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Mechanism of transparent STM images of chemisorbed molecules and outermost layers
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Applied Surface Science 67 (1993) 235-240 North-Holland
applied surface science
Mechanism of transparent STM images of chemisorbed molecules and outermost layers Masaru Tsukada
a
K a t s u y o s h i K o b a y a s h i " a n d N o b u y u k i Isshiki b
Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan b Institute for Knowledge and Intelligence Science, Kao Corporation, Bunka 2-1-3, Sumida-ku, Tokyo 131, Japan Received 10 August 1992; accepted for publication 18 September 1992
There have been many examples of STM image reported, where depending on the bias value the adsorbate molecules become transparent or a moire pattern is formed between the adlayer and the substrate surface. Analytical theory for the mechanism of the transparency is presented based on the transfer matrix formalism of the surface wavefunction. Examples of the g r a p h i t e / b e n z e n e adsorption systems and T i C ( l l l ) / g r a p h i t e monolayer are investigated by the first-principles L D A calculations.
1. Introduction
In spite of recent rapid progress of scanning tunneling microscopy and its extension toward a variety of application fields, there remain several fundamental problems in STM which await theoretical explanation. In this paper, we address the question about the transparent STM images of some weakly adsorbed molecules as well as the mechanism of moire pattern formation between the outermost layer and a weakly binding substrate surface. This kind of p h e n o m e n a has often been reported in literature. For example, Mizutani et al. [1] observed that the liquid crystal molecules such as 7CB or 8CB supported on graphite surfaces look transparent, and the substrate graphite structure can be visible when the bias voltage is reduced to the range of 0.1 V. On the other hand, the STM image of the same molecules is quite clear for the bias range of 1 eV. So the transparency significantly depends on the bias voltages. Examples of the moire pattern have been reported by several authors. Itoh et al. [2] formed a monolayer of graphite on a clean substrate of TiC or other transition metal carbides and found a very clear moire pattern between the graphite and the substrate structures. Similar moire patterns have been observed on the
transition metal chalcogenide layer unit formed on a different chalcogenide by the van der Waals epitaxial method [3]. The transparency of the molecule or the moire pattern formation would indicate that the tunnel current between tip and surface is sometimes influenced not only by the atomic arrangement of the outermost portion of the surface, but also by the atomic structure underneath. Sometimes the latter becomes even more predominant than the former. The purpose of the present article is to propose a physical insight for these p h e n o m e n a through some analytical arguments based on a transfer matrix formalism for the surface electronic states as well as first-principles calculations of electronic states of weakly chemisorbed systems.
2. Transfer matrix formalism for the local density of states
If the effect of the tip electronic states is ignored, the STM image simply reflects the local density of states (LDOS) of the surface at a certain prove point fixed on the tip [4,5]. In this section we consider how the L D O S outsides the surface is determined by the formalism of the
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
236
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
transfer matrix. The wavefunction at the surface can be generally expressed as Ok,,(r 0, z) = eik"rll E
eiGi'rll~)ikll(Z ),
(1)
By eqs. (4)-(6), one gets the following relation between the wavefunctions at z 2 for the system with and without adsorbates, respectively: N
Gi
where kjl is the crystal momentum in the direction parallel to the surface, and the G, is the 2D inverse lattice vector, and r u and z are the coordinates parallel and perpendicular to the surface, respectively. For the following discussions, it is more convenient to express eq. (1) in a 2N-dimensional vector form as (/) i kll( Z ) eiG"r,,
q~Nkll( Z ) e iGNrl'
Ok,,(rll, z) =
,
(2)
~',,,,(z) e
-= F . S i j ( z 2 )~Jkl[ 0 ( Z 2),
where
Kij(z2) = [TA(rll; Z2, Zl)TO(rll;Zl, Z2)]ii X exp(iGij • rrl ) .
Ok,,(ru, z2)
=
T(rll; Z2, z,)O,,,(rll, z , ) .
Z2)
: Y'a(L
where N is the number of the inverse lattice vectors included in the expansion. Since the Schr6dinger equation defines 2N-dimensional coupled first-order differential equation among Oik 's, the wavefunction in the vector form satisfies the following relation:
(8)
Note that TA(rU; z2, z l) is the inverse matrix of TA(rjp; z I, z2). The left band side of eq. (8) does not depend on z~ and rip if we take the position z~ sufficiently close to the surface. The LDOS of the system with the adsorbates can be expressed as pA(rll ,
~N~,,(Z) e'~' r,,
(7)
j-1
E(k,,)) }2 e
kll
=
i(;j'rll
0
,
A:~ ~ A +,~, (~)<~,,(~), 1
]
~a(E- U(k,,)) kll X
[y'Yi, q(rll, pq
z2)e
,,]
io,,r o, , , 'gavk,r(z2)&uk,,(z2)
(9)
,
where Ypq is defined by
(3)
In the above T(rll; z2, Z1) is the so-called transfer matrix of dimension 2 N x 2N. For the pure substrate we represent the corresponding transfer matrix by T0(rll; z2, zl). Then the wavefunction O°(r I[ I;, z 2) of the pure substrate at some position trll, z 2) far outside the surface is given by
Ypq( r l l , Z 2 ) =
EKi*p(z2)Kjq(Z2) ei(%,-C',"r,,. ij
(10)
where z, corresponds to some position below the top layer. On the other hand, the wavefunction ~0A(r, Z2) for the system with the adsorbed II u molecule (layer) inserted is given by
If the matrix K is almost the unit matrix, namely, in the limit of very weak potential of the adsorbates, Yvq = 1 for any values of p, q. This case corresponds to the complete transparency of the adsorbates as verified by the second line of eq. (9). Less complete transparency of the adsorbates is generally resulted, if the off-diagonal matrix elements of K turns out to be very small. In this case the LDOS of the adsorbates is given by
A A Ok,,(rll, z2) = TA(rlI; Z2, Z l ) ~ k l , ( r l l , Zl) ,
pA(rll , z2)
r i*,,t ot r
U' z 2 ) =
o T0(rll,. z2, z,)~k,(rll, Zl),
(4)
(5)
with the transfer matrix TA(rll; z2, z l) for this system. If the interaction between the substrate and the adsorbate is weak, the wavefunction g,~(r,, z l) is almost the same as ~-k, ,t/)(r II, z1): Ok,t ( r, ' z , ) ~
~k,(0 rll, Zl).
(6)
--- E a ( E - E(k,,)) kll Kpp(Z2) Kqq(Z2) e
X
tq
It~Pkll(Z2)~qkrc(Z2)
,
[lq
(ll)
237
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
which generally shows the similar features as those of the bare substrate, p0(rll, z2), which is defined by eq. (11) with Kpp = Kqq = 1. The order of the off-diagonal elements of K is estimated for the larger value of z and for the peak potential V of the adsorbates as 2m K i j ~- h2
× f V(rH, z) eia';r"qbA*(z)dpA(z)drll dz (k,, +
(i~j).
(k,, + ai) 2 (12)
For the stronger potential, V should be replaced by the T-matrix of the scattering. For the case of I Gil 4: I Gj[, the difference of the spatial extent between ~b/A(z) and ~bA(z), as well as the increase of the denominator of the integrand, tends to reduce the value of the off-diagonal element Kij. In the other words, the scattering of the
~bA(z) exp[i(kll + Gi)'rll] to ~bA(z) by the adsorbates is suppressed, and this favors the transparency. It should be remarked that even for a rather strong potential on the adsorbate layer, the off-diagonal elements are not necessarily large. At the energy close to a molecular level of the adsorbates, the potential V is replaced by the scattering T-matrix, the value of which becomes enhanced due to the resonance effect. This explains why the image of the adsorbates becomes stressed in such a energy region. The 2D Fourier components o f Ypq(rll, z ) (eq. (10)) in the direction of rll contain the wave components of the inverse lattice vectors both of the substrate and adsorbate layer. Thus if the off-diagonal elements of K are of the proper range of values, it is quite easy to show that both the periodicity of the substrate and the adsorbate layer appear in the lateral spatial variation of LDOS, which explains the origin of the the moir6 pattern in the STM image.
wavelet
×exp[i(kll+Gj).rll]
L35A i
'i, ,,
3.35A r
, I I
' i
~.35A Ir
Fig. 1. Atomic structure of ~ - × ~/7-C6H 6 on graphite used for calculation. Left and right side show top and side view, respectively. The small open circles and triangles denote carbon and hydrogen atoms of benzene molecule, respectively. Closed circles denote carbon atoms of graphite.
238
M. Tsukada et al. / S T M images of chemisorbed molecules attd outermost layers
3. The STM image of a benzene molecule supported on a graphite surface
In principle the STM image can be obtained by the numerical calculations of the transfer matrix and thereby obtained matrix Kij in the previous section. However, numerical integration for the transfer matrix often causes instability and require a special numerical device, which we are now developing. Therefore at the present stage, we make calculations of the electronic state of a weakly adsorbed molecule by the first-principles L D A m e t h o d [6], and form the STM image [7]. The model we used is shown in fig. 1. The C - C bond length of a benzene molecule and graphite are 1.40 and 1.42 A, respectively. The distance between the benzene molecularoPlane and the graphite surface is taken as 3.35 A. The molecule is arranged in a ~ - × ( 7 superstructure of the graphite lattice. This structure has been observed by experiment [8]. Figs. 2a and 2b show the STM image of the adsorbed b e n z e n e molecule for a bias voltage + 1.0 and +0.1 V, respectively. For the substrate graphite, a slab model with three atomic layers is used. The height between the tip and the molecule is assumed as 2.6 A. As
(a)
C ~
~
the cluster model of the tip, W l 0 [ l l l ] is used, which from our n u m e r o u s experiences [9] is known to give normal images of surfaces. For the larger bias voltage (fig. 2a), the strong current region distributes like a d o u g h n u t showing the electron cloud on the benzene ring. On the other hand, for the smaller bias value (fig. 2b), the strong current region concentrates on the alternate three carbon atoms. These carbon atoms correspond to the B sites of the substrate graphite surfacc. Therefore the STM image of fig. 2b can be regarded as that of the graphite layer which is visible through the benzene molecule. Why the 7r electron cloud on the benzene ring can be observed only for the larger bias value can be explained by the following way. Fig. 3 shows the density of states ( D O S ) of the g r a p h i t e / C , H ~ , system (full line) c o m p a r e d with the D O S of the substrate graphite without the benzene adsorbates (dashed line). On the top of the figure, the levels of the benzene molecules arranged in the same structure as the adlayer are shown. In the D O S of the g r a p h i t e / C 6 H ~ system, the sharp peaks due to the molecules are clearly seen. They are scarcely changed when the interaction with the substrate is introduced. In the energy region
(b)
F~
~
Fig. 2. The contour plot of STM images of ~- x ~- - C6M 6 on graphite. The distance between the tip and the benzene molecule is set to 2.6 ,~. A tungsten tip protruded to [111] direction of crystal is used. Crosses and triangles show the carbon and hydrogen atoms of benzene molecules. Circles show the carbon atoms of graphite. (a) Surface bias is 1.0 eV. (b) Surface bias is 0.1 eV.
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
70.0 I 60.0 f
5o.oI ,_ 40.0 o ~3
30.0 e,,
20.0 10.0 0.0
t~L
-20.0
-15.0
-10.0
-5.0
EF
5.0
Energy (eV)
Fig. 3. Density of states of ~ - × !~--C6H 6 on graphite (solid line) and H O P G (dashed line). Bars on the upper side show the energy level of the benzene molecule.
close to the Fermi level of the adsorbed system, there are no levels of benzene: the highest occupied molecular level ( H O M O ) and the lowest unoccupied molecular level ( L U M O ) are apart from E F by about 3 eV, as seen in fig. 3. Therefore for the energy of the tunnel electron close to E v, the off-diagonal elements of the K-matrix are small. In such a case the L D O S would be determined by eq. (11). Namely, an intervening molecular layer does not significantly destroy the substrate image, as discussed in the previous section. As opposed to this situation, when the energy of the tunnel electron approaches to the molecular level of the adsorbate, the scattering effect by the molecule becomes significant. In this case the tail of the wavefunction of the tunnel electron experiences very strong modification in the lateral direction. This results in the enhancement of the off-diagonal elements of K. Therefore the structure of the admolecule dominates in the vacuum tail and the STM image solely reflects the structure of the molecule.
4. The STM image of a graphite monolayer on TiC(lll) Formation of the graphite monolayer on a clean transition metal or their carbide surfaces has attracted much attention recently. Among
239
many interesting properties of these systems, the formation of the moire pattern provides us a mystery to be solved [7]. For the case of the TIC(111) substrate there observed two periods of the moire pattern, the shorter one of the order of 5 ,~, about twice as large as the graphite lattice o vector, and the longer one of the order of 27 A. The moire pattern changes considerably with the variation of the bias voltage, but the periodicity of the graphite lattice cannot be seen. In order to clarify the effect of the substrate on the STM image of the graphite monolayer, we performed the electronic state calculation on the model as shown in fig. 4a [7]. In this model, the graphite monolayer is placed on the Ti surface of the TIC(111) surface which is formed by six atomic
/
(a)
/ \ 1 \ 0
1st l a y e r Ti ( 4 t h l a y e r C)
•
2nd l a y e r
C
•
3rd l a y e r
Ti
(b) I
i
i
i
i
[
i
i
i
i
I:
Fig. 4. (a) Unit cell of monolayer graphite on T i C ( I l l ) surface. (b) Contour map of the calculated tunneling conductance of monolayer graphite on the TiC(ll 1) surface. Peaks of the tunneling conductance are shown by H, which form a triangular lattice with a twice period of the lattice constant of bulk graphite.
240
M. Tsukada et aL / STM images of chemisorbed moh, cuh, s and outermost layers
layers. In the actual system the graphite structure is incommensurate with that of the substrate. But here we focus on the dominant effect of the electronic interaction introduced by the substrate, so we elongated the C - C bond length of graphite slightly so that it agrees with 1 / 2 of the T i - T i distance. Fig. 4b shows the calculated LDOS of this surface at a plane 5.3 A above the top layer. The energy is 0.5 eV above the Fermi energy. The calculated STM image is quite different from that expected by the graphite layer structure. The strongest current region appears at the center of the carbon network hexagon forming a 2 x 2 superlattice. The weakest current region forms a honeycomb structure, the size of which is twice as large as the original graphite lattice. All the Ti sites on the substrate top layer correspond to the strongest or the weakest current region. The STM image thus reflects strongly the atomic structure of the substrate top layer. The calculated STM image is similar to the short period component of the experimental moir6 pattern.
formation matrix are small. It is discussed under what condition, these situation is realized. To demonstrate numerically the transparency of the admolecule and outermost layer, numerical calculations of the electronic states for the g r a p h i t e / b e n z e n e system, and TIC(111)/graphite monolayer are performed. The benzene on the graphite layer looks more or less transparent and the character of the substrate graphite is visible, when the bias voltage is in the range of 0.1 eV. On the other hand the characteristic ~r electron cloud of the benzene molecule is visible when the bias voltage is increased to about 1.0 eV. Thus the transparency significantly depends on the bias voltage. In the case of T i C ( l i D / g r a p h i t e , the simulated STM image is dramatically different from the normal STM image of graphite surface. Carbon atoms of the top graphite surface cannot be visible in the STM image, but the strong current region rather corresponds to each Ti atom on the substrate layer. This feature of the STM image corresponds to the short period properties of the moird pattern observed in the STM image of this surface.
5. Summary In the present work, the mechanism of the transparency of the adsorbed molecules or the weakly bonded outermost layer is investigated by the analytical theory and the first-principles calculation of the electronic states of the adsorbed systems. The wavefunction of the surface in the far vacuum tail is expressed as a linear combination of two-dimensional plane wave multiplied by the profile function. The profile function for the adsorbate system is written as a linear transformation of the profile functions of the pure substrate: the transformation matrix is a function of the distance from the surface and is obtained by the transfer matrices of the Schr6dinger equations both for the pure substrate and the adsorbate system. The transparency is generally expected, if the off-diagonal elements of the trans-
References [ll w . Mizutani, M. Shigeno, M. On() and K. Kajimura, Appl. Phys. LetI. 56 (1990) 1974. [2] H. Itoh, T. Ichinose, C. Oshima, T. Ichinokawa and T. Aizawa, Surf. Sci. Len. 254 (1991) L437. [3] B.A. Parkinson, F.S. Ohuchi, K. U e n o and A. Koma, Appl. Phys. Lett. 58 (1991) 472. [4] J. Tersoff and D.R. Hamann, Phys. Rev. 31 (1985) 805. [5] M. Tsukada and N. Shim& J. Phys. Soc. Jpn. 56 (1987) 2875. [6] M. Tsukada, H. Adachi and C. Satoko. Prog. Surf. Sci. 14 (1983) 113. [7] K. Kobayashi, Y. Souzu, N. Isshiki and M. Tsukada, Appl. Surf. Sci., to be published. [8] I. Gameson and T. Rayment, Chem. Phys. Len. 123 (1986) 15(1. [9] M. Tsukada, K. Kobayashi, N. Isshiki and H. Kagcshima, Surf. Sci. Rep. 13 (1991) 267.
Applied Surface Science 67 (1993) 235-240 North-Holland
applied surface science
Mechanism of transparent STM images of chemisorbed molecules and outermost layers Masaru Tsukada
a
K a t s u y o s h i K o b a y a s h i " a n d N o b u y u k i Isshiki b
Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan b Institute for Knowledge and Intelligence Science, Kao Corporation, Bunka 2-1-3, Sumida-ku, Tokyo 131, Japan Received 10 August 1992; accepted for publication 18 September 1992
There have been many examples of STM image reported, where depending on the bias value the adsorbate molecules become transparent or a moire pattern is formed between the adlayer and the substrate surface. Analytical theory for the mechanism of the transparency is presented based on the transfer matrix formalism of the surface wavefunction. Examples of the g r a p h i t e / b e n z e n e adsorption systems and T i C ( l l l ) / g r a p h i t e monolayer are investigated by the first-principles L D A calculations.
1. Introduction
In spite of recent rapid progress of scanning tunneling microscopy and its extension toward a variety of application fields, there remain several fundamental problems in STM which await theoretical explanation. In this paper, we address the question about the transparent STM images of some weakly adsorbed molecules as well as the mechanism of moire pattern formation between the outermost layer and a weakly binding substrate surface. This kind of p h e n o m e n a has often been reported in literature. For example, Mizutani et al. [1] observed that the liquid crystal molecules such as 7CB or 8CB supported on graphite surfaces look transparent, and the substrate graphite structure can be visible when the bias voltage is reduced to the range of 0.1 V. On the other hand, the STM image of the same molecules is quite clear for the bias range of 1 eV. So the transparency significantly depends on the bias voltages. Examples of the moire pattern have been reported by several authors. Itoh et al. [2] formed a monolayer of graphite on a clean substrate of TiC or other transition metal carbides and found a very clear moire pattern between the graphite and the substrate structures. Similar moire patterns have been observed on the
transition metal chalcogenide layer unit formed on a different chalcogenide by the van der Waals epitaxial method [3]. The transparency of the molecule or the moire pattern formation would indicate that the tunnel current between tip and surface is sometimes influenced not only by the atomic arrangement of the outermost portion of the surface, but also by the atomic structure underneath. Sometimes the latter becomes even more predominant than the former. The purpose of the present article is to propose a physical insight for these p h e n o m e n a through some analytical arguments based on a transfer matrix formalism for the surface electronic states as well as first-principles calculations of electronic states of weakly chemisorbed systems.
2. Transfer matrix formalism for the local density of states
If the effect of the tip electronic states is ignored, the STM image simply reflects the local density of states (LDOS) of the surface at a certain prove point fixed on the tip [4,5]. In this section we consider how the L D O S outsides the surface is determined by the formalism of the
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
236
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
transfer matrix. The wavefunction at the surface can be generally expressed as Ok,,(r 0, z) = eik"rll E
eiGi'rll~)ikll(Z ),
(1)
By eqs. (4)-(6), one gets the following relation between the wavefunctions at z 2 for the system with and without adsorbates, respectively: N
Gi
where kjl is the crystal momentum in the direction parallel to the surface, and the G, is the 2D inverse lattice vector, and r u and z are the coordinates parallel and perpendicular to the surface, respectively. For the following discussions, it is more convenient to express eq. (1) in a 2N-dimensional vector form as (/) i kll( Z ) eiG"r,,
q~Nkll( Z ) e iGNrl'
Ok,,(rll, z) =
,
(2)
~',,,,(z) e
-= F . S i j ( z 2 )~Jkl[ 0 ( Z 2),
where
Kij(z2) = [TA(rll; Z2, Zl)TO(rll;Zl, Z2)]ii X exp(iGij • rrl ) .
Ok,,(ru, z2)
=
T(rll; Z2, z,)O,,,(rll, z , ) .
Z2)
: Y'a(L
where N is the number of the inverse lattice vectors included in the expansion. Since the Schr6dinger equation defines 2N-dimensional coupled first-order differential equation among Oik 's, the wavefunction in the vector form satisfies the following relation:
(8)
Note that TA(rU; z2, z l) is the inverse matrix of TA(rjp; z I, z2). The left band side of eq. (8) does not depend on z~ and rip if we take the position z~ sufficiently close to the surface. The LDOS of the system with the adsorbates can be expressed as pA(rll ,
~N~,,(Z) e'~' r,,
(7)
j-1
E(k,,)) }2 e
kll
=
i(;j'rll
0
,
A:~ ~ A +,~, (~)<~,,(~), 1
]
~a(E- U(k,,)) kll X
[y'Yi, q(rll, pq
z2)e
,,]
io,,r o, , , 'gavk,r(z2)&uk,,(z2)
(9)
,
where Ypq is defined by
(3)
In the above T(rll; z2, Z1) is the so-called transfer matrix of dimension 2 N x 2N. For the pure substrate we represent the corresponding transfer matrix by T0(rll; z2, zl). Then the wavefunction O°(r I[ I;, z 2) of the pure substrate at some position trll, z 2) far outside the surface is given by
Ypq( r l l , Z 2 ) =
EKi*p(z2)Kjq(Z2) ei(%,-C',"r,,. ij
(10)
where z, corresponds to some position below the top layer. On the other hand, the wavefunction ~0A(r, Z2) for the system with the adsorbed II u molecule (layer) inserted is given by
If the matrix K is almost the unit matrix, namely, in the limit of very weak potential of the adsorbates, Yvq = 1 for any values of p, q. This case corresponds to the complete transparency of the adsorbates as verified by the second line of eq. (9). Less complete transparency of the adsorbates is generally resulted, if the off-diagonal matrix elements of K turns out to be very small. In this case the LDOS of the adsorbates is given by
A A Ok,,(rll, z2) = TA(rlI; Z2, Z l ) ~ k l , ( r l l , Zl) ,
pA(rll , z2)
r i*,,t ot r
U' z 2 ) =
o T0(rll,. z2, z,)~k,(rll, Zl),
(4)
(5)
with the transfer matrix TA(rll; z2, z l) for this system. If the interaction between the substrate and the adsorbate is weak, the wavefunction g,~(r,, z l) is almost the same as ~-k, ,t/)(r II, z1): Ok,t ( r, ' z , ) ~
~k,(0 rll, Zl).
(6)
--- E a ( E - E(k,,)) kll Kpp(Z2) Kqq(Z2) e
X
tq
It~Pkll(Z2)~qkrc(Z2)
,
[lq
(ll)
237
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
which generally shows the similar features as those of the bare substrate, p0(rll, z2), which is defined by eq. (11) with Kpp = Kqq = 1. The order of the off-diagonal elements of K is estimated for the larger value of z and for the peak potential V of the adsorbates as 2m K i j ~- h2
× f V(rH, z) eia';r"qbA*(z)dpA(z)drll dz (k,, +
(i~j).
(k,, + ai) 2 (12)
For the stronger potential, V should be replaced by the T-matrix of the scattering. For the case of I Gil 4: I Gj[, the difference of the spatial extent between ~b/A(z) and ~bA(z), as well as the increase of the denominator of the integrand, tends to reduce the value of the off-diagonal element Kij. In the other words, the scattering of the
~bA(z) exp[i(kll + Gi)'rll] to ~bA(z) by the adsorbates is suppressed, and this favors the transparency. It should be remarked that even for a rather strong potential on the adsorbate layer, the off-diagonal elements are not necessarily large. At the energy close to a molecular level of the adsorbates, the potential V is replaced by the scattering T-matrix, the value of which becomes enhanced due to the resonance effect. This explains why the image of the adsorbates becomes stressed in such a energy region. The 2D Fourier components o f Ypq(rll, z ) (eq. (10)) in the direction of rll contain the wave components of the inverse lattice vectors both of the substrate and adsorbate layer. Thus if the off-diagonal elements of K are of the proper range of values, it is quite easy to show that both the periodicity of the substrate and the adsorbate layer appear in the lateral spatial variation of LDOS, which explains the origin of the the moir6 pattern in the STM image.
wavelet
×exp[i(kll+Gj).rll]
L35A i
'i, ,,
3.35A r
, I I
' i
~.35A Ir
Fig. 1. Atomic structure of ~ - × ~/7-C6H 6 on graphite used for calculation. Left and right side show top and side view, respectively. The small open circles and triangles denote carbon and hydrogen atoms of benzene molecule, respectively. Closed circles denote carbon atoms of graphite.
238
M. Tsukada et al. / S T M images of chemisorbed molecules attd outermost layers
3. The STM image of a benzene molecule supported on a graphite surface
In principle the STM image can be obtained by the numerical calculations of the transfer matrix and thereby obtained matrix Kij in the previous section. However, numerical integration for the transfer matrix often causes instability and require a special numerical device, which we are now developing. Therefore at the present stage, we make calculations of the electronic state of a weakly adsorbed molecule by the first-principles L D A m e t h o d [6], and form the STM image [7]. The model we used is shown in fig. 1. The C - C bond length of a benzene molecule and graphite are 1.40 and 1.42 A, respectively. The distance between the benzene molecularoPlane and the graphite surface is taken as 3.35 A. The molecule is arranged in a ~ - × ( 7 superstructure of the graphite lattice. This structure has been observed by experiment [8]. Figs. 2a and 2b show the STM image of the adsorbed b e n z e n e molecule for a bias voltage + 1.0 and +0.1 V, respectively. For the substrate graphite, a slab model with three atomic layers is used. The height between the tip and the molecule is assumed as 2.6 A. As
(a)
C ~
~
the cluster model of the tip, W l 0 [ l l l ] is used, which from our n u m e r o u s experiences [9] is known to give normal images of surfaces. For the larger bias voltage (fig. 2a), the strong current region distributes like a d o u g h n u t showing the electron cloud on the benzene ring. On the other hand, for the smaller bias value (fig. 2b), the strong current region concentrates on the alternate three carbon atoms. These carbon atoms correspond to the B sites of the substrate graphite surfacc. Therefore the STM image of fig. 2b can be regarded as that of the graphite layer which is visible through the benzene molecule. Why the 7r electron cloud on the benzene ring can be observed only for the larger bias value can be explained by the following way. Fig. 3 shows the density of states ( D O S ) of the g r a p h i t e / C , H ~ , system (full line) c o m p a r e d with the D O S of the substrate graphite without the benzene adsorbates (dashed line). On the top of the figure, the levels of the benzene molecules arranged in the same structure as the adlayer are shown. In the D O S of the g r a p h i t e / C 6 H ~ system, the sharp peaks due to the molecules are clearly seen. They are scarcely changed when the interaction with the substrate is introduced. In the energy region
(b)
F~
~
Fig. 2. The contour plot of STM images of ~- x ~- - C6M 6 on graphite. The distance between the tip and the benzene molecule is set to 2.6 ,~. A tungsten tip protruded to [111] direction of crystal is used. Crosses and triangles show the carbon and hydrogen atoms of benzene molecules. Circles show the carbon atoms of graphite. (a) Surface bias is 1.0 eV. (b) Surface bias is 0.1 eV.
M. Tsukada et al. / STM images of chemisorbed molecules and outermost layers
70.0 I 60.0 f
5o.oI ,_ 40.0 o ~3
30.0 e,,
20.0 10.0 0.0
t~L
-20.0
-15.0
-10.0
-5.0
EF
5.0
Energy (eV)
Fig. 3. Density of states of ~ - × !~--C6H 6 on graphite (solid line) and H O P G (dashed line). Bars on the upper side show the energy level of the benzene molecule.
close to the Fermi level of the adsorbed system, there are no levels of benzene: the highest occupied molecular level ( H O M O ) and the lowest unoccupied molecular level ( L U M O ) are apart from E F by about 3 eV, as seen in fig. 3. Therefore for the energy of the tunnel electron close to E v, the off-diagonal elements of the K-matrix are small. In such a case the L D O S would be determined by eq. (11). Namely, an intervening molecular layer does not significantly destroy the substrate image, as discussed in the previous section. As opposed to this situation, when the energy of the tunnel electron approaches to the molecular level of the adsorbate, the scattering effect by the molecule becomes significant. In this case the tail of the wavefunction of the tunnel electron experiences very strong modification in the lateral direction. This results in the enhancement of the off-diagonal elements of K. Therefore the structure of the admolecule dominates in the vacuum tail and the STM image solely reflects the structure of the molecule.
4. The STM image of a graphite monolayer on TiC(lll) Formation of the graphite monolayer on a clean transition metal or their carbide surfaces has attracted much attention recently. Among
239
many interesting properties of these systems, the formation of the moire pattern provides us a mystery to be solved [7]. For the case of the TIC(111) substrate there observed two periods of the moire pattern, the shorter one of the order of 5 ,~, about twice as large as the graphite lattice o vector, and the longer one of the order of 27 A. The moire pattern changes considerably with the variation of the bias voltage, but the periodicity of the graphite lattice cannot be seen. In order to clarify the effect of the substrate on the STM image of the graphite monolayer, we performed the electronic state calculation on the model as shown in fig. 4a [7]. In this model, the graphite monolayer is placed on the Ti surface of the TIC(111) surface which is formed by six atomic
/
(a)
/ \ 1 \ 0
1st l a y e r Ti ( 4 t h l a y e r C)
•
2nd l a y e r
C
•
3rd l a y e r
Ti
(b) I
i
i
i
i
[
i
i
i
i
I:
Fig. 4. (a) Unit cell of monolayer graphite on T i C ( I l l ) surface. (b) Contour map of the calculated tunneling conductance of monolayer graphite on the TiC(ll 1) surface. Peaks of the tunneling conductance are shown by H, which form a triangular lattice with a twice period of the lattice constant of bulk graphite.
240
M. Tsukada et aL / STM images of chemisorbed moh, cuh, s and outermost layers
layers. In the actual system the graphite structure is incommensurate with that of the substrate. But here we focus on the dominant effect of the electronic interaction introduced by the substrate, so we elongated the C - C bond length of graphite slightly so that it agrees with 1 / 2 of the T i - T i distance. Fig. 4b shows the calculated LDOS of this surface at a plane 5.3 A above the top layer. The energy is 0.5 eV above the Fermi energy. The calculated STM image is quite different from that expected by the graphite layer structure. The strongest current region appears at the center of the carbon network hexagon forming a 2 x 2 superlattice. The weakest current region forms a honeycomb structure, the size of which is twice as large as the original graphite lattice. All the Ti sites on the substrate top layer correspond to the strongest or the weakest current region. The STM image thus reflects strongly the atomic structure of the substrate top layer. The calculated STM image is similar to the short period component of the experimental moir6 pattern.
formation matrix are small. It is discussed under what condition, these situation is realized. To demonstrate numerically the transparency of the admolecule and outermost layer, numerical calculations of the electronic states for the g r a p h i t e / b e n z e n e system, and TIC(111)/graphite monolayer are performed. The benzene on the graphite layer looks more or less transparent and the character of the substrate graphite is visible, when the bias voltage is in the range of 0.1 eV. On the other hand the characteristic ~r electron cloud of the benzene molecule is visible when the bias voltage is increased to about 1.0 eV. Thus the transparency significantly depends on the bias voltage. In the case of T i C ( l i D / g r a p h i t e , the simulated STM image is dramatically different from the normal STM image of graphite surface. Carbon atoms of the top graphite surface cannot be visible in the STM image, but the strong current region rather corresponds to each Ti atom on the substrate layer. This feature of the STM image corresponds to the short period properties of the moird pattern observed in the STM image of this surface.
5. Summary In the present work, the mechanism of the transparency of the adsorbed molecules or the weakly bonded outermost layer is investigated by the analytical theory and the first-principles calculation of the electronic states of the adsorbed systems. The wavefunction of the surface in the far vacuum tail is expressed as a linear combination of two-dimensional plane wave multiplied by the profile function. The profile function for the adsorbate system is written as a linear transformation of the profile functions of the pure substrate: the transformation matrix is a function of the distance from the surface and is obtained by the transfer matrices of the Schr6dinger equations both for the pure substrate and the adsorbate system. The transparency is generally expected, if the off-diagonal elements of the trans-
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