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The inverse scanning tunneling near-field microscope (ISTOM) or tunnel scanning near-field optical microscope (TSNOM) 3D simulations and application to nano-sources
ultramicroscopy ELSEVIER
Ultramicroscopy 61 (I995) 17-20
The inverse scanning tunneling near-field microscope (ISTOM) or tunnel scanning near-field optical microscope (TSNOM) 3D simulations and application to nano-sources Dominique Barchiesi *, Daniel Van Labeke Laboratoire d'Optique P.M. Duffieux, Universit~ de Franche-Comtd, URA CNRS 214, UFR Sciences, Route de Gray, F-25030 Besanqon Cedex, France
Received 9 May 1995
Abstract We propose an application of the ISTOM to characterize nano-sources used in Scanning Near-Field Microscopies. The model takes into account the coupling between the nano-source and the hemispherical lens of the ISTOM set-up. By changing the angle of detection, experimental data are related to the Fourier spectrum of the source. We show "images" calculated with two different distances between tip end and lens surface.
1. Introduction In the field of Scanning Near-Field Optical Microscopy, a new technique appeared recently. The authors called it T S N O M (Tunnel Scanning NearField Optical Microscopy) because the set-up leads to detection of the tunneling photons in far field [1]. This set-up is also called I S T O M (Inverse Scanning Tunneling Optical Microscopy) because of the set-up " s y m m e t r y " between S T O M (Scanning Tunneling Optical Microscopy) and I S T O M if detection is made at supercritical angle [1-3]. Indeed, the light comes from the tip to be detected in far-field after the hemispherical lens in ISTOM, whereas in STOM, light comes from a laser through the hemispherical lens to be detected in near-field by the tip, at a few nanometers from the sample (Fig. 1). W e have
* Corresponding author. Fax: +33 81 66 64 23; E-mail: [email protected].
demonstrated in a previous paper [2] that it was possible to characterize emission of nano-sources with an I S T O M apparatus. But the interaction between the tip and sample has been neglected. W e have used the crude B e t h e - B o u w k a m p model. In this paper, we introduce the coupling between the source and the sample. In a first part, we will describe the background of the model. Previously, nano-sources have been extensively studied with other powerful methods like M M P or Green Function method in the 2D S T O M or S N O M cases [4-6].
2. The model In Fig. 1, we detail the I S T O M head apparatus. It points out the main part of this set-up. At first, we have to model the source emission, then we have to calculate it at the sample location. The interaction between the sample and the illumination must be
0304-3991/96/$15.(/0 © I996 Elsevier Science B.V. All rights reserved SSDI 0304-399 1(95)00096-8
18
D. Barchiesi, D. Van Labeke / Ultramicroscopy 61 (1995) 17-20
described before calculating the signal in the direction of far-field detection. In the previous paper [2], we used the source model of Bethe-Bouwkamp. This model describes analytically the field emitted by a hole in a perfectly conducting screen, but it is not interacting with the sample or the plane of the hemispherically lens. Therefore, electromagnetic coupling is not taken into account. Recently, some of us, have developed a multilayer model to describe STOM and STOM apparatus [7-9]. This model is an application of the perturbative Rayleigh-Fano diffraction theory to the near-field apparatus. It describes analytically low roughness diffractive multilayer systems. 3D nano-sources have been studied with this model, notably the influence of geometry of metal coating in Ref. [9]. Nano-sources are usually the end of an etched optical fiber. In order to increase resolution, the way to diminish the size of the detector is to coat the end of the fiber with aluminum, keeping a small hole in metal coating. In the best case, the size of this aperture is around 20 nm. Therefore, experimental characterization of nanosources is necessary. It seems to be possible with an ISTOM apparatus. For this, we use the multilayer model to calculate the electromagnetic field in the glass of the hemispherical lens (Fig. 1). The multilayer system is composed of 3 layers. The first two layers are the boundaries of the aluminum coating of the nano-source and the third one is the fiat surface of the hemispherical lens (Fig. 1). Then it is neces-
Incident beam
Opti c a l ~
sary to calculate the signal detected in far-field, far away from the hemispherical lens. For this purpose, we introduced the BDC (bidirectional detection coefficient), similar to coefficients used in optical scattering measurements [10]: BDC
1 d/~ I~ d ~ -
4_
__16n3(wa) 971"3
c
]kzE~[~'
where I 1 is the total power incident upon the aperture, d g~ is the solid angle, n is the optical index of the hemispherical lens, a is the radius of the hole, k z is the z component of the wave vector in glass and E~ is the diffracted field calculated in glass at the plane position of the hemispherical lens. This simple formula is derived from the asymptotic expansion of plane wave spectrum [11]. k z is the glass wave vector perpendicular to the hemispherical lens plane component.
3. Results
We apply the model in the case of the coupled nano-source. The nano-sources are better described as in the previous papers [2,3] because the true index of A1 (1.20 - 6.85 i) and the thickness of coating are introduced. We choose the glass index for simplicity equal to 1.5 even for the optical fiber tip. The incident wavelength is 632.8 nm. The incident elec-
Ei t l Ff~;.~ ~ .............~**~*~***~,~
-
Directi~°n4~ angles: eD ! ~D Polarization ~D
(1)
ko k 4r~
Fig. 1. Experimental and theoretical set-up; parameter definitions.
D. Barchiesi, D. Van Labeke / Ultramicroscopy 61 (1995) 17-20
tric field is parallel to the x axis and illumination is at normal incidence. We choose two distances separating tip and hemispherical lens plane: 20 nm (Fig. 2) and 3 nm (Fig. 3). In the two cases, we show the images obtained in ISTOM when the detection is made by varying the detector position. The obtained intensity map is projected on a plane and the two axes are graduated with the associated x and y coordinates of the wave vector in oo/c units. Nevertheless, it is easy to deduce two detection angles associated to any point of the map (Fig. 1); O D is the angle defined by the z axis and the direction of detection (in the plane of detection), ~D is defined by the x axis and the intersection of the xy plane and the plane of detection. The axis ticks are chosen to indicate clearly where the detected signal is associated to high spatial frequencies of the nano-source.
66
40 2O
S
0
t~
~'~- 26 -40 -60 -60
-40
-20
0
kx(cO/c
g
20
40
60
units)
20
-60
-40
-20
0
kx(o~/C
20
20 40 units)
60
Fig. 3. (a) The tip to hemispherical plane diopter separation is 3 nm. The relevant BDC signal is plotted in contour levels. (b) The tip to hemispherical plane diopter separation is 3 nm. The relevant normalized BDC signal is plotted in gray and contour level. Each line and each column of the BDC signal in (a) are normalized sequentially.
J
0
8
(a)
-40
(a)
40
.=
60
19
-'<>'-20 -40 -66 -60
-40
-20
0
kx(tO/c
26 46 units)
60
60 46 20
o
0
~-2o -40 -60 -60
-40
-20
0
20
40
60
kx(ml e units) Fig. 2. (a) The tip to hemispherical plane diopter separation is 20 nm. The relevant BDC signal is plotted in contour levels. (b) The tip to hemispherical plane diopter separation is 20 nm. The relevant normalized BDC signal is plotted in gray and contour level. Each line and each column of the BDC signal in (a) are normalized sequentially.
The low frequencies are located in the circle of radius 1 centered at the origin of the coordinates. If O D is above the critical angle only evanescent waves have contribution to the BDC. Therefore, BDC is very small (about 10 -7 or 10 -9) and contains high frequencies of the source. If O D is lower than the critical angle, images look more symmetric, like conventional SNOM images. The figures (a) show the real BDC whereas figures (b) show the normalized BDC to underline the sensitivity of the set-up to the direction of detection. When the tipplane distance is small, characterization of the nanosource is better because high spatial frequencies that decrease rapidly with distance remain intense enough at the hemispherical plane position to appear in the detected signal.
20
D. Barchiesi, D. Van Labeke / Ultramicroscopy 6l (1995) 17-20
4. Conclusion
References
In this paper, we introduce characterization of nano-sources in the light of ISTOM study. In fact, the best nano-source spectrum contains high frequencies and is plane and is as smooth as possible. Because of the convolution between the source and the sample spectra, it is easy to draw the conclusion that the closer the source is to the sample, the better images we get, because high frequencies of the sample will remain in the images. However, ISTOM can help to characterize nano-sources, if the detector is sensitive enough. It is shown in this paper, that for a given nano-source, results have to be carefully interpreted, because there is a strong dependence of the ISTOM signal on the tip-plane diopter separation.
[3] B. Hecht, H. Heinzelmann and D.W. Pohl, Ultramicroscopy 57 (1995) 228. [2] D. Van Labeke, D. Barchiesi and F. Ba'ida, J. Opt. Soc. Am. A 12 (1995) 695. [3] D. Van Labeke, F. Ba'ida, D. Barcbiesi and D. Courjon, Opt. Commun. 114 (1995) 470. [4] H. Heinzelmann and D. Pohl, Appl. Phys. A 59 (3994) 89. [5] A. Dereux and D.W. Pohl, Near Field Optics, NATO ASI Ser. E 242 (1993) 189. [6] L. Novotny, D.W. Pohl and P. Regli, J. Opt. Soc. Am. 11 (1994) 1768. [7] D. Barchiesi and D. Van Labeke, Ultramicroscopy 57 (1995) 196. [8] D. Barchiesi and D. Van Labeke, Microsc. Microanal. Microstruct. 5 (1994) 435. [9] D. Barchiesi, Opt. Commun., submitted. [10] J.C. Stover, Optical Scattering Measurement and Analysis (McGraw-Hill, New York, 1990) ch. I. [13] JJ. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986).
Ultramicroscopy 61 (I995) 17-20
The inverse scanning tunneling near-field microscope (ISTOM) or tunnel scanning near-field optical microscope (TSNOM) 3D simulations and application to nano-sources Dominique Barchiesi *, Daniel Van Labeke Laboratoire d'Optique P.M. Duffieux, Universit~ de Franche-Comtd, URA CNRS 214, UFR Sciences, Route de Gray, F-25030 Besanqon Cedex, France
Received 9 May 1995
Abstract We propose an application of the ISTOM to characterize nano-sources used in Scanning Near-Field Microscopies. The model takes into account the coupling between the nano-source and the hemispherical lens of the ISTOM set-up. By changing the angle of detection, experimental data are related to the Fourier spectrum of the source. We show "images" calculated with two different distances between tip end and lens surface.
1. Introduction In the field of Scanning Near-Field Optical Microscopy, a new technique appeared recently. The authors called it T S N O M (Tunnel Scanning NearField Optical Microscopy) because the set-up leads to detection of the tunneling photons in far field [1]. This set-up is also called I S T O M (Inverse Scanning Tunneling Optical Microscopy) because of the set-up " s y m m e t r y " between S T O M (Scanning Tunneling Optical Microscopy) and I S T O M if detection is made at supercritical angle [1-3]. Indeed, the light comes from the tip to be detected in far-field after the hemispherical lens in ISTOM, whereas in STOM, light comes from a laser through the hemispherical lens to be detected in near-field by the tip, at a few nanometers from the sample (Fig. 1). W e have
* Corresponding author. Fax: +33 81 66 64 23; E-mail: [email protected].
demonstrated in a previous paper [2] that it was possible to characterize emission of nano-sources with an I S T O M apparatus. But the interaction between the tip and sample has been neglected. W e have used the crude B e t h e - B o u w k a m p model. In this paper, we introduce the coupling between the source and the sample. In a first part, we will describe the background of the model. Previously, nano-sources have been extensively studied with other powerful methods like M M P or Green Function method in the 2D S T O M or S N O M cases [4-6].
2. The model In Fig. 1, we detail the I S T O M head apparatus. It points out the main part of this set-up. At first, we have to model the source emission, then we have to calculate it at the sample location. The interaction between the sample and the illumination must be
0304-3991/96/$15.(/0 © I996 Elsevier Science B.V. All rights reserved SSDI 0304-399 1(95)00096-8
18
D. Barchiesi, D. Van Labeke / Ultramicroscopy 61 (1995) 17-20
described before calculating the signal in the direction of far-field detection. In the previous paper [2], we used the source model of Bethe-Bouwkamp. This model describes analytically the field emitted by a hole in a perfectly conducting screen, but it is not interacting with the sample or the plane of the hemispherically lens. Therefore, electromagnetic coupling is not taken into account. Recently, some of us, have developed a multilayer model to describe STOM and STOM apparatus [7-9]. This model is an application of the perturbative Rayleigh-Fano diffraction theory to the near-field apparatus. It describes analytically low roughness diffractive multilayer systems. 3D nano-sources have been studied with this model, notably the influence of geometry of metal coating in Ref. [9]. Nano-sources are usually the end of an etched optical fiber. In order to increase resolution, the way to diminish the size of the detector is to coat the end of the fiber with aluminum, keeping a small hole in metal coating. In the best case, the size of this aperture is around 20 nm. Therefore, experimental characterization of nanosources is necessary. It seems to be possible with an ISTOM apparatus. For this, we use the multilayer model to calculate the electromagnetic field in the glass of the hemispherical lens (Fig. 1). The multilayer system is composed of 3 layers. The first two layers are the boundaries of the aluminum coating of the nano-source and the third one is the fiat surface of the hemispherical lens (Fig. 1). Then it is neces-
Incident beam
Opti c a l ~
sary to calculate the signal detected in far-field, far away from the hemispherical lens. For this purpose, we introduced the BDC (bidirectional detection coefficient), similar to coefficients used in optical scattering measurements [10]: BDC
1 d/~ I~ d ~ -
4_
__16n3(wa) 971"3
c
]kzE~[~'
where I 1 is the total power incident upon the aperture, d g~ is the solid angle, n is the optical index of the hemispherical lens, a is the radius of the hole, k z is the z component of the wave vector in glass and E~ is the diffracted field calculated in glass at the plane position of the hemispherical lens. This simple formula is derived from the asymptotic expansion of plane wave spectrum [11]. k z is the glass wave vector perpendicular to the hemispherical lens plane component.
3. Results
We apply the model in the case of the coupled nano-source. The nano-sources are better described as in the previous papers [2,3] because the true index of A1 (1.20 - 6.85 i) and the thickness of coating are introduced. We choose the glass index for simplicity equal to 1.5 even for the optical fiber tip. The incident wavelength is 632.8 nm. The incident elec-
Ei t l Ff~;.~ ~ .............~**~*~***~,~
-
Directi~°n4~ angles: eD ! ~D Polarization ~D
(1)
ko k 4r~
Fig. 1. Experimental and theoretical set-up; parameter definitions.
D. Barchiesi, D. Van Labeke / Ultramicroscopy 61 (1995) 17-20
tric field is parallel to the x axis and illumination is at normal incidence. We choose two distances separating tip and hemispherical lens plane: 20 nm (Fig. 2) and 3 nm (Fig. 3). In the two cases, we show the images obtained in ISTOM when the detection is made by varying the detector position. The obtained intensity map is projected on a plane and the two axes are graduated with the associated x and y coordinates of the wave vector in oo/c units. Nevertheless, it is easy to deduce two detection angles associated to any point of the map (Fig. 1); O D is the angle defined by the z axis and the direction of detection (in the plane of detection), ~D is defined by the x axis and the intersection of the xy plane and the plane of detection. The axis ticks are chosen to indicate clearly where the detected signal is associated to high spatial frequencies of the nano-source.
66
40 2O
S
0
t~
~'~- 26 -40 -60 -60
-40
-20
0
kx(cO/c
g
20
40
60
units)
20
-60
-40
-20
0
kx(o~/C
20
20 40 units)
60
Fig. 3. (a) The tip to hemispherical plane diopter separation is 3 nm. The relevant BDC signal is plotted in contour levels. (b) The tip to hemispherical plane diopter separation is 3 nm. The relevant normalized BDC signal is plotted in gray and contour level. Each line and each column of the BDC signal in (a) are normalized sequentially.
J
0
8
(a)
-40
(a)
40
.=
60
19
-'<>'-20 -40 -66 -60
-40
-20
0
kx(tO/c
26 46 units)
60
60 46 20
o
0
~-2o -40 -60 -60
-40
-20
0
20
40
60
kx(ml e units) Fig. 2. (a) The tip to hemispherical plane diopter separation is 20 nm. The relevant BDC signal is plotted in contour levels. (b) The tip to hemispherical plane diopter separation is 20 nm. The relevant normalized BDC signal is plotted in gray and contour level. Each line and each column of the BDC signal in (a) are normalized sequentially.
The low frequencies are located in the circle of radius 1 centered at the origin of the coordinates. If O D is above the critical angle only evanescent waves have contribution to the BDC. Therefore, BDC is very small (about 10 -7 or 10 -9) and contains high frequencies of the source. If O D is lower than the critical angle, images look more symmetric, like conventional SNOM images. The figures (a) show the real BDC whereas figures (b) show the normalized BDC to underline the sensitivity of the set-up to the direction of detection. When the tipplane distance is small, characterization of the nanosource is better because high spatial frequencies that decrease rapidly with distance remain intense enough at the hemispherical plane position to appear in the detected signal.
20
D. Barchiesi, D. Van Labeke / Ultramicroscopy 6l (1995) 17-20
4. Conclusion
References
In this paper, we introduce characterization of nano-sources in the light of ISTOM study. In fact, the best nano-source spectrum contains high frequencies and is plane and is as smooth as possible. Because of the convolution between the source and the sample spectra, it is easy to draw the conclusion that the closer the source is to the sample, the better images we get, because high frequencies of the sample will remain in the images. However, ISTOM can help to characterize nano-sources, if the detector is sensitive enough. It is shown in this paper, that for a given nano-source, results have to be carefully interpreted, because there is a strong dependence of the ISTOM signal on the tip-plane diopter separation.
[3] B. Hecht, H. Heinzelmann and D.W. Pohl, Ultramicroscopy 57 (1995) 228. [2] D. Van Labeke, D. Barchiesi and F. Ba'ida, J. Opt. Soc. Am. A 12 (1995) 695. [3] D. Van Labeke, F. Ba'ida, D. Barcbiesi and D. Courjon, Opt. Commun. 114 (1995) 470. [4] H. Heinzelmann and D. Pohl, Appl. Phys. A 59 (3994) 89. [5] A. Dereux and D.W. Pohl, Near Field Optics, NATO ASI Ser. E 242 (1993) 189. [6] L. Novotny, D.W. Pohl and P. Regli, J. Opt. Soc. Am. 11 (1994) 1768. [7] D. Barchiesi and D. Van Labeke, Ultramicroscopy 57 (1995) 196. [8] D. Barchiesi and D. Van Labeke, Microsc. Microanal. Microstruct. 5 (1994) 435. [9] D. Barchiesi, Opt. Commun., submitted. [10] J.C. Stover, Optical Scattering Measurement and Analysis (McGraw-Hill, New York, 1990) ch. I. [13] JJ. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986).