The dominance of surfaces and interfaces: A view to magnetoconductance and structure in low-dimensional crystalline films



For ultra-thin films, electronic transport properties at surfaces and interfaces are dominated by electronic scattering at the interfaces. Therefore, as our example with Pb on Si(557) shows, d.c. transport is sensitive to confinement, to growth modes, and to (electronic) surface roughness. During the growth of Pb on Si(557) up to more than 10 monolayers, we found classical and quantum size effects, a pronounced conductance anisotropy and conductance oscillations directly related to the anisotropic layer-by-layer growth mode of the Pb film on this regularly stepped surface. In fact, it turned out that the interface anisotropy, which extends up to the seventh layer in conductance, is kept as a memory effect even for thick (isotropic) layers. By adding a magnetic field, details of the scattering mechanism at impurities and defects are revealed, since elastic, inelastic, spin–orbit scattering contributions can be separated.

Strong changes of scattering properties are evident when going from the multilayers to the monolayer, as demonstrated again for the system Pb on Si(557). Contrary to multilayers, spin–orbit scattering dominates for the monolayer, presumably due to the symmetry reduction at the surface and the appearance of spin-split bands split by the Rashba effect. Also the anomaly in spin–orbit scattering close to monolayer completion, coupled with quasi one-dimensional d.c. conductance, can be ascribed to the Rashba effect. The intriguing interplay between bulk and surface conductance with large Rashba split states at the surface is exemplified by a study of multilayer growth of Bi on Si(111). By magnetoconductance we were able to separate bulk from surface contributions. Scattering between strongly spin-polarized Rashba-split states spin can be effectively suppressed, so that only the “classical” magnetoconductance effect remains, as observed in this system.

1 Introduction

Surface and interfaces are not only limiting matter in space or confining electrons, they also break symmetry. This has important consequences for the electronic properties at the interface, e.g., the appearance of spin-split states on centro-symmetric bulk material, known as the Rashba effect 1, 2. Rashba splitting, on the other hand, will directly modify electronic transport, even without magnetic field, since elastic Umklapp scattering between spin-split states in general also requires spin Umklapp.

Concentrating on the confining properties of an interface, electronic systems in cystalline metallic thin films, and in particular in monolayers, seem to be realizations of highly correlated low dimensional electron gases 3–8. Here the formation of chemical bonds between the film and an insulating substrate has two main consequences:

Firstly, accommodation of crystal lattices between film and substrate including the step morphology of the substrate is required, which determines strain relief and growth modes of the film and thus the film morphology. Electronic transport is directly sensitive to these properties. As an example, the formation of quantum well states (QWS), as identified in spectroscopy for Pb layers on Si(111), directly modifies growth by stabilizing certain layer thicknesses – e.g., by formation of islands with “magic” heights – and is also measurable in conductance 9–14. The lattice mismatch in this system of about 9% results first in growth of an amorphous film at low temperatures. This film, however, changes the growth mode to crystalline growth above four monolayers 15. Oscillations of conductance with increasing film thickness have been found only in the crystalline growth regime. They were explained in terms of classical size effects (CSE). Precisely speaking, this variation is due to the varying effective roughness of the vacuum interface during growth, resulting in a varying fraction of specularly reflected electrons during electronic transport measurements from the surface during growth. At the same time, this is a clear indication for layer-by-layer growth 11, 12. Within the Fuchs–Sondheimer model, this surface effect is described by a specularity parameter 16, 17, which is based on the Boltzmann transport equation. For ultrathin films, the discrete energy-level spectrum becomes relevant even at room temperature, and this approach breaks down.

As a second example, both surface and interface effects have also been extensively studied for Bi thin films 18–21. In the bulk, this material exhibits a semimetallic band structure with an extremely long Fermi wavelength (λF ≈ 30 nm) and with high carrier mobilities. Thus quantum size effects, e.g., the predicted semimetal-to-semiconductor transition, become accessible 19. Surface states, e.g., of the (111)-oriented surface, lead to a strongly enhanced electron concentration at EF compared to the bulk. As a consequence, transport properties in epitaxially grown Bi films on Si(111) are dominated by the surface states 22, 23, which turn out to be strongly spin polarized 24. Therefore, this system is an interesting candidate for carrying out magnetotransport measurements, a method that has been rarely applied to thin films so far 25, 26. Since these films are never free of defects, defect scattering of conduction electrons leads to weak localization. Indeed, weak localization effects were found first in Bi films 27. For thin Bi films, even weak antilocalization (WAL) was seen and correlated with the prevailing strong spin–orbit coupling (SOC) in Bi. However, in bulk Bi WAL is not expected because of inversion symmetry. Hence, the WAL effect was attributed to the scattering of bulk electrons at the interface 28, 29. An interesting question arises now for transport along the surface. Electrons originating from spin-polarized states cannot be backscattered easily because spin Umklapp is required. For Bi(111), indeed, strongly reduced backscattering was found by analyzing the standing wave patterns with a scanning tunneling microscope (STM) 30. Therefore, weak localization (or anti-localization) for electronic transport in the surface states is strongly reduced and should become important particularly in the limit of very long elastic mean-free-paths.

Ultra-thin films will behave as low-dimensional electronic systems, in particular, if their electronic states contributing to electronic transport are located within the bulk band gaps of the surrounding material (or vacuum on one side). This opens the possibility to investigate purely two- or even one-dimensional transport behavior. Quasi one-dimensional band structures have indeed been found in strongly anisotropic monolayer systems 31–33. Varying the layer thickness, the transition to three dimensions can be studied. These systems also allow a direct correlation of transport with the structure of the film 34. These films, however, should not be considered as isolated sheets. Chemical bonds are formed at the interface between film and semiconductor, and the topmost occupied electronic states mix with the surface states of the substrate, forming combined interface states. These new states may still be positioned within the Si bandgap so that these states as well as low-lying excitations are electronically decoupled from the Si substrate 35.

Here we present a short overview about many of these aspects by briefly reviewing the correlation between structure and electronic transport, both with and without magnetic field for two systems, Pb on Si(557) and Bi films on Si(111). In both systems, there is a large mismatch between the crystal structures of the adsorbed film and the substrate. Whereas for the Pb/Si(557) system this leads to an intriguing composition of new surface states and new growth modes on the stepped Si surface compared with growth on Si(111), the mismatch allows an effective decoupling of Bi films for thicker layers on the flat surface.

2 Experimental

The sample preparation has been carried out in a UHV chamber operating at a base pressure of 1 × 10−9 Pa. After careful outgassing of the low-doped Si(111) and (557) samples, final heating cycles up to 1100 °C have been performed by electron beam heating from the rear of the sample until the Si(557) surface showed a clear LEED pattern of the alternating arrangement of (111) and (112) facets with 7 × 7 and 2 × 1 reconstructions, respectively, with the characteristic 17-fold splitting of the spots normal to the step direction. Pb and Bi were evaporated out of ceramic crucibles and the coverage was detected by a quartz microbalance. For Pb, exact Pb coverage has been calibrated using the spot splitting of the domain wall phase formed by equation image order on the terraces with equation image domain walls, also known from Pb/Si(111) 36, 37. The Bi coverage was calibrated by the equation image phase on Si(111) 38 and by recording oscillations in conductance with a monolayer period during the evaporation of Bi at 10 K on annealed Bi films. The Pb layers were either prepared at the given surface temperature, or, for the second part described below, the Pb layers were annealed to 640 K in order to remove the original 7 × 7 Si structure of the clean terraces and to allow for reordering of the step structure. Further details for the Pb/Si(557) system can be found in Ref. 36. The Bi layers were grown at 200 K, followed by annealing at 400 K. For further details, see also Refs. 39, 40.

The sample was mounted on a shielded cryostat so that it could be cooled down to about 4 K by equation image. The low temperature regime up to 300 K was measured by a diode within the cryostat bath, whereas higher temperatures were measured pyrometrically direct on the sample. Both temperature regimes were calibrated in advance using Ni/NiCr thermocouples on dummy samples. In addition, a power calibration versus steady-state temperatures was carried out. Eight electrical contacts were made by a mask technique, evaporating Ti onto the Si surfaces with subsequent reaction at 500° in vacuum, so that TiS2 was formed. The samples had machined slit in order to avoid crosstalk between contacts. For further details, see Ref. 42. For magnetotransport measurements, the prepared Pb and Bi films were transferred in situ into a split-coil magnet (±4 T).

3 Results and discussion

3.1 Substrate-induced growth and conductance anisotropy: Pb/Si(557)

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.

Figure 1.

(online color at: (a) LEED image of the clean Si(557) surface. The rows with 16 spots between integer order spots reflect the periodicity normal to the steps. The (7 × 7) structure on the (111)-terraces appears as streaks. A structural model is shown at the bottom. (b) LEED image after adsorption of 6 ML of Pb with isotropic intensity distribution.

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

Angular resolved photoemission experiments on crystalline multilayers of Pb 9 allow the determination of the Fermi velocity, averaged over all subbands to be equation image. Together with the elastic scattering time, equation image determined from magnetoconductance in similar layers 26, an elastic electron mean free path, λ ≈ 5 nm, is obtained. This means that equation image holds up to a layer thickness, d, of least 10 ML, i.e., conductance is dominated by interface scattering in the thickness range investigated here.

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: 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.

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, equation image, 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 equation image, 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 equation image, 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 equation image 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: 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.

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.

3.2 Impurity scattering in ultrathin films: Effects from Rashba splitting

While d.c. transport is already structurally sensitive, the addition of a magnetic field allows the determination of details of the scattering mechanism at imperfections and impurities. We continue to discuss the same system as above, but extend our discussion to the monolayer range on Pb layers annealed at temperatures close to desorption. Under these conditions, the underlying (7 × 7) structure on the (111)-oriented terraces is destroyed, and, depending on Pb coverage, the surface re-facets. In presence of close to one physical monolayer of Pb (1.30–1.5 ML with respect to the Si surface density) the (223)-facet is the stable orientation (The deviation from the (557) orientation is compensated by a few non-periodic steps in the opposite direction.) 36. In this range of concentration a rich phase diagram with metal-to-insulator phase transitions has been found 35, 36, 42, 48. As a peculiarity, 1D metallic conductance appears close to 1.31 ML coverage and at temperatures below 78 K. This phenomenon was ascribed to the electronically stabilized formation of (223) facets, which at this coverage leads to complete band filling in 1D, opening of a gap and Fermi nesting 35. The 1D band gap is gradually reduced with increasing coverage and disappears at 1.5 ML Pb concentration 48. Therefore, this system will be an interesting playground for studies of magnetotransport. While the insulating phases are caused by strong localization, weak localization is expected for conducting phases, for which mobile carriers may also be generated by thermal activation. Here we concentrate on weak localization (WL) of the mobile charge carriers.

Scattering of electrons in transport experiments can be either elastic with a characteristic average time between two scattering events, τ0, inelastic (τi), or it may be due to spin–orbit scattering (τso). WL is influenced by these scattering times in a characteristic way. In case that the elastic scattering rate 1/τ0 is higher than the inelastic rate 1/τi, interference effects between electrons contribute to the total resistance. Although in general the phases of adjacent trajectories are uncorrelated, the condition of backscattering is still well defined, and partial waves elastically backscattered along various scattering paths can interfere constructively, giving rise to WL. An externally applied magnetic field can lift this constructive interference, resulting in negative magnetoresistance 49. In case that spin–orbit scattering is large or even dominant, i.e., τso is of the same order as τ0, the 4π invariance of the spin-wave function can change the constructive interference into a destructive interference, and a positive magnetoresistance will be observed 49.

Both situations are realized in the Pb/Si(557) system, as shown in Fig. 4. Here we compare a multilayer at 6 ML thickness with a layer slightly above one physical monolayer (1.6 ML with respect to Si, this calibration will be used throughout this section). At temperatures far above the transition temperature to superconductivity we find WL for all multilayers independent of thickness, as expected for a non-magnetic material that has no spin-split bands in the bulk. In contrast, the monolayer reveals WAL behavior, which must be caused by Rashba splitting due to the reduced symmetry in the monolayer. Also the relative magnitude of magnetoresistance effects changes from 10−4 to 10−5 in multilayer to typically 10−2 in 2D systems, i.e., by two orders of magnitude.

Figure 4.

(online color at: Magnetoconductivity ΔL of Pb/Si(557) for different film thicknesses along the equation image direction perpendicular to the steps. The conductance at zero magnetic field was 5 and 1 mS for the 6 and 1.6 ML film, respectively.

3.2.1 Monolayer anomaly in Pb/Si(557)

We now concentrate on the physical monolayer on the surface annealed at high temperature, which is governed by WAL. For the 1.5 ML coverage, the anisotropy in d.c. conductance without magnetic field equation image, equation image is also reflected in magnetoconductance, as shown in Fig. 5a. As also shown there, these data can be well described by the Hikami theory 50, which describes electron scattering in terms of the scattering times defined above, neglecting Coulomb scattering. The anisotropy is also reflected in the elastic scattering times (equation image, equation image). Taking the Fermi velocity, vF, in equation image direction of 5 × 105 m/s from spectroscopy 35, the average elastic mean-free path equation image is 2.5 nm, in reasonable agreement with the average step spacing of 1.9 nm for (557)-oriented surface. These values turn out to be independent of Pb concentration in the range 1.2–1.5 ML. Although surface faceting change to a preference of (112) orientations at 1.2 ML coverage. Only the variance of data is higher in the direction normal to the steps, i.e., it is sensitive to the perfectness of step ordering. The inelastic scattering times were found to be around equation image, again independent of Pb coverage.

Figure 5.

(online color at: (a) Magnetoconductance at 40 K measured for 1.5 ML of Pb on Si(557) along (□) and perpendicular (○) to the step direction. (b) Same measurement for 1.3 ML at T = 50 K. Solid lines are fits with the Hikami theory (see text).

Contrary to the elastic and inelastic scattering, the anomaly in d.c. transport at 1.3 ML below 78 K is also reflected in the spin–orbit scattering time, but only in the direction parallel to the steps. As a consequence, a special signature is seen in magnetotransport, shown in Fig. 5b at this Pb concentration. While in perpendicular direction WAL is seen, similar to the situation at 1.5 ML, the magnetoconductance is reversed for the parallel direction. From the Hikami analysis we derive a spin–orbit scattering time, which is larger by 3 orders of magnitude around the Pb concentration of 1.3 ML than outside this coverage range. τso resulting from our fits for both directions are plotted in Fig. 6.

Figure 6.

(online color at: Pb/Si(557): Spin–orbit scattering times, τso, as derived from fits with the Hikami theory 50 of magnetoconductance data parallel (triangles) and perpendicular (circles) to the step direction as a function of Pb coverage.

An explanation seems to be possible with the assumption that, as obvious from strong spin–orbit scattering in these layers, that the electronic band structure close to the Fermi level shows Rashba-split bands.

As shown in Ref. 35, the nested Fermi surface at 1.3 ML consists of characteristic points that are separated in momentum space by equation image, with d as the step separation. It results in complete band filling in the direction normal to the steps and opening of a band gap in this direction. In other words, a one-dimensional Peierls transition takes place at 78 K with insulating properties normal, but metallic properties along the Pb-covered terraces. In the direction parallel to the steps, there are two series of Fermi points from split bands, possibly induced also by spin–orbit coupling. One forms a fundamental gap of approximately 20 meV. Therefore, its contribution to conductance is strongly suppressed also at a temperature of 50 K compared to the second band that is mainly responsible for the observed 1D conductivity. If these bands are spin polarized, it is obvious that scattering of electrons close to the Fermi level from equation image to equation image does not allow spin Umklapp. As a result spin–orbit scattering is strongly reduced under these conditions.

3.3 Surface state conductance in ultra-thin Bi films

As already mentioned in Section 1, spin polarization plays an important role on the surfaces of Bi films as well. As we will show, the intriguing interplay between bulk and surface properties in this system can be well studied in magnetotransport measurements by varying the layer thickness and by adsorption of other material. For this purpose we grew annealed Bi films on Si(111) at room temperature. After growth of a 3 to 4 bi-layers (BL) with preferential (110)-orientation, thicker films grow in (111)-orientation, as checked with LEED 51, and in agreement with Ref. 39, but this change of orientation turned out not to be crucial for the results presented here.

A relative magnetoconductance curve is shown exemplarily in Fig. 7 for a 7 BL thick Bi film. The contributions to this curve can be separated into surface and bulk contributions, as tested by quantitative fits to the curve, systematic variations of film thickness and by adsorption of other metals (see below for Pb). The tip at low magnetic fields can be characterized by weak anti-localization (WAL), in agreement with previous investigations of bulk Bi 27–29. In contrast, the broad “background” with opposite curvature can be quantitatively described by the classical magnetoresistance, assuming a two-carrier model 52.

Figure 7.

(online color at: Relative magnetoconductance G(B)/G(0) of a 7 BL thick Bi film. The changes in conductance in the regime of low and high magnetic fields are attributed to conductance, Gs, of the surface states [dashed-dotted (blue) line] and of bulk states, Gb [dashed (green) line]. For better visibility, both contributions are slightly shifted.

The clearest evidence for the separation in bulk and surface contributions comes from two experiments. The first is the variation of the various contributions as a function of layer thickness (see Fig. 8). Varying the film thickness, the absolute height of the peak in the magnetoconductance curves at low fields remains unchanged. The slopes of the shoulders of the magnetoconductance curves, however, increase gradually in the regime of high magnetic fields with increasing film thickness. Since the slope is strongly influenced by the mobility of the carriers, the scattering of electrons within the surface states is reduced. This is compatible with our LEED investigations, which show that the fraction of (111)-textured grains increases, i.e., the rotational disorder decreases with increasing Bi film thickness.

Figure 8.

(online color at: Magnetoconductance curves obtained for 5 (a) and 22 BL (c) films at a surface temperature of 10 K. The dip visible for a 22 BL film has the same magnitude as at 5 BL. (b) Magnetoconductance after adsorption of 0.5 ML Pb on the 5-BL film. The dash-dotted lines represent the contributions of surface magnetoconductance.

The second, even clearer evidence comes from an adsorption experiment with half a monolayer of Pb on a 5 BL thick Bi film. The magnetoresistance after adsorption is shown in Fig. 8b. The magnitude of the tip at low magnetic field remains essentially unchanged, as expected for a bulk property. On the other hand, the MR effect at magnetic fields above 1 T, assigned to the surface, has almost vanished, or even reversed slope, i.e., it shows signs of WAL. This effect in MR is much more drastic than the change in total d.c. conductance, which is reduced by Pb adsorption only by 20%.

This general scenario is corroborated by a quantitative analysis of the curves indicated in Figs. 7 and 8 using the standard theory for magnetoresistance 52 and the theory by Hikami et al. 50 for the analysis of WL and WAL. From a fit of both contributions we found that for the surface conductance both electrons and holes contribute to conductance at a ratio close to one, independent of layer thickness, but the mobility of electrons, µn, is higher by typically a factor 4 ± 1 than for holes, µp. The presence of both types of carriers is consistent with angle-resolved photoemission spectroscopy (ARPES) measurements, revealing electron pockets at the Γ point and hole lobes along the Γ–M direction 24. The mobility of both carriers, and thus the conductance, increases as a function of layer thickness, reflecting the increasing crystalline quality of the layers. In all cases, µn (µn ≈ 0.1 m2/Vs at 22 BL) and µp are much lower than in macroscopic bulk samples, resulting in conductance values Gs between 0.5 and 1.7 mS.

From the central peak of magnetoconductance we derived elastic, inelastic and spin–orbit scattering times and the absolute value, Gb. The elastic and spin orbit scattering times were found to be both of the order of a few times 10−14 s, corroborating the dominance of WAL for the bulk contribution. The bulk conductance turned out to contribute to the total conductance only between 10−2 and 10−3. This means that the bulk conductivity in these thin layers is typically by a factor of 1000 lower than in macroscopic bulk material, most likely due to the quantum size effect seen very pronounced in photoemission experiments 24.

In agreement with this assignment is the measured temperature dependence of conductance, shown in Fig. 9 for a 15 BL thick film. Below 60 K the temperature dependence is dominated by the metallic surface conductance, which is reduced by phonon scattering that increases as a function of temperature. For higher temperatures, activated transport due to inter-subband transitions in the bulk dominates. Thus the carrier concentration increases from 4 × 1012 cm−2 at 10 K, as determined by own Hall measurements in these layers (not shown) to ≈1013 cm−2 at room temperature, if the carrier concentration is calculated as an effective surface density. Thus these values correlate well with those obtained in an independent d.c. conductance measurement carried out at room temperature 22.

Figure 9.

Conductance of a 15 BL Bi film as a function of temperature. At T = 60 K, activated transport from bulk states sets in. The inset shows a magnification of the low-temperature regime.

It remains to explain why the surface contribution to magnetoconductance does not exhibit weak anti-localization, as expected in systems with spin–orbit split bands. This expectation, however, cannot hold in low-dimensional Rashba-split bands. Here backscattering of electrons close to the Fermi level always requires spin Umklapp. This process, as our results show, is very unlikely in the Bi films investigated here, so that the WAL effect is completely suppressed and only the standard magnetoresistance can be observed.

4 Conclusions

As we have shown, electronic transport at surfaces in ultra-thin layers is a very sensitive and versatile tool for the characterization of mono- and multilayers, ranging from the characterization of growth modes, interface roughness and crystallinity of layers to details of electronic scattering processes and sensitive tests of the electronic band structure close to the Fermi level. It thus complements in a unique manner spectroscopic data as obtained, e.g., by angular resolved photoemission experiments, as well as structural information. Especially in transitions between strong and weak localization, as, e.g., found in the monolayers of Pb on Si(557) and their structural implications 42, 48, d.c. transport proves to be the most sensitive to the typical instabilities of low-dimensional systems.


The support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

Biographical Information

After receiving his physics diploma Herbert Pfnür started his research career at the TU München where he completed his PhD in 1982. For the following two years he was a postdoctoral fellow at IBM in San Jose, California. Since 1990 he is a professor at the Leibniz University in Hannover, Germany. His research activities include, among others, electronic transport in ultra-thin films and one-dimensional structures, fabrication of nanostructures, plasmons in low-dimensional structures as well as molecular electronics.

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