PHYSICAL REVIEW B 81, 035313 (2010)

Low-temperature scanning tunneling microscopy and spectroscopy of spatial oscillations in the density of states near domain boundaries at the Ge(111)2×1 surface

D.A. Muzychenko¹, S.V. Savinov¹, V.N. Mantsevich¹, N.S. Maslova¹,V. I. Panov¹

K. Schouteden², C. Van Haesendonck²

¹ Faculty of Physics, Moscow State University, 119991 Moscow, Russia

² Laboratory of Solid-State Physics and Magnetism, BE-3001 Leuven, Belgium

Abstract

We present the results of low-temperature scanning tunneling microscopy and scanning tunneling spectroscopy investigations of the spatial oscillations of the local electron density of states on clean Ge(111)2×1 surfaces. The oscillations appear in the vicinity of the boundaries between domains with different atomic arrangements. We introduce a tight-binding based model, which consistently explains the observed experimental features in terms of the formation of two-dimensional surface states within the surface band gap due to the breaking of the translational symmetry at the domain boundaries.

Introduction

Electronic properties of elemental semiconductor surfaces have attracted a lot of interest due to their crucial importance both for technological applications and for fundamental scientific issues. The Ge(111) surface with 2×1 reconstruction is among the most intensively investigated. Already in the eighties of last century photoemission studies of heavily doped Ge single crystals as well as theoretical calculations revealed the existence of separate occupied and non-occupied bands for the surface electrons.

Until now, there were no direct observations of effects that are connected with the non-occupied surface states band of the Ge(111)2×1 surface. Here, we show that the existence of non-occupied surface states induces the appearance of spatial oscillations in the local density of states (LDOS) of the surface electrons at domain boundaries that appear on the reconstructed Ge(111)2×1 surface.

Experiment and Results

The main goal of our STM investigation at low temperatures was to clarify the details of the Ge(111)2×1 surface electronic structure. Consequently, we intensively used the STS modes of the STM operation. Spectroscopic measurements were performed using harmonic detection by means of lock-in amplification for measuring the spatial variation of the differential conductance dI/dV (closed feedback loop) at selected values of the tunneling bias voltage V. This spatial variation corresponds to a map of the LDOS at energy eV with respect to the Fermi energy. Everywhere in the text the tunneling bias voltage V refers to the sample voltage, while the STM tip is virtually grounded.

Fig. 1. Topographical STM image as well as a selection of spectroscopic LDOS images at different bias voltages of the clean Ge(111)2×1 surface. These images cover a surface area where a DB of type B is present.

The results of our combined STM/STS experiments for the Ge(111)2x1 surface (Fig.1) can be summarized as follows.

· Spatial oscillations of the electron density were observed on the Ge(111)2x1 surface for both n-type (results are not shown here) and p-type bulk conductivity in the vicinity of DBs. The oscillations become visible in LDOS maps as well as in the CITS data.

· Within the experimental error, the wavelengths of the spatial oscillations originating from different type of DBs are the same.

· The spatial oscillations can be better described in terms of a decaying sine wave oscillation superimposed upon a smooth background. The oscillation amplitude exponentially decays with increasing distance from the DB.

· The spatial oscillations can be observed only within the range of bias voltages between 0.23V to 0.85V, where surface states are the only states that are able to carry the tunneling current.

The nature of the effect

Our experimental observations can be consistently interpreted in the framework of a model relying on the presence of Tamm surface states. The basic idea can be described as follows. It is well known that the breaking of the 3D translational symmetry at the surface of a 3D solid induces the appearance of p-orbital derived surface states that are localized within a narrow surface layer. The Tamm states are decaying exponentially into the vacuum, while they reveal an oscillating decay into the bulk. While the presence of a 2D surface on a 3D solid results in the appearance of 2D surface states, a 1D surface defect (a DB in our case) of the 2D surface causes in a similar way the appearance of 1D surface states.

Dispersion of the spatial oscillation of the electron DOS

Fig. 2. (a) - Spatially resolved map of the differential conductance dI/dV(V) along the line aa' contains the three points I to III, which correspond to the position of the three vertical cross-sections that are marked in (a). (b) - 1D Fourier-transform of the dash-dotted rectangle marked in (a) image, which corresponds to the dispersion behavior, energy versus wave vector, of the spatial oscillations of the electron density of states (DOS). The blue, red and green squares with error bars are data points that are directly derived from cross-sections of the oscillation patterns for three different DBs.

Relying on CITS measurements we were able to extract the energy versus wave-vector dispersion relation of the observed spatial LDOS oscillations. In Fig. 2 we present a constant current STM image of a type-B DB at the Ge(111)2×1 surface, recorded simultaneously during the CITS measurements. It is clear that also the CITS measurements directly reflect the presence of the spatial LDOS oscillations around a DB on the Ge(111)2×1 surface. Figure 2(a) presents a 2D visualization of the dI /dV(V) curves calculated from the CITS measurements along the white arrow. By performing a row by row 1D Fourier transform of the data enclosed by the dash-dotted rectangle in Fig. 2(a), the energy versus wave-vector dispersion relation of the spatial LDOS oscillations can be obtained. The result of this Fourier transform is presented in Fig. 2(b). The extra data points blue triangle, red circle, and green square symbols with error bars, which are presented as well in Fig. 2(b), are inferred from LDOS height profiles for three different type-B DBs, similar to the ones presented in Fig. 1. It is clear that there is an excellent agreement with the dispersion derived from the CITS results.

The model

Fig. 3. Calculated quasi-3D map of the LDOS of the surface electrons in the vicinity of a DB. The abscissa corresponds to the distance from the DB, while the ordinate corresponds to the Vt. A few hyperbola-like branches are clearly visible.

To describe the experimental observation quantitatively we have performed analytical calculations in tight binding approximation. Ge(111)2×1 surface has been modeled by linear atomic chains, consisting of two inequivalent atoms 1/2 with energy levels e1/e2 and tunneling matrix elements T(1-2 tunneling) and t(2-1 tunneling). The interaction between atomic chains has been described by tunneling amplitude t, which has the same value for all atoms in the chain. The potential introduced by domain boundary is modeled by hard wall potential W.

The dependence of the LDOS of the surface states on the distance in the direction perpendicular to the domain boundary is given by equation:

Calculation steps:

1. Calculation of the local density of states for single atomic chain.

2. We have used already calculated LDOS for single atomic chain and have introduced the inter-chain interaction t and relaxation g.

3. We have added scattering at domain boundary rotated by certain angle with respect to atomic chain direction.

Conclusion

In conclusion, we presented the results of our combined LT STM/STS study of the spatial oscillations of the LDOS that appear in the vicinity of boundaries between domains with different atomic arrangement on the reconstructed Ge(111)2×1 surface. The period of the spatial oscillations decreases when the tunneling bias voltage increases within a specific voltage range (between 0.23V and 0.85V). The amplitude of the oscillations exponentially decreases with the distance from the domain boundary. A theoretical model was introduced, which explains the observed effects in terms of the formation of 2D Tamm surface states within the surface band gap due to the breaking of the 2D translational symmetry at the surface domain boundaries.