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Surface Science 275 (1992) 1-15 North-Holland

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Temperature dependence Si( 001) surfaces

of the step structure of vicinal

C.E. Aumann, J.J. de Miguel I, R. Kariotis and M.G. Lagally University of Wuconsin-Madison, Madison, WI 53706, USA

Received 31 December 1991; accepted for publication 5 May 1992

Si(OO1)surfaces miscut slightly towards the [llO] direction consist of alternating domains of (1 x 2) and (2 X 1) reconstruction, separated by inequivalent, single-atomic-height steps; at higher miscut angles, the surface is mainly monodomain, with terraces separated by double-atomic-height steps. High-resolution low-energy electron diffraction has been used to determine the step structure of vicinal Si(OO1)as a function of both temperature and miscut angle. The concentration of double-atomic-height steps continuously increases with miscut angle and, for vicinalities greater than _ 2”, decreases with increasing temperature. From a comparison of the experimental results with the predictions of a one-dimensional model treating the problem in terms of chemical equilibrium in a two-component system we obtain information on the energetics of the structure transformation.

1. Introduction

In recent years, the step structure of the vicinal Si(OOlX2 x 1) surface has revealed itself as a challenging theoretical and experimental problem. Because of its importance, the surface has been the subject of many studies, and much has been learned about the factors that control the structure of this surface and its behaviour with vicinality and temperature. As a result, it has become apparent that Si(OO1) is a nearly ideal model system for investigating adatom interactions and their influence on structure. The Si(OO1) surface reconstructs by forming dimers arranged in parallel rows [l]. Because of the symmetry of the substrate, this reconstruction presents two equivalent degenerate (2 x 1) domains, related by a 90” rotation. If a surface is miscut towards (llO), dimer rows in adjacent terraces run parallel and perpendicular to the terrace edges, respectively. Terraces with dimer rows running perpendicular to the steps are de’ Permanent address: Departamento

de Ffsica de la Materia Condensada, C-3, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain.

0039-6028/92/$05.00

noted (2 x 11, while those with dimer rows parallel to the steps are called (1 x 2). In early diffraction studies [2], only the (2 x 1) reconstruction could be observed in vicinal samples with large miscut angles (> 4”), implying that the surface had only double-atomic-height (DAI-I) steps of the type called D,, i.e., a step perpendicular to the dimer rows. Additional observations using a number of different techniques, including RHEED [3], transmission electron diffraction (TED) and microscopy (TEM) [4], and LEED [5] appeared to support the conclusion that this was the equilibrium state of all vicinal Si(OO1) surfaces. This conclusion was further supported by a calculation [6] that found an energy per unit length of Da-type steps lower than the sum of formation energies for the two types of singleatomic-height CWH) steps, S, and S,. These steps respectively terminate the “down” side of (1 X 2) and (2 X 1) terraces. It was later shown that multiple-scattering effects complicated the interpretation of the diffraction experiments, and that at least nearly flat surfaces contained only monatomic-height steps [7]. An important contribution to the understanding of the structure of the Si(OO1) surface came

0 1992 - Elsevier Science Publishers B.V. All rights reserved

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C.E. Aumann et al. / Step structure of vicinal Si(OO1)

with experiments showing the influence of surface stress [8]. On the basis of these observations it was pointed out [9-111 that the anisotropy in the surface stress should cause even perfectly oriented (001) surfaces to lower their energy by breaking up into terraces with alternating reconstruction domains separated by SAH steps. A number of recent STM experiments [10,12-141 support the following general picture for the equilibrium state of this surface at low temperatures: for high vicinalities the surface is single-domain, presenting (2 x 1) terraces separated by DAH steps, whereas for lower vicinalities alternating terraces of (2 x 1) and (1 x 2) structure are present, separated by SAH steps. However, the way in which the transition from one state to the other occurs is by no means clear. A number of different models have been proposed that will be discussed later, and their predictions will be compared with our results. In this paper we report on detailed high-resolution low-energy electron diffraction (HRLEED) measurements on Si(OO1)(2x l), performed as a function of temperature on samples of different vicinalities. Preliminary results have been presented elsewhere [15,16]. These measurements go beyond earlier diffraction results and supplement recent scanning tunnelling microscopy @TM) observations. Although the interpretation of STM experiments is much easier (because they provide real-space images of the surface), at the present moment they are limited to temperatures of several hundred “C or lower. In contrast, diffraction measurements can be performed at high temperatures with very little complication. Additionally, because diffraction probes the state of the surface averaged over a large sample area, information from diffraction and STM can be combined to obtain a greater understanding of the structure of surfaces than is possible with either alone. In the next section we describe the experiment and the Si samples used in this study. In section 3 we discuss theoretical aspects of diffraction that are relevant to the interpretation of our measurements. In section 4 we present the results of our experiments. We discuss their significance in section 5, where we compare them with previous theoretical and experimental studies; in particu-

lar, we briefly review the successes and limitations of one-dimensional (1D) models, and gain in this way further insight into the mechanisms that control the surface dynamics. Finally, in section 6 we provide the conclusions.

2. Experimental The samples used in this study were cut from well-oriented Si(OO1)wafers. Sample orientations were measured with electron and X-ray diffraction, as well as with STM [17]. These measurements showed the crystals to be well-oriented vicinal surfaces cut towards [llO] having negligible azimuthal miscuts, i.e., the steps had a low density of “forced” kinks. The samples were mounted on the sample holder with the steps running at 45” with respect to the clamping direction to minimize the effect of strain. STM has also confirmed that our heat treatment of these samples yields surfaces free of carbon and oxygen contamination [12]. This treatment consists of high-temperature flashes to 1250°C for approximately 30 s, followed by annealing and slow cooling from 900°C. Extended exposure of surfaces to temperatures below N 1150°C especially at pressures above N 10e9 Torr irreversibly roughens them, because Sic is not removed at these conditions. Long-term exposure of a sample to vacuum with numerous flashes to 1250°C appears to degrade gradually the quality of the surface, producing a higher concentration of surface vacancies. No chemical treatment other than degreasing samples with acetone and methanol before insertion into the UHV chamber was used. Metal contamination was avoided by handling the samples with teflon tweezers, by using silicon spacer material to isolate the sample from the Ta mounting clips and by avoiding all contact of the sample with metal or even ions from an ion gun. No evidence of the (2 x n) structures indicative of nickel or other metal contamination was observed on the samples used in this study, by either STM or HRLEED. The (2 x n) structure can, however, be made at will by deliberately using steel tweezers or touching a chromel-alumel thermocouple to the sample at high temperature. The sample

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C.E. Aumann et al. / Step structure of uicinal Si(OO1)

temperature was measured by means of two pyrometers (optical and infrared). Temperature values determined this way are accurate to within N 20 K. The measurements were made using a HRLEED diffractometer described previously [18]. The high resolution (characterized by a maximum resolvable distance of N 1 pm) results from using a field-emission electron gun, an electron detector with a small entrance aperture, and near-grazing angles of incidence. Angular profiles of diffracted beams are obtained by ramping a current through a Helmholtz coil assembly under computer control while recording the electron count from the detector. The magnetic field from the coil sweeps a particular diffracted beam across the aperture of the detector. Several scans are averaged to yield a profile of this beam with a good signal-to-noise ratio. 3ecause there are two

a>

b)

I

Ma

I

orthogonal sets of coils in the assembly, which can be active simultaneously, a number of scanning modes are available. Two-dimensional (2D) angular profiles can be obtained by taking a line scan with one coil active while the other has a fixed current passing through it and then subsequently incrementing the current in this second coil. Angular profiles can be taken with the sample at temperature by applying a pulsed voltage signal across the sample, while recording the electron count when there is no voltage on the sample. The electron counting is triggered by the down-going edge of a pulsed reference signal synchronous with the sample heating voltage. A time delay is added following the trigger to allow the voltage on the sample to settle completely to zero. Use of direct heating alone leads to spurious profile shapes that result from deflections

2Ma

I

TI” 2

I art/Ma -

2x/L

x/Ma H

R/L

x/d

Fig. 1. Schematic diagrams of reciprocal lattices for simple vicinal surfaces; only the (00) terrace rods are shown. (a) Reciprocal lattice of a vicinal surface containing equispaced, monatomic-height steps. The miscut angle is 8,. The shaded region represents the terrace structure factor; its width is 2x/Ma. (b) Reciprocal lattice of a surface with the same miscut angle but containing diatomic-height steps. Extra rods appear because of the longer periodicity of the surface.

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C.E. Aumann et al. / Step structure of vicinal Si(OO1)

due to the magnetic field set up by the heating current itself. The current flows at 45” with respect to the steps; no influence of the current polarity on the relative occupation of the two reconstruction domains has been observed. Though absolute intensities cannot be measured, the profiles can be scaled to the current in the last lens element of the electron gun. This current is proportional to the actual beam current so that fluctuations in the beam current from the inherently unstable field-emission gun can be filtered out. This normalization makes possible reliable comparison between profiles of single reflections taken at different times; 2D profiles need not be scaled as all diffracted beams in such a profile see the same average fluctuations.

3. Description of the experimental method Atomic steps produce periodic changes in the reciprocal lattice rods of a perfect crystal surface. These characteristic changes are seen as a broadening or splitting of diffracted beams at out-ofphase conditions. A wealth of literature describing the reciprocal lattices for a number of simple stepped surfaces is available [19]. While the presence of atomic-height steps can be readily determined with diffraction, extraction of the actual distribution of step heights is not possible when there is a mixture present on the surface. Because the intensities measured in diffracted beams result from correlations between the separations of scatterers, surface configurations having singleand multiple-atomic-height steps are very difficult to distinguish from surfaces having only SAH steps but unequal “odd” (1 X 2) and “even” (2 X 1) terrace areas. In this sense Si(OO1) surfaces present a challenge for diffraction; they form DAH steps for certain miscuts and strain can cause the surface to have more terrace area of one type than of the other. What follows is a discussion of the information that is available through diffraction and how the measurements we present were performed. Our measurements are best understood by first considering the reciprocal lattices from a few simple surfaces having well defined step heights

and terrace lengths. The reciprocal lattice around the (00) terrace rod for a perfect vicinal surface having all SAH steps is shown in fig. la. The vicinal rods due to the periodic arrangement of steps are inclined with respect to [OOl] by the miscut angle and are modulated by the scattering factor for a terrace of length Mu (the shaded area in the figure). The intersection of the Ewald sphere with this lattice yields the familiar split spots when the sphere cuts through an out-ofphase point (2mr/a, (2n - l)rr/d) for perfect SAH steps. If we now force the SAH steps to group in pairs we will have a surface with the same miscut angle but with terraces twice as long as before, separated by DAH steps. This longer periodicity in real space will create new, additional vicinal rods in reciprocal space half-way between the previous ones at the integral-order positions. The terrace scattering factor will also change, because the width of the terraces now will be 2Mz; the new reciprocal lattice is shown in fig. lb. Characteristic of this situation is the appearance of a single sharp reflection at (0, r/d), which is the first in-phase condition for DAH steps. Next, let us consider the reciprocal lattice for a surface having different but fixed odd- and eventerrace areas, as shown in fig. 2. This surface can be thought of as an intermediate stage between the purely SAH and the purely DAH examples presented above. In this case, the surface would appear to have DAH steps because the lattice shows intensity at (0, r/d). However, the terrace structure factor will be broader than in the purely DAH stepped case because the terraces are narrower than 2Mu; consequently, the adjacent vicinal rods will be visible as well. For simplicity, we will label the different lattice rods observed in a single profile as A, B, C, as shown in the figure. The difference in area between even- and oddterrace levels divided by the sum of odd- and even-terrace areas is denoted as the occupation asymmetry. The asymmetry has a value in the range from zero to one as the surface moves from a condition of equal odd- and even-terrace areas to one having all DAH steps. The asymmetry equals l/3 for the surface shown in fig. 2, where the even terraces have twice the area of the odd

C.E. Aumann et al. / Step structure of vicinal Si(OO1)

terraces. This same information can be found in the integrated intensities associated with the vicinal lattice rods. Specifically, the ratio of integrated intensity scattered into the extra rod (i.e., into the “B” peak) to the total integrated intensity is: zl3

Mf,

- Nfrv

I* + I, + z, = MfM+NfN’

5

1.O deg.

0.3 deg.

I

(1)

where M and N are the average sizes of (2 X 1) and (1 x 2) terraces, respectively, and the f’s are their respective scattering factors. Eq. (1) is a measure of the deviation from the ideal situation depicted in fig. la. This means that for a silicon surface with mostly (2 x 1) area the measured ratio of intensities would be near one, while for a

4.0

2.0 deg.

deg.

I

I

Fig. 3. Set of 2D profiles of the (00) beam at room temperature for samples with different miscut angles, showing all three vicinal rods. The Ewald sphere cuts the central rod (B in previous figures) at the exact out-of-phase condition S, = n-/d.The intensity of this rod increases with vicinality, indicating a growing imbalance of terrace areas.

Fig. 2. Scheme of the geometry of our experiments. The surface generally consists of alternating terraces of different size, which manifests itself in the appearance of intensity in the extra rods (dashed lines). The Ewald sphere as depicted corresponds to an experiment at near-glancing incidence. The conditions are chosen such that rod B (order - 1) is profiled exactly at the first out-of-phase condition (Sz = r/d); rods A and C are then cut at different positions and their intensities must be corrected accordingly (see text). The three rods A, B, and C (of order 0, - 1, and - 2, respectively) make up the (00) fundamental reflection at Sz = r/d.

surface with equal (2 x 1) and (1 x 2) areas the ratio would be zero. This is illustrated by the 2D profiles shown in fig. 3: these profiles were taken at room temperature (RT) on samples with different miscut angles. The increasing ratio of intensity of the central peak to the split ones with increasing miscut that can be observed in the figure clearly shows the tendency of the surface to change the relative domain occupations as a function of miscut angle; we will come back to this later. Realistic surfaces contain a range of odd- and even-level terrace widths as well as rough edges; however, this does not alter the result that the measured integrated intensity ratio gives the occupation asymmetry. Distributions of odd- and even-level terrace areas broaden the even vicinal rods, yet the integrated intensities stay the same for surfaces with the same occupation asymmetry.

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C.E. Aumann et al. / Step structure of uicinal Si(OO1)

Diffraction can measure only the area of terraces of different reconstruction, and thus occupation asymmetries. The observation of any change in this magnitude reveals only that atoms are changing levels and leaves in question the actual mechanism by which this change occurs. However, in combination with additional information from other techniques, specifically STM, one can reasonably assign a physical path for a change in occupation asymmetry.

4. Results In Si(OO11,multiple scattering causes the scattering factors of the two types of terraces to be in general not equal. This effect manifests itself in the appearance of intensity in the position of the extra (odd) vicinal rods [7], thus complicating the analysis purely on the basis of terrace areas. When the azimuth of incidence of the electron beam is along [loo], i.e. 45” with respect to the steps, the scattering factors become equal and the ratio of intensities in eq. (1) gives directly the difference in sizes of both types of terraces, that is, the occupation asymmetry. For this reason, all of the measurements reported in this paper were taken with the incident beam along the [loo] direction. Diffracted beams associated with surface reconstructions (“superlattice reflections”) naturally contain information about the amount of area occupied by their respective domains. Since the (2 X 1) and (1 X 2) reconstructions can never form on the same level, the integrated intensities of their respective diffracted beams give information about the relative area occupied by odd- and even-level terraces as well [20]. The vicinal rods associated with the integral-order beams (“fundamental reflections”), however, offer several advantages over the half-order reflections. The half-order beams are weaker in intensity than the (001 beam. One can follow the integral-order beams to higher temperatures because they can be reached at points lower in Sz, at which the Debye-Waller factor is significantly less than it is for the half-order features. Additionally, as the surface moves towards one having more DAH

steps (i.e., more (2 x 1) area> the intensity in the (1 X 2) superlattice beams, corresponding now to very narrow terraces, is distributed over a very large angular range, limiting the accuracy with which it can be measured. Further, STM has revealed that the area associated with (1 x 2) domains often consists of single dimer rows that would not add intensity to the (1 X 2) superlattice beams at all [17]. The integral-order beams see this area and thus give a more accurate value for the occupation asymmetry. For all these reasons, our measurements were principally made on the (00) reflection at the SAH-step out-of-phase condition. Experimentally, the intensities of the beam profiles are affected by two geometrical factors that complicate the calculation of the asymmetry. The first one, specific to our electron energy analysis and detection scheme, is that the detector employs a flat-grid assembly behind its entrance aperture for retardation of inelastic electrons. Intensities of electrons entering the detector at other than normal incidence will be attenuated because they enter the aperture at an angle with respect to the grid assembly. Because the relative angular separation between various rods increases with vicinality, a correction factor found for one sample is not valid for others with different vicinalities. Furthermore, because of the diffraction geometry, the angular distance of satellite peaks from the central one differs for beams on either side, giving different attenuation factors in the same profile. The attenuation has the effect of making a surface look like it has a larger occupation asymmetry than it actually has. The second geometric factor is related to the necessarily low angle of incidence. To minimize the rate of fall-off of the intensity with temperature due to the Debye-Waller factor it is prudent to take measurements at the lowest Sz value possible. Most of the data reported in this paper have been taken at the first out-of-phase condition (S, = r/d), where the value of the exponent 2M (which determines the rate of decay of the peak intensity due to thermal scattering) is 0.04 at RT. This results in a loss of peak intensity of - 10% in our measurements at 1300 K, with respect to the intensity measured at RT. To reach

C.E. Aumann et al. / Step structure of vicinal Si(OO1)

the first r/d point for Si(OO1) requires a grazing angle of 5.3” with respect to (001) for the usual 600 eV beam energy employed in this study. This means the Ewald sphere can cut only one vicinal rod at the exact r/d out-of-phase condition for a given angle of incidence, a situation shown schematically in fig. 2. However, eq. (1) can only be used to calculate the occupation asymmetry if all three rods are measured at S, = r/d; consequently, asymmetries obtained by applying eq. (1) to the intensities measured in composite 2D profiles that include all three rods (like those shown in fig. 3), are not correct. This is not a problem for the simple schematic vicinal surfaces discussed above because, within the kinematic approximation, the shape of the terrace scattering factor and the position of the Ewald sphere are known precisely for such surfaces, implying that the intensities at the r/d positions can be calculated given their intensities at other known S, values. When there is a distribution of terrace areas, however, one must find a method to correct for this effect and determine the asymmetry accurately. To correct for such factors we have used the following procedure: the integrated intensity of a

LL*bbA

eeeee 0 E-ma

Sz

rod A

rod

rod

B C

(n/d)

Fig. 4. Example of the measurements of the integrated intensities of the three vicinal rods shown in fig. 2 as a function of S, near the first out-of-phase condition, for a 3”-miscut crystal. The arrows show the positions in S, at which each rod is cut with our experimental geometry when the Ewald sphere is set to intersect rod B exactly at S, = r/d. The fact that the intensities vary considerably along S, (due to muhiple scattering) indicates why it is necessary to correct them in order to obtain appropriate values for the occupation asymmetry.

7

single rod centered in the detector is recorded as a function of incidence angle, for all available rods within the Brillouin zone. Data taken this way insure that all reflections see the detector in the same way. Our knowledge of the precise diffraction geometry and therefore the cut of the Ewald sphere across the rods allows us to map the incidence angles to S, values. Fig. 4 shows a typical measurement of the intensities of three different rods centered in the detector as a function of S, at a fixed temperature. The arrows indicate the values of Sz at which each rod would be measured in a typical 2D profile with our diffraction geometry if the central rod is cut at precisely S, = r/d. These measurements reveal the existence of a third factor affecting the calculation of the occupation asymmetry: multiple scattering modulates the intensities along the rods. However, by making use of these measurements of the integrated rod intensities, the appropriate diffraction conditions can be found that give us the correct domain occupations. Let us consider first the results of the measurements at RT. Fig. 3 showed 2D profiles of the (00) beam take? at the first out-of-phase condition (Sz = 2.3 A-‘) at RT for several vicinalities. Fig. 5 shows the behaviour of the integrated rod intensities as a function of S, for the same miscut angles. From the latter curves the occupation asymmetries can be calculated directly using eq. (1) and the values of the integrated intensities at the appropriate value of S,: if the kinematic approximation were valid, peak B should have maximum intensity at S, = r/d. However, the curves shown in fig. 5 appear to be shifted, which could be an effect of the inner potential. We calculate the occupation asymmetries at the values of S, corresponding to the maximum integrated intensity for rod B. The resulting values for the area1 occupation of the minority domain at RT, for all of the vicinalities we have studied, are shown in fig. 6, together with the data published by Tong and Bennett (TB) 1201 and Schroder-Bergen and Ranke (SR) [21], as well as recent STM data [17]. Possible causes for the differences observed in these experimental results will be discussed in the next section. Qualitative agreement is found in an

C.E. Aumann et al. / Step structure of vicinal Si(OOl)

cz

z;

z

00

Sz (n/d)

1.0

2.0

3.0

Sz (n/d)

Fig. 5. Integrated intensities in the three vicinal rods of the (00) reflection at room temperature as a function several vicinalities: (a) 2”; (b) 3”; (c) 4”; (d) 6”. From these measurements, the correct domain occupation calculated and the correction factors for the intensities in the 2D profiles can be found.

aspect: the in the occupation vicinal angle a gradual and there no sharp as had suggested [lo]. the good agreement between those sets data, obtained analyzed by

ANGLE

(")

6. Fractional occupied by minority (1 2) doat room as a of miscut after several triangles, ref. dashed line, [20]; squares, [21]; circles, work. See for discussion.

of S, near asymmetries

r/d for can be

methods, makes confident that is basically Next we concentrate on temperature dependence the occupation For the of experimental we have temperature series 2D profiles all diffracparameters fixed azimuth and dence angle, two of series are in figs. and 8, to samples 2” and respectively. It be clearly that the in the peak, which us the in area1 of the x 1) (1 X domains, decreases increasing temperature to that the other peaks. We used 2D for the ture measurements they can taken much than the rod intensity presented before. thermal exof silicon small, so angular separaof the will not appreciably with this means the diffraction do not with temperature.

C.E. Aumann et al. / Step structure of uicinal Si(OO1)

S, value itself is very small and the differences in S, between beams in such profiles is small enough so that we need not consider any temperature dependence of asymmetry due to different Debye-Waller factors. Finally, since all three rods are profiled in a single measurement, the reproducibility and consistency between the different profiles taken in a temperature series is improved. Knowing that the intensities measured in these profiles do not give us the correct domain occupations, we have used the following correction method. We know from eq. (1) that the occupation asymmetry is a linear function of the total intensity scattered into rod B. Thus, for every miscut we take a 2D profile at RT, obtain the integrated intensity of each rod and calculate the effective correction factor that, applied to the integrated intensity of rod B, gives us the correct occupation asymmetry (obtained from the inte-

T = 743 K

T =

1100K

T = 1273 K

Fig. 7. 2D scans showing the temperature evolution of the diffracted intensity in the (00) beam of a sample miscut by 2” (S, = z-/d for rod B).

Fig. 8. Temperature evolution of the diffracted intensity for a sample miscut by 4”, same as in fig. 7.

grated rod intensity measurements as presented in the previous paragraph and shown in figs. 5 and 6). This factor effectively incorporates all the geometrical and dynamical effects discussed above, and is a constant for every set of measurements, because all experimental parameters are kept fixed except temperature. Then, by making use of eq. (1) and the corrected intensities, the changes in the occupation of each domain can be followed. To check the accuracy of our method of analysis, we performed integrated rod intensity measurements like those in fig. 5 for several miscuts at temperatures other than RT. In all cases the agreement between these measurements and the corrected 2D profiles was satisfactory. Figs. 7 and 8 show very little intensity in the central peak at temperatures near 1300 K, we conclude that the areas occupied by each domain at those temperatures must be almost equal, and that there must be essentially no DAH steps. The sample miscut by 0.3” showed negligible intensity

10

C.E. Aumann et al. / Step structure of vicinal Si(OOl) 2" MISCUT

However, these measurements hadot be done at higher values of S, (typically N 8 A-‘), resulting in a more rapid decrease of the peak intensities, due to the effect of the Debye-Waller factor and a correspondingly higher background. Consequently, we could only extend our measurements to temperatures near 1100 K. We were not able to deduce any significant changes in the occupation asymmetry from these data, in agreement with ref. [20]. An important consideration regarding the experiments of TB is the temperature range in which they were performed. The highest temperature reached in that study was 1100 K, while our data show that the most significant changes in domain occupation occur at temperatures above 1000 K. We believe that this fact, together with the experimental difficulties associated with measuring the half-order beams, discussed above, may account for the failure to observe any temperature dependence in that work.

051

051

3" MISCUT

z s g

0.3 04

g $

05 ! 02

g

0.4

5 2

03

8

"

0

4" MISCUT

00

l

zj 02 i s g 2

04

0 0 6" MISCUT

ir 03 1 02

01

1

0 0

0’2

o”if---5F TEMPERATURE

(K)

Fig. 9. Observed temperature evolution of the occupation of the (1 x 2) (minority) domain for the different vicinalities. These data have not been corrected for the extra row of atoms in Da steps (see text).

in the central peak at all temperatures; the one miscut by 1” showed a higher intensity in that peak, but no temperature dependence in the range we could study. For the rest of the vicinalities studied, the observed temperature dependencies are shown in fig. 9, where the fraction of area occupied by the minority domain is depicted as a function of temperature. A continuous, rather than abrupt, change in this fraction over a large temperature range is observed. It should also be mentioned that the splitting of the diffracted beams remains constant at all temperatures, indicating that no step bunching or facetting occurs. As already mentioned, fractional-order superlattice beams also contain information on domain occupation. We have also attempted to measure the temperature evolution of the intensities in the half-order superlattice spots, (0, *I and (i, 01.

5. Discussion A number of aspects about the data deserve discussion. Let us first comment on the roomtemperature data shown in fig. 6. It is evident that there is good overall agreement in the general trend between our data and those obtained by the other authors. The data of SR show a fairly large amount of dispersion because they have been obtained using two different methods of analysis. It should be mentioned that our experiments and those of SR were performed on the (00) rod, while TB measured the difference in intensities in the half-order beams. The latter measurement should nearly correctly yield the occupation asymmetry at low vicinalities, for which both types of terraces are large enough to accommodate many dimers. However, as the miscut angle increases and the mean terrace width shrinks, conditions are found where the minority terraces are less than two dimers wide, which is the minimum required to have intensity in the corresponding half-order beam. This remaining area will still contribute to the fundamental reflections.

C.E. Aumann et al. / Step structure

The sensitivity of the fundamental reflections to very narrow strips of terrace must be taken into account when analyzing our data at high vicinalities. Because of the diamond crystal structure, D, steps are not perfectly vertical. There is a protruding line of atoms on the lower plane. Although this line is considered to be part of the step, it is seen by the fundamental reflections as non-zero area of the (1 x 2) domain. This area influences our determination of occupation asymmetries in those samples that have miscut angles so large that even the (2 x 1) (i.e., majority) terraces consist of only a few atomic rows. As an example, for a sample misoriented by 6”, the size of the monodomain terraces (when there are only DAH steps on the surface) is _ 26 A, i.e., they can contain a maximum of 7 rows of atoms; in this case, the extra line of atoms in the step amounts to N 12% of the total terrace area, which means that measurements showing < 12% minority domain are not achievable. In fact, our data for that vicinality show a minimum of N 14% minority domain (see fig. 9); this value should therefore be considered as an upper bound to the actual area of (1 X 2) terraces. As the temperature rises and the length of D, steps decreases, the effect diminishes. The effect has been corrected for the data presented in fig. 6 as well as in fig. 10, which summarizes the results of our temperature-dependent measurements in terms of contour lines of equal-minori~-domain occupation plotted on a vi~inali~-versus-temperature diagram. One important consideration in the interpretation of measurements on the temperature dependence of domain occupation is the influence of surface transport and evaporation kinetics. It is well known [221 that the state of the surface observed at RT is not the equilibrium one, but rather corresponds to a higher temperature at which the atomic transport kinetics becomes so slow that the surface appears to be stabIe for ail practical purposes. The changes in domain oceupation involve mass transport across the terraces and movement of the steps. Therefore, the values of the “freeze-out” temperatures are expected to depend on the miscut angle (i.e., on the mean terrace size). To eliminate any possible influence

qf uicinal Si(OO1)

0

0

;------_.--_-_-

11

8oro-_-

_. .-____.~; 1.300

300

‘fEMPEI