spectroscopy

Applied Surface Science 256 (2009) 469–474

Contents lists available at ScienceDirect

Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc

Observation of the screened potential and the Friedel oscillation by low-temperature scanning tunneling microscopy/spectroscopy Masanori Ono 1, Takahiro Nishio 1, Toshu An 2, Toyoaki Eguchi, Yukio Hasegawa * The Institute for Solid State Physics, the University of Tokyo, 5-1-5, Kashiwa-no-ha, Kashiwa, Japan

A R T I C L E I N F O

A B S T R A C T

Article history: Available online 16 July 2009

Using low-temperature scanning tunneling microscopy/spectroscopy we have developed a method for measuring electrostatic potential in high spatial and energy resolutions, and performed a real-space observation of the potential screened by two-dimensional surface electrons around step edges, where extra charges are localized, on the Si(1 1 1)H3  H3-Ag surface. In the potential images, characteristic decay and the Friedel oscillation were clearly observed around the charges. ß 2009 Elsevier B.V. All rights reserved.

Keywords: Scanning tunneling microscopy Scanning tunneling spectroscopy Screening The Friedel oscillation Electron standing waves Two-dimensional electron system

1. Introduction Characterization of atomic structure and electronic states of materials is one of the fundamental issues for understanding their various physical/chemical properties and developing materials having new functionalities. Among the many techniques developed for the material characterization, scanning tunneling microscopy (STM) [1] has established its unique status as a powerful tool for elucidating nano-scale topography, atomic structure and electronic states of materials’ surfaces. Since its invention, STM has extended its versatility, and now it can be operated at low temperatures (LT) below 10 K. Because of the following merits; high energy resolution in tunneling spectroscopy (STS) [2], high stability, and accessibility to low-temperature sciences, LT-STM has been widely utilized for revealing nano-scale phenomena on materials’ surfaces. Here, we review our recent work using LT-STM/S, in particular, using a method called two-dimensional tunneling spectroscopy (2DTS). In this method, a tunneling spectrum (the tunneling current (I) measured during a sweep of the sample bias voltage (Vs)) is taken at each site during the twodimensional scanning over the sample surface. Since differential tunneling conductance (dI/dV) is a good measure of the density of states (DOS) of the probed surface area just below the tip [3],

the resulting three-dimensional data set provides systematic information on DOS near the Fermi energy (EF) over the sample surface. Images visualizing the spatial distribution of DOS at various energy levels can also be extracted from the 2DTS data. Using 2DTS we succeeded in observation of the screening effect and the resulting Friedel oscillation [4]. From the 2DTS data, we obtained a mapping showing spatial distribution of the electrostatic potential from an energy level of surface electronic states on the Si(1 1 1)H3  H3-Ag surface, which is known to have twodimensional (2D) metallic surface states [5]. The observed potential showed a peculiar decaying and oscillatory profile near step edges, where extra charges are presumably localized. Based on a theoretical analysis, we found that the observed potential is well explained with the Coulomb potential screened by the 2D metallic electrons existing on the surface. We also observed an oscillatory potential profile whose period is the half Fermi wavelength of the 2D electron system, which is consistent with that of the Friedel oscillation. The area where the Friedel oscillation was observed is <50 nm from the step edges and the potential variation is in sub-10 meV range, demonstrating high spatial and energy resolutions of this potential measurement method. 2. Instrumentation

* Corresponding author. E-mail address: [email protected] (Y. Hasegawa). 1 Present address: RIKEN, Wako, 351-0198, Japan. 2 Also at: PRESTO, Japan Science and Technology Agency, Japan. 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.07.023

In this work we employed a LT-STM system made by Unisoku (USM-1300), which cools the tip and sample with liquid He down to 2 K. It is operated under UHV conditions whose base pressures are less than 6  109 Pa at RT. The sample and tip can be

M. Ono et al. / Applied Surface Science 256 (2009) 469–474

470

exchanged through a load-lock chamber without breaking the UHV condition. The STM tips used in these experiments are prepared by electro-chemical etching from a W wire. After loaded into the UHV chamber the tips were degassed and characterized in situ by field ion microscope (FIM). The FIM is also used for removing oxide layers on the tip apex by field evaporation, which we believe very crucial for reproducible and reliable tunneling spectroscopy. 3. Screened potential When a charge is situated in a metal, the Coulomb potential induced by the charge is modified by redistribution of the electron density around the charge in the metal. The phenomenon, called screening, is one of the fundamental one in metals. Because of the screening effect, the original long-range Coulomb potential is modified into the short-range Yukawa potential, which has an exponential decaying function. In fact, the Yukawa potential is a result under the Thomas–Fermi approximation, which assumes small spatial variation in the resulting electrostatic potential. Under more precise approximation proposed by Lindhard, which assumes that the induced charge density is proportional to the total potential f, the screened potential oscillates spatially with a wavelength of the half Fermi wavelength of the metal. The oscillation is called the Friedel oscillation [4]. In this section, we briefly explain how to calculate the spatial variation of the screened potential based on the Lindhard’s linear response theory [6–8]. According to the Lindhard approach, the electric susceptibility x(q) or a response function, which describes how the total electrical potential varies with the induced charges with a wavevector of q, is given in the following formula for freely behaving electrons in metals; X f ðEk Þ  f ðEkþq Þ xðqÞ ¼ ; Ekþq  Ek k

is given as a function shown in Fig. 1(b). From the response function x(q), a dielectric function e(q), which is a response of the resulting potential to the external potential, is calculated in the following formula:

 h 2 k þ E0 ; 2m

(3)

Using this we can calculate the screened electrostatic potential for 2DEG. Dielectric function e(q) of 2DEG is obtained from the Lindhard formula and (3). At T = 0, it is 8 q > > q  2kF ; 1 þ TF ; > > q 8 < " #1=2 9   2 = (4) eðqÞ ¼ q < 2kF > > ; q > 2kF ; 1 þ TF 1  1  > > ; q : q : qTF ¼

m e 2 ¼ ; 2pe0 eb aB

(5)

where kF: the Fermi wavenumber of 2DEG; qTF: the Thomas–Fermi screening wavenumber; m*: effective mass of electron in 2DEG; aB:effective Bohr radius. The Fourier transform of the screened potential VSCR(q) is then given using e(q) by V SCR ðqÞ ¼

v2D ðqÞ ; eðqÞ

(6)

where V2D(q) is the two-dimensional Fourier transform of the Coulomb potential given by

v2D ðqÞ ¼

e2 : 2e0 eb q

(7)

(1)

By performing two-dimensional inverse Fourier transformation of VSCR(q), the screened potential f(r) is obtained;

(2)

fðrÞ ¼

2

Ek ¼

e2 xðqÞ: 2eq

eðqÞ ¼ 1 þ

where Ek is an energy of an electronic state with a wavevector k in the electronic system, f(E) is the Fermi distribution function, m* is electron effective mass and E0 is the lowest energy of the electronic state. The response function x depends on the dimension of the electron system. For instance, response functions of 1D, 2D and 3D electron gas are shown in Fig. 1. All functions including the one for 3D electrons have a singularity at q = 2kF; the derivative of x with respect to q diverges there and becomes infinite for 3D electron system. Actually, this singularity causes the oscillation with a wavelength of p/kF (=half Fermi wavelength) in the resulting potential. This is the Friedel oscillation. In the present case, what is observed is the screened potential on a surface having 2DEG. The response function of the 2D system

Z

1 2

ð2pÞ

1

eiqr V SCR ðqÞ dq:

(8)

0

In the cylindrical coordinates the integral can be calculated as following: 1

Z 2p

Z

1

eiqr cos u V SCR ðqÞ dq 4p2Z 0 0 1 1 ¼ qV SCR ðqÞJ0 ðqrÞ dq; 2p 0

fðrÞ ¼

du

(9)

where J0 is the zeroth-order Bessel function satisfying Z 2p 0

eiqr cos u du ¼ 2pJ 0 ðqrÞ:

(10)

We can then calculate the screened potential by numerically integrating Eq. (9).

Fig. 1. Response function x(q) for (a) 1D, (b) 2D and (c) 3D electron gas system. Each function has an inflection point at 2kF, where kF is the Fermi wave number of the electron system.

M. Ono et al. / Applied Surface Science 256 (2009) 469–474

471

Fig. 2. STM images obtained at 5 K with Vs = 1.0 V. The coverage of Ag is (a) 1 ML, (b) <1 ML, and (c) >1 ML. The size of the images is 50 nm  50 nm. The samples (a) and (b) were annealed at 600 8C and (c) was annealed at 500 8C after more than 1 ML Ag depositions.

4. Si(1 1 1)H3 T H3-Ag surface As a sample surface having 2DEG, we used Si(1 1 1)H3  H3-Ag surface [5], which can be formed by depositing 1 monolayer (ML) Ag on the clean Si(1 1 1) 7  7 surface and annealing around 500– 600 8C. It has metallic surface states even at low temperature (4 K) whose energy dispersion is parabolic and isotropic to all surface directions, as will be discussed later. The electrons in the surface states thus behave as 2DEG. The electronic states of the H3  H3-Ag surface have been studied by angle-resolved photoemission spectroscopy (ARPES) [9,10]. Three surface states are found in a band gap of the Si substrate. A surface state named S1 has an isotropic and parabolic dispersion, forming 2DEG on the surface. Electron standing wave (ESW) patterns [11,12], which are characteristic to the freeelectron-like electrons, are observed by STM [13]. In addition to the 2D metallic state, two surface states labeled S2 and S3 are also observed around 1.0 eV below the Fermi level at the G¯ point. Photoemission studies performed so far revealed that the energy level of the surface states depend on sample preparations [9,10], and it has been believed that the dependence is related with the amount of excess Ag atoms on the H3  H3-Ag surface. Nakajima et al. [10] reported that additional small amount of Ag deposition (0.01 ML) on the surface shifts the energy level of the surface states to increase their binding energies. The spectrum shift was explained with electron doping to the S1 state from the Ag adsorbates. Using the 2DTS method, we also observed the shift of the surface states, as demonstrated in Figs. 2–4.

STM images taken on various Ag coverages on the Si(1 1 1)H3  H3-Ag surface, whose amount was adjusted with the post-annealing temperature, are shown in Fig. 2 The Ag coverages for (a), (b), and (c) are 1 ML, <1 ML and >1 ML, respectively. When the Ag amount is 1 ML (a), the whole surface is covered with the H3  H3-Ag structure. A few Ag adsorbates are found in the image, but its density is much less than the image taken on a surface with >1 ML Ag (c). When the amount of Ag is less than 1 ML, a stripe pattern is observed (upper part of (b)). This is a semiconducting 3  1 Ag structure, which has less density of Ag atoms (1/3 ML). In dI/dV images, presenting spatial distribution of DOS, the ESW pattern induced by the S1 state is observed. Fig. 3(b) shows the interference pattern taken on a Si(1 1 1)-H3  H3-Ag surface whose Ag amount is less than 1 ML [14]. The wave number of the S1 state can be obtained through a fast Fourier transformed (FFT) pattern of the dI/dV images, as shown in (c). A circular pattern in (c) indicates that the S1 state has an isotropic dispersion in the surface-parallel directions. The intensity of the circle is, however, not isotropic. The reason for the uneven intensity is because this ESW pattern was mostly induced by steps, which has preferential crystallographic orientations. Six spots found in (c) are due to the H3  H3 structure of the surface. A cross-sectional pattern of a pile of the FFT images taken at various voltages is shown in (d). It shows the energy dispersion relation of the surface states. The energy dispersion curve has a minimum at a G¯ point with the binding energy of approximately 0.07 V above the Fermi energy. The curve is fitted well with a parabolic function in a range of 0.4 eV from the

Fig. 3. (a) STM image on the H3  H3-Ag surface (Vs = 0.8 V, 30 nm  30 nm, T = 5 K). (b) Tunneling conductance (dI/dV) image extracted from 2DTS data set taken on the same area. (c) FFT pattern of (b). Six spots are due to the periodicity of the H3  H3-Ag structure. (d) Dispersion relation obtained from the FFT patterns of the 2DTS data. The dotted line in (d) indicates EF. These images are taken from [14].

472

M. Ono et al. / Applied Surface Science 256 (2009) 469–474

Fig. 5. Schematic principle of potential measurement.

Fig. 4. Dispersion curves of the S1 state taken from 2DTS data sets on samples with two different Ag coverages. The Ag coverage for (a) is less than 1 ML like the case of Fig. 5(b), and the coverage for (b) is slightly higher than 1 ML like Fig. 5(a). The dotted lines indicate EF. Vertical lines at both sides in (b) correspond to the H3  H3-Ag periodicity in the reciprocal space (k// = 0.95 nm1).

bottom. From the fitting the effective mass m* was estimated as 0.11me, where me is a mass of the free electron. The fact that the minimum level of the S1 state is above the Fermi energy indicates that the surface is semiconducting. The binding energy of the states varies with samples and the preparation conditions; we measured the energy dispersion relation on the H3  H3-Ag surfaces whose Ag coverage is <1 ML and >1 ML (see Fig. 4), and found that the measured energy levels are obviously different. When the Ag coverage is <1 ML the binding energy is above EF and the surface is semiconducting, whereas it is located below EF and the surface is metallic on the >1 ML surface. In the energy range above 0.4 eV from the bottom energy, the energy dispersion curve does not follow the parabolic function and shows a straight dispersion. 5. Potential variation around step edges on the Si(1 1 1)H3 T H3-Ag surface We measured the electrostatic potential profile on the Si(1 1 1)H3  H3-Ag surface using the 2DTS method [15]. The principle of the measurement method is schematically illustrated in Fig. 5. When the electrostatic potential spatially changes on the surface, the energy level of the surface states also changes following the potential variation. By measuring the energy level of one of the states, spatial distribution of the potential can be measured and imaged. We measured the energy level of surface states of the Si(1 1 1)H3  H3-Ag surface using 2DTS and obtained a potential profile around a step edge. Fig. 6(a) shows an STM image taken on the Si(1 1 1)H3  H3-Ag surface with an island structure, and (b) is a zoomed image taken near a step edge in the white box drawn in the image of (a). We performed 2DTS in the area, and Fig. 6(c) shows a series of normalized dI/dV spectra taken at positions marked by the arrows in the STM image (Fig. 6(b)). There are two distinctive peaks in the spectra. The peak around 0.85 V, which is attributed to the S2/S3 ¯ states, and the peaks around 0.5 V, which are the S2 state at M point. The position of the peaks shifts to the higher binding energy (lower sample bias voltage) side as the measured site approaches

to the step edge although the entire surface is covered with the H3  H3-Ag structure except the very vicinity of the step edge. Fig. 6(d) shows color-coded tunneling spectra (dI/dV) taken in the same area. It shows that the energy levels of the two peaks shift to higher binding energy side in the same manner as approaching to the step edge. Since this is the exactly same case as that shown in Fig. 5, the observed shift is indeed due to the potential variation presumably induced by the extra charges located on the step edge. The energy-level shift of surface states could be caused by other factors, for instance, by surface strain, as demonstrated by Rastei et al. [16]. In the case of the strain-induced shift, however, the amount and direction of the shifts depend on the characteristics of each state [17]. In our case, since all states moves in the same manner, we believe the shift is really induced by the potential variation. The potential profile obviously exhibits potential shift near the step edge. A cross-sectional plot of the potential, which was obtained from a peak position in Fig. 6(d), is presented in Fig. 6(f) with black dots, together with the topographic profile. In addition to the reduced potential the profile also shows a weak oscillatory structure near the step edge. In order to make the oscillation clear we made a potential image from the energy level shift of the S2/S3 states as shown in Fig. 7(b). In Fig. 7, three images taken on the same area: (a) STM image, (b) the potential image, and (c) LDOS image at EF (dI/dV at Vs = 0 V), are presented. In the LDOS image (c), ESW is clearly visible. In the potential images (See just outside of the island.), oscillatory features can also be seen with the almost same periodicity as the ESW patterns in the LDOS image. Since ESW at EF has the periodicity of the half Fermi wavelength of the 2DEG, the potential also oscillates with the periodicity of the half Fermi wavelength. This suggests us that the oscillatory feature in the potential profile is related with the 2DEG on the surface, and probably due to the Friedel oscillation. In order to confirm that the observed oscillation is really the Friedel oscillation resulting from the screening, we calculated the screened potential following the procedure discussed in Section 3. The calculated potential profile is shown in Fig. 6(e) with the solid line. For the calculation, we needed to know kF of the 2DEG (S1 state) and obtained it by fitting a profile of the ESW with its function, 1  J0(2kFr + f) (Fig. 7(d)), where J0 is the zeroth-order Bessel function. The Fermi wavelength (2p/kF) of the 2DEG measures 14 nm (kF = 0.45 nm1). The calculated potential shows excellent correlation with the measured one including the oscillatory features. The only parameter we adjusted for the fitting is a scaling parameter of the potential profile, which is proportional to the charge density at the step edges. From the fitting we estimated the linear charge density at the step edge as

M. Ono et al. / Applied Surface Science 256 (2009) 469–474

473

Fig. 6. (a) Filled state STM image of the H3  H3-Ag surface. (b) Zoomed image taken in the white box of (a). (c) Tunneling spectra taken at the sites pointed by arrows in (b). (d) Color-coded dI/dV spectra arranged from terrace to the step edge. (e) Cross-sectional plots of the surface-state peak energy shift, which corresponds to the potential, and topography along the direction perpendicular to the step edge. The black dots and blue line-dots are experimental data. The peak energy shift or the potential was fitted by a calculated screened Coulomb potential, which is shown with a red line. The hatched area indicates the area where the H3  H3-Ag structure is not formed around the step edge. These images are taken from [14] and [15]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

0.55 electrons/nm. The fitting result clearly demonstrates that the measured potential profile and the oscillatory feature are indeed due to the screened potential and the Friedel oscillation. It should be emphasized here that the observed Friedel oscillation is obviously different from ESW. The standing waves are often referred to as energy-resolved Friedel oscillation or simply the Friedel oscillation. They are the modulated LDOS, formed by scattering and interference in 2DEG whereas the

genuine Friedel oscillation [4] is a spatial modulation in a total charge density or electrostatic potential caused by the screening. To date, various reports have been published on the observation of the Friedel oscillation in STM. All of them are actually observations of ESW in the precise definition. We thus believe that our study is the first real-space visualization of the Friedel oscillation. As indicated with arrows in Fig. 7(d), the peak positions of the potential oscillation are slightly shifted from those of the ESW,

474

M. Ono et al. / Applied Surface Science 256 (2009) 469–474

Fig. 7. (a) Same STM topographic image as Fig. 6(a). (b) Potential distribution in the same area as (a). Cold color indicates low potential. (c) dI/dV image at EF or Vs = 0 V on the same area. (d) Cross-sectional profiles of the DOS (standing waves) and the potential (Friedel oscillation) taken in the red square area of (a). Both of the experimental data are averaged along the step direction. The arrows indicate the peak positions. These images are taken from [14] and [15]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

clearly demonstrating the difference between the two waves. In fact, after the observation of ESW [11,12], various related phenomena, such as the surface-state-mediated adatom–adatom or adatom–step interactions, were discussed in terms of the LDOS modulation since their characteristic distances seem to be related to the half Fermi wavelength. Obviously, the modulated electrostatic potential affects the interactions and thus should be considered in their analyses. We believe that investigation of the surface potential and its real-space imaging are therefore quite important to understand these nano-scale and atomistic phenomena on the surfaces. Acknowledgements We appreciate devoted help given by former and present members involved in these projects, Masayuki Hamada, Shiro Yamazaki, Qing Li, Atsushi Nomura, Kosuke Miyachi. This work is partly supported by a Grant-in-Aid for Scientific Research (Nos. 17360018 and 19310065) from the Ministry of Education, Science, Sports, and Culture of Japan.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

G. Binning, H. Rohrer, Ch. Gerber, W. Weibel, Phys. Rev. Lett. 49 (1982) 57. R.J. Hamers, R.M. Tromp, J.E. Demuth, Phys. Rev. Lett. 18 (1986) 1972. J. Tersoff, D.R. Hamann, Phys. Rev. Lett. 50 (1998) 1983. J. Friedel, Nuovo Cimento Suppl. 7 (1958) 287. S. Hasegawa, J. Phys.: Condens. Matter 12 (2000) R463. N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders College, Philadelphia, 1976 . J.H. Davies, The Physics of Low-Dimensional Semiconductors, Cambridge University Press, Cambridge, 1998. T. Ando, A.B. Fowler, F. Stern, Rev. Mod. Phys. 54 (1982) 437. L.S.O. Johansson, E. Landemark, C.J. Karlsson, R.I.G. Uhrberg, Phys. Rev. Lett. 63 (1989) 2092. Y. Nakajima, S. Takeda, T. Nagao, S. Hasegawa, X. Tong, Phys. Rev. B 56 (1997) 6782. Y. Hasegawa, Ph. Abouris, Phys. Rev. Lett. 71 (1993) 1071. M.F. Crommie, C.P. Luts, D.M. Eigler, Nature 363 (1993) 6429. N. Sato, S. Takeda, T. Nagao, S. Hasegawa, Phys. Rev. B 59 (1999) 2035. Y. Hasegawa, M. Ono, Y. Nishigata, T. Nishio, T. Eguchi, J. Phys.: Conf. Series 61 (2007) 399. M. Ono, Y. Nishigata, T. Nishio, T. Eguchi, Y. Hasegawa, Phys. Rev. Lett. 96 (2006) 016801. M.V. Rastei, B. Heinrich, L. Limot, P.A. Ignatiev, V.S. Stepanyuk, P. Bruno, J.P. Bucher, Phys. Rev. Lett. 99 (2007) 246102. D. Sekiba, K. Nakatsuji, Y. Yoshimoto, F. Komori, Phys. Rev. Lett. 94 (2005) 016808.