An infrared photon scanning tunnelling microscope for investigations of near-field imaging

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1 J. Opt. A: Pure Appl. Opt. 1 (1999) Printed in the UK PII: S (99) An infrared photon scanning tunnelling microscope for investigations of near-field imaging J C Quartel and J C Dainty Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, UK j.quartel@ic.ac.uk Received 1 March 1999 Abstract. Despite the rapid growth of near-field optical microscopy in the past decade, many questions about the imaging properties of near-field microscopes remain unanswered. In this paper we describe a novel near-field optical microscope, employing CO 2 laser illumination and a silver halide fibre probe, and demonstrate its potential for fundamental investigations of near-field imaging. Keywords: Near-field optics, infrared microscopy, scanning near-field optical microscopy 1. Introduction Since the first realization of the scanning near-field optical microscope (SNOM) in 1984 [1] an explosion of novel instrument designs has ensued, and the technology has now matured to the point where near-field microscopes are employed in a wide variety of applications in biology, material science and surface chemistry [2 4]. Recently, however, serious doubts have been raised concerning the super-resolution claims of many SNOM results. It has been shown, for example, that a near-field image is strongly influenced by the scan path of the probe [5, 6]. That these problems have come to light at such a relatively late stage in the development of SNOM highlights the general lack of understanding of the near-field imaging process. To clarify the nature of the imaging problem in nearfield optics, consider figure 1(a). The near-field image is a product of several variable factors which can be divided into two categories: those which depend on the construction and geometry of the microscope, and those which depend on the object to be imaged. The former includes such factors as the probe shape and coating quality (where metal coatings are used) as well as the type of illumination used, while the latter includes factors such as the surface topography of the object and its optical properties (dielectric, fluorescence, absorption etc depending on the quantity detected). Since almost all instruments in use today employ some form of topographic feedback mechanism to maintain a constant probe sample distance while scanning (such as shear force or atomic force feedback), the scan path of the probe is also an object-dependent factor. The resulting image is therefore unlikely to be a simple mapping of the desired object information. In almost all cases, the desired information is the optical properties of the object, and one would (b) (a) Figure 1. Schematic representations of (a) the SNOM imaging process and (b) the inverse problem. like, therefore, to have an inversion procedure as shown in figure 1(b) whereby a characterization of the microscope, the known (or assumed) information about the object, and the near-field image can be processed in such a way as to extract these properties unambiguously. To our knowledge, very little processing of real nearfield images has been attempted to date (see [7] for a simple scan path correction). This, we believe, is due to the difficulty in describing the imaging process in simple terms, and in characterizing the imaging properties of a real microscope in a meaningful way. Fortunately, recently proposed theoretical treatments of near-field imaging [8] predict the possibility of making the desired inversions in certain circumstances, and /99/ $ IOP Publishing Ltd 517

2 J C Quartel and J C Dainty (a) (b) Figure 3. (a) Conventional micrograph of a pyramidal tip formed at the end of a silver halide fibre using the cleaving technique. (b) A line diagram showing the geometry of the tetrahedral pyramid tips. Figure 2. Schematic diagram of the infrared photon scanning tunnelling microscope experimental set-up. these have been tested with simple numerical simulations [9, 10]. What remains to be achieved is to verify that these ideas can be applied to real SNOMs. In this paper we describe our experimental approach to tackling this difficult problem, whereby a large scale microscope, which takes advantage of the relatively long wavelength of a CO 2 laser, is used to make careful nearfield measurements of simple object structures. Preliminary results are presented and the technical problems which are yet to be overcome are discussed. 2. The infrared experiment Figure 2 shows a schematic diagram of our experimental setup for investigating the near-field imaging process. The most important feature of this design is the use of a CO 2 laser (Edinburgh Instruments, WL-4, 4W linearly polarized continuous-wave) for illumination of the object. With its relatively long wavelength of 10.6 µm we can have a high degree of confidence in the probe and sample geometries in comparison to this scale and, as the samples need only have micron-sized variations to be relevant for nearfield microscopy, straightforward techniques can be used to construct them. In our experiment, a Galilean beam expander is used to produce a4mmdiameter Gaussian beam, and a half-wave plate is employed to permit either s or p polarization. While long-wavelength SNOM is not a new idea (indeed, the very first SNOM images were produced with microwaves [11]), few have used optical fibre probes [12, 13]. Since most of the near-field microscopes in use today employ tapered optical fibre probes, they are the natural choice for an investigation into near-field imaging. In our experiment we use a multimode silver halide fibre (Oxford Electronics) with core and cladding diameters of 600 and 700 µm, respectively. Since silver halide has very different mechanical properties to glass fibre, the standard techniques of producing tapers for near-field probes cannot be used the soft material does not have the viscosity properties of glass which allow it to be melt-drawn into a taper, and as a polycrystalline mixture, there is unlikely to be a solvent which can etch a silver halide fibre evenly and smoothly. We have therefore developed a scheme where the fibre is effectively guillotined in three planes to produce a tetrahedral pyramid. The guillotine consists of a 700 µm diameter hole in a glass plate, drilled at 45 to its surface, together with a simple mechanism which holds the fibre in place, rotates it, and advances it small distances through the hole. Using a sharp blade, 30 µm slices are shaved from the fibre until the desired amount has been cut from it. The fibre is then rotated through 120, withdrawn slightly, and cleaved again in the same manner. A third, similar cleave is made to finally produce a tetrahedral pyramid with smooth walls at 45 to the fibre axis and an apex with a typical radius of curvature of 1 2 µm (see figure 3). Our chosen microscope configuration is that of the photon scanning tunnelling microscope (PSTM) where the illuminating beam is incident on the sample such that it totally internally reflects from (the mean plane of) its upper surface. The PSTM is one of the oldest SNOM 518

3 An infrared PSTM for investigations of near-field imaging configurations, and its popularity has steadily declined due to complicated image effects which arise from its anisotropic illumination [14 16]. Nevertheless, this arrangement is attractive for fundamental investigations since its inherent simplicity makes the interactions between the field and the probe more easily isolated and modelled. Indeed, it is this simplicity which has attracted to this configuration much of the theoretical work in near-field image formation, and there is little doubt that the results have relevance for other SNOM configurations [8]. When used with uncoated probes, the PSTM also generally gives larger signals than its apertured counterparts, which is an important consideration when using (noisy) infrared detection. The sample structures used for the experiments presented here are made from pure silicon wafer which is 500 µm thick, polished on both faces and etched on the upper surface. Reactive ion etching is used to produce precise step-like structures with vertical sidewalls. The sample to be imaged is mounted onto an anti-reflection coated 45 zinc selenide prism (as shown in figure 2) by optical contacting. Thus the incident beam is transmitted into the silicon at an angle of 30 (the critical angle for a silicon air interface is 17 ). A photoconductive mercury cadmium telluride (MCT) detector (New England Research Center, MPC11-1-A1) is used to measure the signal transmitted into the fibre. Since this type of detector suffers from low frequency noise, the incident illumination is modulated and phase sensitive detection is used to measure the modulated part of the signal. We modulate the CO 2 laser output from its power supply at 4 khz and the measurement signal is filtered at the same frequency with a lock-in amplifier (Stanford Research, SR530). An image of the sample is created by scanning the probe above its surface using a piezoelectric flexure stage (Physik Instrumente, P762.2L). The stage, which incorporates position-sensing feedback, can accurately and reproducibly position the fibre to within 40 nm (equivalent to times the illuminating wavelength) of a specified target position, with a total range of 120 µm. The position signal is sent to the stage from a computer, via digital-to-analogue conversion and the stage s control electronics, at a typical rate of 20 Hz. The filtered (single pole filter with a typical time constant of 10 ms) output signal from the detector is measured at the same rate with each measurement constituting one image point. In the experiments presented here, we only investigate one-dimensional structures (that is, those which have variations in only one lateral direction), so scanning is not performed in the direction normal to the plane of figure 2 and the signal is assumed constant in this direction. It is important to note that we incorporate no physical mechanisms to determine the position of the fibre probe relative to the sample structure. Not only would this pose a formidable technical problem with the rather stiff and vibration sensitive silver halide fibre, but we prefer to leave the optical signal entirely undisturbed by unrelated external factors. The means by which we are able to determine the probe position relative to the sample, and thereby avoid crashing the tip, is described in the next section. Figure 4. The signal recorded (dots) as the probe is brought into contact with the bare zinc selenide prism with an s polarized incident beam. The known exponential decay of the intensity in the absence of the probe is shown (solid curve) for comparison. The z origin is placed at the apparent point of contact. 3. Experimental results 3.1. Approach curves In the case of a perfectly flat object, we know that the totally internally reflecting beam in the PSTM produces an evanescent wave in the air above the sample, and the presence of this wave can be detected with the near-field probe. Figure 4 shows the measured intensity as the tip is slowly brought into contact with the bare zinc selenide prism. After contact, the soft fibre tip is squashed flat against the sample surface and a roughly constant signal is observed. Another notable feature of the approach curves is the small, constant background signal. We believe this to arise from those planewave components of the illuminating Gaussian beam whose angle of incidence is smaller than the critical angle, and which are therefore transmitted as propagating waves above the sample. The fact that the background increases when the beam diameter is decreased seems to confirm this theory. As is usually observed with the PSTM configuration [12, 17] the approach curve does not fit well with the known exponential decay of the evanescent wave, which indicates that the probe itself distorts the field it is measuring. Although this may seem to be a fundamental problem with nearfield detection, theoretical studies have shown that a strong interaction between the probe and the substrate need not complicate the imaging problem [8]. In our case, in fact, the probe substrate interaction is an advantage, as it allows the use of the approach curves to initially determine the location of the sample relative to the fibre tip. Surprisingly, in some PSTM experiments, including our own, one finds that the simplest possible model for the probe substrate interaction where the probe is considered to be an infinite half plane of fibre material produces a very good fit to the observed data. Such a model predicts that the power transmitted into the fibre material is given simply by 1+α I(z) = I z0 cosh[(z z 0 )/ζ ]+α, (1) where z and z 0 are the positions, respectively, of the probe air and the substrate air interfaces (the origin is arbitrary). The constants α, I z0, and ζ depend on the refractive indices of the materials involved, and the angle and polarization of the 519

4 J C Quartel and J C Dainty Intensity (arb. units) 1 p - polarization s - polarization (z-- z 0 ) / mm Figure 5. Comparison between experimental approach curves (dots) and the frustrated total internal reflection model (solid curve) in both polarizations. In this case, the bare zinc selenide prism is used, but similar results are obtained with flat silicon samples. incident wave (expressions and values for these are provided in the appendix). The important feature about this curve is that if we allow it to be vertically scaled by an unknown factor, the quantity z 0 can still be deduced, which is not the case for an exponential curve. Several experiments with approaching the fibre to contact point have been carried out using both s and p polarized illumination, and with zinc selenide or silicon as the substrate material. In all cases a nonlinear (Levenberg Marquardt) curve fit to the data using (1), with I z0 and z 0 as the unknown parameters along with a constant offset, produced consistently good fits (see figure 5, for example). The position of the substrate, z 0, was found (in both polarizations) always to be 0.10 ± 0.05 µm less than the apparent contact point (that is, the model is consistent with a half plane of silver halide positioned 0.1 µm behind the tip extremity). Interestingly, although the above model predicts a constant ratio between the I z0 for s polarization and that for p polarization, the observed ratio typically differs from this and varies with the rotational orientation of the probe. Hence, in each experiment the position of the sample surface, z 0, can be first determined by fitting approach curves to the form of (1) (s polarization curves are preferred since the slower decay gives a more accurate determination of the fit parameters). Of course without crashing the probe into the sample we cannot measure the whole approach curve, so fitting is repeatedly performed as the tip approaches the surface until it is 0.15 µm away (according to the fit). Keeping the tip at least this distance from the surface is sufficient to avoid crashing it Standing evanescent waves As an initial test of the microscope s lateral response, a standing evanescent wave was created above the hypotenuse face of the zinc selenide prism by placing a mirror close to the prism s exit face. Figure 6 shows the measured response in the x (lateral) and z (fibre axis) directions over a small area above the prism. The nodes and antinodes are clearly visible (with visibility around 0.3) and have the expected period of 3.12 µm. Another important point to note is the apparent brightening of the fringes in the positive x direction. Analysing the z response at different x positions reveals this Figure 6. Image of a standing evanescent wave produced by placing a mirror at the output face of the prism. Here, and in subsequent images, the length scales have been normalized to the wavelength (10.6 µm) of the illuminating light. to be due to a slight slope in the x-scan direction relative to the prism surface. To compensate for this problem in subsequent measurements, approach curves are first taken at either end of the x-scan range and the scan slope inferred from the apparent positions of the sample surface. All horizontal scans thereafter are made to follow the path calculated to be parallel to the sample surface Images of structured silicon Figure 7 shows four xz images of the near-field produced by long pairs of troughs etched in silicon with s polarized illumination. The troughs were measured to be 0.12 µm deep, 2.4 µm wide, 6 mm long, and separations of the pairs as indicated on the figure. While the positions of the troughs can be seen in these images, there are large, apparently random variations in the lateral signal which obscure the measurement (images using p polarized illumination are not shown since they consist solely of such variations). A cross section of the image in figure 7(b) is shown in figure 8 along with the known field intensity in the absence of the probe (calculated using a perturbation method as described in [15]). It should be noted that as the calculation does not take into account the presence of the probe, we cannot expect the measured signal to resemble it closely. Nevertheless, the main peaks in the measured signal can be matched to the calculated ones in order to estimate the x position of the probe relative to the structure (the profiles shown on the images in figure 7 were positioned this way). Even allowing for the fact that the probe will affect the measurement of the near-field, however, the observed signal variations cannot be attributed to the probe sample interaction alone since similar effects have been observed with flat silicon samples. This extraneous signal is highly repeatable and far above the noise level, its form is very sensitive to small changes in the illumination conditions (such as the the beam diameter), and is not observed when measuring the near-field above the bare zinc selenide prism. These points suggest that the unwanted signal may arise from multiple reflections of scattered waves within the thin silicon wafer. If we consider that the optical contacting could allow an air gap between the silicon wafer and the zinc selenide prism of up to 1.5 µm, then the effective reflectivity of the 520

5 An infrared PSTM for investigations of near-field imaging (a) (b) (c) (d) Figure 7. xz images of the signal measured by the near-field probe when it is scanned above trough pairs in silicon. The distance between the centres of the pairs are (a) 35µm, (b) 25µm, (c) 15µm and (d) 5 µm. The silicon surface profiles are shown at the bases of the images in their approximate position relative to the measurements. The illuminating beam is incident from the bottom left. Figure 8. A horizontal scan (solid curve) taken from figure 7(b) compared with a calculation of the near-field intensity at the same height ( 0.4 µmorλ/25) above the surface (dashed curve). Both curves have been normalized to their mean values I. A surface profile is shown above the curves to indicate the lateral position of the troughs. interface (at the angles used in this experiment) can be as large as 0.72 for s polarization and 0.94 for p polarization. Work is continuing to minimize this effect as, at present, the results give little insight into the imaging properties of our near-field probe. 4. Summary We have presented a simple experimental infrared photon scanning tunnelling microscope. The unique combination of CO 2 laser illumination of the object and a tapered fibre collecting probe allows accurate measurements to be made, relative to the operating wavelength, which can provide valuable information about near-field imaging. Thus far, however, our measurements have been obscured by large signal variations which we believe can be attributed to a high reflectivity between the object structures used and the prism they are mounted on. Although this effect is less likely to be problematic in visible light microscopes, where refractive indices vary less and where index-matching liquids can be used to mount the sample, it should nevertheless be kept in mind wherever SNOM imaging is performed in transmission through a substrate material. We have also described a new technique for forming pyramidal tapers on silver halide fibres. Since silver halide fibres transmit a broad band of wavelengths from 2 14 µm with very little attenuation, they hold significant potential for use in near-field spectroscopy applications. Finally, our analysis of our PSTM approach curves has shown that probe altitude can be determined using only the optical signal. This technique may be useful wherever only constant altitude mode imaging is desired. An accurate model for the approach curve could also be useful in correcting scan path artifacts. Acknowledgments The authors gratefully acknowledge the Royal Society for their support of this work. John Quartel is further supported by the Association of Commonwealth Universities. 521

6 J C Quartel and J C Dainty Appendix The situation modelled by (1) is the transmittance of a single thin-film slab separating two half spaces in the special case where the waves in the slab are evanescent. It can be derived simply from the general formula found elsewhere [18]. In our case, the thin film is air and the two half spaces are the substrate material and the fibre material. Let these have refractive indices denoted by n 1, n 0 and n 2, respectively. If a plane wave (with wavelength λ in vacuum and intensity I 0 ) is incident on the thin film from the substrate material at an angle θ 0, then a simple application of Snell s law gives the direction cosines of the waves in the other two media (the air film and the fibre material, respectively) as cos θ 1 = i (n 0 /n 1 ) 2 sin 2 θ 0 1, (A.1) cos θ 2 = 1 (n 0 /n 2 ) 2 sin 2 θ 0. (A.2) It is important to emphasize that (1) is valid only for the case of frustrated total internal reflection, i.e. n 0 sin θ 0 <n 1 and n 0 sin θ 0 >n 2. This implies that cos θ 0 and cos θ 2 are real and cos θ 1 is imaginary, hence the form of the expressions above. It is convenient to also define the generalized refractive indices as { nj cos θ j for s polarization u j = (A.3) n j / cos θ j for p polarization for each of j = 0, 1, 2. Then the constants in (1) are given by iλ ζ =, (A.4) 4πn 1 cos θ 1 α = (u 0 + u 2 ) 2 + ( u0u2 u 1 + u 1 ) 2 (u 0 + u 2 ) 2 ( u0u2 u 1 + u 1 ) 2, (A.5) I z0 = 4u 2u 0 (u 0 + u 2 ) I 0. (A.6) 2 The (real) constant ζ has units of length and is equal to the decay constant of the intensity in air when the fibre material is absent. With the exception of I z0, values for these constants relevant to the presented experiment are shown in table A1. Since we do not measure absolute intensity in the experiment, Table A1. Values of the approach curve constants relevant for our experiment (the values n 1 = 1 (air), and n 2 = 2.2 (silver halide) were used in the calculations). α s and α p are the values for α corresponding respectively to s and p polarized illumination. Substrate θ 0 ζ material n 0 (deg) (µm) α s α p zinc selenide silicon there is no advantage in calculating I z0. Also note that in the case of a silicon substrate, we do not include the effect of the zinc selenide silicon interface in this model. References [1] Pohl D, Denk W and Lanz M 1984 Appl. Phys. Lett [2] Pohl D and Courjon D (ed) 1993 Near-Field Optics vol 242 NATO ASI Series E (Dordrecht: Kluwer) [3] Nieto-Vesperinas M and García N (ed) 1996 Optics at the Nanometer Scale vol 319 NATO ASI Series E (Dordrecht: Kluwer) [4] Paesler M and Moyer P 1996 Near-field Optics: Theory, Instrumentation, and Applications (New York: Wiley) [5] Hecht B, Bielefeldt H, Inouye Y, Pohl D W and Novotny L 1997 J. Appl. Phys [6] Carminati R, Madrazo A, Nieto-Vesperinas M and Greffet J-J 1997 J. Appl. Phys [7] Martin Y, Zenhausern F and Wickramasinghe H K 1996 Appl. Phys. Lett [8] Greffet J-J and Carminati R 1997 Prog. Surf. Sci [9] Greffet J-J, Sentenac A and Carminati R 1995 Opt. Commun [10] Carminati R and Greffet J-J 1995 Ultramicroscopy [11] Ash E and Nicholls G 1972 Nature [12] Piednoir A, Licoppe C and Creuzet F 1996 Opt. Commun [13] Unger M, Kossakovski D A, Kongovi R, Beauchamp J L, Baldeschwieler J D and Palanker D V 1998 Rev. Sci. Instrum [14] Goudonnet J P, Bourillot E, Adam P M, de Fornel F, Salomon L, Vincent P, Nevière M and Ferrell T L 1995 J. Opt. Soc. Am [15] Sentenac A and Greffet J-J 1995 Ultramicroscopy [16] de Fornel F, Adam P M, Salomon L, Goudonnet J P, Sentenac A, Carminati R and Greffet J-J 1996 J. Opt. Soc. Am [17] Meixner A, Bopp M and Tarrach G 1994 Appl. Optics [18] Macleod H A 1986 Thin-Film Optical Filters (Bristol: Hilger) pp