EUROPHYSICS LETTERS
1 May 2003
Europhys. Lett., 62 (3), pp. 398–404 (2003)
Controlling a tunnel current from the exterior: A new mesoscopic quantum effect A. Otto(∗ ) Lehrstuhl f¨ ur Oberfl¨ achenphysik (IPkM), Heinrich-Heine-Universit¨ at D¨ usseldorf 40225 D¨ usseldorf, Germany (received 9 September 2002; accepted in final form 19 February 2003) PACS. 73.40.Rw – Metal-insulator-metal structures. PACS. 73.40.Gk – Tunneling. PACS. 73.23.-b – Electronic transport in mesoscopic systems.
Abstract. – Surprising new effects are observed, when the thickness of the Ag electrode of an Al/Al-oxide/Ag junction is reduced to the order of the mean free path of the tunneling hot electrons in silver. In this case, strong increases (up to 500%) in the tunnel current at constant tunnel voltage are observed, if, for example, small quantities of silver are condensed on the Ag electrode at cryogenic temperatures. An explanation of this effect in terms of a ballistic model fails. A model is proposed, in which the coherent tunneling state of the electrons is changed by diffusive scattering at the outer Ag surface.
Introduction. – Solid-state physics knows macroscopic quantum effects, such as the quantum Hall effect, the magnetic flux quantum and the Josephson effect. Mesoscopic quantum effects are, for instance, the Coulomb blockade of quantum dots. Metal-insulator-metal tunnel (MIM) junctions may be considered as a mesoscopic system when the thickness of one or both electrodes decreases to the mean free path of the tunneling hot carriers. MIM junctions are a long-standing object of research [1, 2], the oldest reference known to the author is on electron emission [3]. In 1970, Bernard et al. [4] reported that exposure of Al/Al-Ox/Au junctions to 760 Torr of O2 for 1 minute caused a strong decrease of the tunnel current IT . Similar effects were found, when MIM junctions are exposed in UHV to oxygen (decrease of IT ) or potassium (increase of IT ) [5], but were not understood. For an extensive bibliography on light emission of MIM junctions see ref. [5], on internal photoemission, electron emission, filamentary growth and related work see ref. [6], on surface reactions by hot electrons and hot-electron emission into the MIM caused by surface reactions see ref. [7]. Gadzuk [8] pointed out the relation of resonance-assisted hot-electron surface reactions with fs-chemistry. Sensitive linear optical spectroscopy of charge transfer excitations is possible by monitoring internal photoemission into the Ag electrode of MIM junctions [9]. Changing the tunnel current at constant tunnel voltage by altering the coverage or structure of the outer surface of the top electrode, as first reported by Bernard et al. [4] and (∗ ) E-mail:
[email protected] c EDP Sciences
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A. Otto: Controlling a tunnel current from the exterior: etc.
energy / eV
energy / eV
electron tunneling
6
CB 4 2
2.4 eV
3.9 eV
EF (Al) -eUT
0
8.3 eV
EF (Ag)
}
hole tunneling
6 vacuum level 4.5
4
CB
2
eV
0
-2
-eUT
2.4 eV
{
8.3 eV
}
}
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vacuum level 4.5 eV
0
-2
-4
-4 VB
-6
-6 Al
AIOx
Ag
d (Al)
d (Ox)
d (Ag)
vacuum
x
VB
Al d (Al)
AIOx d (Ox)
Ag d (Ag)
vacuum
x
Fig. 1 – Energy scheme of the Al/anodic AlOx/Ag junctions under electron (UT < 0) and hole (UT > 0) tunneling into the silver electrode. CB (VB) is the lower (upper) edge of the conduction (valence) band of AlOx. The vacuum level is the one above the Ag electrode.
H¨anisch and Otto [5] is a “robust”, general and chemically specific effect. It works also with an inhomogeneous oxide film [5]. A very homogeneous silver film thickness in the sense of quantum size effects is not necessary. Equally strong effects are observed for MIM junctions immersed into electrolytes [6]. Applications in sensorics seem possible [6]. A first hypothetical explanation close to that presented below was proposed in [10]. The theory presented here is based on the control of IT “from outside” by manipulating the tunneling wave functions by changing the surface properties. In this sense this is a new mesoscopic quantum effect, not just a ballistic effect. The theory is demonstrated for the example of “roughening” the silver-vacuum interface by cold deposition of small quantities of silver. Experiment. – The substrates for the preparation of the aluminum/aluminum oxide(AlOx)/silver junctions were disks of SiO2 . The 30 nm thick aluminum film was prepared by vapor deposition at a pressure of 10−8 mbar. The Al film is then transferred into a N2 filled chamber, where it is locally oxidized in an electrochemical droplet cell by a controlled oxidation cyclo-voltammogramm, allowing to grow uniform oxides with thickness between 1.4 and 10 nm, see ref. [11]. The anodic oxidized Al film was transferred into a UHV system, where the top silver electrode was added by vapor deposition at room temperature. The contact area of the junction was 2 × 4 mm2 . The band offsets (measurements are described in [7]) are given in fig. 1. For an applied tunnel voltage UT = −1.0 V the electrons tunneling from Al to Ag come from an energy range of about 0.25 eV directly below the Fermi level of Al [7]. Since this width is larger than the spacing of the possible quantum well states in a 20 nm thick silver film, these states play no role here. Results. – An Al/2.3 nm Al-Ox/20 nm Ag junction was cooled to about 42 K in UHV. IT measured at UT = −1.0 V increases from about 15 to 75 µA/cm2 during the vapor deposition of 2.4 nm Ag within 1600 s, as shown in the left panel of fig. 2. By slow annealing of the junction (now with 22.4 nm Ag layer) to 340 K, IT decreases continuously to 25 µA/cm2 . This drop is irreversible; cooling back to 44 K brings IT to 20 µA/cm2 . Figure 3 shows the relative increase of IT after silver deposition of 1.6 nm at low temperatures as a function of the tunnel voltage. The increase is smaller when holes tunnel into the silver electrode (UT < 0), but for both electron and hole tunneling the relative increase becomes more pronounced the smaller the absolute value of UT .
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Fig. 2 – Left side: increase of IT at UT = −1.0 V during the additional evaporation of 2.4 nm silver at 42 K on the silver electrode of a MIM with initial silver electrode thickness d(Ag) of 20 nm; right side: IT during subsequent annealing of the MIM junction from 42 K to 340 K and recooling to 44 K.
Theory and discussion. – The observed effects are assigned to increased scattering of the hot carriers by the structural disorder of the cold-deposited silver. Disorder-induced scattering of electrons at the Fermi level is also observed as an increase ∆R in the electric resistance R when small quantities of Ag are cold-deposited on a smooth Ag film, see figs. 5.1 and 5.21 in ref. [12]. Indeed the drop of IT during annealing (fig. 2, right) resembles closely the eventual disappearance of ∆R by annealing, see figs. 4.2 and 5.6 in [12]. The annealing of the porosity of cold-deposited Ag films is caused by migration of vacancy doublets (activation energy 0.58 eV) to the surface [13]. The surface roughness anneals by two-dimensional adatom
I rough / Ismooth
6
Al /anodic oxide/Ag(18nm) dcold=1.6nm at 48K
4
2
hot electrons into Ag
hot holes into Ag
0
-0,8
-0,6
-0,4
-0,2 UT / V
0,0
0,2
0,4
Fig. 3 – Ratio of the tunnel currents after (Irough ) and before (Ismooth ) cold deposition of 1.6 nm of silver at 48 K on the 18 nm thick silver top electrode of a MIM junction, as a function of the tunnel voltage UT . Negative (positive) values of UT correspond to hot electron (hole) tunneling into the silver electrode.
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evaporation (activation energy 0.71 eV [14]). After annealing to 300–340 K, the cold-deposited silver layer is ordered like a room-temperature–deposited silver film. Firstly, one may try to discuss the results by a ballistic model, assuming a starting flux I0 of electrons at the oxide silver interface. This flux correspond to IT of a MIM junction with a silver film thickness dAg far exceeding the mean free path λee of the starting electrons. For dAg of the order of λee , the ballistic current density at the silver-vacuum interface at first encounter is called Iel . One may tentatively assume a certain return rate of the electrons to the Al side into the initial starting state because this is the only available state. The probability for this process is modeled by an elastic reflection coefficient pel at the silver-vacuum interface and a coefficient tel of tunneling into the initial state after elastic return to the silver-oxide interface. Further reflections are neglected. One derives easily for the tunnel current density IT : 2 Iel IT = I0 1 − pel tel . I0
(1)
Electron-electron (e-e) scattering in Ag at negative tunnel voltages (electron current from Al to Ag) leads to a cascade of secondary electrons and holes in Ag. The secondary hot electrons cannot tunnel to the aluminum side, because they are below the Fermi level of Al. However, secondary hot holes in silver can tunnel to the Al, because there are filled electron states (“empty hole states”) on the Al side. Therefore, after localization in silver and energy relaxation, a charge qt of more than one electron per primary tunneling electron may contribute to IT , which is measured in the outer circuit of the MIM contact as a transport current involving only electrons at the Fermi levels of the circuit. The secondary hole current can be tackled by replacing I0 by I0 qt . Diffuse elastic scattering at the silver-vacuum surface will, of course, change pel but not the distribution of holes in the secondary cascade, provided that inelastic scattering at the silver-vacuum interface can be neglected. If one tries to explain the factor-five change of IT at UT = −1 V (see fig. 2, left), one may choose the favorable condition tel = 1 and pel to vary from 0 to 1 by cold deposition of Ag. This requires the ratio IIel0 ≈ 0.9 after traversing 20 nm of silver. This ratio is possible only with λee about 190 nm, which exceeds by far the accepted value of about 80 nm at 1 eV hot-electron energy [15]. At λee = 80 nm the maximal change of IT cannot exceed a factor of about 2.5, which is distinctly less than 5. Therefore a model is proposed, based on changing the coherent tunneling states by electron scattering at the Ag-vacuum interface. There are two limiting pictures of tunneling: The usual consideration of the tunneling process between two half-spaces (metal 1 (aluminum) and metal 2 (silver), separated by a thin barrier) assumes a free electron approaching the barrier from, e.g., the side of metal 1 and tunneling to metal 2 with a usually small transmission amplitude, calculated by the WKB method or directly [7]. The wave function of the tunneling electron is continuous, in other words coherence is maintained in metal 2 with respect to metal 1. Elastic, inelastic and dephasing scattering processes, altering the coherent tunneling state, are not explicitly considered in the calculations. However, these processes are necessary. Tunneling as measured by an external current meter is only complete after the eventual loss of the primary coherent tunneling wave function and the localization of the tunneling electron and its secondaries in new wave functions restricted to metal 2 (where electrons and holes eventually settle down to the Fermi level). In the case that the thickness of the metal 2 electrode exceeds by far the mean free path of the tunneling electron in metal 2 this condition is always fulfilled by electron-electron scattering, which exceeds the electron-phonon scattering. The other limiting picture for a tunneling process in a MIM junction is the double well system consisting of two thin films. Without a scattering process, the electron originally
EUROPHYSICS LETTERS
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a)
40 R = 0.1
30
I T /I∞
I T (Ws =0.5) / I T (Ws =0.01)
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20 10 0
R = 0.5
0,0
0,5
1,0 1,5 (E - EF )/eV
2,0
2,5
1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0
b)
UT = -1 V
R = 0.5 R = 0.25
0,0
0,2
R = 0.1
0,4
Fig. 4 – Dependencies according to eq. (2) for several parameters R. a) shows of (E − EF ), b) gives the ratio outer surface.
IT (Ws ) I∞
0,6
0,8
1,0
WS IT (Ws =0.5) IT (Ws =0.01)
as a function
for UT = −1 V. Ws is the diffuse scattering probability at the
on side 1 oscillates periodically within times given by the barrier and the electron energy coherently between side 1 and side 2 (as in covalent bonding of a H+ 2 ion), it never settles to side 2. As a more realistic description coherently evolving electron states ϕ1–2 are assumed starting from well 1 (Al) at t > 0 into well 2 (Ag). Scattering processes will eventually weaken the probability of finding the electron in ϕ1–2 and localize it as a hot electron in well 2. The most important scattering processes are e-e scattering in the bulk of Ag or Al and scattering by disorder at the interfaces (mainly elastic), but only the scattering rate at the outer Ag surface can be experimentally influenced from the exterior. The mean free path of electron-phonon interaction is larger than λee at the given electron energies and will be neglected. The mean free path λee in e-e Coulomb scattering is calculated with electrons normalized to probability one within the same volume. This is different in the present case (and was overlooked in [10]) where an electron in ϕ1–2 interacts with the electrons localized in the Fermi sea of well 2 (Ag). This leads formally to an increase of the mean free path λee in well 2 to λRee , where R is the probability to find the electron in state ϕ1–2 in well 2 (Ag). A type of rate equation of intensities was chosen rather than scattering amplitudes, because e-e scattering is always characterized by the ballistic mean free path which is restricted by the quasi-dephasing electron-electron scattering. Therefore the interference between the amplitudes of e-e scattering events and of scattering at the surface can be neglected. Assuming that IT is controlled by two types of scattering processes, electron scattering in the bulk and diffuse scattering with probability Ws (0 ≤ Ws ≤ 1) at the outer surface of the silver electrode, IT is given by RdAg RdAg IT = I∞ 1 − exp − + Ws exp − , (2) λee λee where I∞ is the value of IT for an infinitely thick top silver electrode, and dAg is the actual thickness of the top silver electrode. As in the ballistic model, the secondary hole current can be taken into account by renormalization of I∞ . Note that from dAg λee there follows R < 1 and IT ≈ I∞ Ws . In this limit, at constant UT , the tunnel current IT is fully controlled d ≈ 1, R is a function of I∞ by scattering at the outer surface (see fig. 4b). In the range λAg ee (given by the barrier and UT ), of dAg /λee , and of Ws , which I do not know how to calculate.
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(Ws =0.5) Figure 4a shows the ratio IITT(W as a function of (E − EF ) for two parameters R. The s =0.01) hot-electron energy (E − EF ) = −eUT determines the value of λee in eq. (2). Figure 4b gives s) for UT = −1 V as a function of Ws for several parameters R. the ratio ITI(W ∞ Figure 4b may be considered as qualitative explanation of the observed increase of IT with the amount of cold-deposited Ag in fig. 2, left. Figure 4a does qualitatively explain the results for electron tunneling in fig. 3. Any better fitting would convey a wrong impression, because there is no way to calculate R. Hole tunneling from Al to Ag, see fig. 3, can be formally treated in the same way for a degenerate free-electron gas. In the limit ε → 0 for small energies ε of hot electrons (above EF of Ag) and hot holes (below EF of Ag) the mean free path becomes the same, but for finite ε the mean free path of holes is larger. Contrary to the injected electrons, injected holes are always at small ε, irrespective of the positive value of UT , see fig. 1. The contribution of hot holes and hot electrons at ε ≤ 0.3 eV to IT is about the same at smooth surfaces, but the ratio Irough /Ismooth is about a factor of 2 smaller for holes than for electrons, see fig. 3. Given the relative small influence of the unknown parameter R at small |UT |, this must be assigned to a smaller parameter Ws for primary hot holes with respect to primary electrons at the same energy ε, though one expects for ε → 0 the same diffuse scattering in the unordered cold-deposited layer. However, the flux of electrons and holes into Ag with cold-deposited Ag on top are not symmetric cases. Hole flux from Al to Ag can be described also as electron flux from Ag to Al, with the diffuse scattering at the outer surface of the start well. But for flux of electrons from Al to Ag the diffuse scattering takes place at the outer surface of the destination well.
Summary and concluding remarks. – The tunneling probability in stratified metalinsulator-metal contacts is usually considered as a function only of the tunnel voltage, the properties of the barrier (thickness, barrier height, given by the lower edge of the conduction band in the insulator) and the electronic density of electronic states in the metals. It is implicitly assumed that the thickness of the metal layers exceeds the mean free path of the tunneling electrons. However, new mesoscopic effects are found, when this condition is no longer fulfilled. The tunnel current IT at constant tunnel voltage depends strongly on the conditions at the outer surfaces of the metal electrodes. One of these surfaces will be in contact with the substrate, the other with vacuum, gas or liquid (electrolyte). At the latter surface chemical and structural changes by adsorption or deposition do control the tunnel current at constant tunnel voltage “from the exterior”. In the limit of a thickness of the non-buried film much smaller than the mean free path of the “hot” electrons in this film, the tunnel current can be approximated by IT ≈ I∞ Ws , where I∞ is the tunnel current at thickness of the non-buried film exceeding the mean free path by far, and Ws is the probability of diffuse surface scattering of the tunneling electron out of the coherent tunneling state extended over both sides of the barrier into new states localized in the non-buried film. Ws is a parameter, adjustable through the experimental conditions. In this article Ws was explained by disorder-scattering in the thin cold-deposited silver film. For the other manifestations of this mesoscopic quantum effect, tentative explanations of Ws are given in [7]. ∗∗∗ I thank D. Diesing for performing the measurements and programming eq. (2).
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REFERENCES [1] [2] [3] [4] [5] [6]
[7] [8] [9] [10]
[11] [12] [13] [14] [15]
Duke C. E., Tunneling in Solids (Academic Press, New York) 1969. Hansma P. K. (Editor), Tunneling Spectroscopy (Plenum Press, New York) 1982. Mead C. A., J. Appl. Phys., 32 (1961) 646. Bernard J., Decker M. and Mentalechata Y., C.R. Acad. Sci. Paris B, 270 (1970) 1419. ¨nisch M. and Otto A., J. Phys. Condens. Matter, 6 (1994) 9659. Ha Diesing D., Kritzler G. and Otto A., in Solid Liquid Interfaces, Macroscopic Phenomena and Microscopic Understanding, edited by Thurgate S. and Wandelt K., Topics in Applied Physics, Vol. 85 (Springer, Berlin) 2003, p. 365. Diesing D., Kritzler G., Stermann M., Nolting D. and Otto A., J. Solid State Electrochem., published on-line 29 March 2003. Gadzuk J. W., Phys. Rev. Lett., 76 (1996) 4234. Schatteburg S., Diesing D. and Otto A., Appl. Phys. B, 70 (2000) 573. ¨nisch M., Lohrengel M. M., Ru ¨ ße S., Schaak A., Otto A., Diesing D., Janssen H., Ha ¨ rwer D., Kritzler G. and Winkes H., in Interfacial Science, edited Schatteburg S., Ko by Roberts M. W. (Blackwell Science, Oxford) 1997, p. 163. Diesing D., Hassel A. W. and Lohrengel M. M., Thin Solid Films, 342 (1999) 282. Schumacher D., Springer Tracts in Modern Physics, 128 (1993) 1. Mehren H. and Seeger A., Phys. Status Solidi, 39 (1970) 647. ¨gsgaard E., Besenbacher F. and Comsa G., Phys. Morgenstern K., Rosenfeld G., La Rev. Lett., 80 (1998) 556. Quinn J. J., Phys. Rev., 126 (1962) 1453.
