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Scanning tunneling spectroscopy of d states from a transition metal surface: theoretical study
Vacuum 54 (1999) 131 — 136
Scanning tunneling spectroscopy of d states from a transition metal surface: theoretical study L. Jurczyszyn*, B. Stankiewicz Institute of Experimental Physics, University of Wroc!aw, pl. Maxa Borna 9, 50-204 Wroc!aw, Poland
Abstract We present a theoretical study of the influence of localized d states from a transition metal surface on the tunneling spectra obtained by scanning tunneling spectroscopy (STS). This problem is considered here for the system formed by a Ni(0 0 1) surface and an Al or Ni tip. It is found, that the d band of a Ni(0 0 1) substrate could considerably modify the STS tunneling spectra, but only for very small (around 2.5 As ) tip—sample distances. The obtained results also show that the d band features in STS spectra depend strongly on the properties of the STM tip. 1999 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction The role of d orbitals in electron tunneling between the STM tip and the sample surface is still not clear. For greater tip—sample separation, the influence of strongly localized d states is not very important. But it seems possible that for very small tip—sample distance, the localized d states (which may have a high density near the Fermi level) could be very active in electron tunneling between the tip and the sample [1—3]. In this paper, we present a theoretical study of the scanning tunneling spectroscopy (STS) from a transition metal surface. In particular, we consider an interesting problem of the probable influence of d states from a transition metal substrate on the STS tunneling spectra. Some STS measurements performed for transition metal surfaces indicate the presence of d states features in the obtained spectra [4, 5]. Other experimental results, however, do not confirm any structure related to the d states of the substrate [6]. The aim of the present paper is to determine the conditions necessary for observation of the substrate d states by STS. This problem is discussed here for STS from Ni(0 0 1). It is well-known, that the STS spectra are very sensitive to the electronic and atomic properties of the tip [7, 8].
* Corresponding author.
To consider additionally the effects connected with the electronic properties of a particular tip, we have performed calculations of the STS spectra for two different tips, formed by Al and Ni atoms.
2. Model and method of calculation Description of the tunneling current between the tip and the sample is based on the non-equilibrium Green-function formalism developed by Keldysh [9]. This approach is very useful for studying the coherent tunneling through different orbitals in the tip—sample system, and — because it is not based on any perturbation theory — it is accurate even for small tip—sample separation. This method was used by Carolli et al. [10, 11] in theoretical studies of electronic tunneling in microstructures; later, it was also adopted for an STM study [12, 13]. The method starts from the complete Hamiltonian of the tip—sample system. It can be written as a sum of three terms, describing the tip (H< ), sample (H< ), and the inter2 1 action between them (H< ) ' H< "H< #H< #H< . 2 1 '
(1)
The tip—sample interaction is described as a superposition of the hopping processes between the orbitals of the tip and sample atoms, which leads to the following
0042-207X/99/$ — see front matter 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 9 8 ) 0 0 4 4 8 - 5
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
expression for H< : ' H< " [¹< (aj) c' R (a)c' ( j)#¹< ( ja) c' R ( j)c' (a)] . (2) ' 21 2 1 12 1 2 ? H Summation in (2) is performed over the orbitals from both parts of the system. The elements of the matrix ¹< denote hoppings between the orbitals of the tip and 21 the sample. When the tip—sample system is in a stationary state (defined by the applied voltage), the total current between the tip and the sample can be described as follows [11]:
Fig. 1. Schematic plot of the cluster-Bethe-lattice model representing the tip—sample system: dashed lines denote Bethe lattices connected to the clusters of the tip (5-atom cluster in the form of a pyramid) and the sample (25-atom square cluster).
J"(ie/ ) [ ¹< (a j) 1c' R (a)c' ( j)2!¹< ( ja)1c' R ( j)c' (a)2]. 21 2 1 12 1 2 ? H (3) As it has been shown in previous papers [9, 12], the Keldysh method enables us to pass from a general formula (3) to the following equation for the tunneling current: J"(4ne/ )
>
\ Tr[ (¹< 21 oL 11 (u)D< 011 (u)¹< 12 oL 22 (u)D< 22 (u)]
;[ f (u)!f (u) ] du , 2 1 where
(4)
D< 0 (u)"[ I< !¹< g' 0 (u)¹< g' 0 (u)]\ 11 12 22 21 11 and D< (u)"[ I< !¹< g' (u)¹< g' (u)]\. 22 21 11 12 22
Fig. 2. Density-of-states distributions of the nickel substrate: (a) dotted and solid line denotes total d states and s—p states distributions, respectively; (b) dotted lines represent the density of particular d states, while dashed lines denote s and p states; increase of the length of dash corresponds to s, p , and p —p states, respectively. X V W
Fig. 3. Density-of-states distributions at the apex atom of the Al tip: solid line represents the total density, dotted line denotes the s state, while short- and long-dashed lines correspond to p and p —p states, X V W respectively.
L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
133
Fig. 4. Evolution of the differential conductance dI/d» of the Al-tip—Ni(1 0 0) system for different tip—sample distances (tip is located directly above a surface atom) : (a) 2.0 As , (b) 2.5 As , (c) 3.0 As , (d) 3.5 As , (e) 4.0 As , (f ) 4.5 As . Solid lines denote total differential conductance dI/d», while dotted and dashed lines represent the contributions connected with the tunneling from d and s—p orbitals of the surface Ni atom located below the tip.
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Eq. (4) shows that for the calculation of the tunneling current we need to know the matrices of the Green functions (g' and g' 0 — for the tip; g' and g' 0 — for the 22 22 11 11 sample) and the density of states (oK — for the tip; 22 oL — for the sample) when the tip and the sample are 11 uncoupled (i.e., when ¹< "0). We also have to find the 21 matrix ¹< for hoppings between the orbitals from the 21 tip and the sample; as it has already been shown in [14], these hopping interactions can be calculated via the expression for the Bardeen tunneling current between particular orbitals. Investigation of the influence of d states of the sample on the STS spectra is performed here for the system formed by (1 0 0) nickel surface and the STM tip built by Al or Ni atoms. In our model consideration, the matrices of the Green functions and the density of states of the tip and the sample (necessary for the calculation of the tunneling current) have been calculated within the cluster-Bethe-lattice method. In this approach, the nickel surface is represented by a square cluster of 25 atoms; the influence of the rest of the crystal is simulated here by a Bethe lattice connected to this cluster (cf. Fig. 1). The same approach is used for the description of the tip: the top of it is represented by a cluster of a few atoms, while the influence of the rest of the tip is simulated by a Bethe lattice. We have assumed that the top of the tip has a form of pyramid with a single atom at the apex and four atoms at the basis. Geometry of the clusters representing the tip and the sample is determined by the fcc structure, with distances between the atoms equal to those in the bulk of a metal. To calculate the density of states and the Green function matrices of the tip and the sample, we have used the tight-binding approach with the parameters taken from [15]. We have introduced a self-consistency by imposing a local charge neutrality condition at each atom.
respectively, of the surface nickel atom situated directly below the apex of the tip. The obtained results show that for very small tipsample distances, dI/d» has a wide and high maximum, which appears for about 2 V of the sample voltage. This maximum is built mainly by the conductance contribution connected with the tunneling from d orbitals of the surface nickel atom (cf. parts a and b of Fig. 4). But the increase of the tip—sample separation decreases quickly the d states contribution, so already for the distance of 4 As , the tunneling from d orbitals of Ni surface atoms practically does not influence the tunneling spectra. The small peak below Fermi level of nickel, which still occurs in parts e and f of Fig. 4, represents the complex convolution of s—p states from the Al tip and the Ni surface; it does not contain any contribution from Ni d states, in contrast with cases a and b of Fig. 4. The density-of-states distributions of the apex atom of the Ni tip are presented in Fig. 5. It was assumed (like in the previous case) that the apex of the tip is located directly above a surface Ni atom. The obtained tunneling spectra (cf. Fig. 6) show that the electronic structure of the tip strongly influence the evolution of the differential conductance. The two main maxima, occuring in the tunneling spectra (cf. Fig. 6), are directly connected with the corresponding peaks in the density-of-states distributions shown in Fig. 5. The first one (around !1 V of the sample voltage in Fig. 6) is caused by the narrow band of d states of the Ni tip (a sharp and high peak in
3. Results The density-of-states distribution at a surface atom of the Ni(0 0 1) substrate, with the band of d states, is shown in Fig. 2. Study of the influence of these localized d states of Ni substrate on the STS spectra is based here on the analysis of the evolution of the differential conductance dI/d», calculated for Al and Ni tip. Let us consider first the results obtained within aluminium tip: density-of-states distributions of the apex atom of the Al tip are shown in Fig. 3. The set of dependences in Fig. 4 presents the evolution of the differential conductance dI/d» (as a function of the voltage applied to the sample) for six different distances between the tip and the sample; in all cases, the tip is located directly above the surface Ni atom. Solid curves denote the total dI/d», while dashed and dotted lines represent the contributions connected with the tunneling from s—p and d orbitals,
Fig. 5. Density-of-states distributions at the apex atom of the Ni tip: solid line represents the total density, dotted line denotes d states, while dashed line represents s—p states.
L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Fig. 6. The same as in Fig. 4, but for the Ni-tip—Ni(1 0 0) system.
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Fig. 5, dotted line). The second pronounced feature, which appears in Fig. 6 (around 6 V of the sample voltage), is connected with the peak of the density of states formed by s states of the Ni tip (cf. Fig. 5, dashed line). For small tip-sample separation, the highest peak in the calculated spectra (parts a and b of Fig. 6) is caused by the narrow band of d states of the Ni tip. With increase of the distance, this peak becomes smaller, but — as it follows from parts e and f of Fig. 6 — it remains well visible also for distances greater then 4 As . Comparison of the density-of-states distributions from the nickel tip and the nickel substrate (cf. Figs. 2 and 5) shows that the maximum of d states from the nickel surface (cf. Fig. 2) is much broader and not as high as in the case of the tip apex atom (cf. Fig. 5). As a consequence, the influence of d states from the nickel substrate on the differential conductance in a tip—sample system is much weaker than that of the narrow d band of the nickel tip. Results presented in Fig. 6 show that the band of d states from the nickel surface appears in the spectra only in the form of a weak shoulder (for the sample voltage around 1 V, cf. parts a and b of Fig. 6). This d band shoulder occurs there only for the distance of 2—2.5 As ; for greater tip—sample separations it completely disappears from the tunneling spectra (cf. parts e and f of Fig. 6).
4. Conclusions Calculations of the STS spectra show that the band of d states from the Ni(0 0 1) substrate could be observed by scaning tunneling spectroscopy, but only for very small tip—substrate distances (around 2—3 As ). We have found that in such a case (i.e., for very small tip—sample separation), the d band of the nickel surface could considerably modify the tunneling spectra. Additionally, we have also shown that the d band features, generated by the Ni substrate, depend strongly on the properties of the tip. They have the form of a high peak (for Al tip) or only a weak shoulder (for Ni tip). The obtained results indicate also that in both of the considered cases (i.e., for Al and Ni tips), features connected with d band of the Ni(0 0 1) substrate disappear already for the tip—sample distance
around 3.5 As . As it follows from our calculations, the condition necessary for the detection of the substrate d states depends strongly on the tip—sample distance (it must not be greater than 3 As ) as well as on the properties of the tip. We suggest it to be the reason why some STS measurements indicate the presence of d states features, while the others do not confirm it. On the other hand, the obtained results show that the narrow band of d states of the Ni tip (which are of a very high density) could influence considerably the STS spectra even for larger distances.
Acknowledgements This work has been supported by the University of Wroc"aw within the grant No. 2016/W/IFD/97.
References [1] Doyen G, Koetter E, Barth J, Drakova D. In: Proc NATO Advanced Study Institute on Basic Concepts and Applications of Scanning Tunneling Microscopy. Dordrecht: Kluwer Academic Publishers, 1990; 97. [2] Mingo N, Jurczyszyn L, Garcia-Vidal FJ, Saiz-Pardo R, de Andres PL, Flores F, Wu SY, More W. Phys Rev B 1996;54:2225. [3] Jurczyszyn L, Mingo N, Flores F. Acta Phys Polon A 1997; 93:307. [4] Kaiser WJ, Jaklevic PJ. IBM J Res Dev 1986;30:396. [5] Kuk Y, Silverman PJ, Chua FM. J Microsc 1988;152:449. [6] Brodde A, Toch S, Neddermeyer H. J Microsc 1988;152:441. [7] Tomitori M, Sugata K, Okuyama G, Kimata H. Surf Sci 1996; 335:21. [8] Kubby JA, Boland JJ. Surf Sci Rep 1996;26:1. [9] Keldysh LV. Zh Eksp Teor Phys 1964;47:1515. Sov Phys JETP 1965;20:1018. [10] Caroli C, Combescot R, Nozieres P, Saint-James D. J Phys C 1971;4:916. [11] Caroli, C, Combescot, R, Nozieres P, Saint-James D. J Phys C 1972;5:21. [12] Martin-Rodero A, Flores F, March NH. Phys Rev B 1988;38: 10047. [13] Ferrer J, Martin-Rodero A, Flores F. Phys Rev B 1988;38:10113. [14] Flores, F, Martin-Rodero A, Goldberg EC, Duran JC. Nuovo Cimento D 1988;10:303. [15] Papaconstantopoulos DA. Handbook of the band structure of elemental solids. New York: Plenum Press, 1986.
Scanning tunneling spectroscopy of d states from a transition metal surface: theoretical study L. Jurczyszyn*, B. Stankiewicz Institute of Experimental Physics, University of Wroc!aw, pl. Maxa Borna 9, 50-204 Wroc!aw, Poland
Abstract We present a theoretical study of the influence of localized d states from a transition metal surface on the tunneling spectra obtained by scanning tunneling spectroscopy (STS). This problem is considered here for the system formed by a Ni(0 0 1) surface and an Al or Ni tip. It is found, that the d band of a Ni(0 0 1) substrate could considerably modify the STS tunneling spectra, but only for very small (around 2.5 As ) tip—sample distances. The obtained results also show that the d band features in STS spectra depend strongly on the properties of the STM tip. 1999 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction The role of d orbitals in electron tunneling between the STM tip and the sample surface is still not clear. For greater tip—sample separation, the influence of strongly localized d states is not very important. But it seems possible that for very small tip—sample distance, the localized d states (which may have a high density near the Fermi level) could be very active in electron tunneling between the tip and the sample [1—3]. In this paper, we present a theoretical study of the scanning tunneling spectroscopy (STS) from a transition metal surface. In particular, we consider an interesting problem of the probable influence of d states from a transition metal substrate on the STS tunneling spectra. Some STS measurements performed for transition metal surfaces indicate the presence of d states features in the obtained spectra [4, 5]. Other experimental results, however, do not confirm any structure related to the d states of the substrate [6]. The aim of the present paper is to determine the conditions necessary for observation of the substrate d states by STS. This problem is discussed here for STS from Ni(0 0 1). It is well-known, that the STS spectra are very sensitive to the electronic and atomic properties of the tip [7, 8].
* Corresponding author.
To consider additionally the effects connected with the electronic properties of a particular tip, we have performed calculations of the STS spectra for two different tips, formed by Al and Ni atoms.
2. Model and method of calculation Description of the tunneling current between the tip and the sample is based on the non-equilibrium Green-function formalism developed by Keldysh [9]. This approach is very useful for studying the coherent tunneling through different orbitals in the tip—sample system, and — because it is not based on any perturbation theory — it is accurate even for small tip—sample separation. This method was used by Carolli et al. [10, 11] in theoretical studies of electronic tunneling in microstructures; later, it was also adopted for an STM study [12, 13]. The method starts from the complete Hamiltonian of the tip—sample system. It can be written as a sum of three terms, describing the tip (H< ), sample (H< ), and the inter2 1 action between them (H< ) ' H< "H< #H< #H< . 2 1 '
(1)
The tip—sample interaction is described as a superposition of the hopping processes between the orbitals of the tip and sample atoms, which leads to the following
0042-207X/99/$ — see front matter 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 9 8 ) 0 0 4 4 8 - 5
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
expression for H< : ' H< " [¹< (aj) c' R (a)c' ( j)#¹< ( ja) c' R ( j)c' (a)] . (2) ' 21 2 1 12 1 2 ? H Summation in (2) is performed over the orbitals from both parts of the system. The elements of the matrix ¹< denote hoppings between the orbitals of the tip and 21 the sample. When the tip—sample system is in a stationary state (defined by the applied voltage), the total current between the tip and the sample can be described as follows [11]:
Fig. 1. Schematic plot of the cluster-Bethe-lattice model representing the tip—sample system: dashed lines denote Bethe lattices connected to the clusters of the tip (5-atom cluster in the form of a pyramid) and the sample (25-atom square cluster).
J"(ie/ ) [ ¹< (a j) 1c' R (a)c' ( j)2!¹< ( ja)1c' R ( j)c' (a)2]. 21 2 1 12 1 2 ? H (3) As it has been shown in previous papers [9, 12], the Keldysh method enables us to pass from a general formula (3) to the following equation for the tunneling current: J"(4ne/ )
>
\ Tr[ (¹< 21 oL 11 (u)D< 011 (u)¹< 12 oL 22 (u)D< 22 (u)]
;[ f (u)!f (u) ] du , 2 1 where
(4)
D< 0 (u)"[ I< !¹< g' 0 (u)¹< g' 0 (u)]\ 11 12 22 21 11 and D< (u)"[ I< !¹< g' (u)¹< g' (u)]\. 22 21 11 12 22
Fig. 2. Density-of-states distributions of the nickel substrate: (a) dotted and solid line denotes total d states and s—p states distributions, respectively; (b) dotted lines represent the density of particular d states, while dashed lines denote s and p states; increase of the length of dash corresponds to s, p , and p —p states, respectively. X V W
Fig. 3. Density-of-states distributions at the apex atom of the Al tip: solid line represents the total density, dotted line denotes the s state, while short- and long-dashed lines correspond to p and p —p states, X V W respectively.
L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
133
Fig. 4. Evolution of the differential conductance dI/d» of the Al-tip—Ni(1 0 0) system for different tip—sample distances (tip is located directly above a surface atom) : (a) 2.0 As , (b) 2.5 As , (c) 3.0 As , (d) 3.5 As , (e) 4.0 As , (f ) 4.5 As . Solid lines denote total differential conductance dI/d», while dotted and dashed lines represent the contributions connected with the tunneling from d and s—p orbitals of the surface Ni atom located below the tip.
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Eq. (4) shows that for the calculation of the tunneling current we need to know the matrices of the Green functions (g' and g' 0 — for the tip; g' and g' 0 — for the 22 22 11 11 sample) and the density of states (oK — for the tip; 22 oL — for the sample) when the tip and the sample are 11 uncoupled (i.e., when ¹< "0). We also have to find the 21 matrix ¹< for hoppings between the orbitals from the 21 tip and the sample; as it has already been shown in [14], these hopping interactions can be calculated via the expression for the Bardeen tunneling current between particular orbitals. Investigation of the influence of d states of the sample on the STS spectra is performed here for the system formed by (1 0 0) nickel surface and the STM tip built by Al or Ni atoms. In our model consideration, the matrices of the Green functions and the density of states of the tip and the sample (necessary for the calculation of the tunneling current) have been calculated within the cluster-Bethe-lattice method. In this approach, the nickel surface is represented by a square cluster of 25 atoms; the influence of the rest of the crystal is simulated here by a Bethe lattice connected to this cluster (cf. Fig. 1). The same approach is used for the description of the tip: the top of it is represented by a cluster of a few atoms, while the influence of the rest of the tip is simulated by a Bethe lattice. We have assumed that the top of the tip has a form of pyramid with a single atom at the apex and four atoms at the basis. Geometry of the clusters representing the tip and the sample is determined by the fcc structure, with distances between the atoms equal to those in the bulk of a metal. To calculate the density of states and the Green function matrices of the tip and the sample, we have used the tight-binding approach with the parameters taken from [15]. We have introduced a self-consistency by imposing a local charge neutrality condition at each atom.
respectively, of the surface nickel atom situated directly below the apex of the tip. The obtained results show that for very small tipsample distances, dI/d» has a wide and high maximum, which appears for about 2 V of the sample voltage. This maximum is built mainly by the conductance contribution connected with the tunneling from d orbitals of the surface nickel atom (cf. parts a and b of Fig. 4). But the increase of the tip—sample separation decreases quickly the d states contribution, so already for the distance of 4 As , the tunneling from d orbitals of Ni surface atoms practically does not influence the tunneling spectra. The small peak below Fermi level of nickel, which still occurs in parts e and f of Fig. 4, represents the complex convolution of s—p states from the Al tip and the Ni surface; it does not contain any contribution from Ni d states, in contrast with cases a and b of Fig. 4. The density-of-states distributions of the apex atom of the Ni tip are presented in Fig. 5. It was assumed (like in the previous case) that the apex of the tip is located directly above a surface Ni atom. The obtained tunneling spectra (cf. Fig. 6) show that the electronic structure of the tip strongly influence the evolution of the differential conductance. The two main maxima, occuring in the tunneling spectra (cf. Fig. 6), are directly connected with the corresponding peaks in the density-of-states distributions shown in Fig. 5. The first one (around !1 V of the sample voltage in Fig. 6) is caused by the narrow band of d states of the Ni tip (a sharp and high peak in
3. Results The density-of-states distribution at a surface atom of the Ni(0 0 1) substrate, with the band of d states, is shown in Fig. 2. Study of the influence of these localized d states of Ni substrate on the STS spectra is based here on the analysis of the evolution of the differential conductance dI/d», calculated for Al and Ni tip. Let us consider first the results obtained within aluminium tip: density-of-states distributions of the apex atom of the Al tip are shown in Fig. 3. The set of dependences in Fig. 4 presents the evolution of the differential conductance dI/d» (as a function of the voltage applied to the sample) for six different distances between the tip and the sample; in all cases, the tip is located directly above the surface Ni atom. Solid curves denote the total dI/d», while dashed and dotted lines represent the contributions connected with the tunneling from s—p and d orbitals,
Fig. 5. Density-of-states distributions at the apex atom of the Ni tip: solid line represents the total density, dotted line denotes d states, while dashed line represents s—p states.
L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Fig. 6. The same as in Fig. 4, but for the Ni-tip—Ni(1 0 0) system.
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L. Jurczyszyn, B. Stankiewicz / Vacuum 54 (1999) 131—136
Fig. 5, dotted line). The second pronounced feature, which appears in Fig. 6 (around 6 V of the sample voltage), is connected with the peak of the density of states formed by s states of the Ni tip (cf. Fig. 5, dashed line). For small tip-sample separation, the highest peak in the calculated spectra (parts a and b of Fig. 6) is caused by the narrow band of d states of the Ni tip. With increase of the distance, this peak becomes smaller, but — as it follows from parts e and f of Fig. 6 — it remains well visible also for distances greater then 4 As . Comparison of the density-of-states distributions from the nickel tip and the nickel substrate (cf. Figs. 2 and 5) shows that the maximum of d states from the nickel surface (cf. Fig. 2) is much broader and not as high as in the case of the tip apex atom (cf. Fig. 5). As a consequence, the influence of d states from the nickel substrate on the differential conductance in a tip—sample system is much weaker than that of the narrow d band of the nickel tip. Results presented in Fig. 6 show that the band of d states from the nickel surface appears in the spectra only in the form of a weak shoulder (for the sample voltage around 1 V, cf. parts a and b of Fig. 6). This d band shoulder occurs there only for the distance of 2—2.5 As ; for greater tip—sample separations it completely disappears from the tunneling spectra (cf. parts e and f of Fig. 6).
4. Conclusions Calculations of the STS spectra show that the band of d states from the Ni(0 0 1) substrate could be observed by scaning tunneling spectroscopy, but only for very small tip—substrate distances (around 2—3 As ). We have found that in such a case (i.e., for very small tip—sample separation), the d band of the nickel surface could considerably modify the tunneling spectra. Additionally, we have also shown that the d band features, generated by the Ni substrate, depend strongly on the properties of the tip. They have the form of a high peak (for Al tip) or only a weak shoulder (for Ni tip). The obtained results indicate also that in both of the considered cases (i.e., for Al and Ni tips), features connected with d band of the Ni(0 0 1) substrate disappear already for the tip—sample distance
around 3.5 As . As it follows from our calculations, the condition necessary for the detection of the substrate d states depends strongly on the tip—sample distance (it must not be greater than 3 As ) as well as on the properties of the tip. We suggest it to be the reason why some STS measurements indicate the presence of d states features, while the others do not confirm it. On the other hand, the obtained results show that the narrow band of d states of the Ni tip (which are of a very high density) could influence considerably the STS spectra even for larger distances.
Acknowledgements This work has been supported by the University of Wroc"aw within the grant No. 2016/W/IFD/97.
References [1] Doyen G, Koetter E, Barth J, Drakova D. In: Proc NATO Advanced Study Institute on Basic Concepts and Applications of Scanning Tunneling Microscopy. Dordrecht: Kluwer Academic Publishers, 1990; 97. [2] Mingo N, Jurczyszyn L, Garcia-Vidal FJ, Saiz-Pardo R, de Andres PL, Flores F, Wu SY, More W. Phys Rev B 1996;54:2225. [3] Jurczyszyn L, Mingo N, Flores F. Acta Phys Polon A 1997; 93:307. [4] Kaiser WJ, Jaklevic PJ. IBM J Res Dev 1986;30:396. [5] Kuk Y, Silverman PJ, Chua FM. J Microsc 1988;152:449. [6] Brodde A, Toch S, Neddermeyer H. J Microsc 1988;152:441. [7] Tomitori M, Sugata K, Okuyama G, Kimata H. Surf Sci 1996; 335:21. [8] Kubby JA, Boland JJ. Surf Sci Rep 1996;26:1. [9] Keldysh LV. Zh Eksp Teor Phys 1964;47:1515. Sov Phys JETP 1965;20:1018. [10] Caroli C, Combescot R, Nozieres P, Saint-James D. J Phys C 1971;4:916. [11] Caroli, C, Combescot, R, Nozieres P, Saint-James D. J Phys C 1972;5:21. [12] Martin-Rodero A, Flores F, March NH. Phys Rev B 1988;38: 10047. [13] Ferrer J, Martin-Rodero A, Flores F. Phys Rev B 1988;38:10113. [14] Flores, F, Martin-Rodero A, Goldberg EC, Duran JC. Nuovo Cimento D 1988;10:303. [15] Papaconstantopoulos DA. Handbook of the band structure of elemental solids. New York: Plenum Press, 1986.