One-Dimensional Plasmonic Excitations in Gold-Induced

Article pubs.acs.org/JPCC

One-Dimensional Plasmonic Excitations in Gold-Induced Superstructures on Si(553): Impact of Gold Coverage and Silicon Step Edge Polarization Fabian Hötzel, Nils Galden, Sebastian Baur, and Annemarie Pucci* Kirchhoff Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany S Supporting Information *

ABSTRACT: Free charge carriers confined to atomic chains such as the gold-induced superstructures on the stepped Si(553) surface enable experimental insight into one-dimensional physics. Embedding into the higher dimensional substrate allows for additional couplings between the free charge carriers and their surroundings, which might modify the one-dimensional characteristics. The gold atom superstructures on Si(553) consist of a parallel arrangement of metallic chains from Au and Si atoms on the terraces and of parallel Si step edges with some of the Si atoms having dangling bonds with one unpaired electron. The metallic chains give rise to localized plasmonic excitations. We have studied these plasmonic resonances with infrared spectroscopy that enables the detection of resonance shifts as small as 1 meV or even less. The plasmonic behavior of the conductive chains of the high- and the low-coverage gold superstructures on Si(553) is investigated at various temperatures and additionally after filling electrons into certain electronic states by placing gold adatoms onto the high-coverage structure. When cooling to 20 K, the strong plasmonic signals of the undoped superstructures become even stronger but shift to lower frequencies, which is attributed to the temperature dependent change of the orientational polarization of the Si dangling bonds. Regarding their plasmonic resonance shifts, the conductive atom chains work just like refractive index sensors.

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INTRODUCTION A one-dimensional (1D) linear chain of metallic atoms represents the ultimate lower limit as a conductor for the electric current. However, owing to their inherent instability such freestanding wires cannot grow longer than a few atomic diameters and break after a short time.1 A promising method for the preparation of longer and more stable 1D wire systems is their embedding into the surface of vicinal silicon surfaces.2−4 The atomic steps of these surfaces act as templates for the selfassembly of large areas of straight-lined metallic wires. As ideal candidates for testing theoretical concepts of low-dimensional physics, such as the 1D Tomonaga-Luttinger liquid5,6 or Peierls instability,7,8 these atomic chain systems have attracted increasing attention over the past decades. Among the realizable configurations, the metallic wires of the gold-induced superstructures on Si(553) represent one of the most intriguing systems because of the specific characteristics. The system shows Rashba-split 1D metallic bands.9−12 Furthermore, the metallic wires have parallel Si step edges in their neighborhood. At these step edges, those dangling bonds with the unpaired electron might undergo ordering upon cooling.13−15 So, the metallic chains on Si(553) represent a 1D system embedded in a kind of active environment. Several electronic16 and structural17 modifications of this surface exist, © XXXX American Chemical Society

which allows for the use-oriented tunability for future applications. To realize atomic-scale building blocks like plasmonic resonators or plasmonic waveguides in future nanophotonics and sensor devices,18 a deeper understanding of the behavior of free charge carriers and their excitations in low-dimensional electron systems is of particular importance. Infrared (IR) spectroscopy is a well-suited method for this purpose because it is contact-free, nondestructive and provides a better energy resolution than, for instance, electron energy loss spectroscopy (EELS). Furthermore, in situ measurements are possible, which allows for the simultaneous observation of changing properties while manipulating the metal atom chains.19 In this Article we report on the IR spectroscopic characterization of plasmonic excitations in atomic wires on goldinduced superstructures on Si(553) for which the structural model for the high-coverage wire (HCW) surface with one wire on each of the terraces of the stepped surface was proposed by Krawiec20 in 2010. We carefully study the changes of the plasmonic resonance of finite wires with temperature and with electron filling of certain metallic surface states by Au doping. Received: November 22, 2016 Revised: March 15, 2017 Published: March 21, 2017 A

DOI: 10.1021/acs.jpcc.6b11753 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

energy resolution, for example, if IR spectroscopy is employed. Even more, by some gentle modification of preparation conditions it is possible to change the average chain length and thus shift this resonance into the available spectroscopic window (Supporting Information).

Furthermore, additionally to the HCW surface, the lowcoverage wire (LCW) surface where only every second Si(553) terrace exhibits a Au chain,17 is clearly identified as a metallic phase. Because the measurements were performed at various gold coverages and various temperatures between 20 and 500 K, a broad overview of the metallic behavior of the Au chain-decorated Si(553) surface is developed. We present the results for temperatures up to 300 K. Similar to IR studies on Au chains on Si(111),21 our results underline that the Si(553)-Au surface stays metallic upon cooling to lower temperatures.12,14,17,22 However, we observed a qualitatively different change of the plasmonic resonance at lower temperatures compared to the case of the Si(111)-5×2Au system. The increase of plasmonic signal at lower temperatures surprisingly goes ahead with a lowered resonance frequency. The plasmonic resonance shift to lower energies upon cooling is observed for the HCW and the LCW structure. It turns into a shift toward higher energies (as seen for the step edge free Si(111)-5×2-Au system) if hydrogen is exposed to the reactive step edges. We attribute the plasmonic resonance shift to lower energies to the temperature dependent changes of the orientational polarization of the dangling bonds of Si atoms at the step edges. It is well-known that Si dangling bonds with unpaired electrons increase the IR refractive index of silicon.23 The reduction of fluctuations at lower temperatures raises the contribution of the electric dipole of these dangling bonds to the average polarization24 and thus increases the refractive index further. Plasmonic resonances of finite metallic chains at IR energies and below can be seen as the resonances of very thin cylinders with diameters approaching atomic sizes. For such cylinders, if infinitely long, the plasmon dispersion relation, i.e., the relation between plasmonic resonance frequency and wave vector, becomes very flat. For higher wave vectors it becomes increasingly influenced by electron−hole pair formation and by correlation effects.25 At wave vectors of the order of only 0.01 Å−1 the plasmon dispersion of a 1D metal atom chain is mainly dependent on the electronic band structure at the Fermi level and the plasmonic resonance frequencies are proportional to kF/m* where kF denotes the length of the Fermi wave vector and m* the effective electron mass.25−27 As for other plasmonic systems, the plasmonic dispersion of 1D wires is sensitive to the refractive index (the square root of the dielectric constant) of the embedding medium and thus the dielectric properties of the substrate. For the low-dimensional surface plasmons on insulating substrates, the substrate polarization effect is usually considered in terms of an effective refractive index neff = (1 + εs)/2 for the surface in vacuum by which the plasmonic group velocity is divided.28,29 εs denotes the dielectric constant of the substrate. The temperature and energy dependence of εs have been neglected so far.28−30 For a finite length of the plasmonic object, only certain wave vectors are allowed. They form oscillating standing wave patterns of the charge density.31 Depending on their symmetry, these charge oscillation patterns can yield a net dipole moment that couples to light. For the shortest wave vector, the standing wave gives the strongest dipole. In plasmonics, this kind of mode is known as the fundamental one.32 Because the dispersion relation of a low-dimensional object is so flat, the fundamental mode of metallic atom chains with some 10 nm length are in the IR range where it can be studied with high-

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METHODS Experiments were performed under ultrahigh-vacuum conditions at a base pressure of p < 1 × 10−10 mbar. Si(553) wafers (p-type doped, double side polished, 5−6 Ωcm resistivity) with an offcut angle of 12.3° from the [111] toward the [112]̅ direction were heated overnight at 600 °C and flash-annealed several times up to 1200 °C afterward. The quality of both the bare and the Au decorated surface was checked by reflection high-energy electron diffraction (RHEED). The amounts of 0.46 and 0.19 ML (1 ML = 7.83 × 1014 atoms/cm2) gold were evaporated at a deposition rate of 0.10 ML/min from a PBN crucible onto the sample held at 600 °C. Special care was taken to precisely adjust the rate by a quartz crystal microbalance (QCM) and RHEED diffraction measurements in advance. After the Au deposition, the sample was cooled to room temperature (RT) within 90 s and postannealed afterward at 800−870 °C for 1 s. A dosage of 215 L (10.5 min at 2 × 10−7 mbar) of molecular hydrogen was applied to test the influence of hydrogen adsorption on the temperature dependence of the plasmonic resonance. The molecules are cracked at the filament of the ion gauge inside the UHV chamber. All IR measurements were conducted with a dry air-purged Fourier transform IR (FTIR) spectrometer (Tensor 27, Bruker, mercury cadmium telluride (MCT) detector) directly connected to the vacuum chamber via KBr windows. Measurements were performed in transmittance geometry at normal incidence of light and with a resolution of 8 cm−1. Background spectra were scanned 800 times and sample spectra 400 times which yielded a good signal-to-noise ratio. For the transition temperatures, the scan number was reduced due to time limitations in the warming up process. To check the 1D properties of the plasmon, the electric field of the IR beam was polarized either parallel or perpendicular to the Au chains. The reference spectra of the flash-annealed Si(553) surface were recorded at the corresponding temperature and polarization before Au deposition. Then, the relative transmittance is obtained by dividing the spectra of the Au chains by the references. The 100% line serves as indicator for detector and temperature instabilities during the record of one spectrum. It is obtained by forming the relative transmittance of two relative transmittance spectra of the Si sample at two different points of time.

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RESULTS AND DISCUSSION

HCW Surface. For the preparation of pristine single domain Au chains on Si(553) according to the structural model proposed by Krawiec,20 a coverage of 0.46 ML gold was evaporated at 600 °C sample temperature, followed by a short postannealing at 800−870 °C. Figure 1a shows the RHEED pattern of self-assembled pristine Au chains on Si(553) aligned along the [11̅0] direction. The pattern is in agreement with other RHEED measurements of the HCW Si(553)-Au chain system.33,34 All observed diffraction features fully correspond to those from LEED.12,35,36 The ×2 streaks, marked by white dashed lines in Figure 1a, originate from the 2-fold periodicity along the Au chains.14,15,17,36 Moreover, the RHEED pattern is showing the ×3 streaks due to the ordered atomic and B


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Figure 1. (a) RHEED pattern of pristine Au chains on Si(553) at 20 K. The ×2 streaks originating from the 2-fold periodicity parallel to the Au chains are indicated by white dashed lines. Pink dashed lines mark ×3 streaks that arise from the superstructure at the Si step edges. (b) RHEED pattern, taken at 20 K, of doped Au chains after the deposition of additional 0.05 ML Au onto the structure at RT. ×2 streaks and indications to the ×3 streaks from the pattern (a) are still observable. Electron energy is 20 keV, glancing angle 1.3°, and incident direction [112̅].

Figure 2. Relative normal transmittance spectra of Au chains on Si(553) at different temperatures. The electric field is polarized either parallel to the chains in [110̅ ] direction (solid lines) or perpendicular to them ([112̅], dashed lines). Measurements at 20 K are depicted in blue and red spectra and were recorded at RT. Fits according to eq 1 in ref 21 (Supporting Information) are indicated as thin black lines. In (a) and (b), IR spectra of pristine Au wires are shown. The color gradient spectra in (a) were taken for transition temperatures between 20 K and RT (from blue to red in steps of 10 K within 5 to 10 min). The shift of the absorption maximum with temperature is marked by the black arrow. In (b), spectra of pristine Au chains of a sample with longer chains than those for spectra in (a) are shown. In (c) the spectra of the chains of (b) after the deposition of additional 0.05 ML Au onto this sample at RT are shown. Reference in each panel is the transmittance of the Si(553) surface of the same sample at the same temperature and polarization before Au deposition.

electronic structure of the Si step edges12−15,22,36−38 at lower temperatures. The ×3 streaks arise in the RHEED patterns due to the slightly lower position (by 0.3 Å compared to those of the adjacent atoms)37 of every third Si step edge atom the dangling bond of which exhibits an unpaired electron. These streaks can be seen in Figure 1a (marked by pink dashed lines, Figure 1b is described below). At RT, ×3 streaks are not observable because of thermally activated hopping processes of the electrons destroying the long-range order.37 In Figure 2a IR relative transmittance spectra of the pristine Au chain structure on Si(553) at different temperatures in the range from 20 K to RT are shown (Figure 2b,c are described below). For the polarization of the electric field perpendicular to the Au chains ([112]̅ ), no absorption feature can be detected in the accessible measurement range (see the red and blue dashed lines in Figure 2a). But for parallel polarization ([11̅0], see the red and blue solid lines) a remarkably high-absorption signal of the dipole-like charge oscillation is observed, which underlines the optical anisotropy and thus the 1D property of this system. As done for similarly behaving quasi-1D structures like Si(111)-4×1-In39 or Si(111)-5×2-Au,19,21 investigated by the same measurement technique, this signal is attributed to a surface plasmon excitation of finite chains. Its resonance frequency determines the absorption maximum. The metallic behavior of this system arises from several metallic surface bands associated with the Au chains.11,12,15,16,20 Naturally

occurring structural defects3,40−42 and domain boundaries43 limit the gold chain lengths.19,21 The red solid line in Figure 2a represents the IR spectrum of the sample at RT. The relative transmittance change due to the plasmonic resonance is about 4% at the transmittance minimum, which is twice as large as the signal from Au chains on Si(111)-5×2-Au measured under the same conditions.19 The higher chain density per area and more free charge carriers due to several metallic bands deliver the explanation to this finding. In the polarization sensitive measurements the perfect anisotropy of the plasmonic signal and thus of the Si(553)-Au system is obvious. The stability of the Si(553) surface is certainly stabilized by the Au atoms and so step bunching is suppressed. C


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The Journal of Physical Chemistry C Upon cooling the sample to 20 K the plasmonic signal increases (to 6% transmittance change) and gets sharper (Figure 2a, blue solid line). Surprisingly, it shifts to lower wavenumbers compared to the RT signal (red solid line). This is in contrast to the recent experimental findings of the plasmonic behavior of the Si(111)-5×2-Au system at 20 K, where the absorption maximum shifted to higher wavenumbers with decreasing temperature as an expected anharmonic behavior.21 To investigate the unusual behavior of the Si(553)-Au surface in more detail, additional spectra were taken at approximately every 10 K during the warming up process of the sample after cooling (symbolized by the color gradient from blue to red in Figure 2a). As can be seen, the signal gradually shifts back to higher wavenumbers and finally coincides with the RT spectrum again. This behavior of the plasmonic excitation with temperatures could be reproduced and was observed for a series of several wafer substrates. An analytical model for the absorption cross section of metallic needles (Supporting Information) is fitted to the experimental spectra, as explained and successfully tested in refs 21 and 44. According to that, the spectral line shape is described classically within the electrostatic approximation for the absorption of ultrathin needles with a Drude-type dielectric function. The fit also accounts for the Gaussian broadening due to a random distribution of chain lengths. It provides values for the plasmonic resonance frequency ωres, the electronic scattering rate ωτ, the width Δω of the random distribution of resonance frequencies, and as proportional to the plasma frequency, the one-dimensional system’s parameter kF/m*.21 Such fitting of the IR spectra of Figure 2a yields the width Δω = 332 cm−1 as well as the electronic scattering rate ωτ,RT = 1275 cm−1 at RT and its decrease to ωτ,20 K = 1079 cm−1 at 20 K (with a relative error of 10%), which is due to the decreasing electron−phonon scattering toward lower temperatures. As a result, the plasmonic absorption gets sharper. The resonance frequency shifts from ωres,RT = 1045 ± 5 cm−1 down to ωres,20 K = 905 ± 9 cm−1. Such downward shifts of the plasmonic resonance with decreasing temperature have never been observed for metallic atom chains on Si(111).21,39 The plasmonic peak area is slightly increasing and its analysis yields an increase of kF/m* (see below), and so the shift cannot be explained by a decreasing kF/m*. The most probable explanation of this temperature effect is that the resonance shift for the Si(553)-Au chain system is related to the Si step edges with fluctuating dipoles from unpaired electrons of dangling bonds. As theoretically predicted for low temperatures, every third dangling bond is occupied by only one electron whereas the others contain two electrons with opposite spin.15 This electronic occupation goes hand in hand with a slight structural displacement of every third Si step edge atom on the HCW surface, which could be measured only at low temperature.12,14,38 Related to that displacement also the electronic background polarization near the conducting chains is modified. More important, for high enough temperatures, the thermal fluctuations of the electric dipoles of the unsaturated dangling bonds contribute to the dielectric background. According to the Langevin−Debye relation for the orientational polarization,24,45 the electric polarizability change by permanent dipoles with the dipole component μ∥ in the direction of the electric field is proportional to μ∥2/(kBT) at temperature T (kB is the Boltzmann constant). The higher polarizability at lower temperatures corresponds to a higher electric polarization, a higher dielectric constant, and thus a higher refractive index

neff ∼

μ 2 /(kBT ) , also in the IR if the fluctuations are very

fast (almost no activation barrier to be overcome so that the relaxation rate of the orientational polarization is above the IR; see Supporting Information). Indeed, with the exposure of small amounts of hydrogen that preferentially adsorb at the step edges,46 the tendency of the resonance shift upon cooling is reversed (Figure S1b in the Supporting Information). Hydrogen is well-known to electronically passivate Si dangling bonds. Hence the temperature dependent change of the electric step edge polarization is attenuated. With the plasmonic resonance at hand, the length of the plasmon wave vector can be estimated from the experimental plasmonic dispersion at room temperature28 (300 K). So the average chain length L = 31 ± 6 nm is obtained. Furthermore, the quantitative fit of the plasmonic absorption spectrum yields the number of free charge carriers per chain divided by the effective mass and so, assuming the same chain length L for 300 and 20 K, it follows [kF/m*]RT = 0.69 ± 0.20 (Å·me)−1 at RT and [kF/m*]20K = 0.84 ± 0.22 (Å·me)−1 at 20 K, respectively. The clearly higher value of kF/m* at 20 K contradicts the lower resonance frequency at 20 K (i.e., the shift of the plasmonic dispersion to lower energies) if the influence of the effective refractive index neff(T) of the surroundings is not taken into account. For only one electronic band at the Fermi level, as on the Si(111)-5×2-Au surface, the value of kF/m* from the fit to the plasmonic resonance can be easily compared to the directly determined band-structure data. In the Si(553)-Au chain system several one-dimensional bands at the Fermi level (two pairs of spin−orbit split bands,11 for one of them the splitting is too small for the experimental proof) may contribute to the plasmonic excitation. In the case of the same lifetime for all bands, the plasmonic excitation should correspond to the sum of kF/m* for the bands at the Fermi level. But the typically different lifetimes for the various bands should lead to different and temperature dependent weighting factors of the contributions from the various bands, as it follows already for the dynamic conductivity of bulk metals.47 Therefore, contributions from the bands with the highest lifetime should dominate the plasmonic behavior. How the several electronic surface states contribute to the plasmonic excitation has not been theoretically studied so far. This open problem has to be contemplated while comparing data of Table 1. There, band Table 1. Band Structure Data kF/m* (per One Spin Direction) of Different Reconstructions of the Si(553)-Au Chain Systema surface HCW HCW + 0.05 ML Au LCW

ARPES, S1, S2

ARPES, S3

IR, 300 K

IR, 20 K

0.78 ± 0.05

0.72 ± 0.09 0.73 ± 0.07

0.69 ± 0.20 0.45 ± 0.14

0.84 ± 0.22 0.37 ± 0.08

0.82 ± 0.06

0.88 ± 0.11

0.62 ± 0.25

0.65 ± 0.23

a Values are given in (Å·me)−1. For the ARPES data, kF/m* per spin direction is estimated from the ARPES measurements by Crain et al.10 (HCW, 160−220 K), by Song et al.16 (Au-doped HCW, RT), and by Song et al.17 (LCW, 20 K). The designation of the HCW bands is taken from Krawiec et al.11 Results of this work are derived from the IR absorption cross section of the plasmonic excitation in a finite chain. Details of the data extraction from ARPES and the uncertainties are described in the Supporting Information.

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Au chain structure at RT and 20 K, respectively. Solid lines in Figure 2c show the spectra after Au doping at the same temperatures. Compared to the pristine wires, the plasmonic absorption feature at RT decreased and shifted to higher wavenumbers. Equivalent findings were made for the Si(111)5×2-Au surface with additional Au atoms.19 According to that, a shift of the resonance to higher energies means a chain shortening that can be explained by local disorder induced by the Au dopants.16 The diminished intensity of the plasmonic absorption indicates the changes in the electronic band structure. As per Song et al.,16 upon Au doping, the S1/S2 band with the measurable spin−orbit splitting shows a clear ARPES intensity decrease at the Fermi energy. So the decreasing plasmonic signal can be explained. The remaining plasmonic signal originates from the S3 band only (for which the spin−orbit splitting could not be measured yet). Upon cooling the sample to 20 K, this plasmonic resonance features a behavior similar to that of the undoped Au chains: it gets narrower and shifts from 1014 cm−1 to lower frequencies (by 66 cm−1). In analogy to the undoped HCW Si(553)-Au surface, Table 1 gives an overview of the ratio kF/m* for the doped surface from both ARPES data and IR absorption cross section. The value of the S3 band as estimated from ARPES data did not change although being doped by external electrons. That is because kF and m* both increase to the same extent with doping. The IR result is slightly below the ARPES result for the kF/m* value of the S3 band alone, which may be related to slightly different adsorption conditions for the two kinds of experiments, both without a final annealing step. Under consideration of the errors, the plasmonic resonance shift is in accord with the decrease of kF/m* determined from the IR spectra. So, for the doped surface, there is no obvious change in the effective refractive index with temperature, which might be related to the disorder introduced by the dopants not sitting at well-defined sites. The LCW surface. In 2015, Song et al.17 introduced a modified version of the Au chain-covered Si(553) surface with a coverage of only 0.19 ML Au. They referred to the surface as LCW (low coverage wires) because Au chains are located only on every second terrace. According to the structural model (see Figure 4a in ref 17) the surface consists of alternating pristine Si nanoterraces with a 5 × 5 unit cell and a width of 1.8 nm and, as on the HCW surface, Au atom chains with Si step edges nearby. As calculated, on the LCW surface, spin ordering at the Si step edges with tripled periodicity should be hampered by internal strain originating from the neighboring extended Si terraces. ARPES results indicate the metallicity of the chain-like superstructure on the LCW surface.17 We prepared the LCW system, the structural motifs of which are identified by RHEED, and found a clear plasmonic resonance thereby confirming the metallic property (Figure 4). The RHEED pattern clearly displays the ×5 streaks (pink dashed lines) corresponding to the 5 × 5 symmetry of the pristine Si nanoterraces (Figure 4a). Moreover ×2 streaks, arising from the 2-fold periodicity along the Au chains are visible (white dashed lines) like in the RHEED pattern of the HCW surface (Figure 1a). Therefore, our sample corresponds to that with the structural model presented by Song et al.17 The IR spectra (Figure 4b) for electric field polarization parallel to the chains (solid lines) show surprisingly strong plasmonic absorption (regarding a coverage of only 0.19 ML Au) and thus reveal the metallicity of the surface attributed to the Au wires.17

structure data of the Si(553)-Au chain system that we have estimated from angle-resolved photoemission spectroscopy (ARPES) results by Crain et al.10 as well as the results of this IR study are shown. The individual kF/m* values of the ARPES bands are in good accord to the IR result. So we can say that one of the two bands gives the plasmonic excitation, but at the moment not which one. The one with the longer lifetime (which should determine the plasmonic excitation) could be identified by a thorough line width analysis of ARPES spectra, which has not been done yet, as far as we know. Taking into account the increase in kF/m* upon cooling to 20 K, the plasmonic resonance frequency increase of about 13% observed for the HCW structure is attributed to a relative increase of the effective refractive index neff of about 25% (compared to room temperature). The analysis of the temperature dependent plasmonic peak area and of the resonance frequency yields neff(T)/neff(RT) versus 1/√T; see Figure 3. Down to temperatures of about 85 K the linear slope

Figure 3. Experimental data neff(T)/neff(RT) versus 1/√T for the HCW (black squares) and the LCW (red triangles) structure (with a relative error of about 30%). The linear range is marked (red line).

proves thermally fluctuating electric dipoles. At even lower temperatures the fluctuations disappear and the effective refractive index saturates at the higher value of the lowtemperature superstructure. Au Doping of the HCW Surface. In 2014, Song et al.16 reported on the possibility of selectively controlling one of the two pairs of metallic Au bands of the HCW Si(553)-Au surface11,12,15,16 by externally doped electrons from noble metal atoms. According to ARPES, the extra electrons belong to the S3 band.16 This band is the only one with nonvanishing ARPES intensity at the Fermi energy after additional 0.048 ML Au were deposited onto the pristine structure at RT. Surface free energy calculations16 reveal that the preferred adsorption sites of the extra Au atoms are located near the pristine Au nanowires. In our experiments we deposited additional 0.05 ML Au onto the pristine Au chain structure at RT. RHEED patterns at 20 K show that the ×2 and ×3 streaks are still observable, but with slightly less intensity (Figure 1b). This result supports the findings by Song et al. that, first, the amount of extra Au atoms is too small to destroy the overall atomic structure, and second, due to the presence of the ×3 streaks, more extra Au atoms should have adsorbed near the pristine Au wires instead at the Si step edges.16 The IR relative transmittance spectra of the pristine and doped Au chain surfaces are presented in Figure 2b,c. Red and blue solid lines in Figure 2b represent the spectra of the pristine E


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Taking into account the increase in kF/m* at lower temperature [see the band structure data for the LCW surface in Table 1 (IR data)], it follows a relative change of the effective refractive index neff of ca. 18% from the plasmon resonance shift. The ratio of the relative change of neff of the HCW structure to that of the LCW structure is 0.25:0.18 ≈ 1.4. Taking into account the experimental errors and possible differences in the adsorbate coverage from the residual gas, this value is in very good accord to 1.29, which is the square root of the ratio of the area density of dangling bonds for the HCW and the LCW structure (notice that the refractive index is the square root of the dielectric constant that is proportional to the density of dipoles). Our IR results for the LCW structure correspond to a Fermi velocity vF = ℏkF/m* that is slightly lower than the values for the HCW structure, a result that is supported by recent EELS measurements29 of the LCW system. In contrast, Song et al., through ARPES,17 stated that vF of the S3 band of the LCW surface increases compared to that of the HCW structure. The different results from the various experiments may be related to the different effects of electronic damping on the various excitation processes.

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Figure 4. (a) RHEED pattern of the LCW structure at 20 K. ×5 streaks are marked by pink dashed lines, ×2 streaks by white dashed lines. The two insets show a modified version of parts of the pattern (see red dashed lines) at 20 K and RT for a clearer view of the ×5 streaks. Details of the modification are explained in the Supporting Information. Electron energy is 20 keV, glancing angle 0.5° (20 K) and 1.3° (RT), and incident direction [112̅]. (b) Relative normal transmittance spectra of the 0.19 ML-covered LCW system at RT (red) and 20 K (blue). The electric field is polarized either parallel to the chains in [110̅ ] direction (solid lines) or perpendicular to them ([112̅], dotted lines). Fits according to eq 1 in ref 21 (Supporting Information) are indicated as thin black lines. Reference is the transmittance of the Si(553) surface of the same sample at the same temperature and polarization before Au deposition.

CONCLUSIONS Due to the high-energy resolution of IR spectroscopy, not only the results from ARPES, STM/STS, and EELS could be confirmed but also new insights into one-dimensional plasmons are gained. Arranged in one-dimensional chains, gold atoms on silicon surfaces give strong plasmonic signals in the infrared already at coverages well below 1 ML. With the careful quantitative analysis of such a signal on Si(553), band structure data are derived that enlighten how the various electronic bands contribute to the 1D plasmonic excitation. The behavior of the plasmonic absorption at lower temperatures led us to the conclusion that the temperature dependent ordering and the electronic fluctuations at the Si step edges modify the dielectric background for the 1D plasmonic system of the HCW structure and also for that of the LCW structure. Comparable to plasmonic refractive index sensors, the plasmonic 1D wires’ resonances are shifted due to the changes of the effective refractive index of their surroundings. The temperature dependence of that shift might be useful to clarify the transition between the room temperature and low-temperature structure of the gold covered Si(553) surface.

Upon cooling, the absorption signal gets stronger and narrower and its maximum shifts by about 110 cm−1, from ωres,RT = 852 ± 18 cm−1 to ωres,20K = 741 ± 38 cm−1, to lower wavenumbers, similar to the case of the HCW surface (Figure 2a). For perpendicular polarization (dotted lines) no plasmonic absorption feature can be observed. So the LCW structure exhibits equal 1D property as the HCW. The plasmonic resonance shift is accompanied by a decreasing electronic scattering rate from ωτ,RT = 1613 cm−1 to ωτ,20K = 1307 cm−1 (with a relative error of 10%). For the HCW surface, the shift of the plasmonic resonance to lower energies at low temperature is explained also by the decreasing fluctuations of electric dipoles of dangling bonds and the resulting slight structural change at the Si step edges at low temperatures. For the LCW structure at low temperature, the following strain related displacement of the outermost Si step edge atoms is predicted: Each pair of Si atoms adjacent to a corner hole of the 5 × 5 terrace should be shifted downward by 0.3 Å,17 whereas the other three Si step edge atoms in between remain at their positions (Figure 4 in ref 17). Theoretical calculations in ref 17 predict unpaired electrons in the dangling bonds of one of the two downward shifted Si atoms, respectively (Figure S4 in ref 17). So the predicted portion of unpaired electrons along the step edges is 1/5 for the LCW structure whereas it is 1/3 for the HCW structure. The similar plasmonic shifts of the HCW and the LCW structure with temperature indicate a rather similar polarization change.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11753. Analytical model for the absorption cross section, details of the data extraction from ARPES and the uncertainties, orientational polarization, RHEED and relative transmittance of hydrogenated Si(553)-Au, annealing dependent plasmonic absorptions, modification of the RHEED pattern (PDF)

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AUTHOR INFORMATION

Corresponding Author

*A. Pucci. E-mail: [email protected]. ORCID

Annemarie Pucci: 0000-0002-9038-4110 F


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The Journal of Physical Chemistry C Notes

(17) Song, I.; Goh, J. S.; Lee, S.-H.; Jung, S. W.; Shin, J. S.; Yamane, H.; Kosugi, N.; Yeom, H. W. Realization of a Strained Atomic Wire Superlattice. ACS Nano 2015, 9, 10621−10627. (18) Nagao, T.; Han, G.; Hoang, C.; Wi, J.-S.; Pucci, A.; Weber, D.; Neubrech, F.; Silkin, V. M.; Enders, D.; Saito, O.; et al. Plasmons in Nanoscale and Atomic-Scale Systems. Sci. Technol. Adv. Mater. 2010, 11, 054506. (19) Hötzel, F.; Seino, K.; Chandola, S.; Speiser, E.; Esser, N.; Bechstedt, F.; Pucci, A. Metal-to-Insulator Transition in Au Chains on Si(111)-5 × 2-Au by Band Filling: Infrared Plasmonic Signal and Ab Initio Band Structure Calculation. J. Phys. Chem. Lett. 2015, 6, 3615− 3620. (20) Krawiec, M. Structural Model of the Au-Induced Si(553) Surface: Double Au Rows. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 115436. (21) Hötzel, F.; Seino, K.; Huck, C.; Skibbe, O.; Bechstedt, F.; Pucci, A. Metallic Properties of the Si(111)-5 × 2-Au Surface from Infrared Plasmon Polaritons and Ab Initio Theory. Nano Lett. 2015, 15, 4155− 4160. (22) Snijders, P. C.; Johnson, P. S.; Guisinger, N. P.; Erwin, S. C.; Himpsel, F. J. Spectroscopic Evidence for Spin-Polarized Edge States in Graphitic Si Nanowires. New J. Phys. 2012, 14, 103004. (23) Schwidefsky, F. Increase of the Refractive Index of Silicon Films by Dangling Bonds. Thin Solid Films 1973, 18, 45−52. (24) Jackson, K.; Pederson, M.; Wang, C.-Z.; Ho, K.-M. Calculated Polarizabilities of Intermediate-Size Si Clusters. Phys. Rev. A: At., Mol., Opt. Phys. 1999, 59, 3685−3689. (25) Moudgil, R. K.; Garg, V.; Pathak, K. N. Confinement and Correlation Effects on Plasmons in an Atom-Scale Metallic Wire. J. Phys.: Condens. Matter 2010, 22, 135003. (26) Das Sarma, S.; Hwang, E. H. Dynamical Response of a OneDimensional Quantum-Wire Electron System. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1936−1946. (27) Das Sarma, S.; Lai, W. Screening and Elementary Excitations in Narrow-Channel Semiconductor Microstructures. Phys. Rev. B: Condens. Matter Mater. Phys. 1985, 32, 1401−1404. (28) Lichtenstein, T.; Aulbach, J.; Schäfer, J.; Claessen, R.; Tegenkamp, C.; Pfnür, H. Two-Dimensional Crossover and Strong Coupling of Plasmon Excitations in Arrays of One-Dimensional Atomic Wires. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 161408. (29) Lichtenstein, T.; Tegenkamp, C.; Pfnür, H. Lateral Electronic Screening in Quasi-One-Dimensional Plasmons. J. Phys.: Condens. Matter 2016, 28, 354001. (30) Ando, T.; Fowler, A. B.; Stern, F. Electronic Properties of TwoDimensional Systems. Rev. Mod. Phys. 1982, 54, 437−672. (31) Alber, I.; Sigle, W.; Müller, S.; Neumann, R.; Picht, O.; Rauber, M.; van Aken, P. A.; Toimil-Molares, M. E. Visualization of Multipolar Longitudinal and Transversal Surface Plasmon Modes in Nanowire Dimers. ACS Nano 2011, 5, 9845−9853. (32) Neubrech, F.; Kolb, T.; Lovrinčić, R.; Fahsold, G.; Pucci, A.; Aizpurua, J.; Cornelius, T. W.; Toimil-Molares, M. E.; Neumann, R.; Karim, S. Resonances of Individual Metal Nanowires in the Infrared. Appl. Phys. Lett. 2006, 89, 253104. (33) Kopciuszyński, M.; Łukasik, P.; Zdyb, R.; Jałochowski, M. Ordering of the Si(553) Surface with Pb Atoms. Appl. Surf. Sci. 2014, 305, 139−142. (34) Takayama, T.; Voegeli, W.; Shirasawa, T.; Kubo, K.; Abe, M.; Takahashi, T.; Akimoto, K.; Sugiyama, H. Structural Study of the Si(553)-Au Surface. e-J. Surf. Sci. Nanotechnol. 2009, 7, 533−536. (35) Ahn, J. R.; Kang, P. G.; Ryang, K. D.; Yeom, H. W. Coexistence of Two Different Peierls Distortions within an Atomic Scale Wire: Si(553)-Au. Phys. Rev. Lett. 2005, 95, 196402. (36) Biedermann, K.; Regensburger, S.; Fauster, T.; Himpsel, F. J.; Erwin, S. C. Spin-Split Silicon States at Step Edges of Si(553)-Au. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 245413. (37) Erwin, S. C.; Snijders, P. C. Silicon Spin Chains at Finite Temperature: Dynamics of Si(553)-Au. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 235316.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft via the research unit FOR1700. F.H. thanks the Heidelberg Graduate School of Fundamental Physics (HGSFP). We also thank M. Jałochowski for fruitful discussions concerning the RHEED patterns.

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REFERENCES

(1) Ohnishi, H.; Kondo, Y.; Takayanagi, K. Quantized Conductance through Individual Rows of Suspended Gold Atoms. Nature 1998, 395, 780−783. (2) Crain, J. N.; McChesney, J. L.; Zheng, F.; Gallagher, M. C.; Snijders, P. C.; Bissen, M.; Gundelach, C.; Erwin, S. C.; Himpsel, F. J. Chains of Gold Atoms with Tailored Electronic States. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 125401. (3) Hasegawa, S. Quasi-One-Dimensional Metals on Semiconductor Surfaces with Defects. J. Phys.: Condens. Matter 2010, 22, 084026. (4) Snijders, P. C.; Weitering, H. H. Colloquium: Electronic Instabilities in Self-Assembled Atom Wires. Rev. Mod. Phys. 2010, 82, 307−329. (5) Blumenstein, C.; Schäfer, J.; Mietke, S.; Meyer, S.; Dollinger, A.; Lochner, M.; Cui, X. Y.; Patthey, L.; Matzdorf, R.; Claessen, R. Atomically Controlled Quantum Chains Hosting a TomonagaLuttinger Liquid. Nat. Phys. 2011, 7, 776−780. (6) Jompol, Y.; Ford, C. J. B.; Griffiths, J. P.; Farrer, I.; Jones, G. A. C.; Anderson, D.; Ritchie, D. A.; Silk, T. W.; Schofield, A. J. Probing Spin-Charge Separation in a Tomonaga-Luttinger Liquid. Science 2009, 325, 597−601. (7) Wippermann, S.; Schmidt, W. G. Entropy Explains MetalInsulator Transition of the Si(111)-In Nanowire Array. Phys. Rev. Lett. 2010, 105, 126102. (8) Yeom, H. W.; Takeda, S.; Rotenberg, E.; Matsuda, I.; Horikoshi, K.; Schäfer, J.; Lee, C. M.; Kevan, S. D.; Ohta, T.; Nagao, T.; et al. Instability and Charge Density Wave of Metallic Quantum Chains on a Silicon Surface. Phys. Rev. Lett. 1999, 82, 4898−4901. (9) Barke, I.; Zheng, F.; Rügheimer, T. K.; Himpsel, F. J. Experimental Evidence for Spin-Split Bands in a One-Dimensional Chain Structure. Phys. Rev. Lett. 2006, 97, 226405. (10) Crain, J. N.; Kirakosian, A.; Altmann, K. N.; Bromberger, C.; Erwin, S. C.; McChesney, J. L.; Lin, J.-L.; Himpsel, F. J. Fractional Band Filling in an Atomic Chain Structure. Phys. Rev. Lett. 2003, 90, 176805. (11) Krawiec, M.; Kopciuszyński, M.; Zdyb, R. Different Spin Textures in One-Dimensional Electronic Bands on Si(553)-Au Surface. Appl. Surf. Sci. 2016, 373, 26−31. (12) Yeom, H. W.; Jung, S. W.; Shin, J. S.; Kim, J.; Kim, K. S.; Miyamoto, K.; Okuda, T.; Namatame, H.; Kimura, A.; Taniguchi, M. Direct Observation of the Spin Polarization in Au Atomic Wires on Si(553). New J. Phys. 2014, 16, 093030. (13) Aulbach, J.; Erwin, S. C.; Claessen, R.; Schäfer, J. Spin Chains and Electron Transfer at Stepped Silicon Surfaces. Nano Lett. 2016, 16, 2698−2704. (14) Aulbach, J.; Schäfer, J.; Erwin, S. C.; Meyer, S.; Loho, C.; Settelein, J.; Claessen, R. Evidence for Long-Range Spin Order Instead of a Peierls Transition in Si(553)-Au Chains. Phys. Rev. Lett. 2013, 111, 137203. (15) Erwin, S. C.; Himpsel, F. J. Intrinsic Magnetism at Silicon Surfaces. Nat. Commun. 2010, 1, 58. (16) Song, I.; Oh, D.-H.; Shin, H.-C.; Ahn, S.-J.; Moon, Y.; Woo, S.H.; Choi, H. J.; Park, C.-Y.; Ahn, J. R. Direct Momentum-Resolved Observation of One-Dimensional Confinement of Externally Doped Electrons within a Single Subnanometer-Scale Wire. Nano Lett. 2015, 15, 281−288. G


Article

The Journal of Physical Chemistry C (38) Hafke, B.; Frigge, T.; Witte, T.; Krenzer, B.; Aulbach, J.; Schäfer, J.; Claessen, R.; Erwin, S. C.; Horn-von Hoegen, M. Two-Dimensional Interaction of Spin Chains in the Si(553)-Au Nanowire System. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 161403R. (39) Chung, H. V.; Kubber, C. J.; Han, G.; Rigamonti, S.; SanchezPortal, D.; Enders, D.; Pucci, A.; Nagao, T. Optical Detection of Plasmonic and Interband Excitations in 1-nm-Wide Indium Atomic Wires. Appl. Phys. Lett. 2010, 96, 243101. (40) Crain, J. N.; Pierce, D. T. End States in One-Dimensional Atom Chains. Science 2005, 307, 703−706. (41) Crain, J. N.; Stiles, M. D.; Stroscio, J. A.; Pierce, D. T. Electronic Effects in the Length Distribution of Atom Chains. Phys. Rev. Lett. 2006, 96, 156801. (42) Uetake, T.; Hirahara, T.; Ueda, Y.; Nagamura, N.; Hobara, R.; Hasegawa, S. Anisotropic Conductivity of the Si(111)-4 × 1-In Surface: Transport Mechanism Determined by the Temperature Dependence. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 035325. (43) Zhang, L.; Kim, Y.; Shim, H.; Lee, G. Influence of Substrate Temperature on Submonolayer Au Adsorption on an Si(111)-7 × 7 Surface Studied by Scanning Tunneling Microscopy. J. Phys.: Condens. Matter 2007, 19, 486004. (44) Vogt, J.; Hoang, C. V.; Huck, C.; Neubrech, F.; Pucci, A. How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of Crystalline Lead Nanowires. J. Phys. Chem. C 2016, 120, 19302− 19307. (45) Van Vleck, J. H. On Dielectric Constants and Magnetic Susceptibilities in the new Quantum Mechanics Part I. A General Proof of the Langevin-Debye Formula. Phys. Rev. 1927, 29, 727−744. (46) Beitia, C.; Preyss, W.; Sole, R. D.; Borensztein, Y. Adsorption Kinetics of H on Si(111)7 × 7 by means of Surface Differential Reflectivity. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, R4371−R4374. (47) Ashcroft, N. W.; Mermin, N. D. In Solid State Physics; Crane, D. G., Ed.; Harcourt College Publishers: Cambridge, MA, 1976; pp 250− 253.

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One-Dimensional Plasmonic Excitations in Gold-Induced

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