Here we demonstrate the ability of a strongly stepped surface to significantly modify the growth mode compared to a flat surface and study the consequences for d.c. conductance 43. Our example is Pb layers on Si single crystal surfaces. As already mentioned in Section 1, the mode of growth at low temperatures changes from amorphous to layer-by-layer growth at a critical thickness of 4 ML, while at room temperature and above Stranski–Krastanov type of growth was found. Here the question is whether stepped surfaces are able to accommodate better the large misfit between the lattice constants of Si and Pb (9.5%) and how effective steps can be. For this reason, we adsorbed Pb layers on the stepped Si(557) surface at a temperature close to 70 K. A LEED image of the clean surface is shown in Fig. 1a. This surface consists of a periodic sequence of (112)-oriented minifacets containing three steps (with a height of 3.14 Å each) and small (111) terraces, which still show the (7 × 7) structure. Normal to the steps, these result in an effective lattice constant of 5.7 nm, which results in 16 superstructure spots between the integer order spots of the (111) unit cell. A sideview of this structure is shown in the lower part of Fig. 1.
The misfit accommodation between Pb and Si during Pb adsorption turned out to be remarkably effective: Adsorption of only 3 ML resulted in a hexagonal LEED pattern with spot positions corresponding to the bulk Pb unit cell, though with only nanocystalline lateral order and with considerable rotational disorder, but otherwise isotropic intensity distributions. The intensity of the underlying Si structure has completely disappeared, indicating that the Pb layer is closed. This is also corroborated by the d.c. conductivity experiments described below. Increasing the layer thickness to 6 ML reduces the rotational variation of the grains from ±7° to ±4°, but the LEED pattern remains essentially unchanged.
These experiments show that the introduction of a high density of steps into this system leads to clear modifications of the growth mode to layer-by-layer growth starting at the first monolayer. This means that the step structure of the substrate is completely overgrown already by very thin Pb layer, and thus the anisotropy of the original surface is averaged out, leading to a quasi-floating film on the stepped surface.
This picture, however, turns out to be overly simplistic, since LEED strongly weights the contributions from the topmost layer, but is not very sensitive any more to the interface even at layer thicknesses of only three layers. A method that probes both bulk crystallinity and interface properties is electronic transport. This method is, as we will show, significantly more sensitive to the remaining anisotropy in the films, which is clearly visible up to more than six monolayers.
3.1.1 The first few layers: Surface dominated transport
Figure 2 shows the conductance measured during adsorption of Pb at 70 K substrate temperature along (circles) and perpendicular to the steps (diamonds). These curves show little dependence on deposition rate and on temperature in the range between 15 and 100 K surface temperature. Their overall behavior, neglecting for the moment the characteristic oscillations, can be described as follows: In both directions, the onset of conductance is found close to the percolation threshold at 0.5 ML theoretically expected for random adsorption. This excludes cluster formation in this early stage of layer formation.
Figure 2. (online color at: www.pss-a.com) Conductance of Pb layers as a function of coverage on Si(557) parallel (red) and perpendicular (blue) to steps adsorbed at 70 K. The conductance for Pb/Si(111) adsorbed at low temperatures is shown for comparison (from Ref. 41). Inset: Enlarged section of the first few monolayers.
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The conductance normal to the steps, σ⟂, is found to be significantly lower than in parallel direction (σ||) and increases linearly up to 6 ML. Only above 7 ML the increment in conductance as a function of coverage becomes similar leading to parallel curves, as seen in Fig. 2, but the difference, , remains almost constant up to coverages much larger than 10 ML. In other words, there is a clear memory effect due to the anisotropy of the interface that remains visible for quite thick films, as expected from the estimate for λ. A similar memory effect is seen in the data for the Pb layers on Si(111) (see Fig. 2). They exhibit the same slope for Pb layers above 4 ML as on the stepped surfaces for thick layers. This slope therefore, seems to be characteristic for isotropic cystalline layers, which grow ontop of either an amorphous layer as on Si(111) or on an anisotropic interface (on Si(557)).
Considering the difference , a further mechanism is needed that reduces σ⟂ with respect to σ||. It must be directly related to the electronic transmission probabilities of the steps, as directly demonstrated by us in an experiment on a single Pb wire with monolayer height. Here we found an approximately tenfold increase in resistance per unit length when a substrate step was crossed by the wire 44. We therefore conclude that the strong electron scattering in the direction normal to step edges is the reason for the reduced conductance in this direction. The linear dependence of G⟂ on layer thickness indicates that the electronic transmission probability per layer in this direction remains constant up to six layers, but increases quickly for thicker layers.
In parallel direction, the overall conductance dependence on layer thickness is governed by power laws. Whereas up to 5 ML the data are best described by , the exponent is close to 2 for thicker layers. These dependencies are indeed expected from theoretical models of diffuse interface scattering 45–47 of a nearly-free electron gas, taking into account quantum size effects and the effective increase of the density of states with layer thickness. From these models is predicted for thicker layers, whereas the few subbands involved in very thin layers lead to an effective increase of the exponent close to 3 47, in good agreement with our results.
On top of the general increase of conductance as a function of layer thickness, we found characteristic oscillations of conductance. These are well known even for thick layers in systems with a clear layer-by-layer growth mode 11 and are ascribed to the varying roughness during growth, which is minimal when the layer is completed 16, 17, and is the clearest sign of layer-by-layer growth for this system. Looking at these oscillations more quantitatively, it becomes obvious that the non-monotonous amplitudes and half widths as a function of layer thickness, seen in Fig. 3 in σ||, cannot be explained by this “classical” effect. Therefore, also quantum size effects must play an important role. Indeed, the even-odd layer periodicity seen in ab initio calculations of Pb films 45 for formation energy, surface tension etc. is also reflected here in the amplitudes of the conductance oscillations. Within this picture, a new transport channel is opened when a layer starts to be contiguous. Hence the conductance should increase strongly when the percolation threshold of a new layer is reached and should quickly form a new plateau of conductance by further increase in coverage. This is repeated for each layer, but the multiple crossings of subbands with the Fermi level as a function of layer thickness coupled with band relaxations, do not simply increase the density of states. They result even in changes from dominant n to p-type conduction 45 and thus cause non-monotonous behavior, as observed.
Figure 3. (online color at: www.pss-a.com) Conductance data in the low-coverage regime parallel (upper part) and perpendicular to the step direction. The dashed lines mark the background (see text). After subtraction the peaks marked by black lines remain.
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The appearance of the maxima of these oscillations in σ||before completion of the layers, in contrast to the maxima in σ⟂, may be caused by the opening of new conduction channels, as just described. The kinetic effect of sequential filling of terraces and steps, however, which is well known for the Pb monolayer 36, may also produce such a result, if this sequential filling remains effective for the first few layers. Indeed, an initial filling of the (111) terraces with high conductance, followed by adsorption on the (112)-facets with low conductance, would also explain our results, since the areal fraction of the (111) terraces is close to 0.7 (see inset of Fig. 3). This also explains the maximum in σ⟂ exactly at completion of the layers, since it requires complete filling of the (112)-facets.
This discussion demonstrates the sensitivity of d.c. transport measurements both to structural properties of the sample, and to the interfaces. While the vacuum interface can easily be characterized by supplementary methods, this is much more difficult for internal interfaces, and d.c. transport yields valuable supplementary information about the interfacial properties.