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Enhancement of tunnel current through closed shell atoms
Surface Science Letters 258 (1991) L679-L682 North-Holland
Surface Science Letters
Enhancement
of tunnel current through closed shell atoms
Department of Theoretical Physics, Research School ACT 2601, Australia
of Physical Sciences
& Engineering, The Australian National University, Canberra,
and M. Tsukada Department of Physics, Faculty of Science, University of Tokyo, Hong0 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Received 23 April 1991; accepted for publication 15 August 1991
The self-energy of the tunneling electron due to a foreign atom located in the gap between the surface and the tip of STM is estimated analytically. It is found that the tunnel potential barrier height is significantly reduced in the region directly above the atom. This effect would partly explain the reason why some adsorbed rare gas enhances the tunnel current strongly. A similar enhanced tunnel current would generally be expected when there are intervening molecules in the tunnel gap. An explanation of the bimodal behaviour of the metal/rate gas adsorption system, and direct experimental confirmation thereof through observations on the tunnel current is suggested.
Recent rapid progress of the experimental technique of scanning tunneling microscopy (STM) has made it possible to obtain very clear images of individual atoms on solid surfaces. Nevertheless, many strange phenomena observed in tunneling processes so far, which would be related to some hitherto unknown aspect of the microscopic mechanism of tunneling, have not been understood. One such example is that when a rare gas atom with a closed shell structure is present in the gap between the STM tip and the surface, it sometimes does not block the tunnel current, but on the contrary, enhances it. This has been found in the spectacular experiments of Eigler and Schweizer [l] on manipulations of Xe atoms adsorbed on Ni surface. The Xe atom is observed as a circular hill with a radius larger than the Xe atomic radius. This implies the enhancement of the tunnel current by the adsorbed Xe atom. Another example is the fact that significant tunnel current flows through a layer of
paraffia molecules with a thickness of the order of 100 A [Z], implying that the electron effectively tunnels along the hydrocarbon chain, which is thought to be insulating under usual conditions. In the electron transfer mechanism at the electrode surface of an electrochemical cell, it has long been known that an electron can tunnel over long distances from the electrode surface to a solvent ion. The microscopic mechanism of enhanced electron tunneling in STM in the presence of intervening atoms or molecules in the tunnel gap has not been given due theoretical attention. One of the difficulties in theoretical study is that we must deal with the very tail end of the electron wave function, where many-body effects often play an important role in the dynamics of the electron. The spatial decay rate of the tail of the electron wave function is quite sensitive to its effective potential energy in the tunnel gap. This is usually determined in the self-consistent field approxima-
0039~6028/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved
tion, typical of which is the local density functional (LDA) approach. However, it should be mentioned that LDA is rather poor for accurate description of the potential in the vacuum tail. As discussed in many theoretical works [3-S], the main contribution to the tunneling potential barrier in STM is the image potential. This is essentially the self-energy of the tunneling electron arising from its interaction with the surface and the tip plasmon system. It would be reasonable to suppose that the potential barrier height is lowered by the interaction of the electron with the induced polarization field of the intervening atoms in the tunnel gap. The aim of this Letter is to present an analysis of the effect on the electron self-energy and hence the barrier height, of the induced polarization of an intervening closed shell atom. A foreign atom between the tip and the surface would respond to the field of the tunneling electron through the polarization field induced on it. The potential due to this induced field, for a point atom with static polarizability a(O) this potential has the well-known form [61 e2cy(0)
V,‘,‘:‘(r) = - ~
2r3
= -
I’_ re;3 . r
rc
p(r)
=cy(r;
C0-O)E(r).
(3)
where CX(I-;w + 0) is a tensor giving the polarizability density at r. The potential at r’ due to this induced dipole moment density is, (4) Using (3) and (2) we get for the self-energy the electron due to the induced polarization the atom,
e2
-32
( r - re1
d”,_
of on
a( r; 0)
Ir-rc/i
(r-r,)
(5)
/r-rr,li’
For a spherically symmetric foreign atom we now assume for simplicity that cu(r; w) is of the form, a(r:
’
where r is the distance of the electron from the atom. N(O) for the atom near the surface does not have the same value as for the atom in free space, since the proximity of the surface will alter the polarizability of the atom in the adsorbed state. Here we will treat cu(0) as a phenomenological parameter, and discuss later the implications of its dependence on the substrate. Since we are dealing here with distances in the atomic scale, it is necessary to take into account the effect of the finite size of the foreign atom while evaluating its polarization contribution to the self-energy of the tunneling electron. This can be done in a classical framework as follows. The electric field at r due to the electron at rC is.
E(r)
The resulting polarization of the atom whose centre is at the origin is spread over a region of the order of the size of the atom [7,X]. The induced polarization density at r in the static limit is,
w)
=IcY(w)~(I.).
(6)
where f(r) gives the spatial izability. Then (5) becomes, e’n(0)
Kd(rc) = -
If we take f(r) ian, i.e., f’(r)
f(r)
3
j
= ( l/&/‘a3)
-
Ir-i-J’
7
(7) Gauss-
exp( -r’/u’), value
e7N( 0) =
of polar-
d3r
in the form of normalized
for the principal sion.
Vind(rc)
distribution
of (7) we get the expres-
J. Muhanty,
M. Tsukada
/ Enhancement
For re z=+a this gives the asymptotic result of (1). Fig. 1 gives a comparison between the electron self-energy contributions from the induced pofarization of the foreign atom according to eq. (8) in the gap region, and its form in the absence of the foreign atom. The lowering of the barrier close to the surface in the presence of the foreign atom is substantial and would lead to the observed large increase in the tunnel current. Whereas this analysis reveals the reason for increase in the tunnel current near an adsorbed atom or molecule in a situation in which a(O) of
of tunnel current
through
closed shell atoms
the latter is appreciable in spite of the influence of the substrate, the effect of the substrate on a(O), alluded to earlier, can be quite ~orn~~i~ted, One aspect of the effect of the substrate on polarizability bears on the long standing issue of the bimodal behaviour of the metal/rare gas adsorption systems [9-121. This feature is observed in two different forms, (9 the change induced by adsorption in opticat spectra 191, and (ii) the induced dipole moment of the rare gas atom in the adsorbed state [lo]. These experiments reveal that depending on the combination
TIP 5 E\ radius
Fig. 1. Gives the potential barrier as a function of the distance x parakl to the SUTfaCe,for various vertical diszances z from the surface. The origin is on the surface directly below the tip. z and x are in units of the radius of the tip b = 5 A. The unit of the potential V is (ez/b), with the assumption that (Y(O)= u3, a being the range of the Gaussian representing the spread of the polarizability of the foreign atom. The solid curve is for the potential with the atom present, and the dotted curve is for the bare STM geometry. The dotted curve is computed on the basis of an approximate formula 1131,based on the analysis in ref. f5f.
.I. Mahanty, M. Tsukada / Enhancement
of the surface metal and rare gas atoms species, in one class of adsorption systems drastic changes in optical spectra occur, and a large dipole moment is induced; but in the other class these changes are small. As discussed above, the enhancement of the tunnel current depends directly on the effective polarizability of the adsorbed gas atom. Qualitatively, the polarizability should be large if I* < cp, and small if I * > cp, where I* is the ionization energy of the excited adsorbed rare gas atom and cp is the metal work function. This is because of the fact that in the expression for the polarizability,
the dominant term is the squared transition dipole moment matrix epment for np + (n + 1)s i.e., I(%pl+n+i)s)I Y and this is much enhanced when I * < cp, compared with the case of I * > cp. Therefore, STM images of metal/rare gas systems are expected to show bimodal behaviour, i.e., in one type of system very strong enhanced image of the adsorbed atom should be observed, whereas in the other the image of the adsorbed atom would be weakly resolved. Experimental confirmation of this expected bimodal feature in STM imaging would be interesting. Since the closed shell atom provides a rather shallow, but long range polarization potential, there is the possibility of formation of bound states or resonant states by this potential. In that case, a resonant tunneling feature similar to that observed in the scanning tunneling spectroscopy (STS) of image and field states [14] may be expected in STS of adsorbed inert gas atoms. However, since STM investigation of the neighbourhood of an adsorbed inert gas atom uses much lower bias voltage than in STS, the shape of the relevant tunneling potential would be given ade-
of tunnel current through closed shell atoms
quately by the considerations here.
we have outlined
One of the authors (J.M.) is indebted to the Australian Academy of Science, and the Japan Society for the Promotion of Science, for supporting his visit to the Department of Physics of the University of Tokyo, thereby making this collaboration possible. Some interesting discussions with Dr. M.P. Das are gratefully acknowledged.
References [l] D.M. Eigler and E.K. Schweizer, Nature 344 (1990) 524. [2] G. Travaglini, M. Amrein, B. Michel and G. Gross, in: Scanning Tunneling Microscopy and Related Methods, Eds. R.J. Behm, N. Garcia and H. Rohrer (Kluwer. Dordrecht, 1990) p. 335. [3] H. Morawitz, I.P. Batra, R. Reinish and G.R. Henry, Surf. Sci. 180 (1987) 333. [4] J. Mahanty and M.T. Michalewicz, J. Phys. C 19 tIY86) 5005. [S] J. Mahanty and M.T. Michalewicz. Aust. J. Phys. 40 (1987) 413. [6] J.O. Hirschfelder, C.F. Curtiss and R.B. Bird. Molecular Theory of Gases and Liquids (Wiley, New York. 1954) 013.5, p. 989. [7] J. Mahanty and B.W. Ninham. Dispersion Forces (Academic Press. London. 1976) ch. 4. l81 E. Zaremba, in: Density Functional Theory, Eds. J. Keller and J.L. Gazquez, Lecture Notes in Physics 187 (Springer. Berlin, 1983) p. 167. D.K. Greenlaw and C.P. Flynn. Phys. [91 J.A. Cunningham, Rev. B 22 (1980) 717. I101 C.P. Flynn and Y.C. Chen, Phys. Rev. Lett. 46 (19x1) 447. [ill N.D. Lang, A.R. Williams, F.J. Himpsel, B. Rehl and D.E. Eastman, Phys. Rev. B 26 (1982) 1728. l121M. Tsukada and W. Brenig, Z. Phys. B 57 (1984) lY7; Surf. Sci. 151 (198.5) 503. l131B. Das and J. Mahanty, Phys. Rev. B 36 (1987) 898. l141G. Binnig, K.H. Frank, H. Fuchs, N. Garcia. B. Reihl, I-l. Rohrer, F. Salvan and A.R. Williams, Phys. Rev. Lett. 55 (1985) 991.
Surface Science Letters
Enhancement
of tunnel current through closed shell atoms
Department of Theoretical Physics, Research School ACT 2601, Australia
of Physical Sciences
& Engineering, The Australian National University, Canberra,
and M. Tsukada Department of Physics, Faculty of Science, University of Tokyo, Hong0 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Received 23 April 1991; accepted for publication 15 August 1991
The self-energy of the tunneling electron due to a foreign atom located in the gap between the surface and the tip of STM is estimated analytically. It is found that the tunnel potential barrier height is significantly reduced in the region directly above the atom. This effect would partly explain the reason why some adsorbed rare gas enhances the tunnel current strongly. A similar enhanced tunnel current would generally be expected when there are intervening molecules in the tunnel gap. An explanation of the bimodal behaviour of the metal/rate gas adsorption system, and direct experimental confirmation thereof through observations on the tunnel current is suggested.
Recent rapid progress of the experimental technique of scanning tunneling microscopy (STM) has made it possible to obtain very clear images of individual atoms on solid surfaces. Nevertheless, many strange phenomena observed in tunneling processes so far, which would be related to some hitherto unknown aspect of the microscopic mechanism of tunneling, have not been understood. One such example is that when a rare gas atom with a closed shell structure is present in the gap between the STM tip and the surface, it sometimes does not block the tunnel current, but on the contrary, enhances it. This has been found in the spectacular experiments of Eigler and Schweizer [l] on manipulations of Xe atoms adsorbed on Ni surface. The Xe atom is observed as a circular hill with a radius larger than the Xe atomic radius. This implies the enhancement of the tunnel current by the adsorbed Xe atom. Another example is the fact that significant tunnel current flows through a layer of
paraffia molecules with a thickness of the order of 100 A [Z], implying that the electron effectively tunnels along the hydrocarbon chain, which is thought to be insulating under usual conditions. In the electron transfer mechanism at the electrode surface of an electrochemical cell, it has long been known that an electron can tunnel over long distances from the electrode surface to a solvent ion. The microscopic mechanism of enhanced electron tunneling in STM in the presence of intervening atoms or molecules in the tunnel gap has not been given due theoretical attention. One of the difficulties in theoretical study is that we must deal with the very tail end of the electron wave function, where many-body effects often play an important role in the dynamics of the electron. The spatial decay rate of the tail of the electron wave function is quite sensitive to its effective potential energy in the tunnel gap. This is usually determined in the self-consistent field approxima-
0039~6028/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved
tion, typical of which is the local density functional (LDA) approach. However, it should be mentioned that LDA is rather poor for accurate description of the potential in the vacuum tail. As discussed in many theoretical works [3-S], the main contribution to the tunneling potential barrier in STM is the image potential. This is essentially the self-energy of the tunneling electron arising from its interaction with the surface and the tip plasmon system. It would be reasonable to suppose that the potential barrier height is lowered by the interaction of the electron with the induced polarization field of the intervening atoms in the tunnel gap. The aim of this Letter is to present an analysis of the effect on the electron self-energy and hence the barrier height, of the induced polarization of an intervening closed shell atom. A foreign atom between the tip and the surface would respond to the field of the tunneling electron through the polarization field induced on it. The potential due to this induced field, for a point atom with static polarizability a(O) this potential has the well-known form [61 e2cy(0)
V,‘,‘:‘(r) = - ~
2r3
= -
I’_ re;3 . r
rc
p(r)
=cy(r;
C0-O)E(r).
(3)
where CX(I-;w + 0) is a tensor giving the polarizability density at r. The potential at r’ due to this induced dipole moment density is, (4) Using (3) and (2) we get for the self-energy the electron due to the induced polarization the atom,
e2
-32
( r - re1
d”,_
of on
a( r; 0)
Ir-rc/i
(r-r,)
(5)
/r-rr,li’
For a spherically symmetric foreign atom we now assume for simplicity that cu(r; w) is of the form, a(r:
’
where r is the distance of the electron from the atom. N(O) for the atom near the surface does not have the same value as for the atom in free space, since the proximity of the surface will alter the polarizability of the atom in the adsorbed state. Here we will treat cu(0) as a phenomenological parameter, and discuss later the implications of its dependence on the substrate. Since we are dealing here with distances in the atomic scale, it is necessary to take into account the effect of the finite size of the foreign atom while evaluating its polarization contribution to the self-energy of the tunneling electron. This can be done in a classical framework as follows. The electric field at r due to the electron at rC is.
E(r)
The resulting polarization of the atom whose centre is at the origin is spread over a region of the order of the size of the atom [7,X]. The induced polarization density at r in the static limit is,
w)
=IcY(w)~(I.).
(6)
where f(r) gives the spatial izability. Then (5) becomes, e’n(0)
Kd(rc) = -
If we take f(r) ian, i.e., f’(r)
f(r)
3
j
= ( l/&/‘a3)
-
Ir-i-J’
7
(7) Gauss-
exp( -r’/u’), value
e7N( 0) =
of polar-
d3r
in the form of normalized
for the principal sion.
Vind(rc)
distribution
of (7) we get the expres-
J. Muhanty,
M. Tsukada
/ Enhancement
For re z=+a this gives the asymptotic result of (1). Fig. 1 gives a comparison between the electron self-energy contributions from the induced pofarization of the foreign atom according to eq. (8) in the gap region, and its form in the absence of the foreign atom. The lowering of the barrier close to the surface in the presence of the foreign atom is substantial and would lead to the observed large increase in the tunnel current. Whereas this analysis reveals the reason for increase in the tunnel current near an adsorbed atom or molecule in a situation in which a(O) of
of tunnel current
through
closed shell atoms
the latter is appreciable in spite of the influence of the substrate, the effect of the substrate on a(O), alluded to earlier, can be quite ~orn~~i~ted, One aspect of the effect of the substrate on polarizability bears on the long standing issue of the bimodal behaviour of the metal/rare gas adsorption systems [9-121. This feature is observed in two different forms, (9 the change induced by adsorption in opticat spectra 191, and (ii) the induced dipole moment of the rare gas atom in the adsorbed state [lo]. These experiments reveal that depending on the combination
TIP 5 E\ radius
Fig. 1. Gives the potential barrier as a function of the distance x parakl to the SUTfaCe,for various vertical diszances z from the surface. The origin is on the surface directly below the tip. z and x are in units of the radius of the tip b = 5 A. The unit of the potential V is (ez/b), with the assumption that (Y(O)= u3, a being the range of the Gaussian representing the spread of the polarizability of the foreign atom. The solid curve is for the potential with the atom present, and the dotted curve is for the bare STM geometry. The dotted curve is computed on the basis of an approximate formula 1131,based on the analysis in ref. f5f.
.I. Mahanty, M. Tsukada / Enhancement
of the surface metal and rare gas atoms species, in one class of adsorption systems drastic changes in optical spectra occur, and a large dipole moment is induced; but in the other class these changes are small. As discussed above, the enhancement of the tunnel current depends directly on the effective polarizability of the adsorbed gas atom. Qualitatively, the polarizability should be large if I* < cp, and small if I * > cp, where I* is the ionization energy of the excited adsorbed rare gas atom and cp is the metal work function. This is because of the fact that in the expression for the polarizability,
the dominant term is the squared transition dipole moment matrix epment for np + (n + 1)s i.e., I(%pl+n+i)s)I Y and this is much enhanced when I * < cp, compared with the case of I * > cp. Therefore, STM images of metal/rare gas systems are expected to show bimodal behaviour, i.e., in one type of system very strong enhanced image of the adsorbed atom should be observed, whereas in the other the image of the adsorbed atom would be weakly resolved. Experimental confirmation of this expected bimodal feature in STM imaging would be interesting. Since the closed shell atom provides a rather shallow, but long range polarization potential, there is the possibility of formation of bound states or resonant states by this potential. In that case, a resonant tunneling feature similar to that observed in the scanning tunneling spectroscopy (STS) of image and field states [14] may be expected in STS of adsorbed inert gas atoms. However, since STM investigation of the neighbourhood of an adsorbed inert gas atom uses much lower bias voltage than in STS, the shape of the relevant tunneling potential would be given ade-
of tunnel current through closed shell atoms
quately by the considerations here.
we have outlined
One of the authors (J.M.) is indebted to the Australian Academy of Science, and the Japan Society for the Promotion of Science, for supporting his visit to the Department of Physics of the University of Tokyo, thereby making this collaboration possible. Some interesting discussions with Dr. M.P. Das are gratefully acknowledged.
References [l] D.M. Eigler and E.K. Schweizer, Nature 344 (1990) 524. [2] G. Travaglini, M. Amrein, B. Michel and G. Gross, in: Scanning Tunneling Microscopy and Related Methods, Eds. R.J. Behm, N. Garcia and H. Rohrer (Kluwer. Dordrecht, 1990) p. 335. [3] H. Morawitz, I.P. Batra, R. Reinish and G.R. Henry, Surf. Sci. 180 (1987) 333. [4] J. Mahanty and M.T. Michalewicz, J. Phys. C 19 tIY86) 5005. [S] J. Mahanty and M.T. Michalewicz. Aust. J. Phys. 40 (1987) 413. [6] J.O. Hirschfelder, C.F. Curtiss and R.B. Bird. Molecular Theory of Gases and Liquids (Wiley, New York. 1954) 013.5, p. 989. [7] J. Mahanty and B.W. Ninham. Dispersion Forces (Academic Press. London. 1976) ch. 4. l81 E. Zaremba, in: Density Functional Theory, Eds. J. Keller and J.L. Gazquez, Lecture Notes in Physics 187 (Springer. Berlin, 1983) p. 167. D.K. Greenlaw and C.P. Flynn. Phys. [91 J.A. Cunningham, Rev. B 22 (1980) 717. I101 C.P. Flynn and Y.C. Chen, Phys. Rev. Lett. 46 (19x1) 447. [ill N.D. Lang, A.R. Williams, F.J. Himpsel, B. Rehl and D.E. Eastman, Phys. Rev. B 26 (1982) 1728. l121M. Tsukada and W. Brenig, Z. Phys. B 57 (1984) lY7; Surf. Sci. 151 (198.5) 503. l131B. Das and J. Mahanty, Phys. Rev. B 36 (1987) 898. l141G. Binnig, K.H. Frank, H. Fuchs, N. Garcia. B. Reihl, I-l. Rohrer, F. Salvan and A.R. Williams, Phys. Rev. Lett. 55 (1985) 991.