our model will not be correct for the description of the optical part of the energy spectrum, and, in particular, it will not be able to reproduce the LO-TO splitting at the F point. However, as we are interested here only in the acoustic region, where the long-range interaction does not play a critical role, this limited treatment should suffice. In Figure 4 the calculated bulk dispersion curves are compared with the neutron scattering measurements.26-28In the acoustic region the theoretical calculations yield results that agree very well with the experimental data. But as expected for the optical region, the calculated curves do not reproduce the important features associated with the long-range Coulomb interaction. However, the simple model does appear to contain the physics needed to explain the HAS data lying in the acoustic part of the energy spectrum. The set of force constants yielding the best fit of the bulk phonon measurements are the following:
PKK
PBrBr =
1.60 N/m, &Br = 12.81 N/m,
(TKK
= a B r B r = -0.24 N/m, a K B r = 0.96 N/m
When we apply this simple model without adjusting the force constants to calculate the phonon dispersion curves of a 23-layer KBr(001) slab, Figure 5 , we find that the agreement is fairly good in the acoustic region, namely for the Rayleigh and crossing modes as well as for the longitudinal resonance. Thedisagreement for the Rayleigh mode is about 1 1%. This could be improved by modifying the force constants, but, considering the simplicity of the model, such a modification does not appear warranted. For the optical gap mode, the S2 mode, the agreement is not as good but is much better than one might have expected. One should compare this figure with Figure 3f. To calculate the vibrational properties of the systems of interest weintroducea rigidsubstrate (RS) torepresent theNaCl surface.
j= [1101 ji [loo1 p Figure 5. Calculated dispersion curves for a slab of 23 KBr (001) layers using the force constants from the fit in Figure 4. The data have been taken from ref 18 as in Figure 3 . The reduced coordinates are defined as in Figure 4.
E
6
2.5
LL E
Phonon W a v e Vector (QalPx)
Figure 6. Dispersion curves calculated for (a) two KBr monolayers on a rigid substrate, (b) three monolayers, (c) four monolayers, and (d) seven monolayers. The vibrational modes polarized perpendicular to the surface are labeled by
v.
(While this simplification seems rather drastic, we note that the vibrational coupling between KBr and NaCl is not expected to be very good, since the frequency of NaCl is roughly twice that of KBr for the same phonon wave vector.) The new system (KBr RS) requires additional coupling parameters that describe the interaction between the overlayer and substrate atoms. The fit provides the values of these force constants. The results of the calculations for two, three, four, and seven monolayers are shown in Figure 6. In the acoustic region of the spectrum of a system composed of N Lmonolayers, there exist N L modes with polarization normal to the surface (labeled with V,, where i = 1, ...,NL)at the point. One can see that these modes exhibit the typical dispersion of the modes arising from the presence of two different atomic species in each unit cell. As the films become thicker, these curves merge into the typical Rayleigh wave and crossing modes that have been observed in most of the cleaved alkali halide systems that have been examined with HAS, including the cleaved KBr(001) ~urface.~*-2~ The values of the new force constants are found to be = = 4.0 N/m, and note that they are softer than the KBr force constant This is consistent with a weakening of the Coulomb interaction between oppositely charged ions at the interface due to the structural disorder induced by the poor lattice matching. While Figure 6 shows the energy/wave vector dependence, it
+
rK(RS) rBr(RS)
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2273
Surface Dynamics of KBr Overlayers a) 2 ML
c) 4 ML
2%
6-
si
:?
-4
f ow Phonon Wave Vector
(ae/m)
Phonon Wave Vector
(amt)
d) 7 ML
b) 3ML
longitudinal vibrations should be much more sensitive than transverse modes to surface defects. For the 4-ML case there are two data points that lie below the Rayleigh mode curve. Since the peaks in the TOF spectra corresponding to these points are rather strong, they cannot be easily dismissed. One explanation is that they are interface modes, which have now been reported for the NaCI/Ge system.' The model presented here does not treat such features. We plan to reexamine this system to search for interface modes and to modify the model to predict where they would lie. A different model for thin films, the organ pipe model,ss6has recently been developed to interpret the surface vibrational results of Na deposited epitaxially on Cu(OO1). In this model the frequency w at f varies with the number of layers as 1/NLwhereas for our data we find w 1/NL1l2.In simple terms this means that the lowest energy mode at for our systems is due to the overlayer vibrating as a whole. It acts like a simple harmonic oscillator where w ( k / M i l 2 )where k is a spring constant and Mis the total mass of the layers, which is proportional toNL. The physical basis for the difference between the behavior of the Na/ Cu system and the KBr/NaCI system appears to be just that the coupling of the overlayer to the substrate is stronger than the intrafilm forces in the former and weaker in the latter.
-
r
Phonon wave Vector (amq Figure 7. Surface phonon density of states for vibrations normal to the Phonon Wave Vector (Qd2a)
surface in the case of (a) two, (b) three, (c) four, and (d) seven KBr monolayers on a rigid substrate. The intensity of the peaks is represented logarithmically by the length of the horizontal line calculated for the value of Q a t the horizontal center of each vertical slice. The closed and open points are the experimental values as in Figure 3.
is the spectral density of the surface atoms for each mode that indicates how effectively the incoming helium atoms arescattered by that mode. These spectral densities may be calculated according to the equation
(3) Here, a denotes the Cartesian- direction, 8 is the phonon momentu_m, E is the energy, w(QJ) is the frequency of the jth mode at Qj and u,(&,k = 1) is the related displacement along the a direction for the surface atom k = 1. The quantity pz1 # 0 marks the modes that should be easily detectable by helium atom inelastic scattering and furnishes a rough estimate of the scattering intensity. The results for the calculation from eq 3 relative to displacement normal to the surface in the case of two, three, four, and seven monolayers are shown in parts (a), (b), (c), and (d) of Figure 7, respectively. The intensities are indicated logarithmically by the horizontal lines and only the modes with energies less than 2.5 X 10l3rad/s are displayed. Note that at the lowest mode can be thought of as a longitudinal vibration in the direction normal to the surface that hybridizes with the Rayleigh mode for larger wave vectors. This same behavior occurs with the organ pipe modes discussed below.s.6 From these pictures the behavior of the different modes is easily recognizable and the positions of the energies are in generally rather good agreement with the experimental data where they are available. In every case the fit to the Rayleigh mode data is excellent. Except for the 4-ML case where considerable effort was expended in order to be thorough, the data for higher lying modes are rather sparse. Even so, one can see that there are features that are associated with the crossing mode.29 While the model has been developed to provide a good fit to the low energy acoustic modes, it is surprising to find that it also does a fair job of fitting thedata that areassociated with theS2gapmode (except for the 2-ML case). This seems to suggest that the short-range interactions dominate the dynamics of the perpendicularly polarized surface vibrations. The sagittal plane vibrational modes are not strictly separable into perpendicular and longitudinal motions, rather they couple and become elliptically polarized. Thus, for the cleaved KBr(001) we found substantial intensityfor TOFpeaks corresponding to the longitudinal resonance s 6 . ' * For the KBr overlayers we find that the corresponding peaks are much weaker or absent. This is not surprising in view of the fact that the coherence of the
-
V. Conclusions The dynamics of epitaxially grown thin films on crystal substrates has seen remarkable progress in the last year as three different systems have been measured and modeled. The highlights include (1) an interface mode observed in the NaCI/ Ge(001) system' (and possibly also in this work), (2) organ pipe modes found in the Na/Cu(001) c a ~ e , and ~ . ~(3) the strong intrafilm forces that lead to Rayleigh-like low-energy modes in this work.12 Further work in progress on the Pb/Cu(l 11) is likely to lead to further insights into overlayersubstrate dynamics. All these results appear to be easily understood in terms of the models, which offer physically reasonable and useful pictures to base future work on. We believe that HAS experiments are permitting us to move in the direction of being able to predict the properties of surfaces and how epitaxial growth patterns should evolve and thus perhaps even to building "designer" overlayers with particular vibrational properties.
Acknowledgment. N. S. Luo and P. Ruggerone gratefully acknowledge the support of the Max-Planck-Society. S. A. Safron, G. G. Bishop, J. Duan, E. S.Gillman, and J. G. Skofronick similarly acknowledge the support of the U. S.Department of Energy through Grant DE-FG05-85ER45208 and NATO through Grant 891059. J.G.S. also thanks the Max-Planck-Society and the Director of the Institute, Professor J. P. Toennies for the hospitality and the stimulating environment. References and Notes (1) Brusdeylins, G.; Doak, R. B.; Toennies, J. P.Phys. Reu. E 1983, 27, 3662. (2) Toennies, J. P. In Surface Physics, Springerseries in SurfaceScience; Kress, W., deWette, F. W., Eds.; Springer: Berlin, 1991; Vol. 14, Chapter 5. (3) Hinch, B. J.; Koziol, C.; Toennies, J. P.; Zhang, G.Europhys. Let?. 1989, 10, 341; Vacuum 1991, 42, 309. (4) Koziol, C.; Toennies, J. P.;Zhang, G.in Phonons 8 9 Hunklinger, S., Ludwig, W., Weiss, G.,Eds.; World Scientific: Teaneck, NJ, 1990; Vol. 2, p 880. ( 5 ) Benedek, G.;Ellis, J.; Reichmuth, A.; Ruggerone, P.; Schief, H.; Toennies, J. P. Phys. Reu. Left. 1992, 69, 2951. (6) Toennies, J. P. Europhys. News 1992, 23, 63. (7) Brusdeylins, G.; Luo, N. S.;Ruggerone, P.; Schmicker, D.;Toennies, J. P.; Vollmer, R.; Wach, T. Surf. Sci. 1992, 272, 358. (8) Gibson, K. D.; Sibener, S.J. Phys. Reo. Le??.1985, 44, 1514. (9) Gibson, K. D.; Sibener, S.J.; Hall, B. M.;Mills, D. L.; Black, J. E. J. Chem. Phys. 1985,83, 4256. (IO) Black, J. E.; Mills, D. L.; Phys. Reo. B 1990, 42, 5610.
2274 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 (1 1) Black, J. E,;Mills, D. L.; Daum, W.; Stuhlmann, C.; Ibach, H.Surf. Sci. 1989,21, 529. (12) Duan, J.; Bishop, G. G.; Gillman, E. S.;Chern, G.; Safron, S.A.; Skofronick, J. G. Surf. Sci. 1992, 272, 220. (13) Duan, J.; Bishop, G. G.; Gillman, E. S.;Chern, G.; Safron, S. A.; Skofronick, J. G. J . Vac. Sci. Technol. A 1992,IO, 1999. (14) For example, see: Ibach, H.; Mills, D. L. Electron Energy Loss Spectroscopy and Surface Vibrations; Academic: New York, 1982.
(15) For example, see: Zangwill, A. Physics at Surfaces; Cambridge University Press: Cambridge, 1988; Chapter 7. (16) Lauter, H. J.; Godfrin, H.; Frank, V. L. P.; Leiderer, P. Phys. Reu. Lett. 1992,68, 2484. (17) Mason, B. F.;MacPherson, G.; Williams, B. K. Surf. Sci. 1990,233, 153. (18) Chern, G.; Skofronick, J. G.; Brug, W. P.; Safron, S . A. Phys. Reo. 1989,839,12828. (19) Safron, S. A.; Brug, W. P.; Chern, G.; Duan, J.; Skofronick, J. G.; Manson, J. R. 3. Vac. Sci. Technol. A 1990,8, 2627.
(20) Safron, S.A.; Brug, W. P.; Bishop, G . G.; Chern, G.; Derrick, M. E.;Duan, J.; Deweese, M. E.; Skofronick, J. G. J . Vac. Sci. Technol. A 1991,
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R. W. G. Crystal Structures, Wiley: New York,
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