EFFECT OF THE TIP/SAMPLE-SURFACE ELECTRONIC STATES AND THE ELECTRON-PHONON COUPLING ON THE TUNNELING CURRENT IN STM

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EFFECT OF THE TIP/SAMPLE-SURFACE ELECTRONIC STATES AND THE

ELECTRON-PHONON COUPLING ON THE TUNNELING CURRENT IN STM

M. Tsukada, N. Shima, S. Ohnishi, Y. Chiba

To cite this version:

M. Tsukada, N. Shima, S. Ohnishi, Y. Chiba. EFFECT OF THE TIP/SAMPLE-SURFACE ELECTRONIC STATES AND THE ELECTRON-PHONON COUPLING ON THE TUNNEL- ING CURRENT IN STM. Journal de Physique Colloques, 1987, 48 (C6), pp.C6-91-C6-96.

�10.1051/jphyscol:1987615�. �jpa-00226818�

EFFECT OF THE TIPISAMPLE-SURFACE ELECTRONIC STATES AND THE ELECTRON-PHONON COUPLING O N THE TUNNELING CURRENT IN S T M

M. Tsukada, N. Shirna, S. ~hnishi* and Y. ~hiba*

Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan

*NEC Fundamental Research Laboratories, Miyazaki 4-1-1, Miyarnae-ku, Kawasaki, Japan

R6sum6.-Nous proposons une theorie utilisant le formalisme des fonctions de Green pour le courant tunnel des experiences de STM. Les fonctions d'onde de la pointe et de la surface y sont traitees de maniere analogue.

La decomposition du courant en une s o m e de fonctions de Green de surface multiplihes par le facteur de recouvrrement pointe/surface constitue un outil analytique utile pour Btudier les effects non-lineaires et 5 n-corps.

Des resultats numeriques sont donnes pour le systBme mod8le:pointe de tungstGne/surface de silicium (100). 11s r6vBlent l'effet des Btats Blectroniques microscopiques sur le courant tunnel.

Abstract .-A systematic Green' s function theory of the tunneling current in STM is proposed, in which the wave functions on the tip and the sample surface are treated on equal footing. The decomposition of the tunneling current into the sum over the surface Green's functions multiplied by the tip/surface overlapping factors provides a useful analytical tool for the study of the non-linear and the many body effect.

Some numerical results for the W-tip/Si(100) surface model system are given, which reveal the effect of the microscopic electronic states on the tunneling current.

1. Introduction

In spite of recent rapid development of scanning tunneling microscopy (STM)[1,2], the microscopic mechanism of electron tunneling between the tip and the sample surface is not well understood[3,4]. One of the reasons may be lack of information on the possible structure of the tip in atomic scale. On the other hand, for the quantitative analyses of the STM data, it is crucial to clarify what characteristics of the sample surfaces are actually proved by the STM patterns and how they are influenced by the properties of the tip.

It is expected that the STM is also useful for the spectroscopic measurements of the electronic structure of the surfaces. However, it might be possible that many-body effects, such as electron-phonon coupling or electron correlation effects are essentially involved in the tunneling process. Therefore the tunneling conductance of STM is not necessarily straightforwardly interpreted by means of the local single electron density of state (DOS).

To afford a firm basis for the surface analysis by STM, it is indispensable to elucidate how the tunneling current is determined by the microscopic structure and by the electronic states of the tip/sample- surface system. The effect of the strong electron-lattice coupling on the tunneling conductance should be also clarified. In this paper, we describe some of our recent results concerning on these problems[51.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987615

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2. Relation of the tunneling current and the tip/surface electronic states

Based on the Bardeen's independent electron model of the tunneling process[6], it is straightforward to show that the tunneling current is given by

1=2net(

I I

_-

In the above

are the imaginary part of -the Green's function for the surface (GS,.) and the tip (GT,,) in the LCAO representation. The current matrix element J, is given by

where and @ are atomic orbitals in the tip and the surface, respectively.

Vs(VT) is the potential in the surface (tip) side without the attractive potential in the tip (surface).

Another useful expression of the tunneling current and the tunneling conductance are given by following equations with a suitably chosen point R fixed within the tip,

Configuration of the sample surface and the tip in STM.

Vtotal: the total one-electron potential. Vs: the surface potential, obtained from Vtotal by removing the inner tip potential. VT: the tip potential obtained from Vtotal by removing the inner surface potential.

The tunneling conductance is the total sum of the products of the four factors as shown in Fig. 2. Cvi(R) characterizes the geometrical factors, i.e., overlapping and the matching of the symmetry between the surface and the tip orbitals. On the other hand, GS..(E) bears all the information of the surface electronic states. If thUe variation of GS, within the protrusion in the tip is not so large, AS(R,E,E) is expanded as

where pS(R;E) is the surface local DOS at R, and the tip and

y=?/r.

2(r,rT ;E) is the imaginary part of the Green's function in the real coordinate representation. The prove position R in the tip should be defined as the center of mass of the tip potential weighted by the product of the tip eigen-function and the decay function. The first term of eq.

(2-7) gives essentially the same result as that by Tersoff and Hamann[3].

3. Ef fect of the electron-phonon coupling

By the introduction of the electron-phonon linear coupling, it can be shown that the tunneling current is given by

I =2*&

1 1

and 7~ is the coupling constant divided by the energy of the normal mode frequency %aA. In the limit of the vanishing of the coupling, 7~-0, F ( X ) is just the delta function, and eq. (3-1) reduces to the previous one, eq.

(2-4).

Fig. 2 Schematic representation of the factors composing AS(R,E,E") (eq. (2-5)).

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If the values of lyA12 is much smaller than unify, (3-1) and (3-2) lead the tunneling conductance,

The second term represents the phonon side band. Energy loss or gain by the adsorbate vibration is also described by this term. For the strong coupling case, F(X) takes Gaussian form,

with

Due to the strong coupling with phonons, the energy of thefinal electronic state is always lower than that of the initial state by E. Therefore the occupied (unoccupied) band of the surface is observed at lower (higher) position by E as compared with that by UPS or inverse photoemission. The coarse graining of the order of the energy width o would be also inevitable.

4. Numerical Calculations of tunneling conductance

We have performed preliminary numerical calculations of the tunneling conductance for Si(100) surface scanned by W tip. As for the model of the Si surface, the cluster composed of nine Si atoms is used, in which two atoms are the surface symmetric dimer, four atoms are located in the second layer and the other three are situated in the deeper layer. As the model of the protrusion on the W tip, the tetrahedron cluster of four W atoms is used, an appex atom of which is directly faced on the Si cluster. The W-W distance is chosen as 2.82A.

Electronic states of the clusters are determined by local density approximation (LDA) method with the use of the norm-conserving pseudo- potential method[7]. The wave functions are constructed by the LCAO of Si 3s, 3p and W 5d, 6s, 6p atomic orbitals. The dangling bonds of peripheral

Occupied

states 1 Unoccupied states

Fig. 3 Tunneling conduct- ance dI/dV as the function of the applied voltage V (full line).

Dashed line: UPS or inverse photo- emission spectrum.

geometrical configuration t h a t t h e apex W atom i s located a t 6A above t h e c e n t e r of t h e S i dimer. For t h e sake of g e t t i n g physical idea, only t h e s i n g l e e l e c t r o n i c s t a t e a t E F ( t i p ) i n t h e t i p is used f o r t h e p e r t i n e n t s t a t e o f t h e e l e c t r o n t r a n s f e r . This s t a t e , a s shown i n Fig. 5 ( a ) is mainly composed o f t h e d,p (zlltip, z l S i s u r f a c e ) o r b i t a l o f t h e apex W atom. In Fig. 4, t h e p o l a r i t y o f t h e b i a s corresponds t o t h e e l e c t r o n flow from S i s u r f a c e t o t h e t i p . The d o t t e d l i n e shows t h e DOS of t h e Si(100) s u r f a c e given by our model c l u s t e r . The s h a r p peak A f o r t h e low b i a s region corresponds t o t h e bonding dangling bond f o r t h e s u r f a c e dimer shown i n Fig. 6 ( a ) . The peak B which is a l s o t h e s u r f a c e s t a t e o f a n t i - bonding s t a t e o f t h e s u r f a c e dimer a s shown i n Fig. 6 ( b ) , does n o t c o n t r i b u t e t h e tunneling conductance a t a l l . The tunneling conductance v i a next lower e l e c t r o n i c s t a t e o f t h e W t i p , which i s mainly composed o f dxy-orbitals a s shown i n Fig. 5 ( b ) , is found t o have a d i f f e r e n t spectrum from Fig, 4 b u t becomes smaller by lo-? than t h a t of Fig. 4. The symmetry o f t h e o r b i t a l s both i n t h e t i p accepting t h e e l e c t r o n and i n t h e s u r f a c e s t a t e s c r u c i a l l y i n f l u e n c e s t h e tunneling c u r r e n t .

k 1 4

Bias (Volt)

Fig. 4 Tunneling conductance a s t h e function o f t h e b i a s voltage ( s o l i d l i n e ) together with t h e DOS of t h e Si(100) c l u s t e r .

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Fig. 5 S i n g l e e l e c t r o n charge d e n s i t y f o r t h e W4 c l u s t e r f o r a ) HOMO and b ) t h e next l e v e l below t h e HOMO.

Fig. 6 S i n g l e e l e c t r o n charge d e n s i t y f o r t h e s u r f a c e s t a t e of t h e S i g c l u s t e r f o r a ) peak A and b) peak B i n Fig. 4.

References

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49 (1982157; 50 (1982) 120.

[2] Quate, G.F., Phvsic Todav 39 (1986) 26.

[3] T e r s o f f , J . , and Hamann, D.R., Phys. Rev. B31 (1985) 805.

['I] Lang, N.D., Phvs. Rev. L e t t . , 55 (1985) 230; Phvs. Rev. B34 (1986) 5947.

[5] Tsukada, M., and Shima, N., J. Phys. Soc. Jpn., 56 (1987) i n p r e s s . [6] Bardeen, J., & g ~ R n v . l , 6 (1961) 57

171 Bachelet, G.B., Hamann, D.R., and Schliiter, M, Phvs. Rev. B26 (1982) 4199.