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The electric field under a STM tip apex: implications for adsorbate manipulation
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Surface Science 282 (1993) 400-410 North-HolIand
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The electric field under a STM tip apex: implications for adsorbate manipulation C. Girard ‘, C. Joachim b, C. Chavy b and P. Sautet ’ ” Laboratoire de Physique Maltkulaire, Uniuersite’ de Besump, 25030 Besancon
Cedex, France ” Groupe d’Electronique Molkulaire, CEMES, LOE, 29 rue Jeanne Maruig, BP 4347, 31055 Toulouse Cedex, France ’ Laboratoire de Chimie Theorique, ENS, 45 All;, d’ltalie, 69364 Lyon Cedex 07, France
Received 22 May 1992; accepted for publication 4 November 1992
For a given bias voltage, a self-consistent calculation of the electrostatic poiari~ation of the STM tip apex at tunneling distance to a conducting surface is presented. An effective atomic structure of the tip apex during a scan is constructed by fitting calculated and experimental STM scans on the Au(l10) surface. The local electric field in the tip-sample gap is calculated. This leads to the inductive etectrostatic potential energy gained by a physisorbed atom like xenon when the STM tip apex is approaching this adsorbate. Field induced diffusion processes of this adsorbate are discussed.
1. Introduction The ability of the scanning tunneling microscope @TM) to record both topographic and spectroscopic features of surfaces in real space is now well established [l-3]. More recently, the STM has been used to both locally modify surfaces f4] and manipulate individual atoms and molecules with a sub-nanometer precision [5-101. Thus, the work of Eigler et al. [5] successfully illustrates the potential of the STM for sliding atoms adsorbed on the surface of a conducting substrate. For example, very well resolved images of Xe arrays are obtained if during a scan, the tip-sample distance is sufficiently large for the atoms to remain in their equilibrium sites 151.For a decreasing tip-surface distance, it was proposed that the forces responsible for the sliding of the atoms along the (110) rows of the surface are of the van der Waals type rather than of the electrostatic type [ 111. Moreover, the adsorption energy of Xe on Ni(ll0) is weak and the Xe sliding is performed at low temperature (4.2 K) [5]. In this case and for the experimentally applied tip-substrate tunnel resistance, calculations confirm that the adsorbate in its hollow site can be slided on the surface following the attractive 0039-6028/93/$06.00
van der Waals potential energy depression created by the tip apex [lO,ll]. For more corrugated surface or for chemisorbed adsorbates, the sliding process based on van der Waals forces becomes difficult to control [IO]. In this case, other mechanisms must be used to move an adsorbate with sub-nanometer lateral precision. For example, by applying an appropriate voltage pulse between the sample and the tip, it is possible to concentrate atoms under the tip apex 191,to desorb atoms from the tip apex 1121or from the surface 16,101and even to carve holes of a few nanometers in diameter into the substrate 141. Moreover, such field induced processes do not generally exhibit a precise intensity threshold. This is generally attributed to the difference in the tip apex atomic structure which varies from tip to tip. When moving an adsorbate with intermediate (1 to 2 volt) voltage pulses, these pulses modify the initial adsorption energy by an amount depending on both the muftipblar susceptibilities and the permanent multipolar moments of the adsorbate. Due to the confinement of the electric field under the tip apex as demonstrated in this paper, the diffusion process will happen preferentially in the vicinity of the tip apex. The understanding of the physical mechanisms
0 1993 - Elsevier Science Publishers R.V. All rights reserved
C. Girard et ai. / T?ze ekctricfield
occurring during a voltage pulse is of great interest for the building and studies of sub-nanostructures [lo]. In this paper, it is shown from a self-consistent treatment that the tip apex, responsible for the STM resolution, confines a large amplitude electric field when the tip is at tunneling distance from the surface. Let us insist on the fact that our goal is not to explain the Eigler sliding process invoking the electric field because, as already discussed, it is now known that this sliding occurs via van der Waals interaction [ll]. We want to study, if the electric field under an STM tip apex can also lead to a precise atom by atom manipulation. In section 2, an effective atomic structure of the tip apex during a scan on the reconstructed Au(ll0) surface is proposed to demonstrate, on experimental grounds, that the tip apex cannot be reduced to a jellium sphere. In section 3, the permanent electrostatic polarization of the tip apex is calculated. Furthermore, the electric field and the corresponding fieldgradient in the tip-surface tunneling gap are derived. In section 4, the change in potential energy of an adsorbate under such a field is calculated. Field induced diffusion processes are discussed in conclusion. Most of the predictions of the electric field shape and amplitude in the tunneling gap used so far are based on simple continuous electrostatic models. Only recently, an approach based on the effective charge concept has been introduced [13]. In this approach, the tip apex is an ensemble of metallic spheres of atomic radius. The tip-substrate tunnel junction forms a capacitor and the local electric field is calculated by minimizing its electrostatic energy [13]. In the following, this field is calculated by taking into account the polarization of each atom of the tip apex.
2. The effective atomic structure of a tip apex during a scan There is usually a total incertitude on the precise atomic shape of the tip apex during STM scans which preclude a complete analysis of the electric field under the tip apex. Well characterized tips are usually made by the build-up tech-
under
a STM aper
401
nique [14] or by the deposition technique [15]. In both cases, field ion microscopy provides well resolved images of the atomic structure of the tip apex. For example, starting with an electrochemitally etched tungsten tip, one can build (112) facets ended by a trigonal tip apex consisting of a (111) plan with 1, 3, 7.. . tungsten atoms per layer [14]. The major drawback is that when such a well-fabricated tip approaches the surface at tunneling distance, the tip apex structure is generally modified. This defo~ation is not well understood but noticable since usually some scans are required before atomic resolution is achieved. As noticed by Tsukada et al. in their recent review [Xl, the exact atomic structure of the tip apex is not often taken into account in calculating the tunneling current. For STM image calculations, the Tersoff-Hamann approximation avoids this problem by using only a generic s-orbital [17]. More sophisticated models are now available to take into account the tip atomic structure and to predict surface corrugation [18-201. But in many discussions on manipulations of atoms and molecules by an electric field, the tip apex shape is generally not considered. Furthermore, the tipend is often represented as a metallic sphere of a radius estimated between 10 and 100 nm [10,21]. The atomic protrusion forming the tip apex does not appear on this sphere in these discussions. Therefore, it is important before any calculation of the electric field in the tip-surface gap to show that the tip apex ends with a small cluster of metal atoms. The best way for this purpose is to compare e~e~mental and calculated scans taking into account the tip apex structure. Such a comparison allows us to propose an effective tip apex atomic structure during each scan. As an example of effective apex structure determination, let us consider the Au(ll0) reconstructed surface. Well resolved experimental scans on this surface have been obtained experimentally by Gimzewski et al. using a tungsten tip [22]. Such a surface is appealing because of its atomic protrusions showing (111) and (331) steps. These steps are very useful to optimize the lateral shape of the tip apex. To calculate these scans, it is important to pre-suppose an initial tip structure and to adjust it to reproduce the experimental
402
C. Girard et al. / The electric field under a STM apex
scans. A single atom tip is certainly not enough for such steps. For simpIicity, we have chosen to start with a gold tip apex. In the experiments, the tips were made out of tungsten, but gold tips are sometimes used in STM [23]. This difference is not a problem, since no geometric deformations of the tip apex are considered in our calculations. Moreover, aside from the tungsten d-orbitals which are near the Fermi level, the s-orbitals of the two materials are quite similar. Notice also that the spatial exponential decay of d-orbital tail is generally twice the decay of an s-orbital. Therefore, s-orbitals play the principal role in the tunneling current for the chosen substrate. Only these orbitals are considered in the following to reduce the computing time. But all the valence orbitals can be added if necessary. The extraction of the effective tip structure is presented here only to support the fact that the tip apex in the tunneling regime consists of a sharp protrusion with sub-nanometer dimensions. We have also chosen to fit one scan and not a complete image. The reason is that a direct comparison of the tip shape extracted from an “image-to-image comparison” is not precise enough for a correct fit.
J. Gimzewski provided the experimental scans. The calculated ones were obtained using the STM-ESQC technique already described elsewhere [18]. The extended Huckel molecular orbital theory was used to describe the chemical composition of the tip-substrate tunnel junction [18]. A double c basis set was used to better reproduce the iong distance coupling between the tip and the substrate and to get a good currentdistance characteristic [241. For all the constant current scans presented, the current was fixed to 1.5 nA for a 30 mV bias voltage. Only the relative tip apex-to-surface distance is presented. The absolute tip-Alex-last-atom to surface distance is less than 6 A in average on the flat reconstructed Au(ll0) surface. The tip apex structure chosen for the calculation is a tetragonal tip apex built along a (110) axis. This apex is deposited on an AufllO) surface which is the end of the tip body (fig. 1). This simulates a tip equipped with a sharp apex, four lateral facettes and a flat plane to represent the curvature radius of the tip body. In the extreme case of a flat tip without apex, it is the Au(ll0) surface protrusion which plays the role of the tip
Fig. 1. Representation of tip-substrate atomic structure used to fit the calculated STM image with the experimental one. The Au(ll0) surface is reconstructed with two atomic rows more. This defines a (111) step and a (331) step, on the right and on the left side of the protusion, respectively. The bulk of the substrate is made of a semi-infinite reproduction of the unit cell. The tip is made of four layers of atoms oriented along the (110) direction composed successively of 1, 4, 9 and 16 gold atoms. This apex is deposited on the (110) plane of the tip surface. The bulk of the tip is also made of a semi-infinite reproduction of the unit cell.
C. Girard et al. / The electricfield under a STM apez
apex (fig. 2a). Then, a constant current scan gives the topography of the tip surface instead of the topography of the substrate surface.
,’
,-;
a~
,f,’
:
,’ ,I’ ,’
T 3
A better tip apex can be made with 4 atoms in the same plane on the tip body. This is a flat tip as shown fig. 2b. The resulting simulated scan on
:
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2-
403
*,‘. :
16132
Xi.&
-16:32
(a)
-16:32
16132
a:0
Xl‘&
-16.32
0:o (h)
0.0
16.32
Cd)
-16.32 6.0 1632 (e) (0 Fig. 2. Calculated constant current scans compared with the corresponding experimental data (in dashed line). I = 1.5 nA and V= 30 mV. The tip apex used is presented each calculated scan. The surface and the tip body are the same as in fig. 1. Small circles at the bottom of (a) are the x, z Au atom positions on the surface.
404
C. Girard et al. / The electric field under a STM apex
the A~(1101 surface is presented in fig. 2b. It cannot be compared with the experimental one. For example, on the right of the (111) step and on the left of the (331) step, there is an inverted contrast, This means that the surface protrusion is still too high for the chosen tip apex. It can be reduced to one atom like in many existing theory of STM image calculations but supported here by the surface of the tip body. Again, the resulting scan does not correspond to the experimental one (fig. 2c) because the surface of the tip body is too much coupled to the protrusion on the Au(ll0) surface. To get a better fit, a scan with a 5-atom tip apex arranged in 2 layers is presented in fig. 2d. The best agreement with the experiment is obtained with a small increase in the lateral separation of the 4 atoms of the basal layer. Figs. 2e and 2f present scans using a 3-layers and a 4-layers tip apex, respectively. Some lateral geometric variations on this 3-layer tip apex lead also to a very good reproduction of the experimental scan. The scan with the 4-layer tip apex of the fig. 1 is worse than the one with a 3-layer apex perhaps because the experimental tip was not so sharp or because the electronic structure of the lateral part of tip apex is not well optimized. The step-by-step construction of an effective tip apex to reproduce by calculations an experimental scan shows that the end of a tip body is not flat when imaging a A~(1101 surface with steps. The electric field profile in the tip-surface gap will depend on the atomic structure of this tip apex.
3. The electric field in the tip apex-surface
gap
Let us apply a V, bias voltage between the tip and the substrate of the STM tunnel junction described in fig. 3. In this model, the substrate and the tip body are considered without their atomic structure. The tip body is represented by a sphere of radius “b” with “b” in the 10 to 100 nm range. Only the tip apex is supposed to keep its atomic structure with N atoms structured in 3 layers. As discussed in the previous section, this number of layers have been chosen to get a
Fig. 3. The
tip-substrate
electric field calculations. tip apex terminal
STM
tunnel junction
used for the
R,, = (0, 0, Z,,) is the position of the
atom and h the radius of the metallic sphere surporting
the tip apex.
reasonable lateral tip apex shape for weakly corrugated surfaces. For a large tip-surface distance, the tunneling current intensity passing through the junction is negligible. Then, the electric field E,(r) in the gap is equal to the electric field E,, existing between 2 biased metallic electrodes, a spherical one and a planar one. There is also a small contribution of the tip apex which is weakly polarized by Ea. This polarization creates a small electric field component E,(r) superposed to E, to give E,(r). When the tip is in tunneling distance from the substrate and the atoms of the tip apex are frozen in their equilibrium position, a tunneling current in the nano-ampere range does not perturbe the overall surface charge distribution in the substrate and in the tip sphere. This junction can be discribed as a weakly leaking capacitor. But the E,(r) contribution is enhanced since the E,, amplitude increases when the tip-surface distance is reduced. For a sphere-plane capacitor, the E,, contribution to E,(r) is given in the vicinity of the center of the sphere by the known formula [25]: E,=
5 D,
$(l log@
+u) + Jl+u)
UZ7
(1)
C. Girard et al. / The electric @Id under a STM apex
with u = Do/b and D, the distance between the macroscopic tip edge and the substrate surface. The tip apex does not contribute to eq. (1) since it is too small to be considered without its atomic structure. The E,(r) contribution to E,(r) is calculated from the polarization Z’(r) of the tip apex embedded in the E, field. From this polarization, E,(r) can be written: r, r’) *P(r’) dr’.
Z%(r) = lH,(
(2)
H&r, r’) is the overall electrostatic propagator [261. It gives the E,(r) amplitude at a position r from the polarization at a position r’, both positions taken in the gap. To calculate this propagator, notice that P(r) is a function of the local electric field E(R,) interacting with the ith atom of the apex via the relation:
be written in the standard form: To(r, r’) = [3(r-r’)(r-r’)
=a,
E iS(r-Ri)E(Ri),
- Ir-r’(2Z]r-5, (5)
with Z the identity matrix. S&‘, r) models the electrostatic environment of the tip apex. If ZLis an electric dipole located at a position r in the gap, the electric field E(r’) in r ’ induced by this dipole is given by: E(r’) =&,(r’,
r) *p(r).
(6) To solve eq. (41, it is convenient to use the super-vectors F= (E(R,), E(R,), . . * E(R,)) and 9, = E,(O, 0, 1; 0, 0, 1; . . . >. In this case, eq. (4) can be rewritten F= i&Y,, with M, = [I Z&J-‘. B, is a (3N x 3N) matrix which contains all the informations on the chemical composition and structure of the tip apex. Following eq. (4), this matrix is defined by: Bll(RiT
P(r)
405
Rj)
(3)
i=l
with (Y, the polarizability of the atoms of the apex which are considered to be identical. Note that retarded effects are not taken into account in this approach since the dimension of the junction is very small compared to the main wave length of the Fourier components of the generally used bias voltage pulse. The field E(R,) acting on the ith atom of the apex is a superposition of: the macroscopic field E,, the electric field created by the E, polarization of the other atoms of the apex than the ith one and of the modulation of this polarization by the dielectric environment. This environment is made of the surface and of the tip sphere. Both are polarized by the tip apex. Therefore, E(R,) is the solution of the equation: E(R,)
=E,(Ri)
+ ;
S,(R,,
Rj) X/E(Rj)
j=l
+
5
T,(R,,
Rj)m/E(Rj).
(4)
j#l
T,,(r, r’> is the dipolar propagator through vacuum which gives the electric field inside the tip apex acting on one atom due to the others. It can
where the ZZ&, r’) propagator equal to:
used in eq. (2) is
Z%(r, r’) =&A r, r’) + To(r, r’). (8) Finally, the electric field acting on the ith atom in the tip apex is equal to: E( Ri) = 5 D, lOg(h
2
m
+ \/l+u)
M,(R,,
Rj).
j=l
(9) Using this expression, P(r) is calculated from eq. (3) and E,(r) from eq. (2). With the T,, and S, propagators, the complete E,(r) amplitude in the tunnel junction can be written: Z%(r) =&I + /[%(
r, r’) + Z’,,(r, r’)]P(r’)
dr’. (10)
The E,(r) configuration under the tip apex can be studied for many examples changing the tip apex material, the surface material or the tip
406
C. Girard et al. / The electric field under a STM apex
!O
apex geometry. One example is a (111) oriented copper tip apex interacting with a planar copper surface. S,, and (Y, for copper have been taken from the literature: for (Ye, Teadrout et al. [27] gives 9.2 A’,“. The second rank tensor S, was calculated by one of us elsewhere [28]. Let us recall that contrary to the surface used in section 2, no atomic corrugation has been considered here for the copper surface. This approximation is not valid for highly corrugated surfaces where local charge accumulations may play a role in the tip apex polarization. The tip apex chosen for the calculations has 3 layers of copper atoms, piled up along the (111) axis and supported by a metallic sphere of radius 6 = 20 nm. The electrostatic energy density maps associat$d to I E, I 2 are presented in fig. 4. For a fixed 7 A tip apex-to-surface distance and for V,, = 1 V, I B, I 2 has been calculated for different heights from the surface. A very confined field E, is obtained in the vicinity of the tip apex. Let us insist on the fact that this field takes into account the B, component, (see eq. Cl)), due to the sphere which supports the tip apex. Using a 10 nm sphere radius, one usually gets more than 10 nm lateral extension for this field component. This explaias why it is not visible in fig. 4. In contrast, at 4 A from the apex (fig: 4a), the I E, I ’ half maximum width is only 6 A. Moreover, close to the tip apex terminal atom, the field gradiant is very strong along the z axis. When the tip apex is approaching the copper surface, the field amplitude increases and its lateral extension is reduced.
4. The energy electric field Under molecule)
of an adsorbate
in the tip apex
a STM tip apex, an adsorbate (atom, is polarized by the electric field estab-
Fig. 4. The 1E, 1’ energy Gensity maps for a fixed tip apex-tosurface distance Z, = 7 A. Theomaps are reprtsented at 3 differevt altitudes, (a) for Z = 3 A, (b) for Z = 4 A and (c) for Z = 5 A. To get the corresponding scale in field amplitude, the root of the energy ordinate myst be taken and multiplied byO.l89VA-‘.
C. Girard et al. / The electric field under a STM apex
‘\
3.50
3.00
\
\
\
\
\
1 1.00
zL9
407
lished in the STM tunnel junction [lo]. It results in a change in the electronic energy of the adsorbate which leads to a modification of its adsorption energy. In the semi-classical approach chosen here, all these effects are included in the MC”’ multipolar moments and in the (n)cr(n’) multipolar polarizability of the adsorbate. Moreover, if the number of atoms composing the adsorbate is small and the tip apex maintained at tunneling distances, the polarized adsorbate does not change the polarization state of the tip apex too much. In this approximation, the electrostatic part of the potential energy of the adsorbate can be written as: 1 U(R)=+
n,n’ (2n - 1)!!(2n’-
x
(N&0 l)!!
[n + d]Fg(“)( R)F,(“‘)(R) 1
- F (2n - l)!!
M’“‘[ n]F,(“‘( R) . (11)
F(“)(r) = V(“-r)E&r) are the successive gradients 0; the E (r) field. R is the position of the center of mass’of the adsorbate on the surface. This energy has to be added to the periodic potential energy of the adsorbate on its surface if the surface is considered to be corrugated. An adsorbate with a permanent dipolar moment can also be considered in eq. (11). For an adsorbate with a spherical symmetry, like an atom in its ground state, the two first non-vanishing terms in eq. (11) are the dipolar term: U#( R) = - ~%(‘)[ 21Eg( R) Eg( R) and the quadripolar
term:
U&R) = - &(2h(2)[4]F9(2)( R)F,‘2’( R). L
-90
Fig. 5. Attractive dipolar inductive potential energy UJO, 0, Z) of a xenon atom adsorbed on a copper surface, located under a tungsten tip apex. (- - -_) for V0 = 0.5 V, (- - - - - -1 for V0 = 0.6 V, (. . .) for V0 = 0.7 V and (-T - - -) for V, = O.,S V. The tip to surface distance is Zg= 7 A for (a), Z, = 9 A for (b) and Z, = 12 A for Cc).
(12)
(13)
The polarization of many adsorbates by the tip apex can be studied considering only these two terms and the simplification occurring for isotropic adsorbates. For atoms like Xe in the work of Eigler et al. [6] or for organic molecules like in the work of Foster et al. [S], the local electric field Eg is used to adsorb the adsorbate on the tip apex and to move the attached adsorbate with the tip apex. As an example, let us
408
C. Girctrd et al. / The electric field under a ST34 ape*
Fig. 6. Variation of the quadrupolar inductive energy U&O, 0, Z) of a xenon atom adsorbed on a copper surface and under a tungsten tip apex. Notation are the same as in fig. 5.
consider a Xe atom adsorbed on a copper surface and a tungsten tip. For rare gas atoms, standard values for (Y(I)and a(2) are given in the literature [291. For the tip apex, a (111) pyramid with 3 layers of atoms is used like in section 3. A LY,= 10.5 ii” static poIarizability has been chosen for the tungsten atoms of the tip apex. This apex is supported by a 20 nm metallic sphere. U&R) and U,(R) are calculated from eqs. (12) and (13). For V, < 0.5 V, U,(R) and U,(R) are very small compared to other tip-adsorbate interactions like the van der Waals ones at large tipsubstrate distances or the repulsive ones at short distances ill]. The resulting forces of these inductive terms on the adsorbate point always from
the substrate to the tip. Changing the sign of V,, does not modify the direction of this force since only even terms from eq. (11) have been considered. In Fig. 5, the dipolar contribution U,(O, 0, 21 is presented for different tungsten tip-copper surface distances with 0.5 V < V,, < 0.8 V. Z is the height of the Xe atom above the copper surface. When Xe is close to the tip-apex terminal atom, Uh reaches 180 meV which is comparabte to the 200 meV physisorption energy of a Xe atom on the copper surface 111,301. Therefore, even an intermediate 0.8 V voltage pulse can induce the transfer of a Xe atom on the tip apex. This is valid for a large class of metal surfaces like silver, gold, and nickel, where the Xe adsorption energy is small ( < 200 meV) [30]. Notice also that in first approximation, we do not have to consider the lateral corrugation adsorption energy since this corrugation is one order of magnitude lower 111J than the one calculated here. The quadrupolar inductive term U&R) is also very small compared to the dipolar one of the tip substrate distance chosen as presented in fig. 6. For xenon, this justifies the dipolar approximation which is proposed to explain the operation of the atomic switch reported by Eigler et al. [6]. When the tip apex is kept at a fixed 7 A distance from the surface of the Xe atom, there is also a lateral confinement of this adsorbate due to the E, electric field. The resulting force is
-10
-20
Fig. 7. Lateral variation of the inductive energy induced by the tip apex on a xenonatom adsorbed on a copper surface. The Xe is displaces at constant distance 2 = 3 A along the x direction on the surface keepiag the tip apex posit@ constant. Vr, is the same as in figs. 5 and 6. The tip apex to surface distances are 2, = ‘7 A for (a) and Z,, = IO A for (b).
C. Girard et al. / The electric field under a STM apex
attractive which means, as presented in fig. 7, that an electrostatic trap is created under the tip apex. For V,, = 0.8 V, the deepness of this trap can reach 70 meV which is deeper than a van der Waals trap. For example, for the same 7 A tip apex-surface distance, the deepness of the Xe atom van der Waals trap is less than 20 meV on the copper surface [ll].
Ac~o~~~ents
5. Conclusion
References
409
We like to thank the CNRS program Ultimatech for financial support for one of us and Fujitsu France for computing support during this work. Special thanks go to J. Gimzewski for provinding us with the Au(ll0) experimental scans.
[I] H. Rohrer, in: Scanning Tunneling Microscopy and ReInstead of the standard 10 nm or larger sphere tip apex considered for the understanding of STM electric field tip induced diffusion processes [lO,Zll, the atomic structure at the end of this sphere has been taken into account. This is important in the imaging mode where the atomic resolution relies on a tip apex with a terminal atomic protusion. This is also important in the sub-nanometric manipulation mode since this protusion confines the electric field. This field can serve for adsorbate attachment to the tip apex or for sliding the adsorbate when the tip is moved laterally. When the tip is positioned above an adsorbate, the inductive dipolar and quadrupolar forces due to the tip-to-substrate electric field is attractive. For example, a Xe atom physiosorbed on a copper surface is attracted by the tip apex for bias voltage below one volt. Comparable values have been found for Xe on nickel [6]. The lateral extension of this attractive force over 6 to 10 A makes is possible to slide an atom, since when the tip it moved laterally, the electrostatic trap created by the bias voltage on the adsorbate will follow. The advantage compared to van der Waals sliding processes is that no contact is required to get the attractive trap under the tip apex. Furthermore, this trap can be made deeper than the one created by van der Waals interaction. The major drawback is that this trap is less laterally confined than the van der Waals one: 4 A for van der Waals and more than 10 A for the electrostatic trap. Therefore, it is more convenient to move an adsorbate with the tip electric field when the adsorbates are very far appart from each other.
lated Methods, Eds. R.J. Behm, N. Garcia and II. Rohrer, Nato AS1 Series (Kluwer, Dordrecht, 1990) p. 1. 121 H. Ohtani, R.J. Wilson, S. Chiang and CM. Mate, Phys. Rev. Lett. 60 (1988) 2398; P.H. Lippel, R.J. Wilson, M.D. Miller, CH. Wiill and S. Chiang, Phys. Rev. Lett. 62 (1989) 171; J.K. Gimzewski, E. Stall and R.R. Schlitter, Surf. Sci. 181 (1987) 267. [3] J.A. Stroscio, R.M. Feenstra and A.P. Fein, Phys. Rev. Lett. 58 (1987) 1668; I.W. Lyo and Ph. Avouris, Science 245 (1989) 1369; D.P.E. Smith, M. Kirk and K. Quate, J. Chem. Phys. 86 (1987) 6034. 141 C.J. Roberts, M.C. Davies, D.E. Jackson, S.T.B. Tendler and P.M. Williams, J. Phys. C 3 (1991) 7213; R. Weisendanger, Appl. Surf. Sci. 54 (1992) 271. [5] D.M. Eigler and E.K. Schweizer, Nature 344 (1990) 524. [6] D.M. Eigler, C.P. Lutz and W.E. Rudge, Nature 352 (1991) 600. [7] I.W. Lyo and Ph. Avouris, J. Chem. Phys. 93 (1990) 4479. 181J.S. Foster, J.E. Frommer and P.C. Arnett, Nature 331 (1988) 325. [9] L.J. Whitman, J.A. Stroscio, R.A. Dragoset and R.J. Celotta, Science 251 (1991) 1206. [lo] J.A. Stroscio and D.M. Eigler, Science 254 (1991) 1319. [ll] X. Bouju, C. Joachim, C. Girard and P. Sautet, Phys. Rev. B (19931, in press. [12] Vu Thien Binh and N. Garcia, J. Phys. 11 (1991) 605. [13] D. Atlan, G. Gardet, Vu Thien Binh, N. Garcia and J.J. Sbenz, Uitramicroscopy 42-44 (1992) 154. 1141Vu Thien Binh and J. Marien, Surf. Sci. 202 (1988) L539. [15] H.W. Fink, IBM J. Res. Devel. 30 (19861460. [16] M. Tsukada, K. Kobayashi, N. Isshiki and H. Kageshima, Surf. Sci. Rep. 13 (1991) 265. [17] J. Tersoff and D.R. Hamann, Phys. Rev. Lett. 50 (1983) 1998. [IS] C. Joachim and P. Sautet, in: Scanning Tunneling Microscopy and Related Methods, Eds. R.J. Behm, N. Garcia and H. Rohrer (Kluwer, Dordrecht, 1990) p. 377; P. Sautet and C. Joachim, Chem. Phys. Lett. 185 (1991) 23; P. Sautet and C. Joachim, Ultrami~ros~opy 42-44 (1992) 115.
410
C. Girard et al. / The electric field under a STM apex
1191 S. Watanabe, M. Aono and M. Tsukada, Phys. Rev. B 44 (1991) 8330. [20] G. Doyen, E. Koetter, J.P. Vigneron and M. Scheffler, Appl. Phys. A 51 (1990) 281; C.J. Chen, Phys. Rev. B 42 (1990) 8841; W. Sacks and C. Noguera, Phys. Rev. B 43 (19911 11612. [Zl] T.T. Tsong, Phys. Rev. B 44 (1991) 13703. [22] J.K. Gimzewski, R. Berndt and R.R. Schlitter, Phys. Rev. B 45 (1992) 6844; T. Gritsch, D. Couiman, R.J. Behm and G. Ertl, Surf. Sci. 257 (1992) 297.
1231J.A. Kramar, PhD Thesis (Caltech, 1990). [24] P. Sautet and C. Joachim, Surf. Sci. 271 (1992) 387. t2.51 P. Moon and D.E. Spencer, Field Theory for Engineers (Van Nostrand, Princeton, 1961). /26] C. Girard and X. Bouju, J. Chem. Phys. 95 (1991) 2056. [27] R.R. Teadrout and R.T. Pack, Atomic Data 3 (1971) 195. 1281 C. Girard, J.M. Vigoureux, D. Van Labeke and Ph. Grosset, Chem. Phys. 114 (1987) 209. [29] G. Vidali and M.W. Cole, Surf. Sci. 107 (1981) L374. I301 G. Vidali, G. Ihm, H.Y. Kim and M.W. Cole, Surf. Sci. Rep. 12 (1991) 133.
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Surface Science 282 (1993) 400-410 North-HolIand
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The electric field under a STM tip apex: implications for adsorbate manipulation C. Girard ‘, C. Joachim b, C. Chavy b and P. Sautet ’ ” Laboratoire de Physique Maltkulaire, Uniuersite’ de Besump, 25030 Besancon
Cedex, France ” Groupe d’Electronique Molkulaire, CEMES, LOE, 29 rue Jeanne Maruig, BP 4347, 31055 Toulouse Cedex, France ’ Laboratoire de Chimie Theorique, ENS, 45 All;, d’ltalie, 69364 Lyon Cedex 07, France
Received 22 May 1992; accepted for publication 4 November 1992
For a given bias voltage, a self-consistent calculation of the electrostatic poiari~ation of the STM tip apex at tunneling distance to a conducting surface is presented. An effective atomic structure of the tip apex during a scan is constructed by fitting calculated and experimental STM scans on the Au(l10) surface. The local electric field in the tip-sample gap is calculated. This leads to the inductive etectrostatic potential energy gained by a physisorbed atom like xenon when the STM tip apex is approaching this adsorbate. Field induced diffusion processes of this adsorbate are discussed.
1. Introduction The ability of the scanning tunneling microscope @TM) to record both topographic and spectroscopic features of surfaces in real space is now well established [l-3]. More recently, the STM has been used to both locally modify surfaces f4] and manipulate individual atoms and molecules with a sub-nanometer precision [5-101. Thus, the work of Eigler et al. [5] successfully illustrates the potential of the STM for sliding atoms adsorbed on the surface of a conducting substrate. For example, very well resolved images of Xe arrays are obtained if during a scan, the tip-sample distance is sufficiently large for the atoms to remain in their equilibrium sites 151.For a decreasing tip-surface distance, it was proposed that the forces responsible for the sliding of the atoms along the (110) rows of the surface are of the van der Waals type rather than of the electrostatic type [ 111. Moreover, the adsorption energy of Xe on Ni(ll0) is weak and the Xe sliding is performed at low temperature (4.2 K) [5]. In this case and for the experimentally applied tip-substrate tunnel resistance, calculations confirm that the adsorbate in its hollow site can be slided on the surface following the attractive 0039-6028/93/$06.00
van der Waals potential energy depression created by the tip apex [lO,ll]. For more corrugated surface or for chemisorbed adsorbates, the sliding process based on van der Waals forces becomes difficult to control [IO]. In this case, other mechanisms must be used to move an adsorbate with sub-nanometer lateral precision. For example, by applying an appropriate voltage pulse between the sample and the tip, it is possible to concentrate atoms under the tip apex 191,to desorb atoms from the tip apex 1121or from the surface 16,101and even to carve holes of a few nanometers in diameter into the substrate 141. Moreover, such field induced processes do not generally exhibit a precise intensity threshold. This is generally attributed to the difference in the tip apex atomic structure which varies from tip to tip. When moving an adsorbate with intermediate (1 to 2 volt) voltage pulses, these pulses modify the initial adsorption energy by an amount depending on both the muftipblar susceptibilities and the permanent multipolar moments of the adsorbate. Due to the confinement of the electric field under the tip apex as demonstrated in this paper, the diffusion process will happen preferentially in the vicinity of the tip apex. The understanding of the physical mechanisms
0 1993 - Elsevier Science Publishers R.V. All rights reserved
C. Girard et ai. / T?ze ekctricfield
occurring during a voltage pulse is of great interest for the building and studies of sub-nanostructures [lo]. In this paper, it is shown from a self-consistent treatment that the tip apex, responsible for the STM resolution, confines a large amplitude electric field when the tip is at tunneling distance from the surface. Let us insist on the fact that our goal is not to explain the Eigler sliding process invoking the electric field because, as already discussed, it is now known that this sliding occurs via van der Waals interaction [ll]. We want to study, if the electric field under an STM tip apex can also lead to a precise atom by atom manipulation. In section 2, an effective atomic structure of the tip apex during a scan on the reconstructed Au(ll0) surface is proposed to demonstrate, on experimental grounds, that the tip apex cannot be reduced to a jellium sphere. In section 3, the permanent electrostatic polarization of the tip apex is calculated. Furthermore, the electric field and the corresponding fieldgradient in the tip-surface tunneling gap are derived. In section 4, the change in potential energy of an adsorbate under such a field is calculated. Field induced diffusion processes are discussed in conclusion. Most of the predictions of the electric field shape and amplitude in the tunneling gap used so far are based on simple continuous electrostatic models. Only recently, an approach based on the effective charge concept has been introduced [13]. In this approach, the tip apex is an ensemble of metallic spheres of atomic radius. The tip-substrate tunnel junction forms a capacitor and the local electric field is calculated by minimizing its electrostatic energy [13]. In the following, this field is calculated by taking into account the polarization of each atom of the tip apex.
2. The effective atomic structure of a tip apex during a scan There is usually a total incertitude on the precise atomic shape of the tip apex during STM scans which preclude a complete analysis of the electric field under the tip apex. Well characterized tips are usually made by the build-up tech-
under
a STM aper
401
nique [14] or by the deposition technique [15]. In both cases, field ion microscopy provides well resolved images of the atomic structure of the tip apex. For example, starting with an electrochemitally etched tungsten tip, one can build (112) facets ended by a trigonal tip apex consisting of a (111) plan with 1, 3, 7.. . tungsten atoms per layer [14]. The major drawback is that when such a well-fabricated tip approaches the surface at tunneling distance, the tip apex structure is generally modified. This defo~ation is not well understood but noticable since usually some scans are required before atomic resolution is achieved. As noticed by Tsukada et al. in their recent review [Xl, the exact atomic structure of the tip apex is not often taken into account in calculating the tunneling current. For STM image calculations, the Tersoff-Hamann approximation avoids this problem by using only a generic s-orbital [17]. More sophisticated models are now available to take into account the tip atomic structure and to predict surface corrugation [18-201. But in many discussions on manipulations of atoms and molecules by an electric field, the tip apex shape is generally not considered. Furthermore, the tipend is often represented as a metallic sphere of a radius estimated between 10 and 100 nm [10,21]. The atomic protrusion forming the tip apex does not appear on this sphere in these discussions. Therefore, it is important before any calculation of the electric field in the tip-surface gap to show that the tip apex ends with a small cluster of metal atoms. The best way for this purpose is to compare e~e~mental and calculated scans taking into account the tip apex structure. Such a comparison allows us to propose an effective tip apex atomic structure during each scan. As an example of effective apex structure determination, let us consider the Au(ll0) reconstructed surface. Well resolved experimental scans on this surface have been obtained experimentally by Gimzewski et al. using a tungsten tip [22]. Such a surface is appealing because of its atomic protrusions showing (111) and (331) steps. These steps are very useful to optimize the lateral shape of the tip apex. To calculate these scans, it is important to pre-suppose an initial tip structure and to adjust it to reproduce the experimental
402
C. Girard et al. / The electric field under a STM apex
scans. A single atom tip is certainly not enough for such steps. For simpIicity, we have chosen to start with a gold tip apex. In the experiments, the tips were made out of tungsten, but gold tips are sometimes used in STM [23]. This difference is not a problem, since no geometric deformations of the tip apex are considered in our calculations. Moreover, aside from the tungsten d-orbitals which are near the Fermi level, the s-orbitals of the two materials are quite similar. Notice also that the spatial exponential decay of d-orbital tail is generally twice the decay of an s-orbital. Therefore, s-orbitals play the principal role in the tunneling current for the chosen substrate. Only these orbitals are considered in the following to reduce the computing time. But all the valence orbitals can be added if necessary. The extraction of the effective tip structure is presented here only to support the fact that the tip apex in the tunneling regime consists of a sharp protrusion with sub-nanometer dimensions. We have also chosen to fit one scan and not a complete image. The reason is that a direct comparison of the tip shape extracted from an “image-to-image comparison” is not precise enough for a correct fit.
J. Gimzewski provided the experimental scans. The calculated ones were obtained using the STM-ESQC technique already described elsewhere [18]. The extended Huckel molecular orbital theory was used to describe the chemical composition of the tip-substrate tunnel junction [18]. A double c basis set was used to better reproduce the iong distance coupling between the tip and the substrate and to get a good currentdistance characteristic [241. For all the constant current scans presented, the current was fixed to 1.5 nA for a 30 mV bias voltage. Only the relative tip apex-to-surface distance is presented. The absolute tip-Alex-last-atom to surface distance is less than 6 A in average on the flat reconstructed Au(ll0) surface. The tip apex structure chosen for the calculation is a tetragonal tip apex built along a (110) axis. This apex is deposited on an AufllO) surface which is the end of the tip body (fig. 1). This simulates a tip equipped with a sharp apex, four lateral facettes and a flat plane to represent the curvature radius of the tip body. In the extreme case of a flat tip without apex, it is the Au(ll0) surface protrusion which plays the role of the tip
Fig. 1. Representation of tip-substrate atomic structure used to fit the calculated STM image with the experimental one. The Au(ll0) surface is reconstructed with two atomic rows more. This defines a (111) step and a (331) step, on the right and on the left side of the protusion, respectively. The bulk of the substrate is made of a semi-infinite reproduction of the unit cell. The tip is made of four layers of atoms oriented along the (110) direction composed successively of 1, 4, 9 and 16 gold atoms. This apex is deposited on the (110) plane of the tip surface. The bulk of the tip is also made of a semi-infinite reproduction of the unit cell.
C. Girard et al. / The electricfield under a STM apez
apex (fig. 2a). Then, a constant current scan gives the topography of the tip surface instead of the topography of the substrate surface.
,’
,-;
a~
,f,’
:
,’ ,I’ ,’
T 3
A better tip apex can be made with 4 atoms in the same plane on the tip body. This is a flat tip as shown fig. 2b. The resulting simulated scan on
:
,’
2-
403
*,‘. :
16132
Xi.&
-16:32
(a)
-16:32
16132
a:0
Xl‘&
-16.32
0:o (h)
0.0
16.32
Cd)
-16.32 6.0 1632 (e) (0 Fig. 2. Calculated constant current scans compared with the corresponding experimental data (in dashed line). I = 1.5 nA and V= 30 mV. The tip apex used is presented each calculated scan. The surface and the tip body are the same as in fig. 1. Small circles at the bottom of (a) are the x, z Au atom positions on the surface.
404
C. Girard et al. / The electric field under a STM apex
the A~(1101 surface is presented in fig. 2b. It cannot be compared with the experimental one. For example, on the right of the (111) step and on the left of the (331) step, there is an inverted contrast, This means that the surface protrusion is still too high for the chosen tip apex. It can be reduced to one atom like in many existing theory of STM image calculations but supported here by the surface of the tip body. Again, the resulting scan does not correspond to the experimental one (fig. 2c) because the surface of the tip body is too much coupled to the protrusion on the Au(ll0) surface. To get a better fit, a scan with a 5-atom tip apex arranged in 2 layers is presented in fig. 2d. The best agreement with the experiment is obtained with a small increase in the lateral separation of the 4 atoms of the basal layer. Figs. 2e and 2f present scans using a 3-layers and a 4-layers tip apex, respectively. Some lateral geometric variations on this 3-layer tip apex lead also to a very good reproduction of the experimental scan. The scan with the 4-layer tip apex of the fig. 1 is worse than the one with a 3-layer apex perhaps because the experimental tip was not so sharp or because the electronic structure of the lateral part of tip apex is not well optimized. The step-by-step construction of an effective tip apex to reproduce by calculations an experimental scan shows that the end of a tip body is not flat when imaging a A~(1101 surface with steps. The electric field profile in the tip-surface gap will depend on the atomic structure of this tip apex.
3. The electric field in the tip apex-surface
gap
Let us apply a V, bias voltage between the tip and the substrate of the STM tunnel junction described in fig. 3. In this model, the substrate and the tip body are considered without their atomic structure. The tip body is represented by a sphere of radius “b” with “b” in the 10 to 100 nm range. Only the tip apex is supposed to keep its atomic structure with N atoms structured in 3 layers. As discussed in the previous section, this number of layers have been chosen to get a
Fig. 3. The
tip-substrate
electric field calculations. tip apex terminal
STM
tunnel junction
used for the
R,, = (0, 0, Z,,) is the position of the
atom and h the radius of the metallic sphere surporting
the tip apex.
reasonable lateral tip apex shape for weakly corrugated surfaces. For a large tip-surface distance, the tunneling current intensity passing through the junction is negligible. Then, the electric field E,(r) in the gap is equal to the electric field E,, existing between 2 biased metallic electrodes, a spherical one and a planar one. There is also a small contribution of the tip apex which is weakly polarized by Ea. This polarization creates a small electric field component E,(r) superposed to E, to give E,(r). When the tip is in tunneling distance from the substrate and the atoms of the tip apex are frozen in their equilibrium position, a tunneling current in the nano-ampere range does not perturbe the overall surface charge distribution in the substrate and in the tip sphere. This junction can be discribed as a weakly leaking capacitor. But the E,(r) contribution is enhanced since the E,, amplitude increases when the tip-surface distance is reduced. For a sphere-plane capacitor, the E,, contribution to E,(r) is given in the vicinity of the center of the sphere by the known formula [25]: E,=
5 D,
$(l log@
+u) + Jl+u)
UZ7
(1)
C. Girard et al. / The electric @Id under a STM apex
with u = Do/b and D, the distance between the macroscopic tip edge and the substrate surface. The tip apex does not contribute to eq. (1) since it is too small to be considered without its atomic structure. The E,(r) contribution to E,(r) is calculated from the polarization Z’(r) of the tip apex embedded in the E, field. From this polarization, E,(r) can be written: r, r’) *P(r’) dr’.
Z%(r) = lH,(
(2)
H&r, r’) is the overall electrostatic propagator [261. It gives the E,(r) amplitude at a position r from the polarization at a position r’, both positions taken in the gap. To calculate this propagator, notice that P(r) is a function of the local electric field E(R,) interacting with the ith atom of the apex via the relation:
be written in the standard form: To(r, r’) = [3(r-r’)(r-r’)
=a,
E iS(r-Ri)E(Ri),
- Ir-r’(2Z]r-5, (5)
with Z the identity matrix. S&‘, r) models the electrostatic environment of the tip apex. If ZLis an electric dipole located at a position r in the gap, the electric field E(r’) in r ’ induced by this dipole is given by: E(r’) =&,(r’,
r) *p(r).
(6) To solve eq. (41, it is convenient to use the super-vectors F= (E(R,), E(R,), . . * E(R,)) and 9, = E,(O, 0, 1; 0, 0, 1; . . . >. In this case, eq. (4) can be rewritten F= i&Y,, with M, = [I Z&J-‘. B, is a (3N x 3N) matrix which contains all the informations on the chemical composition and structure of the tip apex. Following eq. (4), this matrix is defined by: Bll(RiT
P(r)
405
Rj)
(3)
i=l
with (Y, the polarizability of the atoms of the apex which are considered to be identical. Note that retarded effects are not taken into account in this approach since the dimension of the junction is very small compared to the main wave length of the Fourier components of the generally used bias voltage pulse. The field E(R,) acting on the ith atom of the apex is a superposition of: the macroscopic field E,, the electric field created by the E, polarization of the other atoms of the apex than the ith one and of the modulation of this polarization by the dielectric environment. This environment is made of the surface and of the tip sphere. Both are polarized by the tip apex. Therefore, E(R,) is the solution of the equation: E(R,)
=E,(Ri)
+ ;
S,(R,,
Rj) X/E(Rj)
j=l
+
5
T,(R,,
Rj)m/E(Rj).
(4)
j#l
T,,(r, r’> is the dipolar propagator through vacuum which gives the electric field inside the tip apex acting on one atom due to the others. It can
where the ZZ&, r’) propagator equal to:
used in eq. (2) is
Z%(r, r’) =&A r, r’) + To(r, r’). (8) Finally, the electric field acting on the ith atom in the tip apex is equal to: E( Ri) = 5 D, lOg(h
2
m
+ \/l+u)
M,(R,,
Rj).
j=l
(9) Using this expression, P(r) is calculated from eq. (3) and E,(r) from eq. (2). With the T,, and S, propagators, the complete E,(r) amplitude in the tunnel junction can be written: Z%(r) =&I + /[%(
r, r’) + Z’,,(r, r’)]P(r’)
dr’. (10)
The E,(r) configuration under the tip apex can be studied for many examples changing the tip apex material, the surface material or the tip
406
C. Girard et al. / The electric field under a STM apex
!O
apex geometry. One example is a (111) oriented copper tip apex interacting with a planar copper surface. S,, and (Y, for copper have been taken from the literature: for (Ye, Teadrout et al. [27] gives 9.2 A’,“. The second rank tensor S, was calculated by one of us elsewhere [28]. Let us recall that contrary to the surface used in section 2, no atomic corrugation has been considered here for the copper surface. This approximation is not valid for highly corrugated surfaces where local charge accumulations may play a role in the tip apex polarization. The tip apex chosen for the calculations has 3 layers of copper atoms, piled up along the (111) axis and supported by a metallic sphere of radius 6 = 20 nm. The electrostatic energy density maps associat$d to I E, I 2 are presented in fig. 4. For a fixed 7 A tip apex-to-surface distance and for V,, = 1 V, I B, I 2 has been calculated for different heights from the surface. A very confined field E, is obtained in the vicinity of the tip apex. Let us insist on the fact that this field takes into account the B, component, (see eq. Cl)), due to the sphere which supports the tip apex. Using a 10 nm sphere radius, one usually gets more than 10 nm lateral extension for this field component. This explaias why it is not visible in fig. 4. In contrast, at 4 A from the apex (fig: 4a), the I E, I ’ half maximum width is only 6 A. Moreover, close to the tip apex terminal atom, the field gradiant is very strong along the z axis. When the tip apex is approaching the copper surface, the field amplitude increases and its lateral extension is reduced.
4. The energy electric field Under molecule)
of an adsorbate
in the tip apex
a STM tip apex, an adsorbate (atom, is polarized by the electric field estab-
Fig. 4. The 1E, 1’ energy Gensity maps for a fixed tip apex-tosurface distance Z, = 7 A. Theomaps are reprtsented at 3 differevt altitudes, (a) for Z = 3 A, (b) for Z = 4 A and (c) for Z = 5 A. To get the corresponding scale in field amplitude, the root of the energy ordinate myst be taken and multiplied byO.l89VA-‘.
C. Girard et al. / The electric field under a STM apex
‘\
3.50
3.00
\
\
\
\
\
1 1.00
zL9
407
lished in the STM tunnel junction [lo]. It results in a change in the electronic energy of the adsorbate which leads to a modification of its adsorption energy. In the semi-classical approach chosen here, all these effects are included in the MC”’ multipolar moments and in the (n)cr(n’) multipolar polarizability of the adsorbate. Moreover, if the number of atoms composing the adsorbate is small and the tip apex maintained at tunneling distances, the polarized adsorbate does not change the polarization state of the tip apex too much. In this approximation, the electrostatic part of the potential energy of the adsorbate can be written as: 1 U(R)=+
n,n’ (2n - 1)!!(2n’-
x
(N&0 l)!!
[n + d]Fg(“)( R)F,(“‘)(R) 1
- F (2n - l)!!
M’“‘[ n]F,(“‘( R) . (11)
F(“)(r) = V(“-r)E&r) are the successive gradients 0; the E (r) field. R is the position of the center of mass’of the adsorbate on the surface. This energy has to be added to the periodic potential energy of the adsorbate on its surface if the surface is considered to be corrugated. An adsorbate with a permanent dipolar moment can also be considered in eq. (11). For an adsorbate with a spherical symmetry, like an atom in its ground state, the two first non-vanishing terms in eq. (11) are the dipolar term: U#( R) = - ~%(‘)[ 21Eg( R) Eg( R) and the quadripolar
term:
U&R) = - &(2h(2)[4]F9(2)( R)F,‘2’( R). L
-90
Fig. 5. Attractive dipolar inductive potential energy UJO, 0, Z) of a xenon atom adsorbed on a copper surface, located under a tungsten tip apex. (- - -_) for V0 = 0.5 V, (- - - - - -1 for V0 = 0.6 V, (. . .) for V0 = 0.7 V and (-T - - -) for V, = O.,S V. The tip to surface distance is Zg= 7 A for (a), Z, = 9 A for (b) and Z, = 12 A for Cc).
(12)
(13)
The polarization of many adsorbates by the tip apex can be studied considering only these two terms and the simplification occurring for isotropic adsorbates. For atoms like Xe in the work of Eigler et al. [6] or for organic molecules like in the work of Foster et al. [S], the local electric field Eg is used to adsorb the adsorbate on the tip apex and to move the attached adsorbate with the tip apex. As an example, let us
408
C. Girctrd et al. / The electric field under a ST34 ape*
Fig. 6. Variation of the quadrupolar inductive energy U&O, 0, Z) of a xenon atom adsorbed on a copper surface and under a tungsten tip apex. Notation are the same as in fig. 5.
consider a Xe atom adsorbed on a copper surface and a tungsten tip. For rare gas atoms, standard values for (Y(I)and a(2) are given in the literature [291. For the tip apex, a (111) pyramid with 3 layers of atoms is used like in section 3. A LY,= 10.5 ii” static poIarizability has been chosen for the tungsten atoms of the tip apex. This apex is supported by a 20 nm metallic sphere. U&R) and U,(R) are calculated from eqs. (12) and (13). For V, < 0.5 V, U,(R) and U,(R) are very small compared to other tip-adsorbate interactions like the van der Waals ones at large tipsubstrate distances or the repulsive ones at short distances ill]. The resulting forces of these inductive terms on the adsorbate point always from
the substrate to the tip. Changing the sign of V,, does not modify the direction of this force since only even terms from eq. (11) have been considered. In Fig. 5, the dipolar contribution U,(O, 0, 21 is presented for different tungsten tip-copper surface distances with 0.5 V < V,, < 0.8 V. Z is the height of the Xe atom above the copper surface. When Xe is close to the tip-apex terminal atom, Uh reaches 180 meV which is comparabte to the 200 meV physisorption energy of a Xe atom on the copper surface 111,301. Therefore, even an intermediate 0.8 V voltage pulse can induce the transfer of a Xe atom on the tip apex. This is valid for a large class of metal surfaces like silver, gold, and nickel, where the Xe adsorption energy is small ( < 200 meV) [30]. Notice also that in first approximation, we do not have to consider the lateral corrugation adsorption energy since this corrugation is one order of magnitude lower 111J than the one calculated here. The quadrupolar inductive term U&R) is also very small compared to the dipolar one of the tip substrate distance chosen as presented in fig. 6. For xenon, this justifies the dipolar approximation which is proposed to explain the operation of the atomic switch reported by Eigler et al. [6]. When the tip apex is kept at a fixed 7 A distance from the surface of the Xe atom, there is also a lateral confinement of this adsorbate due to the E, electric field. The resulting force is
-10
-20
Fig. 7. Lateral variation of the inductive energy induced by the tip apex on a xenonatom adsorbed on a copper surface. The Xe is displaces at constant distance 2 = 3 A along the x direction on the surface keepiag the tip apex posit@ constant. Vr, is the same as in figs. 5 and 6. The tip apex to surface distances are 2, = ‘7 A for (a) and Z,, = IO A for (b).
C. Girard et al. / The electric field under a STM apex
attractive which means, as presented in fig. 7, that an electrostatic trap is created under the tip apex. For V,, = 0.8 V, the deepness of this trap can reach 70 meV which is deeper than a van der Waals trap. For example, for the same 7 A tip apex-surface distance, the deepness of the Xe atom van der Waals trap is less than 20 meV on the copper surface [ll].
Ac~o~~~ents
5. Conclusion
References
409
We like to thank the CNRS program Ultimatech for financial support for one of us and Fujitsu France for computing support during this work. Special thanks go to J. Gimzewski for provinding us with the Au(ll0) experimental scans.
[I] H. Rohrer, in: Scanning Tunneling Microscopy and ReInstead of the standard 10 nm or larger sphere tip apex considered for the understanding of STM electric field tip induced diffusion processes [lO,Zll, the atomic structure at the end of this sphere has been taken into account. This is important in the imaging mode where the atomic resolution relies on a tip apex with a terminal atomic protusion. This is also important in the sub-nanometric manipulation mode since this protusion confines the electric field. This field can serve for adsorbate attachment to the tip apex or for sliding the adsorbate when the tip is moved laterally. When the tip is positioned above an adsorbate, the inductive dipolar and quadrupolar forces due to the tip-to-substrate electric field is attractive. For example, a Xe atom physiosorbed on a copper surface is attracted by the tip apex for bias voltage below one volt. Comparable values have been found for Xe on nickel [6]. The lateral extension of this attractive force over 6 to 10 A makes is possible to slide an atom, since when the tip it moved laterally, the electrostatic trap created by the bias voltage on the adsorbate will follow. The advantage compared to van der Waals sliding processes is that no contact is required to get the attractive trap under the tip apex. Furthermore, this trap can be made deeper than the one created by van der Waals interaction. The major drawback is that this trap is less laterally confined than the van der Waals one: 4 A for van der Waals and more than 10 A for the electrostatic trap. Therefore, it is more convenient to move an adsorbate with the tip electric field when the adsorbates are very far appart from each other.
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