EUROPHYSICS LETTERS 1 June 1991 Europhys. Lett., 15 (3)) pp. 2-293 (1991) Decay Length of Surface Plasmons Determined with a Tunnelling Microscope. N. KROO(*), J.-P. THOST, M. VOLCKER, W. KRIEGER and H. WALTHER Max-Planck-Institut fur Quantenoptik and Sektion Physik, Universitat Munchen Garching, FRG (received 7 January 1991; accepted 2 April 1991) PACS. 61.16D - Electron microscopy determinations (inc. scanning tunnelling microscopy methods). PACS. 73.20M - Collective excitations (inc. plasmons and other charge-density excitations). Abstract. - A tunnelling microscope is used to detect surface plasmons (SP) on a silver-vacuum interface excited by a He-Ne laser. The decay length of the SP is determined experimentally, and the detection mechanism of the SP in the tunnelling microscope is discussed. In the last few years dispersion relations for surface plasmons (SP) on metal-insulator interfaces have been extensively studied [l, 21. Some applications of such structures, e.g., for metal-oxide-metal active elements, are envisaged in integrated optics. For these applications the decay time of SP is important. This decay time can be obtained experimentally from the decay length xo of SP in the infrared region (A > 5 pm), where xo = (0.1 t 10) cm. In the visible spectral range the decay length of SP is too short (xo = (0.1 t 100) pm) to be measured by the conventional two-prism method [3]. First results have recently been obtained, however, by using a pump-probe technique with ps laser pulses [4]. Decay time data in the visible frequency range are very important for answering the question whether a coherent SP light source of the distributed-feedback type is feasible. The scanning tunnelling microscope has previously been used to excite [51 and detect [61 SP. This paper describes the first attempt to measure the decay length of SP in this visible spectral range by using a combination of a laser source for excitation and a tunnelling microscope for detection of the plasmons. If the dispersion relation of these excitations is known, the decay time can be calculated from xo. The experimental set-up is shown in fig. 1. The SP are excited in a 400 A thick silver layer deposited on a smooth fused quartz plate by using the photons of a He-Ne laser at 633 nm. The coupling between photons and plasmons at the silver-vacuum interface is realized by the so-called attenuated total reflection method in the Kretschmann geometry 171, i.e. the light Sciences, Budapest, Hungary. (*) Permanent address: Central Research Institute for Physics of the Hungarian Academy of 290 L/ZpLate EUROPHYSICS LETTERS Fig. 1. - Schematic drawing of the experimental set-up for the decay-length measurement of surface plasmons using a tunnelling microscope. of the laser is focused into the silver film from the substrate side via a 90\" prism. A 30 mm) is used to obtain a small focal spot. The prism and the microscope objective cf= substrate are mounted in the sample holder of a tunnelling microscope with the silver film facing the tungsten tip of the microscope. This means that excitation and detection of the plasmons take place on opposite sides of the film. The tip-sample distance of the tunnelling microscope is controlled in the usual way by keeping the tunnelling current constant with a feedback loop acting on the x-piezo. To measure the laser-induced change of the tunnelling current AI, the laser beam is chopped and a lock-in amplifier is used. The chopping frequency (1 kHz) is chosen higher than the cut- off frequency of the feedback loop. The decay length of the SP is determined by measuring the dependence of the laser- induced signal on the distance between the tip and the laser focal spot. This distance is varied by moving the microscope objective with a micropositioner and thereby shifting the focal spot. Line scans of the focus were performed parallel and orthogonal to the incidence plane in the x- and y-directions, respectively. A A/2 plate allows measurements with polarization directions parallel and perpendicular to the incidence plane (p- and s-polarized light). The maximal change of the tunnelling current is found at the angle of incidence of light when the equation nK sine,, = k is satisfied. Here n is the index of refraction of the substrate, and K and k are the momenta of light and SP, respectively. At the plasmon angle eo, which is near 45\" in our experiment, p-polarized light and SP are ideally coupled. The signal AI strongly depends on the polarization of the exciting laser light. When the light is s- polarized, i.e. when it is not coupled to SP, AI is found to be less than 1% of that of the p- polarized case. Typical results of the plasmon-induced change of the tunnelling current AI ?is. the distance between the tip and focus in the x- and y-directions are shown in fig. 2a) and b), respectively. For these measurements the tunnelling current was 2.5 nA, the tip bias voltage - 40 mV, and the power of the p-polarized laser radiation 2 mW. In our excitation geometry the conservation of momentum rules out plasmon propagation 1.2 1.2 - -0.8- v a) . - -0.8- b) r d- - . d;I - 4 v c.l 40.4- 0 in the y-direction and along the negative x-direction. The evaluation of fig. 2b) therefore gives an estimate of the focal spot size. A value of 10.7pm is obtained. Since the silver surface is not perpendicular to the incident radiation? the focus is expected to be elongated in the x-direction by a factor of 1.4. The slow decrease of the signal along the positive x-axis is identified with the decay of the plasmons. As the decay length and the focal spot size are of the same order of magnitude, the experimental curve of fig. 2a) was approximated by a convolution function of the experimentally determined profile of the focal spot and the exponential decay in the positive x-direction. This calculated function is also shown in fig. 2a). For a best fit a decay length xo of the SP of 9.0 pm is obtained. This value agrees with the decay lengths of 12.8(7) pm and 9.3(6) pm obtained in the experiment by van Exter et al. [4] for silver films of different ages. The measurements shown in fig. 2 were performed 20 hours after deposition of the silver film and 5 hours after exposure to ambient air pressure. Additional experiments were carried out in order to determine the detection mechanisms of the SP in the tunnelling microscope. These mechanisms may be of a thermal nature since the main decay channels of the plasmons are electron excitation and photon emission, both of which result in local heating. This in turn leads to a change of the tunnelling current by thermal expansion or by generation of a thermocurrent. The plasmon field may also be directly detected, however, by rectification at the nonlinear current-voltage characteristic of the tunnelling junction [8]. Above most of the silver surface the response time of the tunnelling current to a rapid change of the laser intensity was observed to be between 0.2 and 2 ms. This suggests that the observed plasmon-induced signal is predominantly caused by a temperature rise. In order to distinguish between the two thermal detection mechanisms, we recorded the current-voltage characteristic of the tunnelling junction. An example typical of the major part of the silver surface is shown in fig. 3a). During the voltage scan the laser radiation was periodically interrupted by an optical chopper. This leads to the modulation of the tunnelling current observed. The time dependence of the laser intensity is displayed in a separate trace marked <> and .laser off.. experiment above most of the silver surface is therefore attributed to thermal expansion. The measured curves displayed in fig. 2 were obtained under such conditions. When the tip was scanned across the surface, small regions were located where the plasmon-induced signal was observed to be several times larger. Current-voltage charac- teristics obtained at such sites are shown in fig. 3b) and e). Here the current modulation does not vanish at zero bias voltage. A comparison of fig. 3b and e) also shows that at different sites the polarity of the plasmon-induced current is reversed. Clearly, at those sites other detection mechanisms dominate thermal expansion. In addition, in those regions shorter response times are observed which are limited by the rise time of the current amplifier. These short response times indicate that the rectification of the plasmon field makes a contribution, as also discussed by Moller et al. [6]. But the observation of polarity reversal implies a dramatic change of the current-voltage characteristic. This polarity reversal is, however, also difficult to reconcile with an interpretation of the signals as a thermocurrent. For a final conclusion additional information about effects relating to the topography and to the contamination of the silver film is needed. Experiments are in progress to use the scanning tunnelling microscope to obtain simultaneous images of the silver surface with the tunnelling current and the plasmon-induced signal. To sum up, to uur knowledge this is the first attempt to use a tunnelling microscope to measure the decay length of SP in a metal film. The combination of laser excitation of SP and their detection with a tunnelling microscope opens up new possibilities to study further details of the behaviour of SP. Finally, the experiments demonstrate that the excitation of SP is an efficient method of coupling laser radiation into the tunnelling junction of a tunnelling microscope. A combination of laser excitation and scanning tunnelling microscopy can result in a powerful method of identifying and locating surface adsorbates or surface states. N. KROO et al.: DECAY LENGTH OF SURFACE PLASMONS DETERMINED ETC, 293 REFERENCES [ll LAKS B. and MILLS D. L., Phys. Rev. B, 22 (1980) 5723. [2] KROO N., SZENTIRMAY ZS. and FELSZERFALVI J., Phys. Lett. A, 101 (1984) 235. [3] AGRANOVICH V. M. and MILLS D. L., Surface Polaritions (North Holland, Amsterdam) 1982. [4] VAN EXTER M. and LAGENDIJK A., Phys. Rev. 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