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Formation and morphology of step bunches during B-segregation on vicinal Si(111)
Surface Science 605 (2011) 861–867
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Surface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u s c
Formation and morphology of step bunches during B-segregation on vicinal Si(111) Daniel Bruns, Sebastian Gevers, Joachim Wollschläger ⁎ Fachbereich Physik, Universität Osnabrück, Barbarastr. 7, 49076 Osnabrück, Germany
a r t i c l e
i n f o
Article history: Received 17 March 2010 Accepted 7 January 2011 Available online 25 January 2011 Keywords: SPA-LEED Silicon Boron Step bunch Si(111) pffiffiffi pffiffiffi ð 3 × 3 ÞR30 ∘ reconstruction Surface passivation
a b s t r a c t Degenerately boron-doped vicinal Si(111) substrates were annealed at high temperatures to achieve completep saturation ffiffiffi pffiffiffi of the ‘dangling bonds’ by surface segregating boron atoms under reconstruction to the Si(111) ð 3 × 3ÞR30∘ phase. Different cooling procedures were applied to obtain well ordered superstructures. The surface morphology of the prepared substrates was studied by spot profile analysis of low energy electron diffraction (SPA-LEED). The splitting of the diffraction peaks into multiple satellites points to the formation of step bunches of different inclination (equivalent to different terrace widths) during the segregation process due to changes in the surface free energy. A model with step bunches consisting of steps with monoatomic or biatomic heights and large (111)-oriented terraces is developed to explain our results. Steep step bunches with short terraces and biatomic step heights are formed independently of the preparation process while flat step bunches with large terraces are dissolved with increasing annealing time. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Vicinal Si(111) surfaces can exhibit (111) terraces which are separated by (more or less) regularly arranged atomic steps due to the misorientation of the surface with respect to the (111) orientation. Another possibility is that the size of the (111) terraces increases significantly so that the atomic steps gather and form step bunches. For instance, Phaneuf et al. reported that vicinal Si(111) surfaces misoriented towards ½110 or ½112 exhibit monoatomic steps beyond the critical temperature of the order–disorder transition (7×7) ↔(1×1), while step bunches are formed for the (7×7) reconstructed Si(111) surface [1–3]. Therefore, the formation of step bunches was attributed to the elastic interaction between (7×7) reconstructed terraces to minimize the surface free energy [4,5]. Beyond this, Hibino et al. clarified that step bunches on vicinal Si(111) surfaces tilted towards ½112 are (331) facets for temperatures below 600 °C [6]. These experiments, however, were performed on weakly doped vicinal Si(111) samples (cf. formation of (7×7) reconstruction) by radiation heating. For direct current heating in step-down or step-up direction the formation of step bunches was also observed for weakly B-doped or P-doped Si(111) at high temperatures (disordered (1 × 1) phase) [7]. For instance, vicinal Si(111) surfaces with misalignment towards ½112 form step bunches with direct heating in step-down direction for the temperature range 1200 °C–1300 °C and below 960 °C while for step-up currents the temperature range 1060 °C–1200 °C and
⁎ Corresponding author. Tel.: +49 541 9692652. E-mail address: [email protected] (J. Wollschläger). 0039-6028/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2011.01.013
temperatures above 1320 °C are necessary to form step bunches [8]. For weakly doped vicinal Si(111) substrates which form the (7 × 7) reconstruction at low temperatures, this process is reversible and was attributed to electromigration of single adatoms or advacancies as discussed in several theoretical studies [9–12]. Therefore, the orientation of the step bunches strongly depends on the misorientation of the sample surface, as well as, on the direction of the current. In contrast to the above reported here, we will present pffiffiffi experiments, pffiffiffi studies on Si(111) surfaces with ð 3 × 3ÞR30∘ reconstruction which is induced by boron segregation. There are mainly two different approaches to deposit boron on Si(111). One approach is through evaporation of boron on the substrate followed by annealing at 900 °C. Here boron adsorbs on T4 sites at first and changes to S5 sub-surface sites during the annealing [13]. The other approach is based on boron segregation underneath the surface of degenerately boron-doped Si(111) during annealing. While annealing the samples at about 1000 °C under UHV conditions the boron atoms diffuse towards the surface and attach directly on S5 sites underneath the silicon adatoms which, on the other hand, move from the S5 site to the T4 site [14–17]. An electron transfer between the unsaturated bonds at the silicon adatoms on T4 sites and the boron atoms on S5 sites takes place. Thus, in both cases the presence of boron atoms underneath the surface a change in the surface free energy, which leads to a pffiffiffi pcauses ffiffiffi ð 3 × 3ÞR30∘ reconstruction of the surface without any dangling bonds. Therefore, this passivated surface is of large interest for various applications (cf. [18] and references therein). The present work focuses on the step bunch structure in dependency to the cooling rate after the annealing B-doped Si(111) pffiffiffi of degenerately pffiffiffi where the surface shows the ð 3 × 3ÞR30∘ reconstruction. For
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different cooling procedures SPA-LEED measurements were performed at room temperature (RT) in order to characterize the surface morphology of the samples.
2. Experiment B-doped Si(111) samples with an electric resistivity of 5 Ωcm (weakly doped, 1015/cm3) and 10− 3Ωcm (degenerately doped, 1020/ cm3), respectively, and a (0.35 ± 0.15)° misorientation from the (111) plane towards the ½112 direction were used for the studies presented here. The samples were transferred into a UHV chamber (base pressure 10− 10 mbar) and outgased at 600 °C for 12 h via resistive heating. The current was directed in ½112 (step-down) direction. Afterwards the samples were flash annealed for some seconds at 1020 °C to remove the native SiO2-layer from the surface. The pressure was kept below 10− 8 mbar during this flash annealing. In order to prove that the surface was not contaminated by adsorbates we performed AUGER electron spectroscopy (AES) measurements on the samples (primary energy 3 keV). The AES system works with a cylindrical mirror analyzer (CMA). The scan rate was 10 eV/min while the modulation amplitude of the lock-in amplifier was 6 eV. It is reported that boron atoms segregate at the surface at temperatures above 900 °C [19,20]. In order to force B-segregation we flash annealed the samples at 1200 °C for a few seconds and then quenched to 900 °C (≈50 K/s) and held at this temperature for 20 min (background pressure 5⋅10− 9 mbar). Afterwards the samples were cooled down to RT in two different ways in order to compare the correlation of the annealing process to the morphology of the surface. In the first procedure the sample was cooled from 900 °C to 800 °C with a cooling rate of 20 K/min (total preparation time 25 min). In comparison we used a much slower cooling procedure where the sample was cooled with a rate of only 0.8 K/min to 800 °C (total preparation time 145 min). From 800 °C to RT we cooled both kinds of samples with a rate of ≈10K/s. From now on these procedures are named ‘slow’ and ‘fast’ cooling procedure, respectively. The absolute temperatures were measured by an infrared pyrometer (impac IGA 12) with an accuracy of ± 30 °C. The pyrometer was calibrated with a Si sample with attached thermocouple prior to the measurements reported above. After the preparation the segregation of boron was controlled by AES with the sample at RT. In addition in situ SPA-LEED measurements were performed at this temperature to characterize the surface morphology. This high resolution technique needs an electrostatic deflection unit, a fine focus electron gun and a channeltron pffiffiffi pffiffiffisingle electron detector [21]. 2D measurements of the ð 3 × 3ÞR30∘ reconstruction and spot profiles of the (00)-spot along the ½112 direction were measured in the range of 64 eV up to 148 eV for the electrons. Due to the fact that the investigations were performed on Si (111) samples, in the following we use the scattering phase S = dmonoK⊥/2π, which is normalized to the monoatomic Si(111) ∘ step height dmono = 3:1354 A instead of the vertical scattering vector K⊥ for all measurements. Therefore we probed the scattering phases S = 3.5 − 6.2 for the energy range used here. As a reference we first performed spot profile measurements on a weakly B-doped Si(111) sample to confirm that the changes of the surface morphology of Si(111), as determined by SPA-LEED, are caused by the presence of surface segregated boron. The twodimensional SPA-LEED pattern of the weakly B-doped Si(111) sample at 95 eV (S = 5) is shown in Fig. 2(a). The surface shows the well known (7×7) reconstruction. One can see sharp diffraction spots at RT after annealing with the slow cooling process. The spot profile analysis of the integer-order spots revealed no preferential broadening during an inphase condition, so it is limited by the transfer width which is t∼55±5nm for the used SPA-LEED optics. The only surface irregularities are statistically arranged monoatomic steps which are clearly detectable for an out-of-phase condition due to the enhanced diffuse diffraction.
Therefore only monoatomic steps without any preferential crystallographic ordering are formed during the annealing process. For the weakly doped Si samples the additional isotropic broadening of the spots in an out-of-phase condition is (0.3 ± 0.05)%BZ which is equivalent to an average terrace width of (70 ± 10)nm. Here 100%BZ ∘ (percentage Brillouinzone, ð100%BZ ¼ ˆ 2π = a with a = 3:3258 A Þ denotes the distance between two fundamental diffraction peaks in reciprocal space). All (7 × 7) superstructure spots were round and the change of their FWHM for different scattering phases was equivalent to the behavior of the integer-order spots. 3. Results To probe the surface stoichiometry of the studied samples we performed AES measurements as shown in Fig. 1 for a degenerately B-doped Si(111) sample after the preparation with the fast cooling procedure. The boron signal at 179 eV had a much lower intensity in comparison to the silicon signal at 92 eV. This result represents the fact that there is only a third of a monolayer of boron in the third atomic layer underneath the surface (boron segregates at S5 sites) [22]. SPA-LEED patterns from degenerately B-doped Si(111) pffiffiffi recorded pffiffiffi samples showed a ð 3 × 3ÞR30∘ reconstruction (Fig. 2(b)) instead of the (7×7) reconstruction (cf. Fig. 2(a)). This change is driven pffiffiffiby the pffiffiffilower surface free energy due to the B incorporation. The ð 3 × 3ÞR30∘ superstructure spots were round and had an additional average FWHM of (0.8±0.05)%BZ compared to the instrumental resolution for all samples, which is equivalent to an average domain size of AD =(42±3)nm. In the following a detailed spot profile analysis of the (00) spot for all degenerately B-doped samples was performed to determine the surface morphology according to the annealing procedures. Integer-order spots, however, were clearly elongated along the ½112 direction. A closer inspection showed that these diffraction peaks consisted of several satellite peaks (depending on the scattering condition). 3.1. The fast cooling procedure First we want to focus on the analysis of the (00) spot profile for the fast cooling procedure. Fig. 3 presents cross sections of the (00) spot in ½112 direction for S = 4.46, S = 4.75 and S = 4.94. All profiles exhibit a strong central peak at K∥ = 0%BZ (solid line) which is attributed to large Si(111) terraces and additional satellites (dotted and dashed lines). On the one hand, for S = 4.75 the spot profile shows two symmetric pairs of satellites with a separation of ΔK∥,flat = 2.5%BZ and ΔK∥,steep = 12.2%BZ due to large and small terraces, respectively, determined from fitting the profiles (see below). On the other hand, for S = 4.46
Fig. 1. AES spectrum of the cleaned, degenerately B-doped Si(111). An intense silicon signal at 92 eV and a very weak boron signal at 179 eV can be seen.
D. Bruns et al. / Surface Science 605 (2011) 861–867
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7
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10 10 10 10
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Data (111) terraces steep step bunches flat step bunches Overall function
6
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5
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S=4.75 10
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10
10
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25
7
Data (111) terraces steep step bunches flat step bunches Overall function
6
5
4
3
10 -25 10
-20
-15
-10
-5
0
5
Intensity [cps]
S=4.46
10
10 Fig. 2. 2D diffraction patterns from (a) weakly and (b) degenerately B-doped Si(111) samples with the × 7) reconstruction for a weakly B-doped Si wafer on the left p(7 ffiffiffi pffiffiffi (95 eV) and the 3 × 3 R30∘ reconstruction for a degenerately B-doped Si Wafer on the right (88 eV). Both measurements were performed at RT after the 2 h annealing process (slow cooling procedure).
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Data (111) terraces steep step bunches residual diffuse intensity Overallfunction
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-5
0
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Scattering vector [%BZ] Fig. 3. Spot profiles of the (00)hspotifor the fast cooling process measured at S = 4.94, S = 4.75 and S = 4.46 along the 112 direction. Besides a central peak (solid line) there are several satellite peaks (dashed and dotted profiles).
and S =4.94 the intensity of the satellites almost vanished. We had to add a small amount of diffuse diffraction (presumably due to non crystalline defects [23]) for S = 4.46 because of the low diffraction intensity. In addition the satellite pairs were asymmetric for intermediate diffraction conditions. This almost in-phase behavior during a nearly out-of-phase condition for monoatomic steps (S = 4.46) indicates the presence of biatomic steps on the surface [2]. In Fig. 3 one can see a shift of the satellite positions with changing scattering phase. This is a characteristic for vicinal surfaces with step bunches. Since there are two different kinds of satellites, two kinds of step bunches have to exist relating to their tilt angle against the (111) surface. A model for the Si surface with large (111) terraces and two different kinds of step bunches is presented in Fig. 4(a). Knowing that the integer-order spots are split along the ½112 direction, the step bunches are tilted against the (111) surface in that direction. We analyzed the K∥ position of the satellite peaks in order to determine the tilt angle of the step bunches against the (111) plane in ½112 direction. Therefore we fitted the full profiles with a GAUSSIAN for the central peak (constant position at K∥ =0%BZ) and used VOIGT-functions for the satellites to take into account the convolution of a LORENTZIAN broadening (due to disorder of the step bunches) with a GAUSSIAN broadening (due to the instrumental function, see above). Therefore the FWHM of the GAUSSIAN part of the VOIGT-function remains constant during fitting. The spot profiles are governed by central peaks at K∥ =0%BZ which have an additional FWHM of (0.8±0.05%BZ) with respect to the instrumental broadening. The average terrace size of the
(111) terraces given by the FWHM of the central GAUSSIAN peak is D111 = (42±3)nm. Thus the pffiffiffiaverage pffiffiffi size of (111) terraces coincides with the average size of the ð 3 × 3ÞR30∘ domains. Two different sets of satellites were detected for the fast cooling procedure. Fig. 5(a) shows the positions of the satellites in reciprocal space obtained from fitting the diffraction profiles. Here the scattering phase S is plotted against the position of the satellite peaks K∥ (in ½112 direction) in units of [%BZ] to obtain the usual reciprocal space mapping. The two sets follow straight lines in reciprocal space. The satellites with the smaller splitting (larger terrace width) are less tilted against the (111) plane than the satellites with the larger splitting due to smaller terrace sizes. Linear fits of the satellite positions S = S(K∥) were used to find the average tilt angle for the stepped areas. We found the tilt angles αflat = (3.2 ± 0.7)° and αsteep = (12 ± 1)° for the step bunches which are also given in Table 1. Furthermore, the average terrace width Γ on a step bunch can be calculated as Γ = d/tan α. Here d is the double atomic step height on the step bunches. Thus the set of satellites with the smaller splitting (flat step bunches) could be attributed to an average terrace size of Γflat = (11 ± 2)nm while the other set (steep step bunches) was caused by step bunches with an average terrace size of Γsteep = (3.0 ± 0.2)nm. The average terrace widths on each step bunch are shown in Table 1, too.
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Dsteep
D(111)
a
Dflat
[111]
flat steep [112]
b
flat
steep
Dsteep
D(111)
Dflat
[111]
flat steep [112]
flat
b
steep
Fig. 4. Schematic model of the surface after annealing. (a) represents the surface after fast cooling where all step bunches exhibit steps of biatomic step heights and (b) shows the surface after the slow cooling procedure with step bunches consisting of both single steps and double steps, respectively.
If the terraces on the step bunches are not equal sized but follow some statistical distribution, the FWHM of the satellites changes quadratically with the scattering phase [24]. The used fitting function FWHMsat ½%BZ = 200%BZ ⋅π⋅
2 σ 2 ⋅a d 2 min ðΔSÞ + FWHMsat 3 ⋅ d Γ mono
ð1Þ
includes the monoatomic step height dmono, the actual step height d, and the standard deviation of the terrace width distribution σ [24]. We found a standard deviation σflat = (4.8 ± 0.4)nm for flat step bunches, while the terraces on the steep step bunches are subject to a much smaller standard deviation of σsteep = (0.70 ± 0.08)nm. Furthermore, we added the constant contribution FWHMmin sat (minimal FWHM for the satellite peaks for an in-phase condition), due to the finite size of the step bunches to Eq. (1). From this the average sizes D of the step bunches can be determined by the minimal FWHMmin sat of the satellites. The satellites of the flat step bunches result in an average size of Dflat = (39 ± 2)nm. At the same time the steep step bunches have an average size of Dsteep = (11 ± 1)nm. The constant FWHM of the GAUSSIAN central peak demonstrates that there are no residual atomic steps (e.g. due to islands) on the (111) terraces (cf. diffuse diffraction for weakly doped surfaces). Table 1 shows the average step bunch sizes D for this cooling process. Comparing the average terrace sizes and step bunch sizes we conclude that both step bunches consist of approximately three to four terraces. The average height H of a step bunch can now be calculated as H = D ⋅ tan α . The resulting values can also be found in Table 1. 3.2. The slow cooling procedure We also used a lower cooling rate of 0.8 K/min during the preparation process (see Section 2) in order to determine the influence on surface morphology by comparing the results of both annealing procedures. Therefore we performed the same SPA-LEED measurements as described in Section 3.1 for the slowly cooled samples. Cross sections of the (00) spot in ½112 direction for S = 4.5, S = 4.8 and S = 5 are shown in Fig. 6. As before the (00)-spot is split
Fig. 5. a) Plot of satellite positions with respect to the scattering phase. The dotted lines represent the satellite positions caused by the flat and the dashed lines the satellite positions caused by the steep step bunches. b) Quadratic behavior of the satellites FWHMs for changing scattering phase. FWHM is deconvoluted with the instrumental broadening. The nearly constant FWHM of the central peak (deconvoluted with the instrumental broadening) is marked as a solid line.
into several satellites along the ½112 direction, so the step bunches are tilted against the (111) plane in this direction. Similar to the results from the fast cooling procedure the spot profiles of the slowly cooled samples were dominated by central GAUSSIAN peaks at K∥ = 0% BZ (cf. Fig. 6). Thus the surface must include large (111) terraces and the satellites were again caused by step bunches. Compared to the diffraction patterns obtained from the samples of the fast cooling procedure the intensity of the diffuse diffraction is significantly decreased as demonstrated for S = 4.8 by Fig. 6. Attempts to fit the diffuse diffraction by one pair of satellites due to one kind of step bunches were not successful. Therefore, similar to the spot profile analysis for the fast cooling procedure, we assumed two pairs of
Table 1 Structure details of the step bunches for both annealing procedures. Errors are calculated from the biggest variation of the linear position fits and the quadratic FWHM fits of the satellite peaks, respectively. Preparation
Fast cooling
Step bunch
Flat
Steep
Slow cooling Flat
Steep
Step height
Double
Double
Mono
Double
α [°] D [nm] H [nm] Γ [nm] σ [nm] σ/Γ
3.2 ± 0.7 39 ± 2 2.2 ± 0.4 11 ± 2 4.8 ± 0.4 0.44 ± 0.12
12 ± 1 11 ± 1 2.3 ± 0.2 3.0 ± 0.2 0.7 ± 0.08 0.23 ± 0.04
2.5 ± 0.2 12 ± 1 0.6 ± 0.07 7.1 ± 0.6 4.2 ± 0.5 0.59 ± 0.12
12 ± 1 13 ± 1.2 2.8 ± 0.4 3.0 ± 0.3 1.2 ± 0.2 0.40 ± 0.11
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a
5
10
10
10 10
Data (111) terraces residual diffuse intensity Overall function
4
3
2
-15
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-5
0
5
Intensity [cps]
S=4.8 10
10 Data (111) terraces steep step bunches flat step bunches Overall function
4
6.5
++ + + + + + ++ + + + + ++ + ++ + + ++ + + + + + (I) +
6
5.5 5 4.5
[112] -10
+
+
(II)
++ + + + + +
4
3.5 -15
+
-5
0
5
10
15
Scattering vector [%BZ] 10
b
3
16 14
10
2
-15 10
-10
-5
0
5
10
15
4
S=4.5 Intensity [cps]
15
5
Data (111) terraces
FWHM [%BZ]
Intensity [cps]
S=5.0
Scattering phase [Kd/2π]
10
865
12 10
central Gaussian-peak linear fit first satellite quadratic fit second satellite quadratic fit
(II)
8 6 4
(I)
2 10
3
0 4.5
5
5.5
Scattering phase
10
2
-15
-10
-5
0
5
10
15
Scattering vector [%BZ] Fig. 6. Spot profiles of the (00) h spot i for the slow cooling process measured at S = 5, S = 4.8 and S = 4.5 along the 112 direction.
satellites due to two different kinds of step bunches. For S = 4.8 one can see one almost symmetric satellite pair (dashed line) which, therefore, stems from step bunches with double atomic step heights. The other satellite pair, however, is far from being symmetric. Thus the other step bunch has monoatomic steps. Extrapolation of the position of these satellites to out-of-phase conditions for monoatomic steps predicted a symmetric splitting of these satellites. Obviously, this could not be observed since it was veiled by the broadening of the central peak and by the low diffraction intensity for this diffraction condition. Fig. 7(a) shows the satellite positions for different scattering phases. One can clearly see that only the positions of the satellites caused by the steep step bunches pass through K∥ = 0%BZ for out-of-phase conditions due to biatomic step heights. A model of the surface morphology due to the slow cooling procedure is presented in Fig. 4(b). Similar to the analysis presented in Section 3.1 for the fast cooling procedure, an analysis of the K∥ position of the satellite peaks was performed to determine the average tilt angle of the step bunches against the (111) plane in ½112 direction. We found the average tilt angles αflat = (2.5±0.2)° for the flat step bunches with monoatomic steps and αsteep = (12±1)° for the steep ones with biatomic steps. (cf. Table 1). We again calculated the average terrace sizes Γ for both kinds of step bunches from the tilt angle α (cf. Table 1). As determined for the minimal FWHM of the satellites the average sizes D of the step bunches for the slow cooling procedure (Dflat = (12 ± 1)nm, Dsteep =
Fig. 7. a) Plot of satellite positions against the scattering phase for the slow cooling procedure. The dotted lines represent the satellite positions caused by the flat and the dashed lines the satellite positions caused by the steep step bunches. b) Quadratic behavior of the satellites FWHMs for changing scattering phase. FWHM is deconvoluted with the instrumental broadening. The nearly constant FWHM of the central peak is marked as a solid line and also deconvoluted with the instrumental broadening.
(13 ± 1)nm) were almost equal (cf. Table 1). In contrast to the step bunches on the fast cooled samples the step bunches with monoatomic steps from the slowly cooled samples consisted of fewer terraces than the other step bunches with steps of biatomic heights. Comparing the terrace widths Γ and the step bunch sizes D the flat step bunches consisted only of one or two terraces, which were separated by monoatomic steps while the steep step bunches had about three terraces in average, which were separated by biatomic steps. Furthermore, the calculated standard deviations σ as determined from Eq. (1), as well as, the resulting values for the average height H of the step bunches can be found in Table 1. 4. Discussion We found that step bunches are clearly detectable by SPA-LEED at RT on degenerately doped Si(111) substrates independently from preparation. In contrast to the reversible formation of step bunches on weakly B-doped Si(111) it seems that the step bunch formation on degenerately B-doped Si(111) is not completely at equilibrium since the results depend on the cooling rate. Our results for both cooling procedures showed that the samples developed two kinds of step bunches during the annealing procedure. The flat step bunches from the slow cooling procedure had monoatomic step heights and consisted of smaller terraces while the flat step bunches from the fast cooling procedure had larger terraces and biatomic step heights, respectively. This behavior was not observed for the steep step bunches which exhibit biatomic step heights and similar terrace
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width distributions independently from the cooling procedure. However, the ratio between the standard deviation σ and terrace width distribution Γ is more narrow for both kinds of step bunches from the fast cooling procedure, compared to the slow cooling procedure (cf. Table 1). Therefore, we assume that the step bunches dissolute with increasing annealing time but the dissolution is kinetically hampered (cf. the long annealing time for the slow cooling procedure). It seems that even the slow cooling procedure used in our studies is too fast to completely dissolve the step bunches, although we exclude that the structures observed at RT are quenched high temperature structures since we used moderate cooling rates even for the fast cooling procedure compared to other studies (cf. [25]). It has to be noted, that step bunches with double height steps have not yet been reported for nondegenerately doped Si(111). Compared to the model presented in Fig. 4, in principal, one could also assume that mixed step bunches with large and short terraces can be formed. This, however, can be excluded, because we did not see any correlation effects between large and short terraces close to in-phase conditions. Thus short and large terraces are separated in two step bunches. In contrast to Fig. 4, however, both step bunches are not necessarily separated by a (111) terrace but can adjoin to another. For the steep step bunches the inclination angle, as well as, the average terrace length Γ and the average step bunch size D was almost the same for both cooling procedures. One possible explanation is given by the tilt angle of the steep step bunches which was (12 ± 1)° in average and matches the orientation of (553) facets, (α553 = 12.3° in ½112 direction) and the terrace width on those facets is Γ553 = 2.86 nm with respect to biatomic steps (cf. Fig. 8). So the steep step bunches may be more energetically stable than the flat ones due to their orientation. Also, the smaller step–step distance leads to larger repulsive interactions between the step edges which limits the fluctuation of terrace widths and may explain the small value of σ. Nevertheless, the increased value of σ/Γ for the slow cooling procedure points to the fact that the steep step bunches are not in thermodynamic equilibrium at RT. This observation differs from the formation of (331) facets reported for weakly doped vicinal Si(111) samples [6] surprisingly. Recent STM studies by Hara et al., however, revealed that weakly doped Si(553) surfaces are instable but consist of (111) and (331) facets with (7×7) reconstruction [26]. Our results indicate that the step bunches with (553) orientation are stablepfor B-doped Si. Probably (553) facets are stabilized by ffiffiffi degenerately pffiffiffi the ð 3 × 3ÞR30∘ reconstruction double steps are formed. Fig. 8 pffiffiffi if p ffiffiffi illustrates that, in this case, four ð 3 × 3ÞR30∘ unit cells perfectly fit to the developed terrace width. Since we did not see any residual intensity of (7×7) superstructure spots in our SPA-LEED we assume that the (553)-like step pffiffiffi patterns pffiffiffi bunches show a ð 3 × 3ÞR30∘ reconstruction (cf. Fig. 8). This is in agreement with pffiffiffi former pffiffiffi studies by Stimpel et al. who found that the formation of ð 3 × 3ÞR30∘ reconstructions on degenerately B-doped Si (111) surfaces starts at the bottom pffiffiffi pofffiffiffi steps [27]. Therefore, a step bunch would even faster form a ð 3 × 3ÞR30∘ reconstruction than a large (111) terrace. The average size of the remaining (111)-oriented areas pffiffiffi is the pffiffiffi same∘ Þ as the determined average domain size of the ðp3 × ffiffiffi p3 ffiffiffi R30 reconstructed areas. Hence, the (111) terraces exhibit ð 3 × 3ÞR30∘ reconstructed single domains and the size of the domains is confined by step bunches. Supposing that also the large terraces of the flat step bunches and the short terraces of the steep step bunches are reconstructed, we did probably not observe any significant broadening of superstructure peaks since the amount of step bunches was too small. The orientation of the flat step bunches (corresponding to their tilt angle) is closer to the (111) oriented terraces than to any other facet with low index and therefore those step bunches may dissolve with increasing annealing time and the emerging steps may be incorporated into the steep (553) step bunches [28].
a T4 S5
553
553
[111]
[553] [112] [3310]
b
[110]
[112]
double step
double step
Fig. 8. (a) Cross-section of (553) facet of silicon with biatomic steps. The inclination angle α553 (solid line) towards (111) is 12.3° which is similar to the inclination angles of the steep step bunches towards (111) from both cooling procedures. The terrace width Γ553 =2.86nm for biatomic steps is marked by a dashed line. Boron atoms at S5 are shown as big, pffiffiffi open pffiffifficircles underneath the Si adatoms T4ffiffiffi sites. (b) Top view on (553) facet with ð 3 × 3ÞR30∘ pffiffiffi at p ∘ ð Þ reconstructed terraces. pffiffiffi pffiffiffi3 × 3 R30 unit cells are marked by dashed lines. Terraces are exactly suited by ð 3 × 3ÞR30∘ unit cells. Si adatoms at T4 sites are not shown here in order to make boron atoms at S5 sites visible (open circles).
The relatively big standard deviation σ of the terrace width distribution from the flat step bunches can be attributed to a larger waviness of these terraces due to a meandering of the steps which do not significantly interact with adjunct steps due to the larger step–step distance. A repulsive interaction between the step edges makes a bigger fluctuation of terrace widths more likely for large terraces while the meandering of steps is more confined for small terraces [29]. Since we used direct heating with the current in step-down direction we assume that step bunches were formed in the temperature range 850 °C–950 °C as observed for weakly doped samples [30]. For this reason, we propose that the flat step bunches are residuals of these high temperature step bunches assuming that the doping induced reconstruction is not important in this temperature range. All in all we can say that the morphology of the flat step bunches depends strongly on the annealing process while the structure of the steep step bunches is independent from the cooling process. It can be concluded, that the formation of steep step bunches with double step heights and an orientation similar to a (553) facet is independent from the cooling procedure. 5. Summary We studied the structure of step bunches on degenerately B-doped Si(111) surfaces formed due to surface segregated boron after direct current heating in step-down direction by SPA-LEED. The dependence of the step bunch structure on the cooling rate was analyzed detail at pffiffiffi inp ffiffiffi RT. The (111) terraces as well as the step bunches are ð 3 × 3ÞR30∘ reconstructed after the annealing process. Two kinds of step bunches were observed for both cooling procedures. The steep step bunches are
D. Bruns et al. / Surface Science 605 (2011) 861–867
more energetically stable than the flat step bunches because of their (553) orientation while flat step bunches are more and more resolved with increasing annealing time. Acknowledgment
[13] [14] [15] [16] [17] [18]
We acknowledge the Deutsche Forschungsgemeinschaft (DFG) via Graduate College 695 for the financial support. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
R.J. Phaneuf, E.D. Williams, Phys. Rev. Lett. 58 (1987) 2563. R.J. Phaneuf, E.D. Williams, Phys. Rev. B 41 (1989) 2991. R.J. Phaneuf, E.D. Williams, N.C. Bartelt, Phys. Rev. B 38 (1988) 1984. R.J. Phaneuf, E.D. Williams, N.C. Bartelt, Phys. Rev. Lett. 67 (1991) 2986. T. Ogino, H. Hibino, Y. Homma, Crit. Rev. Sol. State Mat. Sci. 24 (1999) 227. H. Hibino, Y. Shinoda, Y. Kobayashi, K. Sugii, Jpn. J. Appl. Phys. 30 (1991) 1337. A.V. Latyshev, A.L. Aseev, A.B. Krabsilninov, S.I. Stenin, Surf. Sci. 213 (1989) 157. H. Hibino, T. Ogino, Surf. Sci. 413 (1998) 132. S. Stoyanov, Jpn. J. Appl. Phys. 30 (1991) 1. C. Misbah, O. Pierre-Louis, A. Pimpinelli, Phys. Rev. B 51 (1995) 17283. S. Stoyanov, J.J. Métois, V. Tonchev, Surf. Sci. 465 (2000) 227. S. Stoyanov, Phys. Rev. B 58 (1998) 1590.
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Surface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u s c
Formation and morphology of step bunches during B-segregation on vicinal Si(111) Daniel Bruns, Sebastian Gevers, Joachim Wollschläger ⁎ Fachbereich Physik, Universität Osnabrück, Barbarastr. 7, 49076 Osnabrück, Germany
a r t i c l e
i n f o
Article history: Received 17 March 2010 Accepted 7 January 2011 Available online 25 January 2011 Keywords: SPA-LEED Silicon Boron Step bunch Si(111) pffiffiffi pffiffiffi ð 3 × 3 ÞR30 ∘ reconstruction Surface passivation
a b s t r a c t Degenerately boron-doped vicinal Si(111) substrates were annealed at high temperatures to achieve completep saturation ffiffiffi pffiffiffi of the ‘dangling bonds’ by surface segregating boron atoms under reconstruction to the Si(111) ð 3 × 3ÞR30∘ phase. Different cooling procedures were applied to obtain well ordered superstructures. The surface morphology of the prepared substrates was studied by spot profile analysis of low energy electron diffraction (SPA-LEED). The splitting of the diffraction peaks into multiple satellites points to the formation of step bunches of different inclination (equivalent to different terrace widths) during the segregation process due to changes in the surface free energy. A model with step bunches consisting of steps with monoatomic or biatomic heights and large (111)-oriented terraces is developed to explain our results. Steep step bunches with short terraces and biatomic step heights are formed independently of the preparation process while flat step bunches with large terraces are dissolved with increasing annealing time. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Vicinal Si(111) surfaces can exhibit (111) terraces which are separated by (more or less) regularly arranged atomic steps due to the misorientation of the surface with respect to the (111) orientation. Another possibility is that the size of the (111) terraces increases significantly so that the atomic steps gather and form step bunches. For instance, Phaneuf et al. reported that vicinal Si(111) surfaces misoriented towards ½110 or ½112 exhibit monoatomic steps beyond the critical temperature of the order–disorder transition (7×7) ↔(1×1), while step bunches are formed for the (7×7) reconstructed Si(111) surface [1–3]. Therefore, the formation of step bunches was attributed to the elastic interaction between (7×7) reconstructed terraces to minimize the surface free energy [4,5]. Beyond this, Hibino et al. clarified that step bunches on vicinal Si(111) surfaces tilted towards ½112 are (331) facets for temperatures below 600 °C [6]. These experiments, however, were performed on weakly doped vicinal Si(111) samples (cf. formation of (7×7) reconstruction) by radiation heating. For direct current heating in step-down or step-up direction the formation of step bunches was also observed for weakly B-doped or P-doped Si(111) at high temperatures (disordered (1 × 1) phase) [7]. For instance, vicinal Si(111) surfaces with misalignment towards ½112 form step bunches with direct heating in step-down direction for the temperature range 1200 °C–1300 °C and below 960 °C while for step-up currents the temperature range 1060 °C–1200 °C and
⁎ Corresponding author. Tel.: +49 541 9692652. E-mail address: [email protected] (J. Wollschläger). 0039-6028/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2011.01.013
temperatures above 1320 °C are necessary to form step bunches [8]. For weakly doped vicinal Si(111) substrates which form the (7 × 7) reconstruction at low temperatures, this process is reversible and was attributed to electromigration of single adatoms or advacancies as discussed in several theoretical studies [9–12]. Therefore, the orientation of the step bunches strongly depends on the misorientation of the sample surface, as well as, on the direction of the current. In contrast to the above reported here, we will present pffiffiffi experiments, pffiffiffi studies on Si(111) surfaces with ð 3 × 3ÞR30∘ reconstruction which is induced by boron segregation. There are mainly two different approaches to deposit boron on Si(111). One approach is through evaporation of boron on the substrate followed by annealing at 900 °C. Here boron adsorbs on T4 sites at first and changes to S5 sub-surface sites during the annealing [13]. The other approach is based on boron segregation underneath the surface of degenerately boron-doped Si(111) during annealing. While annealing the samples at about 1000 °C under UHV conditions the boron atoms diffuse towards the surface and attach directly on S5 sites underneath the silicon adatoms which, on the other hand, move from the S5 site to the T4 site [14–17]. An electron transfer between the unsaturated bonds at the silicon adatoms on T4 sites and the boron atoms on S5 sites takes place. Thus, in both cases the presence of boron atoms underneath the surface a change in the surface free energy, which leads to a pffiffiffi pcauses ffiffiffi ð 3 × 3ÞR30∘ reconstruction of the surface without any dangling bonds. Therefore, this passivated surface is of large interest for various applications (cf. [18] and references therein). The present work focuses on the step bunch structure in dependency to the cooling rate after the annealing B-doped Si(111) pffiffiffi of degenerately pffiffiffi where the surface shows the ð 3 × 3ÞR30∘ reconstruction. For
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different cooling procedures SPA-LEED measurements were performed at room temperature (RT) in order to characterize the surface morphology of the samples.
2. Experiment B-doped Si(111) samples with an electric resistivity of 5 Ωcm (weakly doped, 1015/cm3) and 10− 3Ωcm (degenerately doped, 1020/ cm3), respectively, and a (0.35 ± 0.15)° misorientation from the (111) plane towards the ½112 direction were used for the studies presented here. The samples were transferred into a UHV chamber (base pressure 10− 10 mbar) and outgased at 600 °C for 12 h via resistive heating. The current was directed in ½112 (step-down) direction. Afterwards the samples were flash annealed for some seconds at 1020 °C to remove the native SiO2-layer from the surface. The pressure was kept below 10− 8 mbar during this flash annealing. In order to prove that the surface was not contaminated by adsorbates we performed AUGER electron spectroscopy (AES) measurements on the samples (primary energy 3 keV). The AES system works with a cylindrical mirror analyzer (CMA). The scan rate was 10 eV/min while the modulation amplitude of the lock-in amplifier was 6 eV. It is reported that boron atoms segregate at the surface at temperatures above 900 °C [19,20]. In order to force B-segregation we flash annealed the samples at 1200 °C for a few seconds and then quenched to 900 °C (≈50 K/s) and held at this temperature for 20 min (background pressure 5⋅10− 9 mbar). Afterwards the samples were cooled down to RT in two different ways in order to compare the correlation of the annealing process to the morphology of the surface. In the first procedure the sample was cooled from 900 °C to 800 °C with a cooling rate of 20 K/min (total preparation time 25 min). In comparison we used a much slower cooling procedure where the sample was cooled with a rate of only 0.8 K/min to 800 °C (total preparation time 145 min). From 800 °C to RT we cooled both kinds of samples with a rate of ≈10K/s. From now on these procedures are named ‘slow’ and ‘fast’ cooling procedure, respectively. The absolute temperatures were measured by an infrared pyrometer (impac IGA 12) with an accuracy of ± 30 °C. The pyrometer was calibrated with a Si sample with attached thermocouple prior to the measurements reported above. After the preparation the segregation of boron was controlled by AES with the sample at RT. In addition in situ SPA-LEED measurements were performed at this temperature to characterize the surface morphology. This high resolution technique needs an electrostatic deflection unit, a fine focus electron gun and a channeltron pffiffiffi pffiffiffisingle electron detector [21]. 2D measurements of the ð 3 × 3ÞR30∘ reconstruction and spot profiles of the (00)-spot along the ½112 direction were measured in the range of 64 eV up to 148 eV for the electrons. Due to the fact that the investigations were performed on Si (111) samples, in the following we use the scattering phase S = dmonoK⊥/2π, which is normalized to the monoatomic Si(111) ∘ step height dmono = 3:1354 A instead of the vertical scattering vector K⊥ for all measurements. Therefore we probed the scattering phases S = 3.5 − 6.2 for the energy range used here. As a reference we first performed spot profile measurements on a weakly B-doped Si(111) sample to confirm that the changes of the surface morphology of Si(111), as determined by SPA-LEED, are caused by the presence of surface segregated boron. The twodimensional SPA-LEED pattern of the weakly B-doped Si(111) sample at 95 eV (S = 5) is shown in Fig. 2(a). The surface shows the well known (7×7) reconstruction. One can see sharp diffraction spots at RT after annealing with the slow cooling process. The spot profile analysis of the integer-order spots revealed no preferential broadening during an inphase condition, so it is limited by the transfer width which is t∼55±5nm for the used SPA-LEED optics. The only surface irregularities are statistically arranged monoatomic steps which are clearly detectable for an out-of-phase condition due to the enhanced diffuse diffraction.
Therefore only monoatomic steps without any preferential crystallographic ordering are formed during the annealing process. For the weakly doped Si samples the additional isotropic broadening of the spots in an out-of-phase condition is (0.3 ± 0.05)%BZ which is equivalent to an average terrace width of (70 ± 10)nm. Here 100%BZ ∘ (percentage Brillouinzone, ð100%BZ ¼ ˆ 2π = a with a = 3:3258 A Þ denotes the distance between two fundamental diffraction peaks in reciprocal space). All (7 × 7) superstructure spots were round and the change of their FWHM for different scattering phases was equivalent to the behavior of the integer-order spots. 3. Results To probe the surface stoichiometry of the studied samples we performed AES measurements as shown in Fig. 1 for a degenerately B-doped Si(111) sample after the preparation with the fast cooling procedure. The boron signal at 179 eV had a much lower intensity in comparison to the silicon signal at 92 eV. This result represents the fact that there is only a third of a monolayer of boron in the third atomic layer underneath the surface (boron segregates at S5 sites) [22]. SPA-LEED patterns from degenerately B-doped Si(111) pffiffiffi recorded pffiffiffi samples showed a ð 3 × 3ÞR30∘ reconstruction (Fig. 2(b)) instead of the (7×7) reconstruction (cf. Fig. 2(a)). This change is driven pffiffiffiby the pffiffiffilower surface free energy due to the B incorporation. The ð 3 × 3ÞR30∘ superstructure spots were round and had an additional average FWHM of (0.8±0.05)%BZ compared to the instrumental resolution for all samples, which is equivalent to an average domain size of AD =(42±3)nm. In the following a detailed spot profile analysis of the (00) spot for all degenerately B-doped samples was performed to determine the surface morphology according to the annealing procedures. Integer-order spots, however, were clearly elongated along the ½112 direction. A closer inspection showed that these diffraction peaks consisted of several satellite peaks (depending on the scattering condition). 3.1. The fast cooling procedure First we want to focus on the analysis of the (00) spot profile for the fast cooling procedure. Fig. 3 presents cross sections of the (00) spot in ½112 direction for S = 4.46, S = 4.75 and S = 4.94. All profiles exhibit a strong central peak at K∥ = 0%BZ (solid line) which is attributed to large Si(111) terraces and additional satellites (dotted and dashed lines). On the one hand, for S = 4.75 the spot profile shows two symmetric pairs of satellites with a separation of ΔK∥,flat = 2.5%BZ and ΔK∥,steep = 12.2%BZ due to large and small terraces, respectively, determined from fitting the profiles (see below). On the other hand, for S = 4.46
Fig. 1. AES spectrum of the cleaned, degenerately B-doped Si(111). An intense silicon signal at 92 eV and a very weak boron signal at 179 eV can be seen.
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10 Fig. 2. 2D diffraction patterns from (a) weakly and (b) degenerately B-doped Si(111) samples with the × 7) reconstruction for a weakly B-doped Si wafer on the left p(7 ffiffiffi pffiffiffi (95 eV) and the 3 × 3 R30∘ reconstruction for a degenerately B-doped Si Wafer on the right (88 eV). Both measurements were performed at RT after the 2 h annealing process (slow cooling procedure).
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Scattering vector [%BZ] Fig. 3. Spot profiles of the (00)hspotifor the fast cooling process measured at S = 4.94, S = 4.75 and S = 4.46 along the 112 direction. Besides a central peak (solid line) there are several satellite peaks (dashed and dotted profiles).
and S =4.94 the intensity of the satellites almost vanished. We had to add a small amount of diffuse diffraction (presumably due to non crystalline defects [23]) for S = 4.46 because of the low diffraction intensity. In addition the satellite pairs were asymmetric for intermediate diffraction conditions. This almost in-phase behavior during a nearly out-of-phase condition for monoatomic steps (S = 4.46) indicates the presence of biatomic steps on the surface [2]. In Fig. 3 one can see a shift of the satellite positions with changing scattering phase. This is a characteristic for vicinal surfaces with step bunches. Since there are two different kinds of satellites, two kinds of step bunches have to exist relating to their tilt angle against the (111) surface. A model for the Si surface with large (111) terraces and two different kinds of step bunches is presented in Fig. 4(a). Knowing that the integer-order spots are split along the ½112 direction, the step bunches are tilted against the (111) surface in that direction. We analyzed the K∥ position of the satellite peaks in order to determine the tilt angle of the step bunches against the (111) plane in ½112 direction. Therefore we fitted the full profiles with a GAUSSIAN for the central peak (constant position at K∥ =0%BZ) and used VOIGT-functions for the satellites to take into account the convolution of a LORENTZIAN broadening (due to disorder of the step bunches) with a GAUSSIAN broadening (due to the instrumental function, see above). Therefore the FWHM of the GAUSSIAN part of the VOIGT-function remains constant during fitting. The spot profiles are governed by central peaks at K∥ =0%BZ which have an additional FWHM of (0.8±0.05%BZ) with respect to the instrumental broadening. The average terrace size of the
(111) terraces given by the FWHM of the central GAUSSIAN peak is D111 = (42±3)nm. Thus the pffiffiffiaverage pffiffiffi size of (111) terraces coincides with the average size of the ð 3 × 3ÞR30∘ domains. Two different sets of satellites were detected for the fast cooling procedure. Fig. 5(a) shows the positions of the satellites in reciprocal space obtained from fitting the diffraction profiles. Here the scattering phase S is plotted against the position of the satellite peaks K∥ (in ½112 direction) in units of [%BZ] to obtain the usual reciprocal space mapping. The two sets follow straight lines in reciprocal space. The satellites with the smaller splitting (larger terrace width) are less tilted against the (111) plane than the satellites with the larger splitting due to smaller terrace sizes. Linear fits of the satellite positions S = S(K∥) were used to find the average tilt angle for the stepped areas. We found the tilt angles αflat = (3.2 ± 0.7)° and αsteep = (12 ± 1)° for the step bunches which are also given in Table 1. Furthermore, the average terrace width Γ on a step bunch can be calculated as Γ = d/tan α. Here d is the double atomic step height on the step bunches. Thus the set of satellites with the smaller splitting (flat step bunches) could be attributed to an average terrace size of Γflat = (11 ± 2)nm while the other set (steep step bunches) was caused by step bunches with an average terrace size of Γsteep = (3.0 ± 0.2)nm. The average terrace widths on each step bunch are shown in Table 1, too.
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Dsteep
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flat steep [112]
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Fig. 4. Schematic model of the surface after annealing. (a) represents the surface after fast cooling where all step bunches exhibit steps of biatomic step heights and (b) shows the surface after the slow cooling procedure with step bunches consisting of both single steps and double steps, respectively.
If the terraces on the step bunches are not equal sized but follow some statistical distribution, the FWHM of the satellites changes quadratically with the scattering phase [24]. The used fitting function FWHMsat ½%BZ = 200%BZ ⋅π⋅
2 σ 2 ⋅a d 2 min ðΔSÞ + FWHMsat 3 ⋅ d Γ mono
ð1Þ
includes the monoatomic step height dmono, the actual step height d, and the standard deviation of the terrace width distribution σ [24]. We found a standard deviation σflat = (4.8 ± 0.4)nm for flat step bunches, while the terraces on the steep step bunches are subject to a much smaller standard deviation of σsteep = (0.70 ± 0.08)nm. Furthermore, we added the constant contribution FWHMmin sat (minimal FWHM for the satellite peaks for an in-phase condition), due to the finite size of the step bunches to Eq. (1). From this the average sizes D of the step bunches can be determined by the minimal FWHMmin sat of the satellites. The satellites of the flat step bunches result in an average size of Dflat = (39 ± 2)nm. At the same time the steep step bunches have an average size of Dsteep = (11 ± 1)nm. The constant FWHM of the GAUSSIAN central peak demonstrates that there are no residual atomic steps (e.g. due to islands) on the (111) terraces (cf. diffuse diffraction for weakly doped surfaces). Table 1 shows the average step bunch sizes D for this cooling process. Comparing the average terrace sizes and step bunch sizes we conclude that both step bunches consist of approximately three to four terraces. The average height H of a step bunch can now be calculated as H = D ⋅ tan α . The resulting values can also be found in Table 1. 3.2. The slow cooling procedure We also used a lower cooling rate of 0.8 K/min during the preparation process (see Section 2) in order to determine the influence on surface morphology by comparing the results of both annealing procedures. Therefore we performed the same SPA-LEED measurements as described in Section 3.1 for the slowly cooled samples. Cross sections of the (00) spot in ½112 direction for S = 4.5, S = 4.8 and S = 5 are shown in Fig. 6. As before the (00)-spot is split
Fig. 5. a) Plot of satellite positions with respect to the scattering phase. The dotted lines represent the satellite positions caused by the flat and the dashed lines the satellite positions caused by the steep step bunches. b) Quadratic behavior of the satellites FWHMs for changing scattering phase. FWHM is deconvoluted with the instrumental broadening. The nearly constant FWHM of the central peak (deconvoluted with the instrumental broadening) is marked as a solid line.
into several satellites along the ½112 direction, so the step bunches are tilted against the (111) plane in this direction. Similar to the results from the fast cooling procedure the spot profiles of the slowly cooled samples were dominated by central GAUSSIAN peaks at K∥ = 0% BZ (cf. Fig. 6). Thus the surface must include large (111) terraces and the satellites were again caused by step bunches. Compared to the diffraction patterns obtained from the samples of the fast cooling procedure the intensity of the diffuse diffraction is significantly decreased as demonstrated for S = 4.8 by Fig. 6. Attempts to fit the diffuse diffraction by one pair of satellites due to one kind of step bunches were not successful. Therefore, similar to the spot profile analysis for the fast cooling procedure, we assumed two pairs of
Table 1 Structure details of the step bunches for both annealing procedures. Errors are calculated from the biggest variation of the linear position fits and the quadratic FWHM fits of the satellite peaks, respectively. Preparation
Fast cooling
Step bunch
Flat
Steep
Slow cooling Flat
Steep
Step height
Double
Double
Mono
Double
α [°] D [nm] H [nm] Γ [nm] σ [nm] σ/Γ
3.2 ± 0.7 39 ± 2 2.2 ± 0.4 11 ± 2 4.8 ± 0.4 0.44 ± 0.12
12 ± 1 11 ± 1 2.3 ± 0.2 3.0 ± 0.2 0.7 ± 0.08 0.23 ± 0.04
2.5 ± 0.2 12 ± 1 0.6 ± 0.07 7.1 ± 0.6 4.2 ± 0.5 0.59 ± 0.12
12 ± 1 13 ± 1.2 2.8 ± 0.4 3.0 ± 0.3 1.2 ± 0.2 0.40 ± 0.11
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Scattering vector [%BZ] Fig. 6. Spot profiles of the (00) h spot i for the slow cooling process measured at S = 5, S = 4.8 and S = 4.5 along the 112 direction.
satellites due to two different kinds of step bunches. For S = 4.8 one can see one almost symmetric satellite pair (dashed line) which, therefore, stems from step bunches with double atomic step heights. The other satellite pair, however, is far from being symmetric. Thus the other step bunch has monoatomic steps. Extrapolation of the position of these satellites to out-of-phase conditions for monoatomic steps predicted a symmetric splitting of these satellites. Obviously, this could not be observed since it was veiled by the broadening of the central peak and by the low diffraction intensity for this diffraction condition. Fig. 7(a) shows the satellite positions for different scattering phases. One can clearly see that only the positions of the satellites caused by the steep step bunches pass through K∥ = 0%BZ for out-of-phase conditions due to biatomic step heights. A model of the surface morphology due to the slow cooling procedure is presented in Fig. 4(b). Similar to the analysis presented in Section 3.1 for the fast cooling procedure, an analysis of the K∥ position of the satellite peaks was performed to determine the average tilt angle of the step bunches against the (111) plane in ½112 direction. We found the average tilt angles αflat = (2.5±0.2)° for the flat step bunches with monoatomic steps and αsteep = (12±1)° for the steep ones with biatomic steps. (cf. Table 1). We again calculated the average terrace sizes Γ for both kinds of step bunches from the tilt angle α (cf. Table 1). As determined for the minimal FWHM of the satellites the average sizes D of the step bunches for the slow cooling procedure (Dflat = (12 ± 1)nm, Dsteep =
Fig. 7. a) Plot of satellite positions against the scattering phase for the slow cooling procedure. The dotted lines represent the satellite positions caused by the flat and the dashed lines the satellite positions caused by the steep step bunches. b) Quadratic behavior of the satellites FWHMs for changing scattering phase. FWHM is deconvoluted with the instrumental broadening. The nearly constant FWHM of the central peak is marked as a solid line and also deconvoluted with the instrumental broadening.
(13 ± 1)nm) were almost equal (cf. Table 1). In contrast to the step bunches on the fast cooled samples the step bunches with monoatomic steps from the slowly cooled samples consisted of fewer terraces than the other step bunches with steps of biatomic heights. Comparing the terrace widths Γ and the step bunch sizes D the flat step bunches consisted only of one or two terraces, which were separated by monoatomic steps while the steep step bunches had about three terraces in average, which were separated by biatomic steps. Furthermore, the calculated standard deviations σ as determined from Eq. (1), as well as, the resulting values for the average height H of the step bunches can be found in Table 1. 4. Discussion We found that step bunches are clearly detectable by SPA-LEED at RT on degenerately doped Si(111) substrates independently from preparation. In contrast to the reversible formation of step bunches on weakly B-doped Si(111) it seems that the step bunch formation on degenerately B-doped Si(111) is not completely at equilibrium since the results depend on the cooling rate. Our results for both cooling procedures showed that the samples developed two kinds of step bunches during the annealing procedure. The flat step bunches from the slow cooling procedure had monoatomic step heights and consisted of smaller terraces while the flat step bunches from the fast cooling procedure had larger terraces and biatomic step heights, respectively. This behavior was not observed for the steep step bunches which exhibit biatomic step heights and similar terrace
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width distributions independently from the cooling procedure. However, the ratio between the standard deviation σ and terrace width distribution Γ is more narrow for both kinds of step bunches from the fast cooling procedure, compared to the slow cooling procedure (cf. Table 1). Therefore, we assume that the step bunches dissolute with increasing annealing time but the dissolution is kinetically hampered (cf. the long annealing time for the slow cooling procedure). It seems that even the slow cooling procedure used in our studies is too fast to completely dissolve the step bunches, although we exclude that the structures observed at RT are quenched high temperature structures since we used moderate cooling rates even for the fast cooling procedure compared to other studies (cf. [25]). It has to be noted, that step bunches with double height steps have not yet been reported for nondegenerately doped Si(111). Compared to the model presented in Fig. 4, in principal, one could also assume that mixed step bunches with large and short terraces can be formed. This, however, can be excluded, because we did not see any correlation effects between large and short terraces close to in-phase conditions. Thus short and large terraces are separated in two step bunches. In contrast to Fig. 4, however, both step bunches are not necessarily separated by a (111) terrace but can adjoin to another. For the steep step bunches the inclination angle, as well as, the average terrace length Γ and the average step bunch size D was almost the same for both cooling procedures. One possible explanation is given by the tilt angle of the steep step bunches which was (12 ± 1)° in average and matches the orientation of (553) facets, (α553 = 12.3° in ½112 direction) and the terrace width on those facets is Γ553 = 2.86 nm with respect to biatomic steps (cf. Fig. 8). So the steep step bunches may be more energetically stable than the flat ones due to their orientation. Also, the smaller step–step distance leads to larger repulsive interactions between the step edges which limits the fluctuation of terrace widths and may explain the small value of σ. Nevertheless, the increased value of σ/Γ for the slow cooling procedure points to the fact that the steep step bunches are not in thermodynamic equilibrium at RT. This observation differs from the formation of (331) facets reported for weakly doped vicinal Si(111) samples [6] surprisingly. Recent STM studies by Hara et al., however, revealed that weakly doped Si(553) surfaces are instable but consist of (111) and (331) facets with (7×7) reconstruction [26]. Our results indicate that the step bunches with (553) orientation are stablepfor B-doped Si. Probably (553) facets are stabilized by ffiffiffi degenerately pffiffiffi the ð 3 × 3ÞR30∘ reconstruction double steps are formed. Fig. 8 pffiffiffi if p ffiffiffi illustrates that, in this case, four ð 3 × 3ÞR30∘ unit cells perfectly fit to the developed terrace width. Since we did not see any residual intensity of (7×7) superstructure spots in our SPA-LEED we assume that the (553)-like step pffiffiffi patterns pffiffiffi bunches show a ð 3 × 3ÞR30∘ reconstruction (cf. Fig. 8). This is in agreement with pffiffiffi former pffiffiffi studies by Stimpel et al. who found that the formation of ð 3 × 3ÞR30∘ reconstructions on degenerately B-doped Si (111) surfaces starts at the bottom pffiffiffi pofffiffiffi steps [27]. Therefore, a step bunch would even faster form a ð 3 × 3ÞR30∘ reconstruction than a large (111) terrace. The average size of the remaining (111)-oriented areas pffiffiffi is the pffiffiffi same∘ Þ as the determined average domain size of the ðp3 × ffiffiffi p3 ffiffiffi R30 reconstructed areas. Hence, the (111) terraces exhibit ð 3 × 3ÞR30∘ reconstructed single domains and the size of the domains is confined by step bunches. Supposing that also the large terraces of the flat step bunches and the short terraces of the steep step bunches are reconstructed, we did probably not observe any significant broadening of superstructure peaks since the amount of step bunches was too small. The orientation of the flat step bunches (corresponding to their tilt angle) is closer to the (111) oriented terraces than to any other facet with low index and therefore those step bunches may dissolve with increasing annealing time and the emerging steps may be incorporated into the steep (553) step bunches [28].
a T4 S5
553
553
[111]
[553] [112] [3310]
b
[110]
[112]
double step
double step
Fig. 8. (a) Cross-section of (553) facet of silicon with biatomic steps. The inclination angle α553 (solid line) towards (111) is 12.3° which is similar to the inclination angles of the steep step bunches towards (111) from both cooling procedures. The terrace width Γ553 =2.86nm for biatomic steps is marked by a dashed line. Boron atoms at S5 are shown as big, pffiffiffi open pffiffifficircles underneath the Si adatoms T4ffiffiffi sites. (b) Top view on (553) facet with ð 3 × 3ÞR30∘ pffiffiffi at p ∘ ð Þ reconstructed terraces. pffiffiffi pffiffiffi3 × 3 R30 unit cells are marked by dashed lines. Terraces are exactly suited by ð 3 × 3ÞR30∘ unit cells. Si adatoms at T4 sites are not shown here in order to make boron atoms at S5 sites visible (open circles).
The relatively big standard deviation σ of the terrace width distribution from the flat step bunches can be attributed to a larger waviness of these terraces due to a meandering of the steps which do not significantly interact with adjunct steps due to the larger step–step distance. A repulsive interaction between the step edges makes a bigger fluctuation of terrace widths more likely for large terraces while the meandering of steps is more confined for small terraces [29]. Since we used direct heating with the current in step-down direction we assume that step bunches were formed in the temperature range 850 °C–950 °C as observed for weakly doped samples [30]. For this reason, we propose that the flat step bunches are residuals of these high temperature step bunches assuming that the doping induced reconstruction is not important in this temperature range. All in all we can say that the morphology of the flat step bunches depends strongly on the annealing process while the structure of the steep step bunches is independent from the cooling process. It can be concluded, that the formation of steep step bunches with double step heights and an orientation similar to a (553) facet is independent from the cooling procedure. 5. Summary We studied the structure of step bunches on degenerately B-doped Si(111) surfaces formed due to surface segregated boron after direct current heating in step-down direction by SPA-LEED. The dependence of the step bunch structure on the cooling rate was analyzed detail at pffiffiffi inp ffiffiffi RT. The (111) terraces as well as the step bunches are ð 3 × 3ÞR30∘ reconstructed after the annealing process. Two kinds of step bunches were observed for both cooling procedures. The steep step bunches are
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more energetically stable than the flat step bunches because of their (553) orientation while flat step bunches are more and more resolved with increasing annealing time. Acknowledgment
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