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New optical near field developments: some perspectives in interferometry
ultramicroscopy ELSEVIER
Ul~amicroscopy61 (1995) 117-125
New optical near field developments: some perspectives in interferometry Daniel Courjon a, *, Claudine Bainier a, Fadi Baida a, Christian Girard b a Laboratoire d'Optique P.M. Duffieux, CNRS URA 214, Universit£ de Franche-Comt£, U.F.R. Sciences, route de Gray, F-25030 Besanqon Cedex, France b Laboratoire de Physique Mol£culaire, CNRS URA 772, Universit£ de Franche-Comt£, U.F.R. Sciences, route de Gray, F-25030 Besanqon Cedex, France
Received 22 May 1995;accepted 11 July 1995
Abstract
This work deals with the interaction of an evanescent standing wave with nanometer size objects in scanning tunneling optical microscopy (STOM/PSTM). Exploiting both the structure of the fringe pattern perturbed by the object and the last simulation works, we discuss the reality of the near field images. We show that interferometry seems to be a good tool for discriminating the true optical signal from artefacts whose origin is not always understood.
1. Introduction
One of the characteristics of local probe microscopies is the strong interaction between the probe and the sample itself. Near field optical microscopy is no exception to the rule. Any near field optical image can be perturbed by various interactions which can be shared between optical interactions, electronical artefacts and mechanical perturbations. Optical interactions are due to the direct coupling between the light and the sample but also to the tip-sample light coupling. It has been shown in an exhaustive literature that the interaction between the sample and the incident light can create what some authors have defined as a c o n f i n e m e n t [1-4]. Actually this confinement is merely a consequence of the continuity conditions on the boundary between the surface of the interacting objects and the ambient medium, * Corresponding author.
The confinement first depends on the polarization direction of the beam interacting with the object, second, it enhances certain object features such as edges. As a consequence, the images of periodic structures are often completely different from the object topography because of collective and resonant effects inside the structure. We will show that these effects can be strongly reduced by symmetrization of the illumination beam or by choosing suitably the polarization direction of the incident beam. Electronical artefacts are just mentioned here because they are not connected to near field detection. They are first due to the scanning of the object by the tip, and second, to electronic noise such as 50 Hz or other. They can be generally easily discriminated and cancelled. Finally mechanical interactions remain the main problem in near field microscopy whatever the scanning and the detection mode. Because of the exceedingly small distance between the sample and the object (a few 10 nanometers) some long distance
0304-3991/96/$15.00 © 1996 Elsevier ScienceB.V. All rights reserved SSDI 0304-3991(95)00132-8
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D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125
forces such as electrostatic or capillary forces can be strong enough to perturb the pollutant layer on the surface or even to modify the tip position during the scanning. This article addresses the problem of the discrimination between " t r u e " optical image, optical confinement and mechanical artefacts. The basic configuration which is considered here is a STOM/PSTM. For the sake of simplicity the objects to be imaged both experimentally and theoretically are mainly low topography gratings. Finally, near field interferometry will be used to improve the discrimination.
2. Near field optical interferometry In the end of the sixties some holographists proposed a technique to prove the ability of evanescent waves to interfere in a total internal reflection configuration. The technique simply consists of illuminating a prism from its two sides as shown in Fig. 1. The two beams travelling in opposite directions lead to a surface standing wave. This peculiar wave does not propagate, neither in the z nor in the x and y directions. Therefore, this configuration is well adapted to the study of the long distance perturbation effects as explained in the following. Recently, near field microscopy has been used to explore these particular interference patterns [5-7]. Fig. 2 shows the optical configuration. The basic part of the set-up is the tip/prism combination as in any S T O M / P S T M configuration. The microscope itself is set inside a two-mirrors combination allowing the generation of the interference fringe system. By removing the beamsplitter BS, the system be-
"~*Atip
Fig. 1. Basic configuration of the set-up showing the interfering beams and the resulting standing wave detected by the tip.
x,y,zPZT actuator fiber tp rnirro~;~.~ ' ~
.~ beamsplittar
.....
Fig. 2. Experimental set-up showing the optical elements, the piezo-positioners and the electronic device.
haves as a two-waves interferometer microscope whereas it becomes a multiple fringe interference microscope with the beamsplitter (Fabry-Prrot interferometer) [7]. Note the presence of the acousto-optical cell which modulates the light beam in order to increase the signal to noise ratio (by lock-in detection). The half wavelength plate allows us the rotation of the polarization plane of the incident beam. It can be replaced by a Pockels cell in order to avoid mechanical handling during the experiment. The mirror M is mounted on a piezo translator in order to move the fringes on the prism. This facility will be justified in the following. Finally the prism can move by means of an inchworm translator ensuring the coarse approach of the tip.
3. Experimental protocol As explained in the previous section the basic configuration is a STOM/PSTM, the light collector is a tapered monomode fiber made by using a usual hybrid technique. First of all, the fiber is heated and pulled leading to a tapered preform. This preform is then plunged in a hydrofluoric acid bath which etches the preform and leads to a very sharp conical shape. Note that the two step procedure takes benefit of both the pulling and heating technique (simplicity and rapidity) and of the chemical etching. The latter limits the tapering of the fiber core inherent to the pure pulling and heating technique. Since our aim is
D. Courjon et al. / UItramicroscopy61 (1995) 117-125 to estimate the artefacts taking place in such microscopes, no distance control is used neither by optical way nor by shear force technique. To determine the analysis plane, the tip is slowly brought towards the surface until subwavelength structures appear in the signal. This procedure is delicate but can be made easier by exploiting the well known decay of the evanescent standing wave.
119
object elements such as lines, dot circular features, they are therefore rather difficult to discriminate from the object information itself.
5.1.1. Effect of the asymmetry of the microscope illumination To point out the effect of illumination b e a m orientation on the image we have chosen first to model the image of a set of square pads. The geometrical parameters o f this object are gathered in the
4. Theoretical modelling
(a)
Two specific theoretical models have been carried out. The first one is well adapted to localized structures. It is based on the real space Green function method as explained and described in recent papers [1,8]. The main drawback of this technique is the computer m e m o r y requirement that is directly related to the size of the discretization grid used to handle the surface structures. It is thus generally limited to small objects with a moderate analysis point number (about 2000). The second model based on a reciprocal space resolution of Maxwell equations is particularly interesting for investigating repetitive objects such as line gratings [2,9]. Its main drawback is its validity domain restricted to almost flat objects.
[] []
° :I,
[]
[] ×
5. Artefacts First of all let us define what we call artefacts. By definition, an artefact is a non-natural effect appearing in an imaging process but it is not a parasitic effect stricto sensu such as hysteresis or 50 Hz parasitic oscillations. As an example, a numerical sub-sampling whose elementary step is close to the smallest object periodicities can generate artefacts leading to spurious figures with a remote relation with the object itself.
5.1. Optical artefacts If artefacts due to sampling, scanning or external forces can be rather easily isolated (though, not easily cancelled) optical artefacts are more difficult to define. They are generally due to interferences inside the object itself or between the object and the fiber tip. These interference patterns can look like
0
0.25
0.5
0.75
i
1.25
1.5
1,75
Fig. 3. (a) Top-view of a 3D object composed of seven squareshaped nanometer protrusions. Protrusions and support have the same optical index (1.5). The input parameters a r e P 1 = 150 rim, P2 = 560 nm, and the height of the pads ~is 90 nm. k represents the projection in the plane ( x y ) o f the incident wave vector associated with the excitation field. In the calculation the surface protrusions are discretized with a total of 525 cubic meshes. The object is illuminated in pure internal reflection configuration with a surface wave vector directed along the x-axis. (b) Grey scale representation of the field distribution. The observation plane is located 10 nm far from the pad top.
D. Courjon et al. / Ultramicroscopy 61 (i995) 117-125
120
Experimental STOM images
TE
TE
TE
TM i0
20
30
40
50
30
~0
50
TM
Fig. 4. Near field image of two different gratings; in (a) the object is a grating of 383 nm of period and 8 nm in depth scanned in constant height mode; in (b) and (c) the object is a grating of 417 nm of period and 5 nm in depth scanned in constant distance mode.
caption of Fig. 3. This simulation has been performed from the real space Green function approach [1], the tip is not taken into account. Fig. 3b shows the resulting STOM image for a tip distance of 10 nm. We note the asymmetrical distribution of light on the sample. This asymmetry is due to the illumination of the system. Moreover, we observe the long distance effects appearing between the pad images. This effect is not new and has been observed both experimentally and theoretically [10,11]. Fig. 4 shows the images of two slightly different gratings (383 nm of period and 8 nm in depth for the first one, 417 nm of period and 5 nm in depth for the second). Image
0
i0
20
Fig. 5. Simulated image of a F-shaped surface of 7.5 nm in thickness and 35 nm in height with an optical index of 1.5. This simulation has been performed with a quasi-point tip (extremity curvature 2.5 nm, height 10 rim) scanning the surface at 3 nm far from the top of the object. The images are given for two external polarization modes.
(a) has been recorded in constant altitude and TE mode, whereas images (b) and (c) have been obtained in constant distance mode, in TE and TM
Fig. 6. Image simulations with the second model (dipolar model without probe). The object is a grating whose period and track depth are 383 nm and 8 nm respectively. The simulated grating is 45 degrees tilted. The approach distance is 2 nm from the top of the track. The dimensions of the simulated images are 1083 nm by 1083 nm, the optical index is 1.515. Fig. 6a shows simulated images obtained in TE and TM modes in one beam configuration. The black arrows show the propagation direction of the beam. The high contrast is due to normalization in the computing program. Cross-sections show the strong asymmetry of the recorded images. This result is in agreement with experimental images of Fig. 4. Fig. 6b shows the simulated images of the same object in two-beams configuration. The low contrast is due to normalization. We note the symmetrization and the strong reduction of local field enhancements at the edge of the grating. Cross-sections are drawn when exploring the light intensity from a dark fringe to a bright one. Fig. 6c shows the same experiment when the two beams are incoherent together.
D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125
(a)
(b) Asymmetrical illumination
121
Coherent symmetrical illumination
b
a
TE
~TM 0
1gm
1 pm
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1 pm
i~ ~ ; i ~... ;~ "i'M
pm
(c)
0
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6.50
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122
D. Courjonet al. / Ultramicroscopy 61 (1995)117-125
polarization respectively. The consequence of non-illumination symmetry is the non-uniform shadowing appearing both in (a) and in (b) that is in TE polarization whatever the scanning mode. This asymmetry leads to a 3D aspect in the image. Despite the bad quality of image (c) we note the rather good symmetry of the groove image. This point will be confirmed in the theoretical section. 5.1.2. Effect of the long distance propagation inside the sample This effect is more insidious because it depends on the object structure. Because of propagation along the object, the evanescent wave interacts successively with the different features encountered along the beam propagation. This effect has been pointed
out clearly in Ref. [12] where the manifestation of the long distance propagation appears as interference patterns generated by the reflection of the light by the object asperities. This effect can be strongly enhanced in periodic structures, For such objects some resonant phenomena can take place modifying the profile of the image in a very complex way. Using again the Green function model, Fig. 5 shows the simulation of a F-shaped topography of subwavelength size in TE and TM mode. The collector is a quasi-point conical tip the whose apex diameter is 2.5 nm. We observe the noticeable difference between the images. Moreover, the TE image exhibits a strong confinement as a tightening of the isointensity field lines along the vertical bar of the letter. We observe the same effect on the experimental image of the grating of Fig. 6a as shown by the white arrows (this image is recorded in constant intensity mode [4]). Such an effect has also been modelled by means of the reciprocal space perturbative approach. It is shown in Fig. 6a. Both asymmetry and confinement clearly appear. The TE image is very different from the topographic profile (of rectangular shape). The 3D aspect of the image is well visible. For sake of simplicity this simulation has been carried out in constant height mode. However, it has been shown that for almost fiat object the two scanning modes lead to qualitatively similar images.
6. Symmetrization of the illumination beam
Fig. 7. (a) Image of the evanescentfield perturbed by the grating (recorded in TE mode). (b) Same image viewed in contour lines.
Fig. 6b shows the similar modelling assuming two symmetric coherent illumination beams. As expected, we observe the symmetrization of the image cross-sections and the dramatic reduction of the confinement at the edges of the grating lines. This simulation confirms that the origin of the confinement along the grating lines depends both on the polarization (the confinement is enhanced in TE mode) and on the propagation distance along the object. Since in the two-beams configuration the light does not propagate, no confinement can take place. We note that the contrast is strongly reduced, but the image cross-section is well correlated with the topographic profile. Fig. 6c shows the image modelling when the two beams are incoherent together. The image is sym-
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D. Courjon et aL / Ultramicroscopy 61 (1995) 117-125
metrical but because of non-interference between the two opposite beams, the result is a simple summation in intensity. We note first that the confinements are kept and symmetrized in TE mode whereas, in TM mode the contrast is strongly enhanced by suitable compensation of the asymmetry of the two individual images. However, despite its apparent quality this image is not satisfying because it is not really correlated to the profile. It essentially depends on the resonances inside the object structure.
(a)
/.~~.~
(b)
7. Result Fig. 7a shows the image of the grating previously described in the two-beams configuration. We detect the slight perturbation introduced by the object in the fringe pattern, this result fits pretty well the modelling presented in Fig. 8. Note that for the sake of computing allocation memory only a two-lines grating has been imaged, moreover the grating depth in this simulation is 18 nm instead of 8 nm in depth (for similar reasons) but because of quasi static situation the difference could not be significative. For image 7b a suitable look up table has been chosen. The isointensity lines well reproduce the object profile as shown by the arrows. 0
8. Force artefacts In this short section we address the complex problem of force artefacts which can be induced by the exceedingly short distance between tip and sample. We have often observed along the last years some high resolved features in STOM images. These features only appear when the distance object/tip is a few nanometers, that is in the near field working regime. Because of very low contrast and confinement artefacts, such probable artefacts are not easily interpretable. In Fig. 9 we see the image of the grating in "flat-tint" interferometric configuration (see below). From the sharp bending of the fringes we can deduce that the resolution is very good (probably around A/30). Unfortunately, the period is the double of the actual period of the grating. It means that only one edge is imaged and that this image is probably due to a force artefact between tip
0.2
0.~
0,6
0.8
l
Fig. 8. (a) Type of object used in the simulation. The surface structure (index 1.5) is composed of two tracks of 18 nm in thickness and 90 nm in width. The spacing between the tracks is h = 280 nm and kll represents the projection in the plane (xy) of the incident wave vector associated with the excitation field (A = 632 nm). In the calculation the tracks are discretized with a total of 800 cubic meshes. (b) The field intensity collected by the point-probe is calculated in a plane parallel to the reference system at a distance of 22 nm far from the plane surface. The scanned area is 1100× 1100 nm 2.
and sample. The origin of this artefact could be the pollutant layer on the surface which is probably attracted b y the tip introducing some relaxation or capillarity effects.
9. Subwavelength fringe spacing simulation In any local microscope, the image is in fact a series of successive data sequentially recorded. It is
D. Courjon et a L / Ultramicroscopy 61 (1995) 117-125
124
Fig. 9. Image of the 383 n m period grating in tw0-beams fiat-tint configuration. Only one edge of the grating is visible. (Constant altitude mode and TE mode recording, scanning area 2 × 2 /zm).
thus possible to modify the experimental conditions between two successive recordings. In our case, it is thus possible to change the mirror position after each data recording. This can be easily achieved by moving the mirror linearly while scanning. The effect will be a linear displacement of the fringe pattern on 2~,m
2:om -
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I III
I Jl
I|
I
Ill
Ill
j~m
I
1~
l
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/
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the prism. Two cases are of real interest, first if we assume that the fringe pattern moves at the velocity of the tip no fringe will be recorded, the interferometer behaves as if it works in flat tint condition (one single fringe). On the contrary, if the mirror moves in such a way the fringe pattern moves in opposite direction of the tip displacement, the number of recorded fringes could be as high as desired without limitation (except the number of sampling points). This facility offered by near field interferometry could increase the accuracy of phase detection because the fringe shift is similar to a heterodyne process. Fig. 10 shows three grating images reproducing the main situations i.e. subwavelength spacing (a), no mirror motion (b), flat tint (c). In the last case the vertical fringes are due to a residue of interference between the reflected beams on the prism faces. We note the symmetrization of the fringes (no 3D perception effect).
10. Conclusion
In this communication we have address the problem of the artefacts appearing in S T O M / P S T M configuration (and probably in other near field microscopies). We have shown that two symmetrical illumination beams allow us to compensate the asymmetry inherent to this configuration, moreover, the standing wave character of the field allows us to cancel the confinement and resonant effects generally enhanced on periodic structure. Finally it has been shown that the fringe pattern superimposed to the object field enhances the ability of estimating the artefacts such as the capillary forces exerted between tip and object.
(a) (b) (c)
~,
References
O~m
l~m
2j~m
Fig. 10. Synthesis of variable period interference fringes (same experimental conditions as Fig. 9): (a) shows the case where the fringes move in opposite direction to the scanning (the subwavelength) synthesized spacing is here 57 nm); (b) in this case the mirror is fixed; (c) corresponds to the flat-tint field, the fringes on the prism move at the velocity of the scanning.
[1] C. Girard, A. Dereux and O.J.F. Martin, Phys. Rev. B 49 (1994) 13872, and references therein. [2] D. Van Labeke and D. Barchiesi, J. Opt. Soc. Am. A 9 (1992) 732. [3] M. Nevi~re and P. Vincent, in: Near Field Optics, NATO ASI Ser. E 242, Eds. D. Pohl and D. Courjon (Kluwer, Dordrecht, 1993) p. 377, and references therein. [4] D. Comjon C. Bainier and M. Spajer, J. Vac. Sci. Technol. B 10 (1992) 2436.
D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125 [5] A. Meixner, M. Bopp and G. Tarrach, Appl. Opt. 33 (1994) 7995. [6] J. Mertz, M. Hipp, J. Mlynek and O. Marti, Appl. Phys. Lett. 64 (1994) 2338. [7] D. Courjon, C. Bainier and F. Baida, Opt. Commun. 110 (1994) 7. [8] C. Girard and A. Dereux, Phys. Rev. B 49 (1994) 11344. [9] F. Baida, Microscopie hybride: association d'un microscope optiqne en champ proche et d'un microscope h forces atom-
125
iques: principe et r~alisation, Th~se d'Universit6 434, Besan~on, 1995. [10] N.F. van Hulst, F.B. Segerink and B. Biflger, Opt. Commun. 87 (1992) 212. [11] C. Girard, A. Dereux and O.J.F. Martin, in: Photons and Local Probes, Eds. O. Marti and R. M~511er, NATO ASI Set. E 300 (Kluwer, Dordrecht, 1995) p. 1. [12] N.F. van Hulst, F.B. Segerink, F. Achten and B. B~51ger, Ultramicroscopy 42-44 (1992) 416.
Ul~amicroscopy61 (1995) 117-125
New optical near field developments: some perspectives in interferometry Daniel Courjon a, *, Claudine Bainier a, Fadi Baida a, Christian Girard b a Laboratoire d'Optique P.M. Duffieux, CNRS URA 214, Universit£ de Franche-Comt£, U.F.R. Sciences, route de Gray, F-25030 Besanqon Cedex, France b Laboratoire de Physique Mol£culaire, CNRS URA 772, Universit£ de Franche-Comt£, U.F.R. Sciences, route de Gray, F-25030 Besanqon Cedex, France
Received 22 May 1995;accepted 11 July 1995
Abstract
This work deals with the interaction of an evanescent standing wave with nanometer size objects in scanning tunneling optical microscopy (STOM/PSTM). Exploiting both the structure of the fringe pattern perturbed by the object and the last simulation works, we discuss the reality of the near field images. We show that interferometry seems to be a good tool for discriminating the true optical signal from artefacts whose origin is not always understood.
1. Introduction
One of the characteristics of local probe microscopies is the strong interaction between the probe and the sample itself. Near field optical microscopy is no exception to the rule. Any near field optical image can be perturbed by various interactions which can be shared between optical interactions, electronical artefacts and mechanical perturbations. Optical interactions are due to the direct coupling between the light and the sample but also to the tip-sample light coupling. It has been shown in an exhaustive literature that the interaction between the sample and the incident light can create what some authors have defined as a c o n f i n e m e n t [1-4]. Actually this confinement is merely a consequence of the continuity conditions on the boundary between the surface of the interacting objects and the ambient medium, * Corresponding author.
The confinement first depends on the polarization direction of the beam interacting with the object, second, it enhances certain object features such as edges. As a consequence, the images of periodic structures are often completely different from the object topography because of collective and resonant effects inside the structure. We will show that these effects can be strongly reduced by symmetrization of the illumination beam or by choosing suitably the polarization direction of the incident beam. Electronical artefacts are just mentioned here because they are not connected to near field detection. They are first due to the scanning of the object by the tip, and second, to electronic noise such as 50 Hz or other. They can be generally easily discriminated and cancelled. Finally mechanical interactions remain the main problem in near field microscopy whatever the scanning and the detection mode. Because of the exceedingly small distance between the sample and the object (a few 10 nanometers) some long distance
0304-3991/96/$15.00 © 1996 Elsevier ScienceB.V. All rights reserved SSDI 0304-3991(95)00132-8
118
D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125
forces such as electrostatic or capillary forces can be strong enough to perturb the pollutant layer on the surface or even to modify the tip position during the scanning. This article addresses the problem of the discrimination between " t r u e " optical image, optical confinement and mechanical artefacts. The basic configuration which is considered here is a STOM/PSTM. For the sake of simplicity the objects to be imaged both experimentally and theoretically are mainly low topography gratings. Finally, near field interferometry will be used to improve the discrimination.
2. Near field optical interferometry In the end of the sixties some holographists proposed a technique to prove the ability of evanescent waves to interfere in a total internal reflection configuration. The technique simply consists of illuminating a prism from its two sides as shown in Fig. 1. The two beams travelling in opposite directions lead to a surface standing wave. This peculiar wave does not propagate, neither in the z nor in the x and y directions. Therefore, this configuration is well adapted to the study of the long distance perturbation effects as explained in the following. Recently, near field microscopy has been used to explore these particular interference patterns [5-7]. Fig. 2 shows the optical configuration. The basic part of the set-up is the tip/prism combination as in any S T O M / P S T M configuration. The microscope itself is set inside a two-mirrors combination allowing the generation of the interference fringe system. By removing the beamsplitter BS, the system be-
"~*Atip
Fig. 1. Basic configuration of the set-up showing the interfering beams and the resulting standing wave detected by the tip.
x,y,zPZT actuator fiber tp rnirro~;~.~ ' ~
.~ beamsplittar
.....
Fig. 2. Experimental set-up showing the optical elements, the piezo-positioners and the electronic device.
haves as a two-waves interferometer microscope whereas it becomes a multiple fringe interference microscope with the beamsplitter (Fabry-Prrot interferometer) [7]. Note the presence of the acousto-optical cell which modulates the light beam in order to increase the signal to noise ratio (by lock-in detection). The half wavelength plate allows us the rotation of the polarization plane of the incident beam. It can be replaced by a Pockels cell in order to avoid mechanical handling during the experiment. The mirror M is mounted on a piezo translator in order to move the fringes on the prism. This facility will be justified in the following. Finally the prism can move by means of an inchworm translator ensuring the coarse approach of the tip.
3. Experimental protocol As explained in the previous section the basic configuration is a STOM/PSTM, the light collector is a tapered monomode fiber made by using a usual hybrid technique. First of all, the fiber is heated and pulled leading to a tapered preform. This preform is then plunged in a hydrofluoric acid bath which etches the preform and leads to a very sharp conical shape. Note that the two step procedure takes benefit of both the pulling and heating technique (simplicity and rapidity) and of the chemical etching. The latter limits the tapering of the fiber core inherent to the pure pulling and heating technique. Since our aim is
D. Courjon et al. / UItramicroscopy61 (1995) 117-125 to estimate the artefacts taking place in such microscopes, no distance control is used neither by optical way nor by shear force technique. To determine the analysis plane, the tip is slowly brought towards the surface until subwavelength structures appear in the signal. This procedure is delicate but can be made easier by exploiting the well known decay of the evanescent standing wave.
119
object elements such as lines, dot circular features, they are therefore rather difficult to discriminate from the object information itself.
5.1.1. Effect of the asymmetry of the microscope illumination To point out the effect of illumination b e a m orientation on the image we have chosen first to model the image of a set of square pads. The geometrical parameters o f this object are gathered in the
4. Theoretical modelling
(a)
Two specific theoretical models have been carried out. The first one is well adapted to localized structures. It is based on the real space Green function method as explained and described in recent papers [1,8]. The main drawback of this technique is the computer m e m o r y requirement that is directly related to the size of the discretization grid used to handle the surface structures. It is thus generally limited to small objects with a moderate analysis point number (about 2000). The second model based on a reciprocal space resolution of Maxwell equations is particularly interesting for investigating repetitive objects such as line gratings [2,9]. Its main drawback is its validity domain restricted to almost flat objects.
[] []
° :I,
[]
[] ×
5. Artefacts First of all let us define what we call artefacts. By definition, an artefact is a non-natural effect appearing in an imaging process but it is not a parasitic effect stricto sensu such as hysteresis or 50 Hz parasitic oscillations. As an example, a numerical sub-sampling whose elementary step is close to the smallest object periodicities can generate artefacts leading to spurious figures with a remote relation with the object itself.
5.1. Optical artefacts If artefacts due to sampling, scanning or external forces can be rather easily isolated (though, not easily cancelled) optical artefacts are more difficult to define. They are generally due to interferences inside the object itself or between the object and the fiber tip. These interference patterns can look like
0
0.25
0.5
0.75
i
1.25
1.5
1,75
Fig. 3. (a) Top-view of a 3D object composed of seven squareshaped nanometer protrusions. Protrusions and support have the same optical index (1.5). The input parameters a r e P 1 = 150 rim, P2 = 560 nm, and the height of the pads ~is 90 nm. k represents the projection in the plane ( x y ) o f the incident wave vector associated with the excitation field. In the calculation the surface protrusions are discretized with a total of 525 cubic meshes. The object is illuminated in pure internal reflection configuration with a surface wave vector directed along the x-axis. (b) Grey scale representation of the field distribution. The observation plane is located 10 nm far from the pad top.
D. Courjon et al. / Ultramicroscopy 61 (i995) 117-125
120
Experimental STOM images
TE
TE
TE
TM i0
20
30
40
50
30
~0
50
TM
Fig. 4. Near field image of two different gratings; in (a) the object is a grating of 383 nm of period and 8 nm in depth scanned in constant height mode; in (b) and (c) the object is a grating of 417 nm of period and 5 nm in depth scanned in constant distance mode.
caption of Fig. 3. This simulation has been performed from the real space Green function approach [1], the tip is not taken into account. Fig. 3b shows the resulting STOM image for a tip distance of 10 nm. We note the asymmetrical distribution of light on the sample. This asymmetry is due to the illumination of the system. Moreover, we observe the long distance effects appearing between the pad images. This effect is not new and has been observed both experimentally and theoretically [10,11]. Fig. 4 shows the images of two slightly different gratings (383 nm of period and 8 nm in depth for the first one, 417 nm of period and 5 nm in depth for the second). Image
0
i0
20
Fig. 5. Simulated image of a F-shaped surface of 7.5 nm in thickness and 35 nm in height with an optical index of 1.5. This simulation has been performed with a quasi-point tip (extremity curvature 2.5 nm, height 10 rim) scanning the surface at 3 nm far from the top of the object. The images are given for two external polarization modes.
(a) has been recorded in constant altitude and TE mode, whereas images (b) and (c) have been obtained in constant distance mode, in TE and TM
Fig. 6. Image simulations with the second model (dipolar model without probe). The object is a grating whose period and track depth are 383 nm and 8 nm respectively. The simulated grating is 45 degrees tilted. The approach distance is 2 nm from the top of the track. The dimensions of the simulated images are 1083 nm by 1083 nm, the optical index is 1.515. Fig. 6a shows simulated images obtained in TE and TM modes in one beam configuration. The black arrows show the propagation direction of the beam. The high contrast is due to normalization in the computing program. Cross-sections show the strong asymmetry of the recorded images. This result is in agreement with experimental images of Fig. 4. Fig. 6b shows the simulated images of the same object in two-beams configuration. The low contrast is due to normalization. We note the symmetrization and the strong reduction of local field enhancements at the edge of the grating. Cross-sections are drawn when exploring the light intensity from a dark fringe to a bright one. Fig. 6c shows the same experiment when the two beams are incoherent together.
D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125
(a)
(b) Asymmetrical illumination
121
Coherent symmetrical illumination
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D. Courjonet al. / Ultramicroscopy 61 (1995)117-125
polarization respectively. The consequence of non-illumination symmetry is the non-uniform shadowing appearing both in (a) and in (b) that is in TE polarization whatever the scanning mode. This asymmetry leads to a 3D aspect in the image. Despite the bad quality of image (c) we note the rather good symmetry of the groove image. This point will be confirmed in the theoretical section. 5.1.2. Effect of the long distance propagation inside the sample This effect is more insidious because it depends on the object structure. Because of propagation along the object, the evanescent wave interacts successively with the different features encountered along the beam propagation. This effect has been pointed
out clearly in Ref. [12] where the manifestation of the long distance propagation appears as interference patterns generated by the reflection of the light by the object asperities. This effect can be strongly enhanced in periodic structures, For such objects some resonant phenomena can take place modifying the profile of the image in a very complex way. Using again the Green function model, Fig. 5 shows the simulation of a F-shaped topography of subwavelength size in TE and TM mode. The collector is a quasi-point conical tip the whose apex diameter is 2.5 nm. We observe the noticeable difference between the images. Moreover, the TE image exhibits a strong confinement as a tightening of the isointensity field lines along the vertical bar of the letter. We observe the same effect on the experimental image of the grating of Fig. 6a as shown by the white arrows (this image is recorded in constant intensity mode [4]). Such an effect has also been modelled by means of the reciprocal space perturbative approach. It is shown in Fig. 6a. Both asymmetry and confinement clearly appear. The TE image is very different from the topographic profile (of rectangular shape). The 3D aspect of the image is well visible. For sake of simplicity this simulation has been carried out in constant height mode. However, it has been shown that for almost fiat object the two scanning modes lead to qualitatively similar images.
6. Symmetrization of the illumination beam
Fig. 7. (a) Image of the evanescentfield perturbed by the grating (recorded in TE mode). (b) Same image viewed in contour lines.
Fig. 6b shows the similar modelling assuming two symmetric coherent illumination beams. As expected, we observe the symmetrization of the image cross-sections and the dramatic reduction of the confinement at the edges of the grating lines. This simulation confirms that the origin of the confinement along the grating lines depends both on the polarization (the confinement is enhanced in TE mode) and on the propagation distance along the object. Since in the two-beams configuration the light does not propagate, no confinement can take place. We note that the contrast is strongly reduced, but the image cross-section is well correlated with the topographic profile. Fig. 6c shows the image modelling when the two beams are incoherent together. The image is sym-
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D. Courjon et aL / Ultramicroscopy 61 (1995) 117-125
metrical but because of non-interference between the two opposite beams, the result is a simple summation in intensity. We note first that the confinements are kept and symmetrized in TE mode whereas, in TM mode the contrast is strongly enhanced by suitable compensation of the asymmetry of the two individual images. However, despite its apparent quality this image is not satisfying because it is not really correlated to the profile. It essentially depends on the resonances inside the object structure.
(a)
/.~~.~
(b)
7. Result Fig. 7a shows the image of the grating previously described in the two-beams configuration. We detect the slight perturbation introduced by the object in the fringe pattern, this result fits pretty well the modelling presented in Fig. 8. Note that for the sake of computing allocation memory only a two-lines grating has been imaged, moreover the grating depth in this simulation is 18 nm instead of 8 nm in depth (for similar reasons) but because of quasi static situation the difference could not be significative. For image 7b a suitable look up table has been chosen. The isointensity lines well reproduce the object profile as shown by the arrows. 0
8. Force artefacts In this short section we address the complex problem of force artefacts which can be induced by the exceedingly short distance between tip and sample. We have often observed along the last years some high resolved features in STOM images. These features only appear when the distance object/tip is a few nanometers, that is in the near field working regime. Because of very low contrast and confinement artefacts, such probable artefacts are not easily interpretable. In Fig. 9 we see the image of the grating in "flat-tint" interferometric configuration (see below). From the sharp bending of the fringes we can deduce that the resolution is very good (probably around A/30). Unfortunately, the period is the double of the actual period of the grating. It means that only one edge is imaged and that this image is probably due to a force artefact between tip
0.2
0.~
0,6
0.8
l
Fig. 8. (a) Type of object used in the simulation. The surface structure (index 1.5) is composed of two tracks of 18 nm in thickness and 90 nm in width. The spacing between the tracks is h = 280 nm and kll represents the projection in the plane (xy) of the incident wave vector associated with the excitation field (A = 632 nm). In the calculation the tracks are discretized with a total of 800 cubic meshes. (b) The field intensity collected by the point-probe is calculated in a plane parallel to the reference system at a distance of 22 nm far from the plane surface. The scanned area is 1100× 1100 nm 2.
and sample. The origin of this artefact could be the pollutant layer on the surface which is probably attracted b y the tip introducing some relaxation or capillarity effects.
9. Subwavelength fringe spacing simulation In any local microscope, the image is in fact a series of successive data sequentially recorded. It is
D. Courjon et a L / Ultramicroscopy 61 (1995) 117-125
124
Fig. 9. Image of the 383 n m period grating in tw0-beams fiat-tint configuration. Only one edge of the grating is visible. (Constant altitude mode and TE mode recording, scanning area 2 × 2 /zm).
thus possible to modify the experimental conditions between two successive recordings. In our case, it is thus possible to change the mirror position after each data recording. This can be easily achieved by moving the mirror linearly while scanning. The effect will be a linear displacement of the fringe pattern on 2~,m
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the prism. Two cases are of real interest, first if we assume that the fringe pattern moves at the velocity of the tip no fringe will be recorded, the interferometer behaves as if it works in flat tint condition (one single fringe). On the contrary, if the mirror moves in such a way the fringe pattern moves in opposite direction of the tip displacement, the number of recorded fringes could be as high as desired without limitation (except the number of sampling points). This facility offered by near field interferometry could increase the accuracy of phase detection because the fringe shift is similar to a heterodyne process. Fig. 10 shows three grating images reproducing the main situations i.e. subwavelength spacing (a), no mirror motion (b), flat tint (c). In the last case the vertical fringes are due to a residue of interference between the reflected beams on the prism faces. We note the symmetrization of the fringes (no 3D perception effect).
10. Conclusion
In this communication we have address the problem of the artefacts appearing in S T O M / P S T M configuration (and probably in other near field microscopies). We have shown that two symmetrical illumination beams allow us to compensate the asymmetry inherent to this configuration, moreover, the standing wave character of the field allows us to cancel the confinement and resonant effects generally enhanced on periodic structure. Finally it has been shown that the fringe pattern superimposed to the object field enhances the ability of estimating the artefacts such as the capillary forces exerted between tip and object.
(a) (b) (c)
~,
References
O~m
l~m
2j~m
Fig. 10. Synthesis of variable period interference fringes (same experimental conditions as Fig. 9): (a) shows the case where the fringes move in opposite direction to the scanning (the subwavelength) synthesized spacing is here 57 nm); (b) in this case the mirror is fixed; (c) corresponds to the flat-tint field, the fringes on the prism move at the velocity of the scanning.
[1] C. Girard, A. Dereux and O.J.F. Martin, Phys. Rev. B 49 (1994) 13872, and references therein. [2] D. Van Labeke and D. Barchiesi, J. Opt. Soc. Am. A 9 (1992) 732. [3] M. Nevi~re and P. Vincent, in: Near Field Optics, NATO ASI Ser. E 242, Eds. D. Pohl and D. Courjon (Kluwer, Dordrecht, 1993) p. 377, and references therein. [4] D. Comjon C. Bainier and M. Spajer, J. Vac. Sci. Technol. B 10 (1992) 2436.
D. Courjon et al. / Ultramicroscopy 61 (1995) 117-125 [5] A. Meixner, M. Bopp and G. Tarrach, Appl. Opt. 33 (1994) 7995. [6] J. Mertz, M. Hipp, J. Mlynek and O. Marti, Appl. Phys. Lett. 64 (1994) 2338. [7] D. Courjon, C. Bainier and F. Baida, Opt. Commun. 110 (1994) 7. [8] C. Girard and A. Dereux, Phys. Rev. B 49 (1994) 11344. [9] F. Baida, Microscopie hybride: association d'un microscope optiqne en champ proche et d'un microscope h forces atom-
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iques: principe et r~alisation, Th~se d'Universit6 434, Besan~on, 1995. [10] N.F. van Hulst, F.B. Segerink and B. Biflger, Opt. Commun. 87 (1992) 212. [11] C. Girard, A. Dereux and O.J.F. Martin, in: Photons and Local Probes, Eds. O. Marti and R. M~511er, NATO ASI Set. E 300 (Kluwer, Dordrecht, 1995) p. 1. [12] N.F. van Hulst, F.B. Segerink, F. Achten and B. B~51ger, Ultramicroscopy 42-44 (1992) 416.