J . Phys. Chem. 1993,97, 1749-1757
1749
FEATURE ARTICLE Investigation of Epitaxial Growth via High-Resolution Helium Atom Scattering: KBr onto RbCl(001) S. A. Safron,' J. Duan, G. G. Bishop, E. S. Gillman, and J. G. Skofronick' Departments of Chemistry and Physics and the Center for Materials Research and Technology (MARTECH), The Florida State University, Tallahassee, Florida 32306 Received: September 30, 1992; In Final Form: December 17, 1992
-
High-resolution He atom scattering experiments have been employed to study the growth of KBr onto a cleaved RbCl(001) surface in the temperatures range 184L220 K. Three kinds of measurements were carried out: deposition curves (specular intensity vs deposition time), angular distributions (total scattering intensity vs incident angle), and time-of-flight spectra. The oscillations in the deposition curves show the characteristic behavior of layer-by-layer growth. However, the analysis of the data indicates that the step height of the first layer is different from that of subsequent layers, 3.71 A compared with 3.32 A expected from the bulk lattice spacing. The results also suggest that the growth mode in this temperature range is to form numerous small islands initially which then merge together with continued deposition. At the same time the defect density is very low for the first monolayer, but it increases with the number of layers grown. Analysis of the time-of-flight spectra for the one monolayer film yields surface phonon dispersion branches consisting of the Rayleigh wave, a longitudinal resonance, and a surface optical mode lying in the gap between the bulk optical and acoustic bands. The Rayleigh wave appears very nearly the same as that for cleaved RbCl and KBr (001) surfaces (very similar to each other); the other branches are significantly softened.
I. Introduction The mystery and beauty of crystal growth have attracted the attention of natural philosophers for a very long time. However, in recent years developing a microscopic framework for understanding the orderly assembly of molecules into a crystal has become a central scientificconcern and a technological necessity. Growth of materials by molecular beam epitaxy (MBE) and by vapor deposition1 has been examined principally by reflection high-energy electron diffraction (RHEED)" augmented by other surface-sensitive analysis techniques such as Auger electron spectroscopy ( A S ) and electron energy loss spectroscopy (EELS) ,33 RHEED provides the structural information;3,496the others provide the chemical analysisof the surfaceand near surface species. Low-energy electron diffraction (LEED)7is also capable of providing structural information about the surface and indeed becomes a very powerful tool for probing the character of the surface during growth when used in a spot profile analysis mode (SPA-LEED).' Although not as widespread as RHEED and LEED, highresolution helium atom scattering (HAS)+I8 has some advantages over electron scattering techniques, particularly for insulating materials. The low-energy He atoms are electrically neutral, nonpenetrating and nonreactive. Hence, they are sensitive only to the outermost layer and are totally nondestructiveto the surface. In contrast, care must be taken in RHEED studies of crystal growth to avoid damaging the surface with the probe electron beam.19J0 Coherent atom scattering is exquisitely sensitive to the presenceof defects on the crystalline surface. Thus, the layerby-layer growth may be followed by monitoring the specular beam intensity, and the details of the growth mechanisms can be established by measuring thedependenceofthe scatteringintensity on the coverage of the deposited material and on the deposition parameters of substrate temperature, deposition rate, and deposition energy.ll-16 Further, He atom diffractive scattering can be employed to determine the geometry and other structural 0022-3654/93/2097-1749S04.00/0
features of the surface at any point during the growth, and these features can be studied as a function of the deposition parameters.lsJ6 HAS instruments capable of time-of-flight (TOF) measurementsls-18can investigate the surface dynamics of the overlayer including modifications of surface forces that result from the growth, such as overlayer lattice strain and substratboverlayer interaction~.I~+2~-~~ Additionally, the TOF can cleanly separate the elastic scattering from the inelasticscattering. The very small fractional order diffraction peaks arising from charge density waves are much more clearly resolved in the elastic angular distributions than in the total scattering angular distributions.24 Similarly, the slight oscillations found in the angular distribution at large angles which are due to interference effects in the elastic scattering from defects can be analyzed via TOF to determine the defect sizes.2s Recent HAS experiments on metal-on-metal growth have explored a variety of sometimes unexpected effects. Some examples include reentrant layer-by layer (two-dimensional) growth for Pt/Pt( 111) at temperatures for which one would normally expect three-dimensional growth to occur,26 an alternation in single- and double-layer growth (quantum size effects) for Pb/Cu( 111),14 the transition from pseudomorphic to strained layer to undistorted Cu(ll1) structure in successive layers of growth of Cu/W( 1lo)," and the "organ pipe" vibrational modes in sodium overlayers from Na/Cu(001).21 Fewer studies have been carried out so far with insulators. HAS experiments for NaCl/Ge(001) have been done which suggest that the NaCl deposits initially perpendicular to the surface.22 This conclusion is somewhat different than is given for a RHEED study of the similar NaCl/GaAs ~ystem.2~The homoepitaxy of NaC1/NaC1(001)15and the heteroepitaxyof KBr/ NaCI(001)l6 and NaC1/KBr(001)28 have been carried out in this laboratory. They show markedly different initial growth patterns which seem to be related to the lattice mismatch (- 17%) Q 1993 American Chemical Society
1750 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
Safron et al.
Time of Flight
the number of atoms reflecting from the detector chamber walls into the ionizer region. The data acquisition system consists of Detector a computer-controlledCAMAC interfacewhich interacts directly I with the instrument. The ionizer region of the QMS is estimated to be at most 10 mm long, and therefore, for a He beam with a wave vector of 7 A-1 or atom speed 1100 m/s, it contributes -9 cis to the width of peaks in the TOF spectra. If one assumes the He velocity spedmeter distribution, the chopper function and the ionizer function are approximately Gaussian, then the meusured TOF width should be the square root of the sum of the squares of the contributing widths. For our path length (see Figure 1) the measured full width at half-maximum (fwhm) is 18 ps, which corresponds to Chopper an intrinsic beam width (182 - 72 - g2)Il2 = 14 ps. This means Skimmer that the intrinsic velocity spread of the beam, b / u , is only lg.31 7 7 Beam Source The He beam is calculatedto have a cross-sectional area of roughly 5 mm2 at the target, and the angular resolution (fwhm) of the Nozzle detector is -0.1O. 7t The incident He beam energies, Ei, in this instrument can be Figure 1. Schematic of the apparatus showing the relation of the beam varied currently from about 20 to 60 meV by suitably cooling the sourcewithnozzle andchopper,thescattering chamber withcrystal target nozzle source. These values correspond to He atom wave vectors, and evaporation source, and the detector with the quadrupole mass ki, of -6-1 1 A-1 or wavelengths (2r/ki) of about 0.6-1.1 A. spectrometer. With the beam source and detector fixed, 8i + Or = 90'. This range provides a good match with both the surface lattice spacings for He atom diffraction and the energies and momenta in the KBr-NaCl systems. But, after as few as four monolayers of the surface phonons for determining the surface phonon of KBr have been deposited on NaCl, the surface phonon dupersion dispersion. appears very similar to that of cleaved single-crystal KBr. This work complements several RHEED studies on the heteroepitaxy The crystal target is mounted onto a manipulator which allows of alkali-metal halides, filling in many of the details of the initial the surface to be aligned in the proper orientation by permitting growth mechanism.2'JJgJ'J translation in the x, y , and z directions, azimuthal rotation, and several degrees of tilting. The scattering geometry is shown more In this paper we focus on the KBr/RbCl heteroepitaxy. clearly in Figure 2. With the sourceand detector ftxed,the crystal Although the lattice constants of the two materials arevery nearly is aligned so that the atoms scattering in the plane perpendicular the same, the individual ions differ in size and polarizability, and these differences give rise to features in the growth which we to the surface can be detected. The heating and liquid nitrogen really did not foresee. In the next section the HAS instrument cooling attachments of the manipulator also permit variation of is described. In section I11 the results for the measurements of the temperature of the crystal holder from approximately 110 to the specular beam intensity vs deposition time, of the angular 1300 K. The manipulator itself is attached onto a differentially distributions,and finally,of the timaof-flit spectra are presented pumped rotatable platform so that the incident angle of the He and discussed. In section IV these results are compared with beam onto the crystal, Oi, may be changed without disturbing the previous alkali-metal halide growth experiments and the conalignment controls. A stepper motor under computer control is clusions summarized. used to drive the platform. For the experiments reported here the RbCl(001) surface was II. ExperiwnWSection prepared by cleaving a single crystal of RbCl in air and then quickly mounting the target onto the manip~lator.3~J~J8 The The apparatus employed for thesc experiments is shown vacuum system was then pumped down and baked for about 24 schematically in Figure lS3l Its design is similar in a number of h at 400 K, after which the crystal was heated in vacuum for respects to HAS instruments which have been described in the approximately 2 h at about 675 K. The base pressure in the literature in that it is composed of several vacuum chambers scattering chamber at this point is about 2 X 1O-IoTorr. After connected together.9J2-35 The He beam36 is produced by this procedure the alignment and measurementscould be started. continuous expansion of helium gas from a nozzle in the source The quality of the starting surface could be judged by comparing chamber, which then passes through a skimmer into the chopper the measured angular distributions (total He scattering intensity chamber. For the inelastic scattering experiments the beam is as a function of Oi) with those that had been obtained previously.38 chopped into pulses (7 ps) which are employed in a time-of-flight The deposition of KBr was carried out as in earlier deposition (TOF) technique for determining the energy transfer; for the studieslsJ6 by heating a picce of single-crystal KBr3' mounted deposition measurementsand the angular distribution experiments about 10cm from the target so that sublimation could take place the chopper is displaced out of the beam path. In either from a broad effusive source.39 (However, despite this design arrangement theatoms then pass through two stagesof differential there is some evidence that the depositionmay have been occurring pumping to the scattering chamber where they collide with the at very slightly different rates over the region probed by the He crystal. For this instrument theangle between the incomingbeam beam, which becomes noticeable only after many layers have and the detector axis is fixed at 9Oo.)l The He atoms which been put down.6 A better design would have the depositing KBr scatter from the surface such that the sum of the incident and issue from a small orifice much further removed from the target.) scattering angles Oi + Of = 90° (measured with respect to the A shutter was opened to expose the target RbCl crystal to the surface normal) then pass through four stages of differential source. A thickness monitor was omploycd as a check on the pumping to the detector chamber where their flux is measured by a quadrupole mass spectrometer (QMS)operated in a pulsedeposition rate measured by the He specular beam intensity counting mode. Not shown in Figure 1 is a "sump" chamber (described below). It was found that the growth could be turned which follows the detector. Helium atoms not ionized in the on and off repeatably if the substrate temperature was not too detector pass through the QMS into the sump chamber where high. It was also found from angular distribution measurements they are pumped away; this reduces the background by minimizing that a clean RbCl surface could be regenerated after deposition 1060 mm
I
-
h
The Journul of Physical Chemistry, Vol. 97, No. 9, 1993 1751
Feature Article
3
KBr/RbC1(001) Deposition Curve stan
Deposition
-B
Helium
C
Source Detector Q M k Q
, 6.60A
2ool 100
I
" 0
Figure 2. Scattering plane geometry showing the incident and scattering wave vectors ki and kfand their parallel and perpendicular components Ki,ki, and Kf,kf,,respectively.
ki =7.13A1 T-215 K
I 50
100
Figure4. DepositioncurveforKBrontoRbCl(001)showingtheintensity of the specular beam as a function of deposition time. The initial wave vector of the beam is 7.13 A-1, and the substrate temperature is 215 K.
I
I-
KBrFtbCl(001) e1 00s Deposition Curves
k , -0.45 A'
k ,- 7 . 1 3 t
6.58A
Figure 3. Bulk crystal lattice spacings for RbCl and KBr and for RbBr and KCI. The latter values might influence thedistancc between the first layer of KBr and the RbCl substrate. The si= of the circles represent the ionic radii. The values are taken from ref 41.
of KBr by heating the target for approximately 0.5 h at -675 K. In this work a 1-h cleaning by the sublimation procedure was used.
III. Results md Discussion Three types of measurements were made with this HAS instrument: helium atom scattering intensity vs deposition thickness for the specular and Bragg peaks, angular distributions of thescatteredHeatoms, andTOFmeasurementsofthescattered He atoms. The latter two were carried out after interrupting the deposition with the shutter at the desired coverage. The results of these measurements are presented in turn. A. Deposition Curves. Becauseof the periodicity of the crystal surface, the interaction potential between the surface and the helium atoms is periodic in the coordinates parallel to the surface plane. This gives rise to the Bragg scattering relation for parallel momentum transfer AK for the coherent elastic reflection from a perfect surfacea
K,- Ir, I hI( = C
(1) where C is a surface reciprocal lattice vector and from Figure 2 Ki= kisin Bi and Kr= krsin Br = ki cos Bi for elastic scattering on this 90° instrument. For RbCl and KBr which have the rocksalt structure with a face-centered cubic lattice, C., = ( 2 m / a , ) f (2rm/as)jwhere 1and j are the unit vectors of the surface mesh, n and m are integers, and usis the length of the square surface net which is given by the bulk lattice constant a b / d . Figure 3 gives the bulk lattice dimensions for RbCl and KBr and shows the relative sizes of the four ionic species.41 The relation given by eq 1 arises from the surface periodicity and applies only to the coherent scattering. The intensity of the Bragg peaks can thus be used to probe the condition of the surface and, hence, to monitor growth. For the most part we have relied on the specular beam intensity for this purpose (Le., the intensity of the He atoms scattered such that AK = COO = 0), but for the homoepitaxy of NaCl on NaCl(001) we also have monitored the growth using both the first- and second-order Bragg peab.ls Figure 4 shows the specular intensity as a function of deposition
+
150
Deposition Time (s)
10
IO 1 0 30 40
Coverage
(ML)
Figure 5. A series of deposition curvw for KBr onto RbCI(001) showing the variation in the oscillation intensities with incident wave vector. The curves are obtained as in Figure 4 except that the abscissa is the coverage in monolayers (ML)instead ofdepositiontime. Thesubstrate temperature is 215 K.
time for ki = 7.13 A-1. One can see that the intensity begins to fall as soon as deposition commences, and then it displays an irregular oscillatory behavior with shoulders, dips, and bumps until it settles down to a long-time value of below 10% of the initial intensity. In F w r e 5 is shown a seriesof similarlymeasured depositions for a range of incident He beam wave vectors. These curves also have irregular oscillatory behavior, which seem to differ from each other except for the first with ki = 7.13 A-1 and the last with ki = 8.45 A-1. Oscillations in the specular intensity during deposition have been seen before with RHEED4 as well as with HAS,11-16 and this behavior has been interpreted in terms of two-dimensional growth involving a competition in the growth mechanism between diffusion and nucleation.11-13 The initial surface, however good, has steps and other defects which give rise to some small amount of incoherent scattering. When the depositing molecules amve, they migrate on the surface at a rate which depends on the temperature until they become tightly bound at a defect or nucleation site. If they diffuse rapidly to the step edges, then the growth occurs by propagating the step edge across the surface. In doing so, the step length changes little, and consequently the amount of incoherent or defect scattering and thus the monitoring intensity will also change little. If the molecules instead nucleate on the terraces, forming islands which grow with further deposition, then the total step length also grows and the coherent intensity begins to fall. After about a half-monolayer coverage is attained, further growth causcs thecoalescencebetween islands, producing a net decrease in step length with the increasein terrace
Safron et al.
1752 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
area and hence an increase in the monitored signal. The coherent scatteringreaches a relativemaximum at one monolayer coverage, and then the cycle begins again. This oscillating intensity tends to fall off with increasing coverage since the new terraces are usually not as defect free as the old ones. In addition, a new layer may begin to form before the previous one has been completed so that the newer terrace widths are smaller than the older terrace widths. Eventually the step separations become close enough that growth takes place via addition to the step edges rather than by island growth." Threedimensional growth usually sets in at lower temperatures when the diffusion rate is slow and new islands build up on top of growing islands, well before the latter form completed terraces. This regime manifests itself by a simple monotonic falloff in the specular intensity. Kunkel et al. have reported a reentrant two-dimensional growth mechanism at temperatures below the three-dimensionalgrowth regime for relatively high deposition rates.26 These authors attribute this behavior under these conditions to the nucleation of many islands too small to sustain three-dimensional growth because their barriers for arriving admolecules to jump down are low. However, when the deposition rate becomes sufficiently slow, the admolecules have time to diffuse to the step edges of existing islands before nucleation, and hence, larger islands are formed which are able to sustain three-dimensional growth. For this mechanism, the specular intensity should oscillate with the coverage if the deposition rate is greater than the diffusion rate at this low temperature, but it should fall off very much more rapidly than in the higher temperature two-dimensional growth regime. Since the specular intensity, as shown in Figures 4 and 5 , oscillates with coverage, one can interpret the results as implying that the KBr overlayer on RbCl grows twodimensionally. It is also well established11-13that interference effects can arise in the coherent scatteringfrom terraces at differing heights. Simply stated, if the new and old terraces are separated in height by D, then the scattering from each to the same Bragg peak with"
(k,
- kJ = Ak, = kfz+ kiz= 2rNID
will be in-phase when N is an integer and out-of-phase when N is a half-integer. In the former case one should observe constructive interference in the scattering intensity and in the latter case destructive interference. What is striking about the datainFigure5 isnot that therelativeintensitiesoftheoscillations depend on the initial wave vector, but rather that the relative intensities for the first and second oscillations vary differently with the perpendicular momentum transfer Akz. This can be seen in Figure 6 where the relative intensity differences between a maximum and its preceding minimum are plotted for the first and second oscillations against Akz. The different phase relation for the first and second oscillations implies that the step height D for the first monolayer is different than the step height for the s m n d monolayer. For KBr one would expect the height to be one-half the bulk lattice constant (see Figure 3) or 3.30 A, which is very close to the value obtained for the second oscillation. The greater value obtained for the first oscillation seems to imply that the size mismatching of the individual ions gives rise to a repulsive interaction even though the lattice constants for KBr and RbCl are very nearly the same. The reason for this effect is not clear at this time. One should note that this height is substantially larger than one would expect even from the Rb+-Br lattice spacing. The shapes of the deposition curves provide further evidence that the growth of the KBr layer is by two-dimensional island formation. Engel and co-workers13have argued that when the growth of the islands is two-dimensional and the decrease in the coherent scattering is primarily due to scattering from the step
0.6 I
1
0.4
0.2
0.0 10
12
11
13
0.6 Second Oscillation 0-3.32A
6 N
0.4 -
0.0 10
12
11
13
Figure 6. Variation in the relative intensity difference between the oscillation maximum and minimum with change in the perpendicular component of the wave vector, A&z. I I and I2 are the intensities of the first and second maxima, respectively,and 1112 and 1312 are the intensities of the first and sicond minima, respectively. As discussed in the text, the oscillation period depends on the step height D For the first layer D = 3.71 A and for the second and subsequent layers D = 3.32 A. The uncertainties are estimated to be approximately M. 1 A.
KBr/RbC1(001) 1.o
I
\ T-215 K
.$
0.8
-
-o! 2 Q€
0.6
-
0.4
- intercept=l.O5
3
0.2 I
0.0
I
I
0.2
0.1
I
I
I
I
0.3
0.4
0.5
0.6
0.7
Square Root of Coverage
Figure 7. Plot of the intensity of the deposition curve in Figure 4 against the square root of the coverage for the range 0 < 8 5 0.5. From the model in the text the slope yields an r ~ =p 16 A.
edges, then the specular beam intensity should decrease with the square root of the coverage for the in-phase scattering condition in eq 2. This is basically because for two-dimensionalgrowth the area of the islands is proportional to the coverage 8, but island perimeters grow as W 2 . If one models the growth as taking place from a fmed number of nucleation sites, forming roughly circular islands with a radius r1/2 at half-monolayer coverage, one would expect the specular intensity Z to follow13
(3) where 100is the specular beam intensity before the deposition and 2~is the cross section per unit length of step. Based on a number of HAS experiments primarily on metal surfaces, the value of ZL has been found to be 13 A2/A.11-13Figure 7 has a plot of Z/Zm against W 2 , which gives a reasonably straight line except at very small coveragesand near one-half monola er coverage. The slope yields a radius at 8 = 0.5 of about 16 (assuming the above value of &), which is close to that found in the homoepitaxial
-
x
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1753
Feature Article
Angular Distribution (k,-7.78A")
growth of NaCI/NaC1(001) (-21 A).Is Since the cross section for alkali-metalhalides has not been determined,the precise values obtained through the model are probably not as important here as the square root of the coverage relation which seems to be reasonably well obeyed. However, the small value for rl/2does suggest that the growth in the alkali-metal halides may be occurring via the reentrant two-dimensional growth mechanism rather than by the more usually observed high-temperature mechanismsz6 Higher temperature studies to check this point are not possible for these systems because the Debye-Waller factor reduces the specular beam intensity too drastically," and experiments in which the deposition rates are varied still need to be carried out. Thedeviationfromeq 3forlowcoverages(8SO.O5)isprobably that in this regime the defects behave as isolated admolecules rather than as islands. In this case the scattering of the He atoms out of the coherent beams due to the adsorbed molecules should lead to a Beer's law-like expression with the specular intensity I given by12
I = z,(i
- zn,e)
(4)
Here ,Z is again the specular scattering intensity from the clean surface, Z is the atom-admolecule cross section, and n, is the number density of adsorbate sites (here, number of surface cells per unit area). The cross section obtained for KBr on RbCl from the initial slope is -60 A2,which is slightly smaller than that for NaCI/NaCl(-80 A2 15) but dramatically smaller than that for KBr/NaCI(-200A2 16). For thelattersystemit wasspeculated that the largecrosssectionwasdue to theorientation perpendicular to the surface of the initially deposited KBr molecules as a result of the large lattice mismatch (17%). The deviation from the @I2 dependencenear 8 = 0.5 probably arises from the breakdown of the linear approximation made to obtain eq (3).IzJ3 In this experiment (Figure 7) thevalue of I/Z, has dropped to about 30% at 8 = 0.5, whereas in previous work on metal deposition it has dropped only to about 80%. B. Angular Llistribution Experiments. Angular distribution experiments are performed by measuring the total scattering intensity of the He beam arriving at the detector as a function of the incident angle of the beam. The condition for Bragg scattering given in eq 1 can be rewritten for the 90° apparatus geometry of this HAS instrument as
AK = JG,,I = hi COS (ei + a/4)
(5)
and one expects a Bragg scattering peak only at those angles for which the conditions of eq 5 are met. We note further that for the experiments reported in this paper the crystal was aligned so that the (100) direction lay in the scattering plane defined by the beam and the detector axis. This restricts the scattering events which can be detected to those where AK = G,, (Le., reciprocal lattice vectors with m = n.) Figure 8 presents for comparison the angular distributions of cleaved RbCl, one monolayer (1 ML)KBr/RbCI, seven monolayers (7 ML)KBr/RbCl, and cleaved KBr. As expected, the Bragg peaks occur at the same angles since the surface lattice constants of RbCl (4.65 A) and KBr (4.67 A) give surface reciprocal lattice constants too close to be resolved in this instrument. The heights of the peaks depend on the corrugation of the surface and on ki. A very rough eikonal approximation treatment using a simple sine function to represent the corrugationa gave about 0.1 A for the peak-to-valley height for R b C P and about 0.3 A for cleaved KBr.)' For 1 ML KBr/RbCI the corrugation appears to be in between these values; from the ratios of the heights of the first-order Bragg peaks to the that of the specular, the 7 ML KBr/RbCl has a corrugation close to that of cleaved KBr but is still not quite there.
01
1
'
20
30
40
50
0
70
Incident Angle 8, (degree) Figure 8. Angular distributions in the (100) direction of He atoms scattered from the surface as a function of incident angle, Bi. In the top panel the surface is cleaved RbCl(001); in the next panel, the surface is 1 ML KBr deposited onto RbCl(001); in the next panel, 7 ML KBr have been deposited; in the bottom panel the surface is cleaved KBr(001), for comparison. The labels of the peaks (n,n)give the order of the Bragg diffraction as discussed in the text for cq 5, indices with bars are the negative values.
The widths of the diffraction peaks depend on the dimensions of the surface features, such as islands, which give rise to the diffractivescattering, but only if they are smaller than the transfer width (related to the resolving power) of the instrument.'* For such islands one should also observe interference effects in the intensities of the Bragg peaks as the perpendicular component of the incident wavevector is varied (as in eq 2). For this apparatus under the conditionsof Figure 8, the transfer width for the specular beam is -550 A. Since the full width at half-maximum (fwhm) of the specular peak of the 1 ML overlayer is only very slightly larger than those of the cleaved crystals (0.15O) and since the widths do not change significantly with ki,one is led to conclude that the surface features or islands have diameters on the order of several hundred angstroms. Further, the narrow peak widths, but substantial background, in the 7 ML KBr overlayer suggest that the defects that do build up are predominantly isolated ones, possibly missing ions or perhaps interchanged ions (C1- for B r , for example) arising from interlayer diffusion.20 We note also that the size inferred here is substantially larger than was found above for half-monolayer coverage, suggesting again that in forming the completed layer the islands have for the most part coalesced to eliminate step edges. This result is also consistent with the low-temperature, two-dimensional growth mechanism discussed above. There is one important point that should be made regarding depositioncurves and diffractivescattering. Because theelectrons
1754 The Journal of Physical Chemistry, Vol. 97, No. 9. 1993
Safron et al.
1 ML KBr/RbC1(001)
8
First Order Bragg Peak KBr/RbC1(001) ki ~ 7 . 7 A' 2 T=193 K 100
3Ooo2Ooo-
m
0
lo00
v
-
60 C
g! C
0
1000
500
Deposition Time
(s)
Figure9. Depositioncurvefor KBr ontoRbCl(001) showingtheintensity of the first-order Bragg peak as a function of time. The intensity of this peak begins to rise above the predeposition value just before thedeposition time for one-half monolayer is reached.
in metallic surfaces "spread out" into the vacuum, the surface corrugation is greatly decreased, and low-energy atom diffraction from metals yields a large specular beam and very small other Bragg diffraction peaks. Thus, the loss of intensity from the specular beam in a deposition curve can always be attributed to defects. With other materials, such as ionic insulators,deposition to form an overlayer can in effect change the surface corrugation and therefore can shift intensity into or out of the specular beam. This means, as in the case here, when the deposition curve shows a substantial decrease in intensity for the specular beam, an important part of the decrease may simply be the corresponding increase in the intensities of the other diffraction peaks. This is shown very clearly in Figure 9 where the deposition is followed by monitoring tho intensity of the first-order Bragg peak. Thus, depositioncurves alone are not sufficient for studies of the growth of nonmetals; angular distributions need to be carried out, too. C. Time-of-Flight Experiments. Helium scattering time-offlight experiments are used to determine the energy transferred to or picked up from the surface at different incident laboratory angles. These data provide several very important pieces of information. First, and most obvious, is that TOFmcasurements can separate the elastic and inelastic contributions to the total scattering intensity measured in the angular distributions. Equation 1 or 5 restricts the coherent elastic scattering to a small set ofanglessatisfyingthe Braggcondition. Any elasticscattering at other angles (called the diffuse elastic scattering) must arise entirely from defects and therefore is another measure of the surface defect density. Figure 10 shows a representative series of TOF spectra for 1 ML KBr/RbCI at non-Bragg angles. An elastic scattering peak (labeled E) is evident in each case but appears to represent only a small fraction of the total scattering at each angle. In fact, the diffuse elastic peaks found here are only marginally larger than those observed for the TOF spectra from cleaved KBr.31 For comparison, in the study of KBr/NaCI16 where the lattice mismatch results in a rather disorderly initial surface overlayer, the diffuse elastic peak is larger by far than the Rayleigh mode surface phonon peaks (labeled R and described below). Qualitatively, then, the surface here appears to be only marginally poorer than the excelknt surface obtained by cleaving and annealing single-crystal KBr. These spectra in Figure 10 also show a large background intensity compared with similar TOF spectra that have been reported for the cleaved alkali-metal halides. This increase is attributable to greater multiphonon scattering due to the somewhat higher temperature? of the crystal in these experiments42(180 K vs 120 K in previously reported experiments on cleaved KBr (OOl)3l.
1500 lo00
500 01 1
1
I
1.5
2
I
2.5
Time of Flight (ms) Figure 10. Representative series of TOF spectra for He scattering from a one monolayer KBr overlayer on RbCl(001) in the (100) direction. The positions labeled E are the arrival times for elastically scattered He atoms. The peaks labeled R correspond to single phonons at the energy expected for Rayleigh wave vibrations of the surface; those labeled 0 are at energies near those of a surface optical band gap mode for KBr; and those labeled I are intermediate in energy between thesc, probably related to the longitudinally polarized mode as discussed in the text. Peaks occurring at later times than (to the right of) E have lost energy to the surface (creation of phonons) while those arriving at earlier times than (to the left of) E have p i n e d energy (annihilation of phonons). The numbered peaks are marked in Figures 11 and 12 with error bars to illustrate the uncertainties in the measurements due to peak widths. The data in these spectra have been smoothed by averaging the number of counts in each 4 ps 'bin" with the number of counts in the two bins immediately before and after it.
Another feature of the spectra in Figure 10 is that the peaks due to single-phonon scattering events (see below) are somewhat broader than were observed in the cleaved crystal experiments. In a harmonic crystal the phonons represent eigenstates of the crystal, and their lifetimes are determined by the spontaneous transition rates. Defects mean that the phonon representation of the crystal states is only approximate; they are not rigorously eigenstates,and their lifetimes becomeshortenedand thespectral lines broadened. The more defects, the broader the lines should become. Normally, the width of the diffuse elastic peaks is the same as that of the specular beam, but in these spectra the widths of the diffuse elastic peaks also seem greater. Such broadening was observed at high temperatures in the premelting of lead43 and in the quasielastic scattering from mobile adsorbates.44 However, it is unlikely that this explanationcanapply here because it does not seem probable that a KBr would be very mobile at these temperatures once it becomes attached to a step edge or terrace nucleation site. More likely is that t L broadening here is due to the enhanced multiphonon scattering (annihilation and creation events) with near zero net energy transfer.4* A most important aspect of the TOF measurements is that the data from single-phononscattering events can be used to map out the surface phonon dispersion curves which, in turn, characterize
Feature Article 3.O 0 A
A
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1755
KBr(001) IML KBr/RbCI(O e A
IML KBrRbCl(001) 0
‘*“
0.0 I loo
>
0
Phonon WnveVector (Qn / 2 ~ r) Figure 1-l.- Surface phonon dispersion calculated from the TOF spectra for the I‘M region of the surface Brillouin zone using eq 8. The open points (0,A) are from previous experiments on cleaved KBr(OO1) ( 100) in ref 31; the solid points (0,A) are from this work. The circles represent well-defined TOF peaks while the triangles are only of moderate quality. The solid lines and shaded regions have been taken from a calculation for the KBr surface by Benedek and M i g l i ~ . The ~ ~ numbered points correspond to the numbered points in Figure 10, and the error bars are calculated from the peak widths. The energy scale is given in 10’)rad/s on the left and in meV on the right.
1 .o
Phonon Wave Vector (Qa /27c )
0
Figure 12, Surface phonon dispersion calculated from the TOF spectra for the I’M region of the surface Brillouin zone using eq 8. The open points (0,A)are from previousexperimentsoncleavedRbCl(001) (100) in ref 46; the solid points (0,A) are from this work. The symbols and energy scales used are as described in Figure 1 1. The numbered points correspoond to the numbered points in Figure 10, and the error bars are calculated from the peak widths. The curve drawn through the lowest energy p i n t s is a sine curve which matches the value of the RbCl data at the M point. S6;48and
the interactionsamong the surfacespecies and between the surface and the bulk species. The kinematic requirements for coherent single-phonon creation and annihilation scattering events modify eq 1 to40
AK=G+Q (6) where Q is the surface projection of the phonon wave vector; and the phonon energy is given by ho = h2(k; - ki2)/2m
(7)
where m is the mass of the helium atom. A negative value for o means that a phonon has been created in the atom-surface collision, and a positive value means that a phonon has been annihilated. Thus, by using eq 6 and 7, one can convert the inelasticpeaks in the TOF to points on the dispersioncurve w(Q). More convenient for this purpose is to combine these equations into that of a “scan ~ u r v e ” . ~
ho/Ei = ([AK+ki sin 8,]’/ki2 cos’ Oi) - 1
(8)
At a given angle 8i and incident energy Ei = h2ki2/2m,eq 8 gives the possible values of phonon energy and crystal momentum consistent with eq 6 and 7. That is, the single-phonon peaks in the TOF spectrum at angle 8i must correspond to intersections of the scan curve with the surface dispersion curves (or possibly with bulk bands). In Figures 11 and 12 are presented the TOF data converted via eq 8 to points on the dispersion curves for 1 ML KBr/RbCl (solid points). Alsoshown in Figure 11 are the data (open points) for cleaved KBr(O01)31on top of a calculation for the KBr(OO1) s~rface;~s in Figure 12 are presented recent data (open points) for cleaved RbC1(001).46 For the cleaved KBr and RbCl surfacesfour distinct dispersion branchesare observed: (i) the Rayleigh wave, which is the lowest energy surface acoustic mode polarized in the sagittal plane; (ii) a crossing resonance, which is a bulk phonon mode polarized perpendicular to the surface that has a high density of states at the surface and crosses the bulk acoustic band from the top of the Rayleigh wave at the M point of the surface Brillouin zone with negative group velocity to the ?1 point4’ (at 1.3 X 1013 rad/s here); (iii) a longitudinally-polarized resonance labeled
-
(iv) an optical mode lying in the gap between the bulk acoustic and optical bands labeled S2,48 For KBr there are some weak points for a higher lying surface mode S4 in the optical band.48 The phonon spectra of KBr and RbCl appear generally rather similar because the masses of the ions (Rb+ and Br,K+ and C1-) are very similar.48 This is especially so for the lowest energy vibrations, the Rayleigh modes, but is less true for the higher energy modes which tend to be more sensitive to secondaryeffects, such as polarizability differences, in the interspecies forces. A comparison of Figures 11 and 12 shows that the RbCl data for the S2 mode do not extend over the entire Brillouin zone and lie at slightly higher energies than for KBr. Another difference between KBr and RbCl is that it has been predicted that the crossing resonance should be weaker for RbCl than for KBr,4’ which appears to be the case. The data from the 1 ML overlayer of KBr seem to lie in three groups: the lowest energy phonons (labeled R in Figure 10) lie close to the Rayleigh phonons of both KBr and RbCl; an intemediate group (labeled I in Figure 10) lies just below the data near the s6 mode for the cleaved crystals and well above the crossing resonance except possibly near the zone center the data for the highest energy phonons (labeled 0 in Figure 10) lie nearly in a straight line near but distinctly below the KBr S2 mode and do not extend to the zone boundary (M). The fair agreement of the 1 ML data with the Rayleigh mode of the cleaved crystals is not surprisingconsideringthe good match between KBr and RbCl frequencies in this region. However, theredoes appear to be a slight stiffeningof thevibrations (higher frequencies) in the middle of the surface Brillouin zone. The reason for this is not clear at this time. The origin of the intermediate group points is not certain, but most likely they are longitudinally polarized modes. The crossing resonance found for the cleaved KBr surface comes from the bulk mode projected onto the surface and is not expected to be evident for a single monolayer of KBr. For KBr/NaCl the crossing resonance was found, but only weakly, for a 4 ML overlayer.16 The fact that these longitudinal acoustic and optical phonons are softened (lower frequencies) from the cleaved crystal values should be.connected with the much larger than expected height of the first layer seen in Figure 6. However, a detailed examination of this relationship will require extensivemodel calculationssuch
(r);
Safron et al.
1756 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 as have been recentlycamed out for NaC1/GeZ2and KBr/NaCLZ3 A further observation may also pertain to the coupling between the overlayer and substrate; whereas in the 4 ML KBr/NaCI measurements a low-frequency band (below the Rayleigh wave) was found that might be an interface vibrational mode,23in the KBr/RbCI system no such low-frequency vibrations have been detected.
IV. Concluding Discmion RHEED studiesof homo- and heteroepitaxialgrowth of alkalimetal halides by vapor deposition have been carried out by Yang and Flynn20 and by Koma et a1.27,29J0 Both groups have reported that the second alkali-metal halide grows pseudomorphically on the (100) cleaved surface of the first for a few layers but then grows as smooth unstrained (100) planes oriented in the same azimuth as the substrate. The exceptions to this pattern are the alkali-metal fluorides which do not seem to grow well on nonfluorides. Yang and Flynn also conclude that the growth is consistent with a picture in which the growth occurs at the step edges rather than at nucleation sites on the terraces. The results of the experiments carried out so far on NaCI/ NaCI, KBr/NaCI, NaCI/KBr, and KBr/RbCl are in partial agreement with this mechanism. Our interpretation of the data suggests that the growth of alkali-metal halides is epitaxial twodimensional growth, forming islands around nucleationsites which then coalesce with continuing deposition. From the size of the islands at one-half monolayer coverage, diameters on the order of 30-40 A, it would appear that the growth mechanism may be the low-temperature mechanism proposed by Comsa and coworkers.26 The overlayers form (001) surfaces which align with the substrate orientation. The quality of the surface that is produdinitially seemstobeverysensitiveto thelatticemismatch. For the cases of NaCI/NaCI and KBr/RbCI the defect density of the first layer is very small but increases with deposition as defect sites accumulate. In contrast, for the KBr/NaCI and NaCl/KBr systems the angular distributions show that the initial surface (after two monolayers have been deposited) is somewhat disordered, perhaps forming as a bilayer, and that there is a superstructure corresponding to the least commensurate length of the two materials which persists for at least six layers. (We note that six KBr's fit very nearly onto seven NaCl's.) After many layers these systems behave much like the other two. For the NaCl/NaCl homoepitaxy, theoriginal specular beam intensity could be restored, after a large number of deposited layers, simply by gently annealing at -400 K for an hour. This annealing procedurewas not carried out in the heteroepitaxialcases to avoid any possibility of interlayer diffusion of ions which could confuse the results. RHEED studies show that the surface quality is rather good after a large number of layers have been deposited, except possibly for alkali-metal fluorides. However, HAS is more sensitive to isolated defects which appear to accumulate with continued deposition. For 2 ML KBr/NaCI the TOF spectra show only a Rayleighlike mode whereas in the work reported here for a singlemonolayer of KBr on RbCI, three distinct modes (including an optical mode) can be recognized. One needs to have four monolayers of KBr on NaCl before one can discern clearly the higher energy modes. The difference between the two systems is the coupling between the substrate and the overlayer. The phonon spectral densities of KBr and NaCl are very different from each other, while for KBr and RbCl they are quite similar. Hence, the vibrational frequencies match quite well in the latter case although there is some evidence for stiffening in the Rayleigh wave and softening in the longitudinal and optical modes. For KBr/NaCI the frequency matching is poor, and there is some evidence that a dispersionlessinterface mode may exist at frequencies below those of the Rayleigh The results for KBr/RbCl give no evidence for such an interface mode.
The major findings of this work for KBr/RbCI are the following: (1) The growth of the initial KBr overlayer appears to be by two-dimensional island formation at nucleation sites on the terraces, probably by the low-temperature, two-dimensional growth mechanism proposed by Comsa and co-workers. (2) The step height for the first layer appears to be larger than the step heights of subsequent layers, and the corrugation of this first layer is intermediate between those of KBr and RbCl. (3) The vibrationalcoupling between overlayer and substrate is very good, permitting the observation of a longitudinal resonancc and an optical mode from a 1 ML KBr overlayer in addition to the Rayleigh wave. (4) There appears to be significant softening in the longitudinal and, particularly, the optical modes that are found for the 1 ML KBr film, which is probably related to the step height change found for this layer. Additional experimental and modeling work is continuing in this laboratory on these fascinating systems. As the alkali-metal halidea are the prototypical ionic insulator materials, we expect to be able to extend the methods and models developed for them to the more interesting, and more difficult to work with, families of metal oxides. These include materials with the rocksalt structure such as MgO% and Ni0,51.s2for which some HAS experiments on surface dynamics have already been carried out, and the perovskites such as BaTiOa and the superconducting cuprates which have been grown by MBE techniques.s3,s4 In the former group of materials not only are the electronic coupling between the ions more involved than in the alkali-metal halides, but magnetic interactions are also possible. For example, NiO has an antiferromagnetic to paramagnetic transition at 523 K. The perovskites often have piezoelectric properties, and in some cases phaae transitions to ferroelectric states occur. These additional features make these ionic insulators more intriguing for fundamental science and more interesting for technology.
AcLwwIledgwat. The authors thank Prof. J. P. Toennies and Drs. N. S.Luo and P. Ruggerone of the Max-Planck-Institut fiir Strbsnungsforschung, Gbttingen, Germany, and Prof. J. R. Manson, Clemson University, South Carolina, for many helpful discussions. We also gratefully acknowledge the support from the U. S. Department of Energy through Grant DE-FGO585ER45208 and NATO under Grant 891059. References md Notes (1) For example, see: Herman, M. A.; Sitter, H. Mofecular Beam Epiraxy; Springer-Verlag: Berlin, 1989. (2) For discussions of the theory and uscs of RHEED, sce for examples: (a) Farrow, R. F. C., Parkin, S. S. P., Dobson, P. J., Neave, J. H., Arrot, A. S., Eds. Thin Film Growrh Techniques for bw-DimensioM/ Srrucrures, NATO ASI Series, Series B: Physics Vol. 163; Plenum: New York, 1986; (b) Larsen, P. K., Dobson, P. J.. Eds. Reflection High Energy Elecrron Di/fracrion and Reflecrlion Electron Imaging ofSut$aces, NATO ASI Series, Series E Physics Vol. 188; Plenum: New York, 1988. (3) For general references to surface science techniques, eec for examplw: Woodruff, W. P.; Dclchar,T. A. Miniern Techni~uesofSurfaceScie~e; Cambridge University: Cambridge, 1986. Zangwill, A. Physics or Surfaces; Cambridge University: Cambridge, 1988. (4) Koziol, C.; Lilienkamp, G.; Bauer, E. Appl. Phys. Lcrr. 1987, 51, 901. Lilienkamp. G.; Koziol, C.; Bauer, E. In ref 2b, pp489-499. Lilienkamp, G.; Koziol, C.; Bauer, E. Surf. Sei. 1990, 226, 358. (5) For example, see: Mills, D. L.; Ibach. H. Elecrron Energy Loss Spectroscopy; Academic: London, 1982. (6) Van Hove, J. M.; Pukite, P. R.; Cohen, P. 1. J . Yac. Sci. Technol. B 1905, 3, 563. (7) For example, see: Clark, L. J. Surface Crysralfography;John Wiley and Sons: Chichester, 1985. (8) Henzlu, M. Appl. Surf. Sci. 1982, f f / I 2,450. Henzler. M.Appl. Phys. A 1984, 34, 205. Bush, H.; Henzler, M. Surf. Sci. 1986, 167, 534. Wollschltiger, J.; Falta, J.; Henzler,M. Appl. Phys. A 1990, 50, 57. (9) Brusdeylins. G.; Doak, R. B.; Tannies, J. P. Phys. Reo. B 1983,27, 3662. ( 10) Tannies, J. P. InSurfanPhysics,SpringcrScrtcsinSurfaceSciem, Vol. 14; Kress, W., de Wette, F. W., Eds.; Springer-Verlag: Berlin, 1991; Chapter 5. (1 1 ) De Miguel, J. J.;Sanchez, A.; Cebollada, A,; Gallego, J. M.;Ferr6n. J.; Ferrer, S.Surf. Sci. 1987, 189/f90, 1062. Dc Miguel. J. J.; Cebollada. A.; Gallego, J. M.; FerrC, J.; Ferrer, S.J . Crysr. Growrh 1988,88, 442.
Feature Article (12) Poelsema, B.; Comsa, G. Scatferingof Thermal Energy Aromsfrom Disordered Suflaces; Springer-Verlag: Berlin, 1989. (13) Xu, H.; Yang. Y.; Engel, T. Surf.Sci. 1991, 255, 73. (14) Hinch, B. J.; Koziol, C.; Toennies, J. P.; Zhang, G. Europhys. Left. 1989, 10, 341. (15) Duan, J.; Bishop, G. G.; Gillman, E. S.; Chem, G.; Safron, S.A,; Skofronick, J. G. J. Vac. Sci. Technol. A 1992, I O , 1999. (16) Duan, J.; Bishop, G. G.; Gillman. E. S.;Chern, G.; Safron, S.A.; Skofronick, J. G. Surf.Sei. 1992, 272, 220. (17) Koziol, C.; Toennies, J. P.; Zhang. G. I n Phonons 89, Vol. 2; Hunklinger, S., Ludwig, W., Weiss. G., Eds; World Scientific: Teaneck, NJ.
1990; p 880. (18) Gibson, K. D.; Sibener, S.J.; Hall, B. M.; Mills, D. L.; Black, J. E. J. Chem. Phys. 1985,83.4256. (19) Mason, B. F.; MacPherson, G.; Williams, B. K. Surf.Sci. 1990,233, 153. (20) Yang, M. H.; Flynn, C. P. Phys. Reo. Lerr. 1989,62,2476. Yang, M. H.; Flynn, C. P. Phys. Reo. E 1990, 41, 8500. (21) Toennies. J. P. Europhys. News 1992,23,63. Benedek, G.; Ellis, J.;
Reichmuth, A.; Ruggerone, P.; Schief, H.; Toennies, J. P. Phys. Reo. Lett.
1992, 69, 295 1. (22) Brusdeylins, G.; Luo, N. S.;Ruggerone, P.; Schmicker, D.; Toennies, J. P.; Vollmer, R.; Wach, T. Surf.Sci. 1992. 272, 358. (23) Safron, S.A.; Bishop, G. G.; Duan. J.; Gillman, E. S.; Skofronick,
J. G.; LUO,N. S.;Ruggerone, P. J. Phys. Chem., in press. (24) Ernst, H.-J.; Hulpke, E.; Tocnnies, J. P. Europhys. Lett. 1989, 10. 747. Hulpke, E. J. Electron Spectrosc. Relar. Phenom. 1990, 54/55, 299. (25) Lahee, A. M.; Manson, J. R.; Toennies, J. P.; W611, C. Phys. Reo. Left. 1986,57,471. Lahee, A. M.; Manson, J. R.; Toennies, J. P.; Wdll, C. J . Chem. Phys. 1987,86, 7194. (26) Kunkel, R.; Poelsema, 8.; Verheij, L. K.; Comsa, G. Phys. Rev. Lert. 1990,65,733. (27) Nakamura, Y.; Saiki, K.; Koma, A. J. Vac. Sci. Technol. A 1992, IO, 321. (28) Duan, J. Private communication. (29) Saiki, K.; Nakamura, Y.; Koma, A. Surf.Sci. 1991, 250, 27. (30) Saiki, K.; Nakamura, Y.; Koma, A. Activity Report of rhe Institute for Synchrotron Radiation; University of Tokyo: Tokyo, 1991. (31) Chern, G.; Skofronick, J. G.; Brug, W. P.; Safron, S.A. Phys. Rev. B 1989.39, 12828. (32) Lilienkamp, G.; Toennies, J. P. J. Chem. Phys. 1983, 78, 5210. (33) Doak, R. B.; Nguyen, D. B. J. Electron Spectrosc. Relat. Phenom. 1987, 44, 205. (34) Gibson, K. D.; Sibener, S . J. J. Chem. Phys. 1988,88, 7862. (35) David, R.; Kern, K.; Zeppenfeld, P.; Comsa, G. Reo. Sci. Insrrum. 1986, 57, 2771. (36) Toennies, J. P.; Winkelmann, K. J. Chem. Phys. 1977, 66, 3965.
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1757 (37) The single crystals of RbCl and KBr were obtained from the Crystal Growth Laboratory, Department of Physics, University of Utah, Salt Lake City, UT 841 12. (38) Chern, G.; Brug, W. P.; Safron, S.A.; Skofronick, J. G. J. Vac.Sci.
Technol. A 1989, 7, 2094. (39) Wasilewski, 2.R.; Aers, G. C.; SpringThorpe, A. J.; Miner, C. J. J. Var. Sci. Technol. B 1991, 9, 120. (40) For example, see: Boato, G.; Canthi, P. Ado. Electron. Elecrron Phvs. 1983. 60. 95. (41) Wyckoff, R. W. G. CrysfalSrructures, Vol. I; John Wileyand Sons:
New York, 1964. (42) Skofronick, J. G.; Bishop, G. G.; Brug, W. P.; Chern, G.; Duan, J.; Safron, S. A.; Manson, J. R.SuperlarricesMicrosrruct. 1990,7,239. Manson, J. R. Phys. Rev. B 1991, 43, 6924. (43) Frenken, J. W. M.; Toennies, J. P.; W611, C. Phys. Reo. Lerr. 1988, 60, 1727. Frenken, J. W. M.;Hinch, B. J.; Toennies, J. P. Surf.Sci. 1989,
211/212,21. (44) Hinch, B. J.; Frenken, J. W. M.; Zhang, G.;Toennies, J. P.Surf.Sci. 1991,259, 288. (45) Benedek, G.; Miglio, L. In Ab Inirio Calculations of PhononSpecrra;
Devrecse, J., van Doren, V. E., van Camp, P. E., Eds.; Plenum: New York, 1982. (46) Bishop, G. G. Private communication. (47) Safron, S. A.; Chern, G.; Brug, W. P.; Skofronick, J. G.; Benedek, G. Phys. Reo. B 1990, 41, 10146. (48) The designation of the modes is that of de Wette and co-workers.
The surface phonon dispersion of RbCl has been calculated by: Chen, T. S.; de Wette, F. W.; Alldredge,G. P. Phys. Reo. B 1977,15,1167. Thecalculation for KBr has been carried out in ref 45 and by: Kress, W.; de Wette, F.W.; Kulkarni, A. D.; Schroeder, U. Phys. Reo. B 1987, 35, 5783. (49) Duan, J. Private communication. (50) Mahgerefteh, M.; Jung, D. R.; Frankl, D. R. Phys. Reo. B 1989,39, 3900. Jung, D. R.; Mahgerefteh, M.; Frankl, D. R. Phys. Reo. B 1989,39, 11164. In addition, MgO has been examined in this group (Brug, W. P. Ph.D. Dissertation, Florida State University, 1991) and by the Gdttingen group (private communication). (51) Brug, W. P.; Chern, G.; Duan, J.; Bishop, G. G.; Safron, S.A.; Skofronick, J. G. J. Vac. Sci. Technol. A 1992, IO, 2222. (52) NiO has also been grown by MBE techniques; see: Chern. G.; Berry, S.D.; Lind, D. M.; Mathias, H.; Testardi, L. R. Appl. Phys. Left. 1991,58, 2512. Lind, D. M.; Berry, S . D.; Chern. G.; Mathias, H.; Testardi, L. R. Phys. Rev. B 1992, 45, 1838. (53) Feenstra, R.; Boatner, L. A.; Budai, J. D.; Christen, D. K.; Galloway, M. D.; Poker, D. B. Appl. Phys. Lett. 1990.54, 1063. (54) Terashima, T.; Bando, Y.; Iijima, K.; Yamamoto, K.; Hirata, K.; Hayashi, K.; Kamigaki, K.; Terauchi, H. Phys. Reo. Lett. 1990, 65, 2684.
