Substitutional adsorption geometry for Pb(1 1 1)-(√3 × √3)R30°-K

Intermixed structures for alkalis (larger than Li) on close-packed substrates have previously been observed only on Al(1 1 1). This study shows that K forms an ordered intermixed structure on Pb(1 1 1). The structures of clean Pb(1 1 1) and Pb(1 1 1)-(√3 × √3)R30°-K were studied using dynamical low-energy electron diffraction (LEED). The clean Pb(1 1 1) surface at 47 K was found to be a relaxed version of the bulk structure, in agreement with an earlier study of the same surface [Y.S. Li, F. Jona, P.M. Marcus, Phys. Rev. B 43 (1991) 6337]. At room temperature, adsorption of K on this surface results in a (√3 × √3)R30° structure, which was shown using dynamical LEED to consist of K atoms substituted in surface vacancies. The K-Pb bond length was found to be 3.62 ± 0.3 Å, with no significant change to the Pb interlayer spacings.     

Phase mixing and phase separation accompanying the catalytic oxidation of CO on Ir{1 0 0}

The co-adsorption of CO and O on the unreconstructed (1 × 1) phase of Ir{1 0 0} was examined by low energy electron diffraction (LEED) and temperature programmed desorption (TPD). When CO is adsorbed at 188 K onto the Ir{1 0 0} surface precovered with 0.5 ML O, a mixed c(4 × 2)-(2O + CO) overlayer is formed. All CO is oxidised upon heating and desorbs as CO₂ in three distinct stages at 230 K, 330 K and 430 K in a 2:1:2 ratio. The excess oxygen left on the surface after all CO has reacted forms an overlayer with a LEED pattern with p(2 × 10) periodicity. This overlayer consists of stripes with a local p(2 × 1)-O arrangement of oxygen atoms separated by stripes of uncovered Ir. When CO is adsorbed at 300 K onto the surface precovered with 0.5 ML O an apparent (2 × 2) LEED pattern is observed. LEED IV analysis reveals that this pattern is a superposition of diffraction patterns from islands of c(2 × 2)-CO and p(2  × 1)-O structures on the surface. Heating this co-adsorbed overlayer leads to the desorption of CO₂ in two stages at 330 K and 430 K; the excess CO (0.1 ML) desorbs at 590 K.LEED IV structural analysis of the mixed c(4 × 2) O and CO overlayer shows that both the CO molecules and the O atoms occupy bridge sites. The O atoms show significant lateral displacements of 0.14 Å away from the CO molecules; the C-O bond is slightly expanded with respect to the gas phase (1.19 Å); the modifications of the Ir substrate with respect to the bulk-terminated surface are very small.     

Structural evolution of sulfur overlayers on Pd(1 1 1)

Low energy ion scattering spectroscopy (LEISS) has been used to characterize the evolution of ordered structures of S on the Pd(1 1 1) surface during annealing. During exposure of the Pd(1 1 1) surface to 0.7 L H₂S at 300 K—conditions that produce the S(√3 × √3)R30 overlayer—the intensity of the Pd LEIS signal decreases and a feature assigned to adsorbed S appears as the adsorbed layer forms. When the surface is held at 300 K after exposure to H₂S is stopped, the LEIS Pd intensity partially recovers and the S signal weakens, presumably as surface S atoms assume their equilibrium positions in the S(√3 × √3)R30 overlayer. Subsequent annealing of the S(√3 × √3)R30 structure at 700 K causes it to convert into a S(√7 × √7)R19 overlayer, whose LEIS spectrum is identical to that of clean Pd(1 1 1). The absence of LEIS evidence for S atoms at the exposed surface of the S(√7 × √7)R19 overlayer is at odds with published models of a mixed Pd-S top layer. Despite the similarity of the LEIS spectra of Pd(1 1 1) and Pd(1 1 1)-S(√7 × √7)R19, their activities for dissociative hydrogen adsorption are very different—the former readily adsorbs hydrogen at 100 K, while the latter does not—suggesting that S exerts its influence on surface chemistry from subsurface locations.     

Sulfur-induced mobilization of Au surface atoms on Au(1 1 1) studied by real-time STM

The interaction of sulfur with gold surfaces has attracted considerable interest due to numerous technological applications such as the formation of self-assembled monolayers and as a chemical sensor. Here, we report on the interaction of sulfur with Au(1 1 1) at two different temperatures (300 K and 420 K) studied by real-time scanning tunnelling microscopy, low energy electron diffraction and Auger electron spectroscopy. In the low coverage regime (<0.1 ML), S adsorption lifts the herringbone reconstruction of the clean Au(1 1 1) surface indicating a lateral expansion of the surface layer. An ordered (√3 × √3)R30° sulfur adlayer develops as the coverage reaches ∼0.3 ML. At higher S coverages (>0.3 ML) gold surface atoms are removed from regular terrace sites and incorporated into a growing gold sulfide phase. At 300 K this process leads to the formation of a rough pit and mound surface morphology. This gold sulfide exhibits short-range order and an incommensurate, long-range ordered AuS phase develops upon annealing at 450-525 K. In contrast, formation of an ordered AuS phase via rapid step-retraction rather than etch pit formation is observed during S-interaction with Au(1 1 1) surfaces at 420 K. Our results shed new light on the S-Au(1 1 1) interaction.     

Surface structure and phase transition of Ge(1 1 1)-3 × 3-Pb studied by reflection high-energy positron diffraction

We studied the structures and the phase transition of Pb/Ge(1 1 1) surface by using the reflection high-energy positron diffraction. The surface structures at 60 K and 293 K have the 3 × 3 and √3 × √3 periodicities, respectively. The rocking curves measured at both temperatures are nearly the same. This indicates that the equilibrium positions of the surface atoms do not change according to the phase transition. From the analysis of the rocking curve based on the dynamical diffraction theory, we found that at both temperatures the surface structures are composed of the so-called one-up and two-down model. The 3 × 3-√3 × √3 phase transition for the Pb/Ge(1 1 1) surface is interpreted in terms of order-disorder transition.     

The adsorption geometry of sulphur on Ir{1 0 0}: A quantitative LEED study

A quantitative low energy electron diffraction (LEED) analysis has been performed for the p(2 × 2)-S and c(2 × 2)-S surface structures formed by exposing the (1 × 1) phase of Ir{1 0 0} to H₂S at 750 K. S is found to adsorb on the fourfold hollow sites in both structures leading to Pendry R-factor values of 0.17 for the p(2 × 2)-S and 0.16 for the c(2 × 2)-S structures. The distances between S and the nearest and next-nearest Ir atoms were found to be similar in both structures: 2.36 ± 0.01 Å and 3.33 ± 0.01 Å, respectively. The buckling in the second substrate layer is consistent with other structural studies for S adsorption on fcc{1 0 0} transition metal surfaces: 0.09 Å for p(2 × 2)-S and 0.02 Å for c(2 × 2)-S structures. The (1 × 5) reconstruction, which is the most stable phase for clean Ir{1 0 0}, is completely lifted and a c(2 × 2)-S overlayer is formed after exposure to H₂S at 300 K followed by annealing to 520 K. CO temperature-programmed desorption (TPD) experiments indicate that the major factor in the poisoning of Ir by S is site blocking.     

The dense α-√3 × √3Pb/Si(1 1 1) phase: A comprehensive STM and SPA-LEED study of ordering, phase transitions and interactions

The T-θ phase diagram for the system Pb/Si(1 1 1) was determined in the coverage range 6/5 ML < θ < 4/3 ML from complementary STM and SPA-LEED experiments. This coverage is within the range where a “Devil’s Staircase” (DS) has been realized. The numerous DS phases answer conflicting information in the Pb/Si(1 1 1) literature and update the previously published phase diagram. The measurements reveal the thermal stability of the different linear DS phases with the transition temperature found to be a function of phase period. Because of additional complexity in the experimental system (i.e. two-dimensionality and 3-fold symmetry) the linear DS phases transform at higher temperature into commensurate phases of 3-fold symmetry HIC (historically named “hexagonal incommensurate phase”). Different types of HIC phases have been discovered differing in the size of the supercell built out of √3 × √3 domains separated by domain walls of the √7 × √3 phase. The detailed structures of these HIC phases (coverage, binding site, twist angle, etc.) have been deduced from the comparison of STM images and diffraction patterns. After heating the system to even higher temperature the HIC phase transforms into the disordered phase. For sufficiently high coverage a SIC (“striped incommensurate phase” which is also built from √3 × √3 domains but meandering √7 × √3 domain walls) is observed which also disorders at high temperatures.     

Surface phase transition and electronic structure of c(5√2 × √2)R45°-Pb/Cu(1 0 0)

The c(5√2 × √2)R45°-Pb/Cu(1 0 0) surface phase is investigated by means of angle resolved ultraviolet photoemission and low energy electron diffraction in the temperature range between 300 and 550 K. We identify and characterize a temperature-induced surface phase transition at 440 K from the room temperature c(5√2 × √2) R45° phase to a (√2 × √2)R45° structure with split superstructure spots. The phase transition is fully reversible and takes place before the two-dimensional melting of the structure at 520 K. The electronic structure of the split (√2 × √2)R45° phase is characterized by a metallic free-electron like surface band. This surface band is backfolded with c(5√2 × √2)R45° periodicity phase at room temperature, giving rise to a surface band gap at the Fermi energy. We propose that a gain in electronic energy explains in part the stability of the c(5√2 × √2)R45° phase.     

Sulfidation of a Cu submonolayer at the Au(1 1 1)/electrolyte interface - An in situ STM study

We describe the electrochemical preparation of an ultrathin copper sulfide film on Au(1 1 1) and its structural characterization by in situ STM. The first step, underpotential deposition of a Cu submonolayer from CuSO₄/H₂SO₄ solution, is followed by two electrolyte exchanges for (i) Cu-free (blank) H₂SO₄ solution and (ii) NaOH/Na₂S solution. The well-known (√3 × √3)R30° structure of the upd Cu layer is stable in the blank electrolyte for at least 2 h. After exposure to bisulfide, the Cu layer contracts and forms two-dimensional islands of two distinct ordered surface phases, i.e. a rectangular and, at higher potentials, a hexagonal phase, with Cu-free Au(1 1 1) regions between them, the latter exhibiting the characteristic (√3 × √3)R30°-S adlayer structure. Potential changes lead to a complex phase behaviour including HS⁻ ? S_x oxidation/reduction and, at strongly anodic potentials, dissolution of the Cu adlayer.     

Composition and structure of chemically prepared GaAs(1 1 1)A and (1 1 1)B surfaces

The (1 1 1)A and (1 1 1)B surfaces of GaAs chemically treated in HCl-isopropanol solution (HCl-iPA) and annealed in vacuum were studied by means of X-ray photoelectron spectroscopy (XPS), low-energy electron diffraction (LEED) and electron energy loss spectroscopy (EELS). To avoid uncontrolled contamination, chemical treatment and sample transfer into UHV were performed under pure nitrogen atmosphere. The HCl-iPA treatment removes gallium and arsenic oxides, with about 0.5-3 ML of elemental arsenic being left on the surface, depending on the crystallographic orientation. With the increase of the annealing temperature, a sequence of reconstructions were identified by LEED: (1 × 1) and (2 × 2) on the (1 1 1)A surface and (1 × 1), (2 × 2), (1 × 1), (3 × 3), (√19 × √19) on the (1 1 1)B surface. These sequences of reconstructions correspond to the decrease of surface As concentration. The structural properties of chemically prepared GaAs(1 1 1) surfaces were found to be similar to those obtained by decapping of As-capped epitaxial layers.     

A structural parallel between Ge- and Si-induced 4 × 4 and 3 × 3 reconstructions on SiC(0 0 0 1) drawn from comparative RHEED oscillations

The initial Ge growth stages on a (√3 × √3)R30°-reconstructed SiC(0 0 0 1) surface (√3) have been studied using a complete set of surface techniques such as reflection high energy electron diffraction (RHEED), low energy electron diffraction (LEED), atomic force microscopy (AFM) and photoemission and compared with similar Si surface enrichments in place of Ge. The investigations essentially focus on the wetting growth-regimes that are favoured by the use of the √3 surface as a starting substrate, this surface being the closest to a smooth and ideally truncated Si-terminated face of hexagonal SiC(0 0 0 1). Depending on temperature and Ge or Si coverages, varying surface organizations are obtained. They range from unorganized layer by layer growths to relaxed Ge(1 1 1) or Si(1 1 1) island growths, through intermediate attempts of coherent and strained Ge or Si surface layers, characterized by 4 × 4 and 3 × 3 surface reconstructions, respectively. RHEED intensity oscillation recordings, as a function of Ge or Si deposited amounts, have been particularly helpful to pinpoint the limited (by the high lattice mismatch) existence domains of these interesting coherent phases, either in terms of formation temperature or surface coverages. Prominently comparable data for these two Ge- and Si-related reconstructions allow us to propose an atomic model for the still unexplained Ge-4 × 4 one. It is based on a same local organization in trimer and ad-atom units for the Ge excess as admitted for the Si-excess of the 3 × 3 surface, the higher strain nevertheless favouring arrangements, for the Ge-units, in 4 × 4 arrays instead of 3 × 3 Si ones. Admitting such models, 1.25 and 1.44 monolayers of Ge and Si, should, respectively, be able to lie coherently on SiC, with respective lattice mismatches near 30% and 25%. The experimental RHEED-oscillations values are compatible with such theoretical ones. Moreover, these RHEED coverage determinations (for layer completion, for instance) inform us in turn about the initial Si richness of the starting √3 reconstruction and help us to discriminate between earlier contradictory atomic models proposed in the literature.     

Scanning tunneling microscopy study on a BC3 covered NbB2(0 0 0 1) surface

We have investigated a BC₃ covered NbB₂(0 0 0 1) surface using scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and low energy electron diffraction (LEED). The STM images reveal characteristic features of a Moiré pattern reflecting an incommensurate relation of the BC₃ sheet with the substrate: bright protrusions with the periodicity of the substrate lattice are modulated in intensity with the periodicity of the BC₃ lattice. As a result, the surface exhibits nm-scale patchy regions with either the √3 × √3 or the 1 × 1 structure of the substrate. The two-dimensional Fourier transformation pattern of the STM image is consistent with the LEED pattern proving the epitaxial and incommensurate relationship between BC₃ surface sheet and substrate. No feature of a predicted superconducting gap was found in STS spectra measured at 5 K.     

Mixed water/OH structures on Pd(1 1 1)

Chemisorbed O and water react on Pd(1 1 1) at low temperatures to form a mixed OH/H₂O layer with a (√3 × √3)R30° registry. Reaction requires at least two water molecules to each O before the (2 × 2)O islands are consumed, the most stable OH/water structure being a (OH + H₂O) layer containing 0.67 ML of oxygen, formed by the reaction 3H₂O + O → 2(H₂O + OH). This structure is stabilised compared to pure water structures, decomposing at 190 K as OH recombines and water desorbs. The (√3 × √3)R30° − (OH + H₂O) phase cannot be formed by O/H reaction and is distinct from the (√3 × √3)R30° structure formed by O/H coadsorption below 200 K. Mixed OH/water structures do not react with coadsorbed H below 190 K on Pd(1 1 1), preventing this phase catalyzing the low temperature H₂/O₂ reaction which only occurs at higher temperatures.     

STM study of Bi-on-Cu(1 0 0)

Scanning tunneling microscopy (STM) has been used to study the various possible structures of adsorbed Bi on the Cu(1 0 0) surface, after equilibration at a temperature of 520 K. All of the structures previously identified by X-ray diffraction (lattice gas, c(2 × 2), c(9√2 × √2)R45°, and p(10 × 10), in order of increasing Bi-coverage) were found to be present on a single sample produced by diffusing Bi onto the Cu(1 0 0) surface from a 3-d source. By investigating the possible coexistence of various pairs of phases, it was demonstrated that the c(2 × 2) phase transforms to the c(9√2 × √2)R45° phase by a first order transition, whereas the transition from c(9√2 × √2)R45° to p(10 × 10) is continuous. In addition, the structure of surface steps was studied as a function of Bi-coverage. The results showed that the presence of Bi changes the nature of the step-step interactions at the Cu(1 0 0) surface from repulsive to attractive. The attractive step-step interactions transform any small deviations from the nominal (1 0 0) orientation of the Cu substrate into (3 1 0) microfacets. When compared with the known equilibrium crystal shape (ECS) of Bi-saturated Cu, the observed microfaceting may imply that the ECS of Cu-Bi alloys is temperature dependent.     

Influence of the surface-termination of hexagonal SiC(0 0 0 1) on the temperature dependences of Ge growth modes and desorption

With the aim of comparing initial Ge adsorption and desorption modes on different surface terminations of 4H-SiC(0 0 0 1) faces, 3 × 3, √3×√3R30° (R3) and 6√3×6√3R30° (6R3) reconstructions, of decreasing Si surface richness, have been prepared by standard surface preparation procedures. They are controlled by reflection high energy electron diffraction (RHEED), low energy electron diffraction and photoemission. One monolayer of Ge has been deposited similarly at room temperature on each of these three surfaces, followed by the same set of isochronal heatings at increasing temperatures up to complete Ge desorption. At each step of heating, the structural and chemical status of the Ge ad-layer has been probed. Marked differences between the Si- (3 × 3 and R3) and C-rich (6R3) terminations have been obtained. Ge wetting layers are only obtained up to 400 °C on 3 × 3 and R3 surfaces in the form of a 4 × 4 reconstruction. The wetting is more complete on the R3 surface, whose atomic structure is the closest to an ideally Si-terminated 1 × 1 SiC surface. At higher temperatures, the wetting layer stage transiets in Ge polycrystallites followed by the unexpected appearance on the 3 × 3 surface of a more ordered Si island structure. It denotes a Si clustering of the initial Si 3 × 3 excess, induced by the presence of Ge. A phase separation mechanism between Si and Ge prevails therefore over alloying by Ge supply onto a such Si-terminated 3 × 3 surface. Conversely, no wetting is obtained on the 6R3 surface and island formation of exclusively pure Ge takes place already at low temperature. These islands exhibit a better epitaxial relationship characterized by Ge(1 1 1)//SiC(0 0 0 1) and Ge〈1 1 −2〉//SiC〈1 −1 0 0〉, ascertained by a clear RHEED spot pattern. The absence of any Ge-C bond signature in the X-ray photoelectron spectroscopy Ge core lines indicates a dominant island nucleation on heterogeneous regions of the surface denuded by the 6R3 graphite pavings. Owing to the used annealing cycles, the deposited Ge amount desorbs on the three surfaces at differentiated temperatures ranging from 950 to 1200 °C. These differences probably reflect the varying morphologies formed at lower temperature on the different surfaces. Considering all these results, the use of imperfect 6R3 surfaces appears to be suited to promote the formation of pure and coherent Ge islands on SiC.     

Comparative investigation of the c(2 × 2)-Si/Cu(0 1 1) and (√3 × √3)R30°-Cu2Si/Cu(1 1 1) surface alloys using DFT

The electronic structure of the c(2 × 2)-Si/Cu(0 1 1) surface alloy has been investigated and compared to the structures seen in the three phases of the (√3 × √3)R30°Cu₂Si/Cu(1 1 1) system, using LCAO-DFT. The weighted surface energy increase between the alloyed Cu(0 1 1) and Cu(1 1 1) surfaces is 126.7 meV/Si atom. This increase in energy for the (0 1 1) system when compared to the (1 1 1) system is assigned to the transition from a hexagonal to a rectangular local bonding environment for the Si ion cores, with the hexagonal environment being energetically more favorable. The Si 3s state is shown to interact covalently with the Cu 4s and 4p states whereas the Si 3p state, and to a lesser extent the Si 3d state, forms a mixture of covalent and metallic bonds with the Cu states. The Cu 4s and 4p states are shown to be altered by approximately the same amount by both the removal of Cu ion cores and the inclusion of Si ion cores during the alloying of the Cu(0 1 1) surface. However, the Cu 3d states in the surface and second layers of the alloy are shown to be more significantly altered during the alloying process by the removal of Cu ion cores from the surface layer rather than by the addition of Si ion cores. This is compared to the behavior of the Cu 3d states in the surface and second layers of the each phase of the (√3 × √3)R30°-Cu₂Si/Cu(1 1 1) alloy and consequently the loss of Cu-Cu periodicity during alloying of the Cu(0 1 1) surface is conjectured as the driving force for changes to the Cu 3d states. The accompanying changes to the Cu 4s and 4p states in both the c(2 × 2)-Si/Cu(0 1 1) and (√3 × √3)R30°-Cu₂Si/Cu(1 1 1) alloys are quantified and compared. The study concludes with a brief quantitative study of changes in the bond order of the Cu-Cu bonds during alloying of both Cu(0 1 1) and Cu(1 1 1) surfaces.     

Structure and electronic properties of gold adsorbed on Ti(0 0 0 1)

The Au/Ti(0 0 0 1) adsorption system was studied by low energy electron diffraction (LEED) and photoemission spectroscopy with synchrotron radiation after step-wise Au evaporation onto the Ti(0 0 0 1) surface. For adsorption of Au at 300 K, no additional superstructures were observed and the (1 × 1) pattern of the clean surface simply became diffuse. Annealing of gold layers more than 1 ML thick resulted in the formation of an ordered Au-Ti surface alloy. Depending on the temperature and annealing time, three surface reconstructions were observed by LEED: (√3 × √3) R30°, (2 × 2) and a one-dimensional incommensurate (√3 × √3) rectangular pattern. The Au 4f core level and valence band photoemission spectra provided evidence of a strong chemical interaction between gold and titanium. The data indicated formation of an intermetallic interface and associated valence orbital hybridization, together with diffusion of gold into the bulk. Au core-level shifts were found to be dependent on the surface alloy stoichiometry.     

Observation of a (√3 × √3)-R30° reconstruction on GaN(0 0 0 1) by RHEED and LEED

A new reconstruction of √3 × √3-R30° has been observed on a GaN film grown on a 6H-SiC (0 0 0 1)-√3 × √3 surface using RHEED and LEED experimental techniques. The experimental LEED PF shows that the GaN film is Ga-terminated hexagonal. The surface is a mixture of two structures with a single bilayer height difference between them. One is a √3 × √3-R30° reconstruction with Ga-adatoms occupying the T4 sites. Another is a Ga-terminated 1 × 1 with no extra Ga on top. The area ratio of the √3 × √3 part to the 1 × 1 part is slightly larger than 1. The first principle total energy calculations and Tensor-LEED I-V curves simulations further confirm this structure model.     

Electron and lattice structure of ultra thin Ag films on Si(1 1 1) and Si(0 0 1)

We studied the low temperature (T ? 130 K) growth of Ag on Si(0 0 1) and Si(1 1 1) flat surfaces prepared by Si homo epitaxy with the aim to achieve thin metallic films. The band structure and morphology of the Ag overlayers have been investigated by means of XPS, UPS, LEED, STM and STS. Surprisingly a (√3 × √3)R30° LEED structure for Ag films has been observed after deposition of 2-6 ML Ag onto a Si(1 1 1)(√3 × √3)R30°Ag surface at low temperatures. XPS investigations showed that these films are solid, and UPS measurements indicate that they are metallic. However, after closer STM studies we found that these films consists of sharp Ag islands and (√3 × √3)R30°Ag flat terraces in between. On Si(0 0 1) the low-temperature deposition yields an epitaxial growth of Ag on clean Si(0 0 1)-2 × 1 with a twinned Ag(1 1 1) structure at coverage’s as low as 10 ML. Furthermore the conductivity of few monolayer Ag films on Si(1 0 0) surfaces has been studied as a function of temperature (40-300 K).     

Structural investigation of the c(√2 × 5√2)R45° surface alloy formed by Ti deposition on Cu(0 0 1)

The alloying process of Ti deposited on Cu(0 0 1) was studied by means of XPS, LEIS, XPD and LEED intensity analysis. With the sample held at 570 K, a linear decrease of the Cu LEIS signal as a function of the amount of Ti deposited is observed in the early stages of deposition until a constant value is reached. At the onset of the plateau a c(√2 × 5√2)R45° LEED pattern starts to be visible. XPD and LEED intensity measurements were performed for the c(√2 × 5√2)R45° phase prepared depositing ca. 1.5 monolayer of Ti. The angle-scanned XPD curves measured for the phase c(√2 × 5√2)R45° reveal that Ti atoms substitute Cu atoms in the fcc lattice of the substrate. The polar XPD curves show that at least the first four layers of the substrate are involved in the alloying process. We found that the (3 1 0) plane of the Cu₄Ti alloy (D1_a type-structure) fits, without significant contraction or expansion of the lattice parameters, the c(√2 × 5√2)R45° structure. The intensity versus energy curves of the diffracted beams were calculated on the basis of this structural model using the tensor LEED method. The results of the LEED intensity analysis provide a further evidence of the formation of a slab of Cu₄Ti(3 1 0) layers.