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Field evaporation in the configuration of a scanning tunneling microscope
Ultramicroscopy 73 (1998) 147—155
Field evaporation in the configuration of a scanning tunneling microscope Zhiyang Li!,*, Wu Liu!, Xingjiao Li" ! Department of Physics, Central China Normal University, Wuhan 430079, People+s Republic of China " Department of Solid State Electronics, Huazhong University of Science and Technology, Wuhan 430074, People+s Republic of China Received 7 July 1997; received in revised form 10 November 1997
Abstract The paper introduced an effective binding energy K@ and emphasized the role it plays in the field evaporation in the %&& configuration of a scanning tunneling microscope (STM). With this K@ an important modification has been made to %&& Tsong’s CE model formula for STM [Tien T. Tsong, Phys. Rev. B 44 (1991) 13 703]. As a consequence, for tip—sample distance 5(d(13 A_ , the high evaporation fields from Tsong’s original formula were found greatly reduced. When d"7.23 A_ , the recalculated evaporation field for Au~1 is 0.6 V/A_ , which is in good agreement with Chang’s experiment [Phys. Rev. Lett. 72 (1994) 574]. Further the evaporation field was found highly localized. For d"7.52 A_ , the evaporation field of Au~1 on top of a Au(1 1 1) surface atom was found several times lower than that at a hollow site. In the calculation we have proposed a universal binding function. In addition selected experimental results on nanostructure formation by positive or negative voltage pulses with Au, Ni, Cu, Pt(Ir) and W tips on Au(1 1 1) substrate with a STM working in atmosphere were presented. The processes were found to bear important feature of field evaporation. ( 1998 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Recently making nanostructures by field evaporation in the configuration of a scanning tunneling microscope (STM) has been the interest of many researchers [1—13]. It is now clear that field evaporation in STM is much different than that in field ion
* Corresponding author. Tel.: #86 27 7865701 3524; fax: #86 27 7876070; e-mail: [email protected].
microscope (FIM). First the evaporation field in STM is found several times lower. Next both positive and negative ions could be evaporated. Further the evaporation rate could be several orders higher than that in FIM. Theories concerning the physical process, though far from complete solution of the problem, have emerged from two different ways resulting in two different classes of theories, namely the phenomenological theory and the microscopic one. In the former class Tsong, in the spirit of classical field evaporation theory in FIM, constructed charge-exchange (CE) and image-hump (IH)
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
model for STM [14], and the evaporation fields of a large number of metals were calculated. Unfortunately the calculated evaporation fields were some how high above the experimental values. For example, the calculated evaporation field for Au~1 was 1.7 V/A_ at a tip—sample distance of 6 A_ and an evaporation rate of only 1 s~1, while Chang’s experiment turned out to be about 0.6 V/A_ at a tip sample distance d"6.4$1 A_ and with an evaporation rate that was several orders higher. Because of this theoretical failure to account for the low evaporation field in STM, Pascual et al. denied the atom mounds formation in STM to be a field evaporation process [15]. In the latter class, Lang first gave a microscopic calculation by modeling STM as two jellium electrodes with an adatom between them [16]. The force, energy, and electron density were all calculated self-consistently. A little later Hirose offered a first principle calculation in which the atomic structure of the tip was considered [17]. While microscopic theory is helpful in deepening our understanding of the physical nature of the field evaporation process, the phenomenological theory has been found very useful in the prediction of evaporation field in FIM and we expect it continue to do so in STM. In this paper first we will introduce in Section 2 an effective binding energy K@ to replace the total %&& binding energy K@ in Tsong’s CE model formula. %&& To calculate K@ , in Section 3, the atomic potential %&& curves for Au/Au, Cu/Cu, Ag/Ag, and W/W adatom—metal systems are calculated, then a universal binding energy function for the adatom— metal system was proposed. In Section 4, the evaporation fields for Au/Au, Cu/Cu, Ag/Ag, and W/W tip/sample combinations were calculated with the new formula. And further the localization of evaporation field is discussed. In Section 5, some selected experimental results on nanostructure formation with Au, Cu, Ni, Pt(Ir), and W tips on Au(1 1 1) substrate in atmosphere are presented.
2. Effective binding energy For convenience of discussion we first review briefly the CE model, which Tsong adapted from FIM to STM [14]. It is assumed that a STM might
Fig. 1. Total atomic potential º and ionic potential º (F) (or ! * º (0) when no field applied) (solid lines) separately as the sum of * that of the tip and the sample (dashed lines) in STM. With subscript t denotes tip, s for sample, a for atomic, and i for ionic. K@ is the total binding energy, K is the binding energy of an isolated electrode (sublime energy). The height of the hump, K@ %&& in the middle of º is the effective binding energy defined in the ! context (here the tip and sample are made of identical metal).
be regarded as a double electrode system. And the atomic(ionic) potential in STM could be taken as the sum of the potentials of the two isolated electrodes as shown in Fig. 1. For simplicity the tip has been approximated by a flat surface and the external field applied between the tip and substrate is assumed to be uniform. At a critical point where the ionic potential curve intersects with the atomic one, the atom would first be field ionized and then evaporated away from the surface. In low-temperature evaporation, the field should be large enough to pull the intersection point down to the equilibrium position of the adatom, that is to K@, where K@ is the total binding energy. Neglecting the shortrange repulsive interaction, Tsong arrived at the following equation for the evaporation field in STM:
C
1 n n2e2 F " K@# + I !n U! STM nr i 16pe r 0 00 i/1 v n2e2 ! !K¹ ln V/A_ , i 16pe (d!r ) 0 0
A BD
(1)
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
where r is the atomic radius, taken to be the radius 0 of ions in the 12-coordinated metal, v the vibration frequency of atom and i the evaporation rate. As for K@, Tsong first approximated it by K (the sublimation energy of the emitter), but later used the present one numerically [18]. +n I is the total i/1 i ionization energy and U the work function of the metal. The 4th and 5th terms in the brackets are the image potentials of the tip and the sample, respectively, and d denotes the distance between them. From Fig. 1 we may see also that as the two electrodes are brought together their atomic potentials overlap and a double well structure is formed. To move an atom from one electrode to the other, a much smaller energy K@ is needed %&& [1,14,19]. However K@ has not been used in %&&
149
Eq. (1). This is somehow strange. Let us bring the tip closer to the sample and see what would happen. K@ will now get smaller. That is to say, the %&& surface effect tends to decrease, and the atom could move between two surfaces as if in the body of a solid. So the evaporation will become easier. On the other hand, K@ gets larger. According to Eq. (1) this will tend to make field evaporation in STM more difficult. Here we encounter a contradiction. In Figs. 2a—2c we have illustrated the atomic potentials (see the small filled squares on the right side) of an adatom at three different sites (see the left side). In Fig. 2a the adatom is at its equilibrium position near one electrode (here the tip). In Fig. 2b it is at somewhere in the remote field free space. In Fig. 2c it is at its equilibrium position near the
Fig. 2. The atomic potential (filled small square on the right side) of adatom A at three different sites (see left side): (a) near the tip; (b) at somewhere in the remote field free space; (c) near the substrate.
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counter electrode (here the substrate). To evaporate an adatom from its equilibrium position (Fig. 2a) to far infinity (Fig. 2b) one should overcome the barrier height K@. To evaporate the adatom only to the counter electrode (Fig. 2c) one has to overcome a much reduced barrier height of K@ , if the dis%&& tance between the two electrodes is sufficiently small. In Tsong’s CE model K@ is used, so the adatom is implied to be evaporated to far infinity (Fig. 2b). While in STM the adatom would only be evaporated to the counter electrode (Fig. 2c). This is how the above-mentioned contradiction originates. Therefore to describe the field evaporation in STM we should replace K@ in Eq. (1) by K@ , %&& [20], and we get,
C
1 n F " K@ # + I !nU!º (r ) STM nr %&& i *.' 0 0 i/1 !K¹ ln
A BD v i
.
(2)
For the role K@ plays we may give it a name, the %&& effective binding energy. In a double electrode system of STM the image potential º (z) could be *.' presented by [21]
C
A B BD
found that there existed a universal binding energy curve for metals and bimetallic interfaces [22], E(z)"E(z )(1#bz@) exp(!bz@), (4) 0 where z@"(z!z )/j, z is the equilibrium separ0 0 ation, j the Thomas—Fermi screening length, j" (9p/4)1@3 r1@2/3 a.u., r could be determined from 4 4 bulk electron density n "3/4pr3. For the total 4 ` cohesive energy curves, which is calculated as a function of the separation between atoms for a uniformly dilated lattice, b"1.16 and it reduces to 0.9 for adhesive energy curves of metal—metal interface. This is partly because all atoms change their positions in the bulk cohesive energy calculation while the adhesive energy curves assume that atomic planes are moved rigidly. We guess that for an adatom—metal system, there also existed a universal function for the binding energy curve, which is also of the form of Eq. (4), and b will further decrease. To confirm this we have calculated the binding energy curves for adatom— metal systems of Au/Au, Cu/Cu, Ag/Ag, and W/W using an effective binding potential method (EBPM) developed by Gollisch [23], and fitted them with Eq. (4). The results are shown in Fig. 3 and b is 0.75$0.09. It was found that for adatom
(ne)2 z!1d 2 2 º (z)"! (ln 2!1)# *.' d d
A
#
d2 d2!4(z!1d)2 2
.
(3)
To calculate the evaporation field for a negative ion, +n I !nU in Eq. (2) should be replaced by i/1 i nU!+n E [14], where E is the electron affini/1 !&& !&& ity of the atom.
3. Universal binding energy function for adatom—metal system To apply Eq. (2), one has to determine the effective binding energy K@ , which depends on the type %&& of the metal, and is also a function of the tip—sample distance d. From the definition of K@ , one could %&& first find the binding energy function of the adatom—metal system. Not long ago Rose has
Fig. 3. Binding energy curves for Au—Au(1 0 0), Cu—Cu(1 0 0), Ag—Ag(1 0 0) and W—W(1 0 0) adatom—metal systems calculated using EBPM method developed by Gollish [23], and scaled using Eq. (4).
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 4. Binding energy curve of an Au adatom at four sites a,b,c and d on Au(1 1 1) surface. (Inset: large circle denote the surface atom, a is a surface atom site, d is a hollow site, b and c are equally located on the line ad.)
on a hollow site the resulting atomic potential curve obeys Eq. (4) quite well, while for other sites Eq. (4) fails to give a good fitting to the whole curve. The atomic potential curves for adatom at four different sites on Au(1 1 1) surface are shown in Fig. 4. As could be seen, the right parts of the curves to their minimum still stick to the curve given by Eq. (4), but the value and the location of the minimum changed considerably. 4. Test calculation and localized evaporation fields With the universal binding energy function Eq. (4), the total atomic potential for a STM system, in which the tip and substrate are made of identical metal and separated by an interval d, could be written as E(z)#E(d!z). The calculation of K@ reduces to the determination of the min%&& imum and maximum of E(z)#E(d!z). Fig. 5 shows the K@ at different tip—sample distances for %&& Au—Au(1 0 0), Cu—Cu(1 0 0), Ag—Ag(1 0 0), and W—W(1 0 0) adatom—metal systems. As could be seen, in all cases, K@ reduces nearly to zero when %&& d(5.0 A_ , and approaches the binding energy (sublime energy) K of each metal for d'13 A_ . In the calculation of evaporation fields the evaporation rate is taken to be, i"1011 s~1. This is
151
Fig. 5. Effective binding energy at various tip—sample distances for different tip/sample combinations.
estimated from the observation [1,4,12] that an atom mound consisting of about 104 atoms could be created by field evaporation within some 102 ns. Fig. 6a—d show the calculated evaporation fields at hollow sites for positive and negative ions at various tip—sample distances for Au/Au(1 0 0), Cu/Cu(1 0 0), Ag/Ag(1 0 0), and W/W(1 0 0) tip/ sample combinations [24]. For comparison, the results calculated with Eq. (1) are also shown (dashed line) (note that the total image potential, that is, the 4th term plus the 5th term in Eq. (1), has been replaced by a form given by Eq. (3). As could be seen, for d'13 A_ , as K@ +K, they tend to %&& reach each other. Starting from about 13 A_ , as K@ %&& diverges from K and decreases to nearly zero when d"5 A_ , our calculation decrease rapidly. For d(3 A_ the image potential becomes dominant (Fig. 7) and the evaporation fields decrease dramatically. In Fig. 6a, When d"7.23 A_ , the calculated evaporation field for Au~1 is 0.6V/A_ , which agrees well with Chang’s experiment (0.6 V/A_ at d"6.4$1.0 A_ ) [4]. As the distance d further decreases the evaporation field reduces to zero. Although the accuracy of the results at this small distance is doubtable, it explains qualitatively the experiments of Pascual [15] that nanometer scale structures could be made by bringing the tip very
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 6. Evaporation field at different tip—sample distances calculated using Eq. (2) for (a) Au/Au(1 0 0), (b) Cu/Cu(1 0 0), (c) Ag/Ag(1 0 0) and W/W(1 0 0) tip/sample combination. For comparison the results from Eq. (1) are also shown (dashed line). With temperature ¹"300 K, and evaporation rate i"1011 s~1.
close to substrate without applying any additional voltage pulse, because the bias voltage is enough to generate field evaporation. As shown in Section 3, the binding energy function and thus the effective binding energy K@ %&& depends on the site of the adatom on the surface (Fig. 4). This will in turn produce the localized evaporation field. We have calculated the evaporation fields F(x, y) at 36 selected pairs (x, y) on Au(1 1 1) surface using Eq. (2) with d"7.52 A_ ,
¹"300 K, and i"1011 s~1. To get an analytic expression F(x, y) has been further fitted to the Fourier series
A
B
2pJ2 hx a AU 2pJ2 ]cos (2k!h)y a J3 AU (h, k"0,$1,$2,2), F(x, y)"+c(h,k) cos
C
D (6)
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 7. The change of the image potential at r with the 0 tip—sample distance. Image potential in the form of Eq. (3) is plotted in solid line, while that in the form of the 4th term combined with 5th term in Eq. (1) is plotted in dashed line.
where a is the lattice constant of gold. Fig. 8 gives A6 a contourplot of F(x, y) on Au(1 1 1). Directly above a surface atom the evaporation field reaches its minimum of 0.113 V/A_ , which is more than five times lower than that above a hollow site where it reaches its maximum of 0.624 V/A_ . For single atom transfer it is likely that when the tip is positioned above a hollow cite on Au(1 1 1) surface, the three adjacent atoms around the hollow will stay where they were while the top atoms of the tip where the field is stronger will be evaporated. If the tip is positioned directly above an atom of the sample, the atom will likely be pulled out, that is, evaporated to the tip. In Chang’s experiment atom mounds and pits, which involved the transfer of thousands of atoms, were observed to appear randomly with nearly equal probability. It is true that during the formation of the nanostructures the Au(1 1 1) surface is not maintained. However in the early stage of field evaporation once the stream of atoms starts to flow, the atom that would try to come out from the counter electrode is pushed back. So the direction of the first few evaporated atoms is of vital importance, for they determine the flow direction of the following atoms. In this sense
153
Fig. 8. Contour plot of evaporation fields of Au~1 on Au(1 1 1) surface at a tip—sample distance d"7.52 A_ , with ¹"300 K and i"1011 s~1. The filled circles denote the first layer Au atoms of Au(1 1 1). The evaporation field reaches a minimum of about 0.113 V/A_ directly above each surface atom and a maximum of about 0.624 V/A_ above a hollow site. The thicker contour line stands for stronger evaporation field, and dashed contour line for weaker one. The evaporation field difference between two contour lines is about 0.051 V/A_ .
we think that Chang’s observation seems a result of localized field evaporation.
5. Nanostructure fabrication with Au, Ni, Cu, Pt(Ir) and W tips in atmosphere We have fabricated nanostructures on Au(1 11) surface in atmosphere with Au, Cu, Ni, Pt(Ir), and W tips by positive or negative voltage pulses. The STM used is a self-built one [25] except for the head of the scanner, which was purchased. Details of the experiments have been reported elsewhere [12]. Fig. 9 gives some selected results. In our experiments the sharp threshold voltage for the generation of nanostructures was confirmed. And we further found that for such metals as Au, Ni, and Cu, atom mounds were formed regardless of the field polarity. For PtIr alloy a positive pulse will produce an atom pit while a negative pulse creates an atom mound. For W both positive and negative pulses create atom pits. In atmosphere it is impossible to get a clean metal surface. Therefore, the
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 9. Nanometer structures fabricated by positive or negative voltage pulses with various STM tips on Au(1 1 1) substrate. (a) Au tip, #4 V, 300 ns, 280]360 nm2; (b) Au tip, !4 V, 300 ns, 300]390 nm2; (c) Ni tip, #5 V, 300 ns, 350]400 nm2; (d) Ni tip, !5 V, 300 ns, 340]360 nm2; (e) Cu tip, #5 V, 300 ns, 280]320 nm2; (f) Cu tip, !5 V, 300 ns, 280]320 nm2; (g) PtIr tip, #3.5 V, 16 ls, 50]80 nm; (h) PtIr tip, !4 V, 16 ls, 250]340 nm2; (i) W tip, #5 V, 16 ls, 60]80 nm2; (j) W tip, !5 V, 16 ls, 60]80 nm2.
process on this contaminated surface is much more complicated. However, the above dependence of pits and mounds formation on tip material is still in general agreement with our experience from FIM. As we know in FIM the measured evaporation fields for Au, Cu and Ni are, respectively, 3.5, 3.0 and 3.5 V/A_ [26], so they are relatively easier to evaporate. While for Pt, Ir and W the measured evaporation fields are 4.8, 5.3 and 5.7 V/A_ they appear more difficult to evaporate. The calculated evaporation field of these metals in STM at a tip—sample distance d"15 A_ are listed in Table 1. At this distance K@ +K, so Eq. (1) was %&& used again with ¹"300 K and i"1011 s~1. As the field at the sharp tip is usually higher than that at the flat substrate, for ions on the substrate to be evaporated their evaporation field must be lower by a certain amount than that of a tip ion. According to Table 1 we may assume this amount to be about 1.6 V/A_ . As could be seen, only the evaporation fields for Pt~1, W~1 and W`3 exceed that for Au`1 or Au~1 by an amount larger than 1.6 V/A_ , so the Au atoms of the sample are evaporated, creating a pit. In all other cases the atoms of the tip are evaporated, giving atom mounds. This explains qualitatively the atom mounds and pits formation in Fig. 9. To sum up, we have introduced an effective binding energy K@ and constructed a new formula by %&&
Table 1 Evaporation fields of Au,Cu,Ni,Pt,Ir and W(V/A_ ) (¹"300 K, i"1011 s~1)
Au Cu Ni Pt Ir W
!1
#1
#2
#3
F` !Au~1 F~1 !Au`1 .*/ .*/
2.57 3.43 4.85 5.78 7.35 9.35
4.09 2.74 3.10 4.77 5.71 6.51
4.78 3.88 3.05 4.08 3.94 5.07
5.94 6.99 5.98 4.74 4.38 4.66
1.52 0.17 0.98 1.37 2.09
!1.52 !0.66 0.76 1.69 5.26
Note: The underlined numbers are the minimum evaporation fields for positive ions F` or negative ions F~ of the tip. Au~1 .*/ .*/ (Au`1) denotes the evaporation field for negative (positive) ion of the Au substrate.
replacing the total binding energy K@ by K@ in %&& Tsong’s CE mode formula for field evaporation in STM. After the modification not only the intrinsic contradiction in the original formula disappears, but the accuracy of the formula is found much improved. For tip—sample distance d ranging from about 5 to 13 A_ , the evaporation fields reduce greatly. The recalculated evaporation field for Au~1, for the first time, agrees well with experiment. Further the evaporation field is found highly localized. The evaporation field of Au~1 on top of a Au(1 1 1) surface atom could be several times
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
lower than that at a hollow site. For the calculation of K@ a universal binding function proposed in the %&& paper is found very helpful. In addition the nanostructure formation by positive or negative voltage pulses using STM in atmosphere bears important feature of field evaporation.
Acknowledgements We would like to give our heartfelt thanks to Dr. Forbes for many helpful discussions. We thank Dr. Chuangyun Xiao for many good suggestions. This work was supported by the National Natural Science Foundation of China, and partly by the State Key Laboratory of Wuhan University of Technology for Advanced New Technique for Material Synthesis and Process.
References [1] H.J. Mamin, P.H. Guethner, D. Rugar, Phys. Rev. Lett. 65 (1990) 2418. [2] In-Whan Lyo, Phaedon Avouris, Science 253 (1991) 173. [3] S.E. McBride, G.C. Wetsel, J. Appl. Phys. Lett. 59 (1991) 3056. [4] C.S. Chang, W.B. Su, Tien T. Tsong, Phys. Rev. Lett. 72 (1994) 574. [5] A. Kobayashi, F. Grey, R.S. Williams, M. Aono, Science 259 (1993) 1724. [6] Masakazu Aono, Ataru Kubayashi, Francois Grey et al., Jpn. J. Appl. Phys. 32 (1993) 1470. [7] D. Huang et al., Jpn. J. Appl. Phys. 33 (1994) L190. [8] F. Grey, D.H. Huang, A. Kobayashi, E.J. Snyder, H. Uchida, M. Aono, J. Vac. Sci. Technol. B12 (1994) 1901.
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[9] K. Bessho, S. Hashimoto, Appl. Phys. Lett. 65 (1994) 2142. [10] S. Hosaka, H. Koyanagi, J. Vac. Sci. Technol. B 12 (1994) 1872. [11] H. Koyanagi, S. Hosaka, R. Imura, Appl. Phys. Lett. 67 (1995) 2609. [12] Zhiyang Li, Wu Liu, Liming Liu, Susun Ye, Xingjiao Li, Proc. 6th National Symp. on Field Evaporation and Vacuum Microelectronics, Wuhan, China, August, 1996. [13] M.S. Gupalo, I.L. Yarish, V.M. Zlupko, Yu. Suchorski, J.H. Block, Surf. Sci. 350 (1996) 176. [14] Tien T. Tsong, Phys. Rev. B 44 (1991) 13703. [15] J.I. Pascual, J. Mendez et al., Phys. Rev. Lett. 71 (1993) 1852. [16] N.D. Lang, Phys. Rev. B 45 (1992) 13 599; 49 (1994) 2067. [17] K. Hirose, M. Tsukada, Phys. Rev. Lett. 73 (1994) 150. [18] N.M. Miskovsky, Tien T. Tsong, Phys. Rev. B 46 (1992) 2640. [19] R. Gomer, IBM J. Res. Dev. 30 (1986) 428. [20] By an electrothermodynamic analysis [see R.G. Forbes, J. Phys D: Appl. Phys. 15 (1982) 1301] of the field evaporation in STM one could found that the process could be equivalently subdivided into two steps. First we evaporate the atom to far infinity (Fig. 2b), then bring it back (Fig. 2c). In the former step Eq. (1) could be used. In the latter step some energy is returned. As a result only the barrier height K@ should be overcome. And the whole %&& process is not a simple charge exchange (CE) one (private discussion with Dr. Forbes, to be published in Chinese Phys. Lett.). [21] G. Binnig, N. Garcia, H. Rohrer et al., Phys. Rev. B. 30 (1984) 4816. [22] J.H. Rose, J. Ferrante, J.R. Smith, Phys. Rev. Lett. 47 (1981) 675. [23] H. Gollish, Surf. Sci. 166 (1986) 87. [24] Generation of high charge state ions by post ionization in the configuration of STM is unlikely. The evaporation fields plotted for them are merely for reference. [25] Zhiyang Li, Wu Liu, Liming Liu, Xingjiao Li, Proc. 4th National Symp. on STM/STS, Beijing, P.R. China, June, 1996. [26] T.T. Tsong, Surf. Sci. 70 (1978) 211.
Field evaporation in the configuration of a scanning tunneling microscope Zhiyang Li!,*, Wu Liu!, Xingjiao Li" ! Department of Physics, Central China Normal University, Wuhan 430079, People+s Republic of China " Department of Solid State Electronics, Huazhong University of Science and Technology, Wuhan 430074, People+s Republic of China Received 7 July 1997; received in revised form 10 November 1997
Abstract The paper introduced an effective binding energy K@ and emphasized the role it plays in the field evaporation in the %&& configuration of a scanning tunneling microscope (STM). With this K@ an important modification has been made to %&& Tsong’s CE model formula for STM [Tien T. Tsong, Phys. Rev. B 44 (1991) 13 703]. As a consequence, for tip—sample distance 5(d(13 A_ , the high evaporation fields from Tsong’s original formula were found greatly reduced. When d"7.23 A_ , the recalculated evaporation field for Au~1 is 0.6 V/A_ , which is in good agreement with Chang’s experiment [Phys. Rev. Lett. 72 (1994) 574]. Further the evaporation field was found highly localized. For d"7.52 A_ , the evaporation field of Au~1 on top of a Au(1 1 1) surface atom was found several times lower than that at a hollow site. In the calculation we have proposed a universal binding function. In addition selected experimental results on nanostructure formation by positive or negative voltage pulses with Au, Ni, Cu, Pt(Ir) and W tips on Au(1 1 1) substrate with a STM working in atmosphere were presented. The processes were found to bear important feature of field evaporation. ( 1998 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Recently making nanostructures by field evaporation in the configuration of a scanning tunneling microscope (STM) has been the interest of many researchers [1—13]. It is now clear that field evaporation in STM is much different than that in field ion
* Corresponding author. Tel.: #86 27 7865701 3524; fax: #86 27 7876070; e-mail: [email protected].
microscope (FIM). First the evaporation field in STM is found several times lower. Next both positive and negative ions could be evaporated. Further the evaporation rate could be several orders higher than that in FIM. Theories concerning the physical process, though far from complete solution of the problem, have emerged from two different ways resulting in two different classes of theories, namely the phenomenological theory and the microscopic one. In the former class Tsong, in the spirit of classical field evaporation theory in FIM, constructed charge-exchange (CE) and image-hump (IH)
0304-3991/98/$19.00 ( 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 3 9 9 1 ( 9 7 ) 0 0 1 4 8 - 4
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
model for STM [14], and the evaporation fields of a large number of metals were calculated. Unfortunately the calculated evaporation fields were some how high above the experimental values. For example, the calculated evaporation field for Au~1 was 1.7 V/A_ at a tip—sample distance of 6 A_ and an evaporation rate of only 1 s~1, while Chang’s experiment turned out to be about 0.6 V/A_ at a tip sample distance d"6.4$1 A_ and with an evaporation rate that was several orders higher. Because of this theoretical failure to account for the low evaporation field in STM, Pascual et al. denied the atom mounds formation in STM to be a field evaporation process [15]. In the latter class, Lang first gave a microscopic calculation by modeling STM as two jellium electrodes with an adatom between them [16]. The force, energy, and electron density were all calculated self-consistently. A little later Hirose offered a first principle calculation in which the atomic structure of the tip was considered [17]. While microscopic theory is helpful in deepening our understanding of the physical nature of the field evaporation process, the phenomenological theory has been found very useful in the prediction of evaporation field in FIM and we expect it continue to do so in STM. In this paper first we will introduce in Section 2 an effective binding energy K@ to replace the total %&& binding energy K@ in Tsong’s CE model formula. %&& To calculate K@ , in Section 3, the atomic potential %&& curves for Au/Au, Cu/Cu, Ag/Ag, and W/W adatom—metal systems are calculated, then a universal binding energy function for the adatom— metal system was proposed. In Section 4, the evaporation fields for Au/Au, Cu/Cu, Ag/Ag, and W/W tip/sample combinations were calculated with the new formula. And further the localization of evaporation field is discussed. In Section 5, some selected experimental results on nanostructure formation with Au, Cu, Ni, Pt(Ir), and W tips on Au(1 1 1) substrate in atmosphere are presented.
2. Effective binding energy For convenience of discussion we first review briefly the CE model, which Tsong adapted from FIM to STM [14]. It is assumed that a STM might
Fig. 1. Total atomic potential º and ionic potential º (F) (or ! * º (0) when no field applied) (solid lines) separately as the sum of * that of the tip and the sample (dashed lines) in STM. With subscript t denotes tip, s for sample, a for atomic, and i for ionic. K@ is the total binding energy, K is the binding energy of an isolated electrode (sublime energy). The height of the hump, K@ %&& in the middle of º is the effective binding energy defined in the ! context (here the tip and sample are made of identical metal).
be regarded as a double electrode system. And the atomic(ionic) potential in STM could be taken as the sum of the potentials of the two isolated electrodes as shown in Fig. 1. For simplicity the tip has been approximated by a flat surface and the external field applied between the tip and substrate is assumed to be uniform. At a critical point where the ionic potential curve intersects with the atomic one, the atom would first be field ionized and then evaporated away from the surface. In low-temperature evaporation, the field should be large enough to pull the intersection point down to the equilibrium position of the adatom, that is to K@, where K@ is the total binding energy. Neglecting the shortrange repulsive interaction, Tsong arrived at the following equation for the evaporation field in STM:
C
1 n n2e2 F " K@# + I !n U! STM nr i 16pe r 0 00 i/1 v n2e2 ! !K¹ ln V/A_ , i 16pe (d!r ) 0 0
A BD
(1)
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
where r is the atomic radius, taken to be the radius 0 of ions in the 12-coordinated metal, v the vibration frequency of atom and i the evaporation rate. As for K@, Tsong first approximated it by K (the sublimation energy of the emitter), but later used the present one numerically [18]. +n I is the total i/1 i ionization energy and U the work function of the metal. The 4th and 5th terms in the brackets are the image potentials of the tip and the sample, respectively, and d denotes the distance between them. From Fig. 1 we may see also that as the two electrodes are brought together their atomic potentials overlap and a double well structure is formed. To move an atom from one electrode to the other, a much smaller energy K@ is needed %&& [1,14,19]. However K@ has not been used in %&&
149
Eq. (1). This is somehow strange. Let us bring the tip closer to the sample and see what would happen. K@ will now get smaller. That is to say, the %&& surface effect tends to decrease, and the atom could move between two surfaces as if in the body of a solid. So the evaporation will become easier. On the other hand, K@ gets larger. According to Eq. (1) this will tend to make field evaporation in STM more difficult. Here we encounter a contradiction. In Figs. 2a—2c we have illustrated the atomic potentials (see the small filled squares on the right side) of an adatom at three different sites (see the left side). In Fig. 2a the adatom is at its equilibrium position near one electrode (here the tip). In Fig. 2b it is at somewhere in the remote field free space. In Fig. 2c it is at its equilibrium position near the
Fig. 2. The atomic potential (filled small square on the right side) of adatom A at three different sites (see left side): (a) near the tip; (b) at somewhere in the remote field free space; (c) near the substrate.
150
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
counter electrode (here the substrate). To evaporate an adatom from its equilibrium position (Fig. 2a) to far infinity (Fig. 2b) one should overcome the barrier height K@. To evaporate the adatom only to the counter electrode (Fig. 2c) one has to overcome a much reduced barrier height of K@ , if the dis%&& tance between the two electrodes is sufficiently small. In Tsong’s CE model K@ is used, so the adatom is implied to be evaporated to far infinity (Fig. 2b). While in STM the adatom would only be evaporated to the counter electrode (Fig. 2c). This is how the above-mentioned contradiction originates. Therefore to describe the field evaporation in STM we should replace K@ in Eq. (1) by K@ , %&& [20], and we get,
C
1 n F " K@ # + I !nU!º (r ) STM nr %&& i *.' 0 0 i/1 !K¹ ln
A BD v i
.
(2)
For the role K@ plays we may give it a name, the %&& effective binding energy. In a double electrode system of STM the image potential º (z) could be *.' presented by [21]
C
A B BD
found that there existed a universal binding energy curve for metals and bimetallic interfaces [22], E(z)"E(z )(1#bz@) exp(!bz@), (4) 0 where z@"(z!z )/j, z is the equilibrium separ0 0 ation, j the Thomas—Fermi screening length, j" (9p/4)1@3 r1@2/3 a.u., r could be determined from 4 4 bulk electron density n "3/4pr3. For the total 4 ` cohesive energy curves, which is calculated as a function of the separation between atoms for a uniformly dilated lattice, b"1.16 and it reduces to 0.9 for adhesive energy curves of metal—metal interface. This is partly because all atoms change their positions in the bulk cohesive energy calculation while the adhesive energy curves assume that atomic planes are moved rigidly. We guess that for an adatom—metal system, there also existed a universal function for the binding energy curve, which is also of the form of Eq. (4), and b will further decrease. To confirm this we have calculated the binding energy curves for adatom— metal systems of Au/Au, Cu/Cu, Ag/Ag, and W/W using an effective binding potential method (EBPM) developed by Gollisch [23], and fitted them with Eq. (4). The results are shown in Fig. 3 and b is 0.75$0.09. It was found that for adatom
(ne)2 z!1d 2 2 º (z)"! (ln 2!1)# *.' d d
A
#
d2 d2!4(z!1d)2 2
.
(3)
To calculate the evaporation field for a negative ion, +n I !nU in Eq. (2) should be replaced by i/1 i nU!+n E [14], where E is the electron affini/1 !&& !&& ity of the atom.
3. Universal binding energy function for adatom—metal system To apply Eq. (2), one has to determine the effective binding energy K@ , which depends on the type %&& of the metal, and is also a function of the tip—sample distance d. From the definition of K@ , one could %&& first find the binding energy function of the adatom—metal system. Not long ago Rose has
Fig. 3. Binding energy curves for Au—Au(1 0 0), Cu—Cu(1 0 0), Ag—Ag(1 0 0) and W—W(1 0 0) adatom—metal systems calculated using EBPM method developed by Gollish [23], and scaled using Eq. (4).
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 4. Binding energy curve of an Au adatom at four sites a,b,c and d on Au(1 1 1) surface. (Inset: large circle denote the surface atom, a is a surface atom site, d is a hollow site, b and c are equally located on the line ad.)
on a hollow site the resulting atomic potential curve obeys Eq. (4) quite well, while for other sites Eq. (4) fails to give a good fitting to the whole curve. The atomic potential curves for adatom at four different sites on Au(1 1 1) surface are shown in Fig. 4. As could be seen, the right parts of the curves to their minimum still stick to the curve given by Eq. (4), but the value and the location of the minimum changed considerably. 4. Test calculation and localized evaporation fields With the universal binding energy function Eq. (4), the total atomic potential for a STM system, in which the tip and substrate are made of identical metal and separated by an interval d, could be written as E(z)#E(d!z). The calculation of K@ reduces to the determination of the min%&& imum and maximum of E(z)#E(d!z). Fig. 5 shows the K@ at different tip—sample distances for %&& Au—Au(1 0 0), Cu—Cu(1 0 0), Ag—Ag(1 0 0), and W—W(1 0 0) adatom—metal systems. As could be seen, in all cases, K@ reduces nearly to zero when %&& d(5.0 A_ , and approaches the binding energy (sublime energy) K of each metal for d'13 A_ . In the calculation of evaporation fields the evaporation rate is taken to be, i"1011 s~1. This is
151
Fig. 5. Effective binding energy at various tip—sample distances for different tip/sample combinations.
estimated from the observation [1,4,12] that an atom mound consisting of about 104 atoms could be created by field evaporation within some 102 ns. Fig. 6a—d show the calculated evaporation fields at hollow sites for positive and negative ions at various tip—sample distances for Au/Au(1 0 0), Cu/Cu(1 0 0), Ag/Ag(1 0 0), and W/W(1 0 0) tip/ sample combinations [24]. For comparison, the results calculated with Eq. (1) are also shown (dashed line) (note that the total image potential, that is, the 4th term plus the 5th term in Eq. (1), has been replaced by a form given by Eq. (3). As could be seen, for d'13 A_ , as K@ +K, they tend to %&& reach each other. Starting from about 13 A_ , as K@ %&& diverges from K and decreases to nearly zero when d"5 A_ , our calculation decrease rapidly. For d(3 A_ the image potential becomes dominant (Fig. 7) and the evaporation fields decrease dramatically. In Fig. 6a, When d"7.23 A_ , the calculated evaporation field for Au~1 is 0.6V/A_ , which agrees well with Chang’s experiment (0.6 V/A_ at d"6.4$1.0 A_ ) [4]. As the distance d further decreases the evaporation field reduces to zero. Although the accuracy of the results at this small distance is doubtable, it explains qualitatively the experiments of Pascual [15] that nanometer scale structures could be made by bringing the tip very
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 6. Evaporation field at different tip—sample distances calculated using Eq. (2) for (a) Au/Au(1 0 0), (b) Cu/Cu(1 0 0), (c) Ag/Ag(1 0 0) and W/W(1 0 0) tip/sample combination. For comparison the results from Eq. (1) are also shown (dashed line). With temperature ¹"300 K, and evaporation rate i"1011 s~1.
close to substrate without applying any additional voltage pulse, because the bias voltage is enough to generate field evaporation. As shown in Section 3, the binding energy function and thus the effective binding energy K@ %&& depends on the site of the adatom on the surface (Fig. 4). This will in turn produce the localized evaporation field. We have calculated the evaporation fields F(x, y) at 36 selected pairs (x, y) on Au(1 1 1) surface using Eq. (2) with d"7.52 A_ ,
¹"300 K, and i"1011 s~1. To get an analytic expression F(x, y) has been further fitted to the Fourier series
A
B
2pJ2 hx a AU 2pJ2 ]cos (2k!h)y a J3 AU (h, k"0,$1,$2,2), F(x, y)"+c(h,k) cos
C
D (6)
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 7. The change of the image potential at r with the 0 tip—sample distance. Image potential in the form of Eq. (3) is plotted in solid line, while that in the form of the 4th term combined with 5th term in Eq. (1) is plotted in dashed line.
where a is the lattice constant of gold. Fig. 8 gives A6 a contourplot of F(x, y) on Au(1 1 1). Directly above a surface atom the evaporation field reaches its minimum of 0.113 V/A_ , which is more than five times lower than that above a hollow site where it reaches its maximum of 0.624 V/A_ . For single atom transfer it is likely that when the tip is positioned above a hollow cite on Au(1 1 1) surface, the three adjacent atoms around the hollow will stay where they were while the top atoms of the tip where the field is stronger will be evaporated. If the tip is positioned directly above an atom of the sample, the atom will likely be pulled out, that is, evaporated to the tip. In Chang’s experiment atom mounds and pits, which involved the transfer of thousands of atoms, were observed to appear randomly with nearly equal probability. It is true that during the formation of the nanostructures the Au(1 1 1) surface is not maintained. However in the early stage of field evaporation once the stream of atoms starts to flow, the atom that would try to come out from the counter electrode is pushed back. So the direction of the first few evaporated atoms is of vital importance, for they determine the flow direction of the following atoms. In this sense
153
Fig. 8. Contour plot of evaporation fields of Au~1 on Au(1 1 1) surface at a tip—sample distance d"7.52 A_ , with ¹"300 K and i"1011 s~1. The filled circles denote the first layer Au atoms of Au(1 1 1). The evaporation field reaches a minimum of about 0.113 V/A_ directly above each surface atom and a maximum of about 0.624 V/A_ above a hollow site. The thicker contour line stands for stronger evaporation field, and dashed contour line for weaker one. The evaporation field difference between two contour lines is about 0.051 V/A_ .
we think that Chang’s observation seems a result of localized field evaporation.
5. Nanostructure fabrication with Au, Ni, Cu, Pt(Ir) and W tips in atmosphere We have fabricated nanostructures on Au(1 11) surface in atmosphere with Au, Cu, Ni, Pt(Ir), and W tips by positive or negative voltage pulses. The STM used is a self-built one [25] except for the head of the scanner, which was purchased. Details of the experiments have been reported elsewhere [12]. Fig. 9 gives some selected results. In our experiments the sharp threshold voltage for the generation of nanostructures was confirmed. And we further found that for such metals as Au, Ni, and Cu, atom mounds were formed regardless of the field polarity. For PtIr alloy a positive pulse will produce an atom pit while a negative pulse creates an atom mound. For W both positive and negative pulses create atom pits. In atmosphere it is impossible to get a clean metal surface. Therefore, the
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Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
Fig. 9. Nanometer structures fabricated by positive or negative voltage pulses with various STM tips on Au(1 1 1) substrate. (a) Au tip, #4 V, 300 ns, 280]360 nm2; (b) Au tip, !4 V, 300 ns, 300]390 nm2; (c) Ni tip, #5 V, 300 ns, 350]400 nm2; (d) Ni tip, !5 V, 300 ns, 340]360 nm2; (e) Cu tip, #5 V, 300 ns, 280]320 nm2; (f) Cu tip, !5 V, 300 ns, 280]320 nm2; (g) PtIr tip, #3.5 V, 16 ls, 50]80 nm; (h) PtIr tip, !4 V, 16 ls, 250]340 nm2; (i) W tip, #5 V, 16 ls, 60]80 nm2; (j) W tip, !5 V, 16 ls, 60]80 nm2.
process on this contaminated surface is much more complicated. However, the above dependence of pits and mounds formation on tip material is still in general agreement with our experience from FIM. As we know in FIM the measured evaporation fields for Au, Cu and Ni are, respectively, 3.5, 3.0 and 3.5 V/A_ [26], so they are relatively easier to evaporate. While for Pt, Ir and W the measured evaporation fields are 4.8, 5.3 and 5.7 V/A_ they appear more difficult to evaporate. The calculated evaporation field of these metals in STM at a tip—sample distance d"15 A_ are listed in Table 1. At this distance K@ +K, so Eq. (1) was %&& used again with ¹"300 K and i"1011 s~1. As the field at the sharp tip is usually higher than that at the flat substrate, for ions on the substrate to be evaporated their evaporation field must be lower by a certain amount than that of a tip ion. According to Table 1 we may assume this amount to be about 1.6 V/A_ . As could be seen, only the evaporation fields for Pt~1, W~1 and W`3 exceed that for Au`1 or Au~1 by an amount larger than 1.6 V/A_ , so the Au atoms of the sample are evaporated, creating a pit. In all other cases the atoms of the tip are evaporated, giving atom mounds. This explains qualitatively the atom mounds and pits formation in Fig. 9. To sum up, we have introduced an effective binding energy K@ and constructed a new formula by %&&
Table 1 Evaporation fields of Au,Cu,Ni,Pt,Ir and W(V/A_ ) (¹"300 K, i"1011 s~1)
Au Cu Ni Pt Ir W
!1
#1
#2
#3
F` !Au~1 F~1 !Au`1 .*/ .*/
2.57 3.43 4.85 5.78 7.35 9.35
4.09 2.74 3.10 4.77 5.71 6.51
4.78 3.88 3.05 4.08 3.94 5.07
5.94 6.99 5.98 4.74 4.38 4.66
1.52 0.17 0.98 1.37 2.09
!1.52 !0.66 0.76 1.69 5.26
Note: The underlined numbers are the minimum evaporation fields for positive ions F` or negative ions F~ of the tip. Au~1 .*/ .*/ (Au`1) denotes the evaporation field for negative (positive) ion of the Au substrate.
replacing the total binding energy K@ by K@ in %&& Tsong’s CE mode formula for field evaporation in STM. After the modification not only the intrinsic contradiction in the original formula disappears, but the accuracy of the formula is found much improved. For tip—sample distance d ranging from about 5 to 13 A_ , the evaporation fields reduce greatly. The recalculated evaporation field for Au~1, for the first time, agrees well with experiment. Further the evaporation field is found highly localized. The evaporation field of Au~1 on top of a Au(1 1 1) surface atom could be several times
Z. Li et al. / Ultramicroscopy 73 (1998) 147—155
lower than that at a hollow site. For the calculation of K@ a universal binding function proposed in the %&& paper is found very helpful. In addition the nanostructure formation by positive or negative voltage pulses using STM in atmosphere bears important feature of field evaporation.
Acknowledgements We would like to give our heartfelt thanks to Dr. Forbes for many helpful discussions. We thank Dr. Chuangyun Xiao for many good suggestions. This work was supported by the National Natural Science Foundation of China, and partly by the State Key Laboratory of Wuhan University of Technology for Advanced New Technique for Material Synthesis and Process.
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[9] K. Bessho, S. Hashimoto, Appl. Phys. Lett. 65 (1994) 2142. [10] S. Hosaka, H. Koyanagi, J. Vac. Sci. Technol. B 12 (1994) 1872. [11] H. Koyanagi, S. Hosaka, R. Imura, Appl. Phys. Lett. 67 (1995) 2609. [12] Zhiyang Li, Wu Liu, Liming Liu, Susun Ye, Xingjiao Li, Proc. 6th National Symp. on Field Evaporation and Vacuum Microelectronics, Wuhan, China, August, 1996. [13] M.S. Gupalo, I.L. Yarish, V.M. Zlupko, Yu. Suchorski, J.H. Block, Surf. Sci. 350 (1996) 176. [14] Tien T. Tsong, Phys. Rev. B 44 (1991) 13703. [15] J.I. Pascual, J. Mendez et al., Phys. Rev. Lett. 71 (1993) 1852. [16] N.D. Lang, Phys. Rev. B 45 (1992) 13 599; 49 (1994) 2067. [17] K. Hirose, M. Tsukada, Phys. Rev. Lett. 73 (1994) 150. [18] N.M. Miskovsky, Tien T. Tsong, Phys. Rev. B 46 (1992) 2640. [19] R. Gomer, IBM J. Res. Dev. 30 (1986) 428. [20] By an electrothermodynamic analysis [see R.G. Forbes, J. Phys D: Appl. Phys. 15 (1982) 1301] of the field evaporation in STM one could found that the process could be equivalently subdivided into two steps. First we evaporate the atom to far infinity (Fig. 2b), then bring it back (Fig. 2c). In the former step Eq. (1) could be used. In the latter step some energy is returned. As a result only the barrier height K@ should be overcome. And the whole %&& process is not a simple charge exchange (CE) one (private discussion with Dr. Forbes, to be published in Chinese Phys. Lett.). [21] G. Binnig, N. Garcia, H. Rohrer et al., Phys. Rev. B. 30 (1984) 4816. [22] J.H. Rose, J. Ferrante, J.R. Smith, Phys. Rev. Lett. 47 (1981) 675. [23] H. Gollish, Surf. Sci. 166 (1986) 87. [24] Generation of high charge state ions by post ionization in the configuration of STM is unlikely. The evaporation fields plotted for them are merely for reference. [25] Zhiyang Li, Wu Liu, Liming Liu, Xingjiao Li, Proc. 4th National Symp. on STM/STS, Beijing, P.R. China, June, 1996. [26] T.T. Tsong, Surf. Sci. 70 (1978) 211.