Optical properties of magic clusters formed in both reactive and non-reactive systems

Magic clusters are the smallest ordered quantum dots; hence, they represent promising materials for optoelectronics. However, their optical properties still have not been studied. Therefore, the purpose of this work is investigation of optical properties of magic clusters formed both in reactive (Cr/Si(111)) and non-reactive (In/Si(111)) systems. The ’adsorbate-silicon’ system named ’reactive’, if reactions resulting in silicide(s) formation take place in it. Using differential reflectance spectroscopy, optical functions of Indium and Chromium magic clusters were obtained. Having analyzed obtained spectra, we conclude that Cr magic clusters are CrSi islands and Si surface covered by In magic clusters is a semiconductor. A new method of obtaining saturation coverage of studied surface structures was proposed. [DOI: 10.1380/ejssnt.2006.650]


I. INTRODUCTION
Magic clusters are the smallest ordered quantum dots; for this reason they represent promising materials for optoelectronics. However, their optical properties still have not been studied. Formation of magic clusters (MC) in reactive systems [1] differs from those in non-reactive ones [2] ('adsorbate-silicon' system is named 'reactive', if reaction resulted in silicide(s) formation takes place in it). The resulting compounds can differ in optical and conducting properties. For this reason the purpose of this work is investigation of optical properties of MC formed both in reactive (Cr/Si(111)) and nonreactive (In/Si(111)) systems. The choice (In/Si(111) and Cr/Si(111) systems) is explained by formation of MC at relatively low temperature (100 • C) in these systems. In order to further decrease the temperature of MC formation, we reduced the deposition rate.
In this work, we report the results on optical properties of Indium and Chromium MC obtained by differential reflectance spectroscopy (DRS) that is a powerful in situ method. Using a new method of DRS data processing, named 'the method of dynamic standard', we can obtain the optical function of these MC for the first time.

II. EXPERIMENTAL DETAILS
The experiments were carried out in two ultra high vacuum (UHV) chambers: 'Varian' (base pressure 2 × 10 −8 Pa) and 'Omicron' (base pressure 1 × 10 −8 Pa). The former is equipped with Auger electron spectroscopy (AES), DRS, low energy electron diffraction (LEED). The latter is equipped with AES, scanning tunneling microscopy (STM) techniques. AES and LEED were used for estimation of film composition and surface periodicity. The data obtained by these methods are auxiliary, they are not presented in the article. The samples were cut from n-type Si(111) wafer (7.5 Ω·cm) and cleaned by toluene before insertion into the sample holder. The initial Si(111)7 × 7 surface was prepared by flash cleaning, i.e. the sam- * Corresponding author: docenko@iacp.dvo.ru ple was outgassed at 500 • C for several hours and then heated at 1250 • C for a few seconds. RT deposition of indium and chromium atoms on silicon was performed from tantalum tubes. The deposition rate measured by quartz microbalance sensor was 0.05 ML/min (1 ML (monolayer)= 7.8 × 10 14 atoms/cm 2 ) and 0.01 nm/min, respectively.
The DRS technique has been described in [3]. The experimental value obtained either during DRS study or after the experiments have been finished is differential reflection coefficient (DRC) where R 0 and R a (h) are the substrate reflectance before deposition (i.e. Si(111)7 × 7) called "standard" in DRS and after formation of a film having the thickness h, respectively. The DRC spectra were recorded by multichannel analyzer having 3684 photodiodes. The spectral range extended from infrared (0.8 eV) up to visible light (2.8 eV). The sample was illuminated by unpolarized light, the incidence angle was 17 • . The obtained DRC spectra contain information about optical properties of all components the film contains. When DRC is proportional to the film thickness Aspnes and McIntyre equation [4] can be applied to obtain the optical properties of the film where ε b = ε b − iε b is the dielectric function of substrate, and ε b and ε b are its real and imaginary parts, respectively. h is the film thickness, c, light velocity, ω, light frequency, ϕ, incidence angle, k, slope of the dependence of DRC versus film thickness ΔR/R(h). Δε S = Δε S − iΔε S is change of the dielectric function of the film, and Δε S and Δε S are its real and imaginary parts, respectively. In the spectral range investigated (1.1 − 2.8 eV) ε b ≈ 0; hence, Eq. (2) is easy to solve For the spectra of changes of imaginary part of the dielectric function of the film Δε S (CIPDF) to interpret, e-Journal of Surface Science and Nanotechnology information about crystallinity and homogeneity of the film obtained by another techniques should be used.
However, the experimental dependence ΔR/R(h) is not linear in the whole range. It consists of several linear regions that we attribute to the stages of the film growth ( Fig. 3(a)). Therefore, we use different standards for calculating the DRC for each region. The number of standards equals to that of linear regions. For each region where the dependence is linear, Eqs. (2) and (3) can be applied. It suffices to use ΔR where h i is film thickness used as the standard for this region, ΔR/R(h i ) is DRC for this standard, then the dependence ΔR/R * versus h * is proportional, as in Eq. (2). The described procedure is named the 'method of dynamic standard' (MDS) [3]. Equation (2) is correct for 3D objects (chemical compounds and crystallites of bulk materials); Eq.
(3) was used in this work to process the DRC spectra obtained for the reactive system (Cr/Si(111)).
For studying the non-reactive system (In/Si(111)), the equation of Bagchi [5] containing the optical function of 2D objects δΛ should be used. In order to solve it we inserted a new variable δΛ Θ named the imaginary part of the normalized variation of the response function (IPN-VRF). It is proportional to the slope K of dependence of DRC versus In coverage ΔR/R(Θ) ( Fig. 1(a)): The meaning of the IPNVRF is the changes of optical properties of a 2D object in the phase transition involving 1 ML of adsorbate (Indium). Using MDS and Eq. (4) for dependence ΔR/R(Θ) we found a solution of the Bagchi equation: where δΛ is the imaginary part of variation of response function (IPVRF), Θ i and Θ i−1 are saturation coverage of next and previous surface phase (reconstruction), respectively, δΛ Θ is IPNVRF of this phase transition, N is the number of phase transition, and Θ 0 = 0 ML.   changes of optical properties during phase transition and has no units. Moreover, the shapes of IPVRF and IPN-VRF spectra are usually different (Figs. 1(b,c)) except those for the 1st phase transition.

III. RESULTS AND DISCUSSION
The dependence of DRC versus In coverage obtained for In/Si(111) system is presented in Fig. 1(a). It con-tains four linear regions. Because the number of points at each linear regions is not enough for the boundary positions to determine precisely in Fig. 1(a), the points of bending (0.12, 0.25 and 0.38 ML) were obtained by averaging the values calculated for dependence ΔR/R(Θ) at several photon energies. The regions (0 − 0.12 ML, 0.12 − 0.25 ML, 0.25 − 0.38 ML, and 0.38 − 0.55 ML) correspond to the four stages of In film growth. According to STM data, the 1st and 2nd stages are attributed to MC formation (Figs. 2(a,b)). The 1st type MC consists six In atoms located mainly at faulted half unit cell (FHUC) of Si(111)7 × 7 [2] (Fig. 2(a)). It appears at the 1st stage ( Fig. 2(a)) and its saturation coverage is 0.12 ML [2]. In the 2nd type MC both unfaulted half unit cell (UFHUC) and FHUC of Si(111)7 × 7 are occupied by In atoms (six per each half) (Fig. 2(b)). These MC cover Si surface at the 2nd stage; its saturation coverage is 0.24 ML [2]. The positions of the 1st and 2nd bending points (0.12 and 0.25 ML) are close to the saturation coverage for MC formed at the 1st and 2nd stages (0.12 and 0.24 ML) ( Fig. 1(a)). Therefore, for saturation coverage of the studied surface structures to obtain, bending points should be found in the dependence ΔR/R(Θ). This statement is the basis of the new method we propose for obtaining the saturation coverage.
Applying this method, we suggested that 3rd bending point (0.38 ML) is close to the saturation coverage of clusters growing at the 3rd stage (Fig. 2(c)). This value corresponds to 18 In atoms per a unit cell of Si(111)7×7 or nine In atoms per a half unit cell because of symmetric filling of both half unit cells (Fig. 2(c)). Therefore, the 3rd type cluster contains 18 atoms per a unit cell and its saturation coverage is 0.38 ML. At the last (4th) stage the next layer of In atoms grows atop the 3rd type clusters (Fig.  2(d)). Unfortunately, the dependence ΔR/R(Θ) does not contain the 4th bending point; we used STM data ( Fig.  2(d)) and the saturation coverage for the 3rd type cluster to find that for the 4th type clusters. We calculated that the saturation coverage of the 4th type clusters is close to 0.65 ML. In order to verify the obtained value we deposited 0.65 ML of IN onto Si(111)7×7 at RT (Fig. 2(e)). One can see the surface is completely covered by the 4th type clusters (compare Fig. 2(d) and Fig. 2(e)).
Optical spectra of the studied MC are presented in Figs.  1(b,c). IPVRF spectrum for the 3rd type clusters is not shown in Fig. 1(c) because the saturation coverage for them (0.38 ML) required for IPVRF calculation (see Eq. (5)) should be found accurately before using it. IPNVRF spectra are shown in Fig. 1(b). They describe changes of optical properties during phase transition (number 'i-1' phase → number 'i' phase) and are related with their band structures: where p v,c (k i ) and p v,c (k i−1 ) are the momentum operators (contains density of state (DOS)) between initial (v) and final (c) slab states at the point in 2D Brillouin zone (BZ) for number 'i' (next) and number 'i − 1' (previous) phases respectively and A is the sample area. According to Eq. (6), if DOS of the next phase is lower than that of the previous one, i.e. the phase transition results in DOS decreasing, IPNVRF is negative and vise versa. Therefore studying IPNVRF spectrum one can find a tendency of DOS changing during phase transition. Because metal-semiconductor phase transition is accompanied by reducing of DOS, it results in negative IPNVRF spectrum. On the contrary, semiconductor-metal phase transition is characterized by a positive IPNVRF spectrum.
It should be noticed that the 2nd spectrum in Fig. 1(b) describing the changes of optical properties during the 1st type→2nd type MC phase transition is located below the photon energy axis. On the contrary, 2nd type MC→3rd type cluster phase transition is characterized by positive value of IPNVRF in the studied photon energy range. It suggests that the former (1st type→type MC phase transition) results in decreasing the density of states (DS) in this energy range and vice versa. The 1st IPNVRF spectrum contains both positive and negative values. This character of the spectrum implies that DS is relocated during 1st type MC formation (Si(111)7 × 7 →1st type phase transition). For the type of each phase to find definitely, IPVRF spectra of In clusters should also be studied.
During the previous studying of In-Si(111) system at 410 • C [6] we found that IPVRF spectrum of metallic surface phase contains peaks located below Si band gap (see spectrum of 4 × 1 in Fig. 1(d)). The peaks of semiconductor surface phase are located at high energies and IPVRF spectrum is usually negative in wide photon energy range (see spectra of 7 × 7-In and √ 3 × √ 3 in Fig.  1(d)). IPVRF spectrum of the 2nd type MC presented in Fig. 1(c) contains only negative values too. Moreover, as mentioned above, during these cluster formation DS reduces. Summarizing all these results we conclude that the surface covered by the 2nd type MC is semiconductor. The hollows in IPVRF spectrum of 7 × 7-In surface phase (see Fig. 1(d)) result from reducing DS of Si adatoms and rest-atoms. Positions of them are close to those in the spectrum II in Fig. 1(c); hence, the formation of 2nd type MC is accompanied by reducing DS of Si adatoms and rest-atoms, too. The hollow located at the center of the spectrum I in Fig. 1(c) suggests that noticeable reducing DS of Si rest-atoms occurs during the 1st type MC formation. Their spectrum contains a broad peak below Si band gap (spectrum I in Fig. 1(c)); thus, the surface phase containing these clusters is metallic.
According to the dependence ΔR/R(h) presented in Fig. 3(a) the process of formation of Cr clusters in Cr/Si(111) system has three stages (0 − 0.03 nm, 0.03 − 0.11 nm and 0.11 − 0.26 nm). The growth of small Cr clusters occurs at the 1st stage ( Fig. 4(a)). However, they have different sizes. One can see both small and big clusters (Figs. 4(a,b)). Therefore they are named the 1st type 'quasi magic' clusters [1]. These clusters occupy mainly FHUC of Si(111)7 × 7 and grow there. This selectivity results in formation of ordered Cr clusters at the 2nd stage ( Fig. 4(b)). However, their height varies considerably and so they are named the '2nd type quasi MC'. The last (3rd) stage corresponds to filling of the area located between these clusters by some substance. It seems to differ from that of clusters (Fig. 4(c)). The growth of this substance results in formation of a non-homogenous continuous film. CIPDF spectrum of this film is smooth (Fig. 3(b)). The peak positions do not coincide with those of both well-known Cr silicides and bulk Cr crystallites [7]. It suggests the film consists of two substances at least.
Unlike the spectrum of a continuous film, the CIPDF of quasi MC contain sharp peaks (Fig. 3(b)). Positions of peaks are not changed and they are close to those of CrSi ones [7]. Therefore growth of 2D and 3D CrSi crystallites was suggested at the 1st and 2nd stages, respectively. The CrSi crystallites growth in FHUC implies that atomic structure of top layers of FHUC of 7 × 7 surface phase, namely the 2nd and 3rd ones, is more suitable for CrSi formation than that of UFHUC. Decreasing and broadening of peaks height observed in the 2nd spectrum results from non-regular increasing of CrSi island sizes. The double increasing of Cr deposition rate results in considerable peaks broadening and the shape of the 2nd spectrum becomes metallic-type up to 2.3 eV, i.e. Δε S ∼ (E) −a , where a > 0 (spectrum III in Fig. 7(b) in [3]). It suggests noticeable increasing of CrSi crystallite size variation. The 1st stage of Cr film growth is also changed: formation of CrSi 2 -like compound occurs. However, CIPDF of the last stage (spectrum IV in Fig. 7(b) in [3]) is close to that of the 3rd one in Fig. 3(b). It means that double increasing of Cr deposition rate does not influence noticeably the film growth at the last stage [6]. Therefore, at the 3rd stage, formation of both CrSi crystallites and CrSi 2 -like compound between them occurs. Finally, the difference in optical properties between reactive and non-reactive clusters should be noticed. The spectra of reactive (Cr) clusters are positive ( Fig. 3(b)) while those of non-reactive (In) ones contain negative values ( Fig. 1(c)).

IV. CONCLUSIONS
Using differential reflectance spectroscopy, optical functions of Indium MC and Chromium quasi MC were obtained. We found that during formation of clusters the positions of peaks in spectra of optical function of Cr quasi MC do not change. It suggests that Cr clusters keep their composition during growth. Having analyzed the obtained spectra, we conclude that Cr quasi MCs are 2D (when Cr film thickness is lower than 0.03 nm) and CrSi crystallites are 3D. Indium MC form surface phases. The Si surface covered by the 1st type In MC is a metallic surface phase while that consisting of the 2nd type In MC is semiconducting one.