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Scanning gate microscopy on a graphene quantum point contact
Physica E 44 (2012) 1002–1004
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Scanning gate microscopy on a graphene quantum point contact S. Neubeck a,n, L.A. Ponomarenko a, A.S. Mayorov a, S.V. Morozov b, R. Yang a, K.S. Novoselov a a b
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK Institute for Microelectronics Technology, Chernogolovka 142432, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 August 2010 Received in revised form 10 October 2010 Accepted 11 October 2010 Available online 13 December 2010
In this paper, we present scanning gate microscopy (SGM) measurements on a graphene quantum point contact, carried out under ambient conditions. Images obtained in SGM display two-dimensional maps of sample resistance, as a function of the position of a biased AFM tip and the voltage applied to the tip. In our studies, a graphene quantum point contact was fabricated using local anodic oxidation. Performing SGM imaging on the resulting device structure shows that the resistance through the graphene QPC is strongly affected by the electric field of the AFM tip at the position of the QPC. & 2010 Elsevier B.V. All rights reserved.
1. Introduction Graphene nanostructures, such as nanoribbons [1–3], quantum point contacts (QPC) [4], single electron transistors [5,6] and quantum dots (QD) [4,7] offer intriguing new possibilities in the field of nanoelectronics. It is yet possible to routinely fabricate these graphene-based nanoelectronic devices, using either standard electronbeam lithography with subsequent reactive ion etching [1,2,4,6], or employing AFM tip assisted etching of graphene [7–12] (by applying a voltage between a conductive AFM tip and a grounded graphene flake in humid atmosphere to achieve direct etching of the graphene crystal into the desired device structure). In both cases the electronic structure of graphene is altered (band-gap opened up) due to size quantization in nanostructured graphene. However, the transport properties of such structures depend strongly on the particular distribution of the Coulomb potential along their edges [13–15], so one would benefit from the detailed information about the spatial distribution of the energy gap introduced [16,17]. While the electronic properties of nanostructured graphene devices are most commonly studied using either the global electrostatic back-gate [1,2,4,8,13,14] or side-gates [3,6,13,14], conducting transport experiments using local scanning electrostatic gating of such nanostructures is relatively new [16,17], and is yet to be further explored. Local electrostatic gating of graphene nanostructures complements experiments employing a global back-gate, in that it allows for precise local control of the charge carrier density inside the final device structure. The local gating leaves the remaining part of the device, such as source and drain contacts, unaffected. It thus yields additional information on the electronic transport properties of these nanostructured devices, which allow for an exclusive characterization of the working part, i.e., the respective nanostructure, of the graphene device. n
Corresponding author. Tel.: + 44 161 275 4074; fax: + 44 161 275 7584. E-mail address: [email protected] (S. Neubeck).
1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.10.017
A powerful tool in accessing this regime of electronic transport measurements is scanning gate microscopy (SGM). In SGM, the biased tip of a scanning probe microscope serves as a local top-gate, which can be moved across the sample surface. This enables one to measure changes in the conductance of a sample, when the charge carrier concentration in the sample is altered by the voltage applied to the tip, as a function of tip position. A further advantage of SGM over static local top-gates, as used, e.g., in Refs. [15,18], is the possibility to vary the coupling of the electric field of the top-gate (here the AFM tip) as the distance between the top-gate and the graphene device can be continuously changed. First examples of the two-dimensional mapping of differences in the local conductance of graphene devices consisting of micrometer-sized graphene sheets using SGM were already given [19–21]. But so far, only two studies [16,17] investigated the local conductance of a graphene nanostructure using SGM, at low temperature. In this paper, we present the successful operation of this technique applied to a graphene quantum point contact under ambient conditions.
2. Experimental method and sample fabrication The principle measurement setup for SGM is shown in Fig. 1. In SGM, a voltage (in the case shown it is the AC reference voltage of a lock-in amplifier) is applied to a conductive tip of a scanning probe microscope that is raster scanned across the device structure to be investigated. While a DC current is applied to the sample, one now measures the voltage drop across the sample as a function of the position of the biased AFM tip. Alternatively, one could also apply a DC bias voltage to the AFM tip and an AC current through the sample to be investigated. The voltage drop across the sample is then displayed simultaneously with the AFM topography, yielding a two-dimensional map of the sample resistance as a function of the voltage applied to the AFM tip.
S. Neubeck et al. / Physica E 44 (2012) 1002–1004
1003
Fig. 1. Left: schematic of the scanning gate microscopy (SGM) set-up being used. The modulation voltage of a lock-in amplifier is applied to a conductive AFM tip that is rasterscanned across the surface of a graphene flake. The graphene flake is equipped with metal contacts to allow for monitoring of its electronic properties. In the middle of the graphene flake, an oxidized area, which defines a graphene quantum point contact (QPC), is sketched. In order to detect changes in the sample conductance induced by the AFM tip voltage, a DC current is applied to the graphene sample and the voltage drop across the sample is measured using a lock-in amplifier. The signal measured at the lock-in is monitored simultaneously to the AFM-topography and displayed on screen. This allows for obtaining two-dimensional maps of sample resistance. Right: top view of the measurement set up. The graphene QPC is defined by two lines oxidized in graphene using local anodic oxidation.
Fig. 2. On the left, a contact mode AFM image of a quantum point contact (QPC) created in single layer graphene by AFM-based local anodic oxidation is shown. The graphene QPC is about 80 nm long and 35 nm wide. On the right, the device resistance, obtained on the same area as the topography shown on the left, is shown as a function of the position of the DC biased AFM tip (Vtip ¼ 0.5 V) on the sample surface. Clearly, the resistance of the sample under the influence of the electric field of the biased AFM tip only changes at the position of the graphene QPC, corresponding to the center of both images (left and right) that appears as a bright spot in the resistance map (right). All other areas on the right image show the same color, indicating that no changes in sample resistance were detected when the AFM tip was gating these positions. Before conducting the scanning gate experiment, the sample resistance was found to be about 15 kO. Scanning the biased tip across the sample led to an increase in sample resistance at the position of the QPC to a maximum of about 120 kO. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Graphene flakes were exfoliated from natural graphite and deposited on top of an oxidized silicon wafer. After selecting single layer flakes using optical microscopy and Raman spectroscopy [22,23], Ti/Au-contacts were lithographically defined on the graphene flake. To confine these flakes to nanostructures, we have employed local anodic oxidation [7–12]. Using contact mode AFM, we were scanning the biased AFM tip (Vtip ¼ 7 V with respect to grounded sample) in a humid atmosphere (relative humidity of 70%) with a velocity of 200 nm/s to locally oxidize graphene to create the desired nanostructure geometries. The spring force applied to the AFM tip was set close to zero, but such that we were still able to obtain stable height images.
3. Experimental results and discussion A QPC fabricated in this way in single layer graphene, as well as the corresponding scanning gate microscopy image, is shown in Fig. 2.
On the left, a contact mode AFM topography of the final nanostructured graphene device is shown. A dark vertical line in the middle of the image can be seen, which corresponds to the area of the graphene sheet that was oxidized by AFM local anodic oxidation. Left and right of this line are intact graphene areas (bright color). The dark line is only interrupted by a small area, about 35 nm wide and 80 nm long, which can be seen at the center of the image. This small area is the graphene quantum point contact. The image on the right in Fig. 2 was obtained on the same area as shown on the topography image on the left. It corresponds to the voltage drop across the sample, measured with the lock-in technique at each position of the AFM tip, under ambient conditions. For the measurement shown, a DC voltage of Vtip ¼ 0.5 V with respect to ground was applied to the AFM tip (Nanosensors PPP–CONTR highly doped silicon tips). An AC current of 1 mA was applied across the QPC shown on the left. We chose contact mode AFM to scan the biased AFM tip across the sample, while simultaneously measuring the sample resistance. This is slightly different
1004
S. Neubeck et al. / Physica E 44 (2012) 1002–1004
to the common operational mode of SGM of lifting the biased AFM tip to a certain height (e.g., about 5 nm [20]) above the sample. We assumed the resistance between AFM tip and sample to be on the order of several hundreds of kO, and hence chose contact mode scanning to have the strongest coupling of the electric field of the AFM tip to the graphene nanostructure (due to minimal distance between the AFM tip and the sample). The rather uniform background (all areas of the image except the center part) on the right image of Fig. 2 justifies our assumption that there is no ohmic current between the biased AFM tip and the sample. The lifetime of the AFM tip for this kind of experiment can be estimated from the usage of the same tips in performing the local anodic oxidation of graphene. For the local anodic oxidation we apply voltages of around 7 V to the AFM tip in contact mode, which is one order of magnitude larger than what we use in our scanning gate experiments. Using the same tip, we were able to perform this AFM lithography up to 50 times without noticeable decrease in lithographic resolution or noticeable change in the radius of the AFM tip, as evidenced by SEM imaging of the tips (images not shown here). Hence, we assume the same number of scanning gate passes to be possible with the same tip without appreciable changes. As is clearly visible, the only significant change in the sample conductance happens at the position of the quantum point contact. This manifests itself in the bright spot seen at the center of the right image in Fig. 2, at exactly the same position where the QPC is found in the sample topography, as shown on the left side. All other areas of the sample show a more or less uniform color, indicating that the sample conductance in these areas was not affected at all by the local gating exerted by the AFM tip.
4. Conclusions This experiment successfully demonstrates the ability to locally change the conductance of a graphene nanostructure by means of a biased AFM tip under ambient conditions. It opens the possibility for more refined studies, examining either the electronic transport behavior for any user-defined geometry of the graphene nanostructure. Alternatively, one could also vary the voltage being applied
to the AFM tip, or the distance between AFM tip and sample, to study in more detail how this will affect the charge carrier transport through the nanostructures.
References [1] M.Y. Han, B. Ozyilmaz, Y.B. Zhang, P. Kim, Phys. Rev. Lett. 98 (2007) 206805. [2] Z.H. Chen, Y.M. Lin, M.J. Rooks, P. Avouris, Physica E 40 (2007) 228. ¨ [3] F. Molitor, A. Jacobsen, C. Stampfer, J. Guttinger, T. Ihn, K. Ensslin, Phys. Rev. B 79 (2009) 075426. [4] L.A. Ponomarenko, F. Schedin, M.I. Katsnelson, R. Yang, E.W. Hill, K.S. Novoselov, A.K. Geim, Science 320 (2008) 356. [5] A.K. Geim, K.S. Novoselov, Nat. Mater. 6 (2007) 183. [6] C. Stampfer, J. Guttinger, F. Molitor, D. Graf, T. Ihn, K. Ensslin, Appl. Phys. Lett. 92 (2008) 012102. [7] S. Neubeck, L.A. Ponomarenko, F. Freitag, A.J.M. Giesbers, U. Zeitler, S.V. Morozov, P. Blake, A.K. Geim, K.S. Novoselov, Small 6 (2010) 1469. [8] A.J.M. Giesbers, U. Zeitler, S. Neubeck, F. Freitag, K.S. Novoselov, J.C. Maan, Solid State Commun. 147 (2008) 366. [9] L. Weng, L. Zhang, Y.P. Chen, L.P. Rokhinson, Appl. Phys. Lett. 93 (2008) 093107. [10] L.P. Biro, P. Lambin, Carbon 48 (2010) 2677. [11] S. Masubuchi, M. Ono, K. Yoshida, K. Hirakawa, T. Machida, Appl. Phys. Lett. 94 (2009) 082107. [12] S. Neubeck, F. Freitag, R. Yang, K.S. Novoselov, Phys. Status Solidi (b) 247 (2010) 2904. [13] C. Stampfer, J. Guettinger, S. Hellmueller, F. Molitor, K. Ensslin, T. Ihn, Phys. Rev. Lett. 102 (2009) 056403. [14] K. Todd, H.-T. Chou, S. Amasha, D. Goldhaber-Gordon, Nano Lett. 9 (2009) 416. [15] X. Liu, J.B. Oostinga, A.F. Morpurgo, L.M.K. Vandersypen, Phys. Rev. B 80 (2009) 121407. ¨ [16] S. Schnez, J. Guttinger, M. Huefner, C. Stampfer, K. Ensslin, T. Ihn, 2010, /arXiv:1005.2024v1S. [17] M.R. Connolly, K.L. Chiu, A. Lombardo, A. Fasoli, A.C. Ferrari, D. Anderson, G.A.C. Jones, C.G. Smith, 2010, /arXiv:1009.1103v2S. [18] B. Oezyilmaz, P. Jarillo-Herrero, D. Efetov, P. Kim, Appl. Phys. Lett. 91 (2007) 192107. [19] R. Jalilian, L.A. Jauregui, G. Lopez, J. Tian, C. Roecker, M.M. Yazdanpanah, R.W. Cohn, I. Jovanovic, Y.P. Chen, 2010 /arXiv:1003.5404S. [20] M.R. Connolly, K.L. Chiou, C.G. Smith, D. Anderson, G.A.C. Jones, A. Lombardo, A. Fasoli, A.C. Ferrari, Appl. Phys. Lett. 96 (2010) 113501. [21] J. Berezovsky, M.F. Borunda, E.J. Heller, R.M. Westervelt, Nanotechnology 21 (2010) 274013. [22] P. Blake, E.W. Hill, A.H. Castro Neto, K.S. Novoselov, D. Jiang, R. Yang, T.J. Booth, A.K. Geim, Appl. Phys. Lett. 91 (2007) 063124. [23] A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, A.K. Geim, Phys. Rev. Lett. 97 (2006) 187401.
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Scanning gate microscopy on a graphene quantum point contact S. Neubeck a,n, L.A. Ponomarenko a, A.S. Mayorov a, S.V. Morozov b, R. Yang a, K.S. Novoselov a a b
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK Institute for Microelectronics Technology, Chernogolovka 142432, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 August 2010 Received in revised form 10 October 2010 Accepted 11 October 2010 Available online 13 December 2010
In this paper, we present scanning gate microscopy (SGM) measurements on a graphene quantum point contact, carried out under ambient conditions. Images obtained in SGM display two-dimensional maps of sample resistance, as a function of the position of a biased AFM tip and the voltage applied to the tip. In our studies, a graphene quantum point contact was fabricated using local anodic oxidation. Performing SGM imaging on the resulting device structure shows that the resistance through the graphene QPC is strongly affected by the electric field of the AFM tip at the position of the QPC. & 2010 Elsevier B.V. All rights reserved.
1. Introduction Graphene nanostructures, such as nanoribbons [1–3], quantum point contacts (QPC) [4], single electron transistors [5,6] and quantum dots (QD) [4,7] offer intriguing new possibilities in the field of nanoelectronics. It is yet possible to routinely fabricate these graphene-based nanoelectronic devices, using either standard electronbeam lithography with subsequent reactive ion etching [1,2,4,6], or employing AFM tip assisted etching of graphene [7–12] (by applying a voltage between a conductive AFM tip and a grounded graphene flake in humid atmosphere to achieve direct etching of the graphene crystal into the desired device structure). In both cases the electronic structure of graphene is altered (band-gap opened up) due to size quantization in nanostructured graphene. However, the transport properties of such structures depend strongly on the particular distribution of the Coulomb potential along their edges [13–15], so one would benefit from the detailed information about the spatial distribution of the energy gap introduced [16,17]. While the electronic properties of nanostructured graphene devices are most commonly studied using either the global electrostatic back-gate [1,2,4,8,13,14] or side-gates [3,6,13,14], conducting transport experiments using local scanning electrostatic gating of such nanostructures is relatively new [16,17], and is yet to be further explored. Local electrostatic gating of graphene nanostructures complements experiments employing a global back-gate, in that it allows for precise local control of the charge carrier density inside the final device structure. The local gating leaves the remaining part of the device, such as source and drain contacts, unaffected. It thus yields additional information on the electronic transport properties of these nanostructured devices, which allow for an exclusive characterization of the working part, i.e., the respective nanostructure, of the graphene device. n
Corresponding author. Tel.: + 44 161 275 4074; fax: + 44 161 275 7584. E-mail address: [email protected] (S. Neubeck).
1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.10.017
A powerful tool in accessing this regime of electronic transport measurements is scanning gate microscopy (SGM). In SGM, the biased tip of a scanning probe microscope serves as a local top-gate, which can be moved across the sample surface. This enables one to measure changes in the conductance of a sample, when the charge carrier concentration in the sample is altered by the voltage applied to the tip, as a function of tip position. A further advantage of SGM over static local top-gates, as used, e.g., in Refs. [15,18], is the possibility to vary the coupling of the electric field of the top-gate (here the AFM tip) as the distance between the top-gate and the graphene device can be continuously changed. First examples of the two-dimensional mapping of differences in the local conductance of graphene devices consisting of micrometer-sized graphene sheets using SGM were already given [19–21]. But so far, only two studies [16,17] investigated the local conductance of a graphene nanostructure using SGM, at low temperature. In this paper, we present the successful operation of this technique applied to a graphene quantum point contact under ambient conditions.
2. Experimental method and sample fabrication The principle measurement setup for SGM is shown in Fig. 1. In SGM, a voltage (in the case shown it is the AC reference voltage of a lock-in amplifier) is applied to a conductive tip of a scanning probe microscope that is raster scanned across the device structure to be investigated. While a DC current is applied to the sample, one now measures the voltage drop across the sample as a function of the position of the biased AFM tip. Alternatively, one could also apply a DC bias voltage to the AFM tip and an AC current through the sample to be investigated. The voltage drop across the sample is then displayed simultaneously with the AFM topography, yielding a two-dimensional map of the sample resistance as a function of the voltage applied to the AFM tip.
S. Neubeck et al. / Physica E 44 (2012) 1002–1004
1003
Fig. 1. Left: schematic of the scanning gate microscopy (SGM) set-up being used. The modulation voltage of a lock-in amplifier is applied to a conductive AFM tip that is rasterscanned across the surface of a graphene flake. The graphene flake is equipped with metal contacts to allow for monitoring of its electronic properties. In the middle of the graphene flake, an oxidized area, which defines a graphene quantum point contact (QPC), is sketched. In order to detect changes in the sample conductance induced by the AFM tip voltage, a DC current is applied to the graphene sample and the voltage drop across the sample is measured using a lock-in amplifier. The signal measured at the lock-in is monitored simultaneously to the AFM-topography and displayed on screen. This allows for obtaining two-dimensional maps of sample resistance. Right: top view of the measurement set up. The graphene QPC is defined by two lines oxidized in graphene using local anodic oxidation.
Fig. 2. On the left, a contact mode AFM image of a quantum point contact (QPC) created in single layer graphene by AFM-based local anodic oxidation is shown. The graphene QPC is about 80 nm long and 35 nm wide. On the right, the device resistance, obtained on the same area as the topography shown on the left, is shown as a function of the position of the DC biased AFM tip (Vtip ¼ 0.5 V) on the sample surface. Clearly, the resistance of the sample under the influence of the electric field of the biased AFM tip only changes at the position of the graphene QPC, corresponding to the center of both images (left and right) that appears as a bright spot in the resistance map (right). All other areas on the right image show the same color, indicating that no changes in sample resistance were detected when the AFM tip was gating these positions. Before conducting the scanning gate experiment, the sample resistance was found to be about 15 kO. Scanning the biased tip across the sample led to an increase in sample resistance at the position of the QPC to a maximum of about 120 kO. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Graphene flakes were exfoliated from natural graphite and deposited on top of an oxidized silicon wafer. After selecting single layer flakes using optical microscopy and Raman spectroscopy [22,23], Ti/Au-contacts were lithographically defined on the graphene flake. To confine these flakes to nanostructures, we have employed local anodic oxidation [7–12]. Using contact mode AFM, we were scanning the biased AFM tip (Vtip ¼ 7 V with respect to grounded sample) in a humid atmosphere (relative humidity of 70%) with a velocity of 200 nm/s to locally oxidize graphene to create the desired nanostructure geometries. The spring force applied to the AFM tip was set close to zero, but such that we were still able to obtain stable height images.
3. Experimental results and discussion A QPC fabricated in this way in single layer graphene, as well as the corresponding scanning gate microscopy image, is shown in Fig. 2.
On the left, a contact mode AFM topography of the final nanostructured graphene device is shown. A dark vertical line in the middle of the image can be seen, which corresponds to the area of the graphene sheet that was oxidized by AFM local anodic oxidation. Left and right of this line are intact graphene areas (bright color). The dark line is only interrupted by a small area, about 35 nm wide and 80 nm long, which can be seen at the center of the image. This small area is the graphene quantum point contact. The image on the right in Fig. 2 was obtained on the same area as shown on the topography image on the left. It corresponds to the voltage drop across the sample, measured with the lock-in technique at each position of the AFM tip, under ambient conditions. For the measurement shown, a DC voltage of Vtip ¼ 0.5 V with respect to ground was applied to the AFM tip (Nanosensors PPP–CONTR highly doped silicon tips). An AC current of 1 mA was applied across the QPC shown on the left. We chose contact mode AFM to scan the biased AFM tip across the sample, while simultaneously measuring the sample resistance. This is slightly different
1004
S. Neubeck et al. / Physica E 44 (2012) 1002–1004
to the common operational mode of SGM of lifting the biased AFM tip to a certain height (e.g., about 5 nm [20]) above the sample. We assumed the resistance between AFM tip and sample to be on the order of several hundreds of kO, and hence chose contact mode scanning to have the strongest coupling of the electric field of the AFM tip to the graphene nanostructure (due to minimal distance between the AFM tip and the sample). The rather uniform background (all areas of the image except the center part) on the right image of Fig. 2 justifies our assumption that there is no ohmic current between the biased AFM tip and the sample. The lifetime of the AFM tip for this kind of experiment can be estimated from the usage of the same tips in performing the local anodic oxidation of graphene. For the local anodic oxidation we apply voltages of around 7 V to the AFM tip in contact mode, which is one order of magnitude larger than what we use in our scanning gate experiments. Using the same tip, we were able to perform this AFM lithography up to 50 times without noticeable decrease in lithographic resolution or noticeable change in the radius of the AFM tip, as evidenced by SEM imaging of the tips (images not shown here). Hence, we assume the same number of scanning gate passes to be possible with the same tip without appreciable changes. As is clearly visible, the only significant change in the sample conductance happens at the position of the quantum point contact. This manifests itself in the bright spot seen at the center of the right image in Fig. 2, at exactly the same position where the QPC is found in the sample topography, as shown on the left side. All other areas of the sample show a more or less uniform color, indicating that the sample conductance in these areas was not affected at all by the local gating exerted by the AFM tip.
4. Conclusions This experiment successfully demonstrates the ability to locally change the conductance of a graphene nanostructure by means of a biased AFM tip under ambient conditions. It opens the possibility for more refined studies, examining either the electronic transport behavior for any user-defined geometry of the graphene nanostructure. Alternatively, one could also vary the voltage being applied
to the AFM tip, or the distance between AFM tip and sample, to study in more detail how this will affect the charge carrier transport through the nanostructures.
References [1] M.Y. Han, B. Ozyilmaz, Y.B. Zhang, P. Kim, Phys. Rev. Lett. 98 (2007) 206805. [2] Z.H. Chen, Y.M. Lin, M.J. Rooks, P. Avouris, Physica E 40 (2007) 228. ¨ [3] F. Molitor, A. Jacobsen, C. Stampfer, J. Guttinger, T. Ihn, K. Ensslin, Phys. Rev. B 79 (2009) 075426. [4] L.A. Ponomarenko, F. Schedin, M.I. Katsnelson, R. Yang, E.W. Hill, K.S. Novoselov, A.K. Geim, Science 320 (2008) 356. [5] A.K. Geim, K.S. Novoselov, Nat. Mater. 6 (2007) 183. [6] C. Stampfer, J. Guttinger, F. Molitor, D. Graf, T. Ihn, K. Ensslin, Appl. Phys. Lett. 92 (2008) 012102. [7] S. Neubeck, L.A. Ponomarenko, F. Freitag, A.J.M. Giesbers, U. Zeitler, S.V. Morozov, P. Blake, A.K. Geim, K.S. Novoselov, Small 6 (2010) 1469. [8] A.J.M. Giesbers, U. Zeitler, S. Neubeck, F. Freitag, K.S. Novoselov, J.C. Maan, Solid State Commun. 147 (2008) 366. [9] L. Weng, L. Zhang, Y.P. Chen, L.P. Rokhinson, Appl. Phys. Lett. 93 (2008) 093107. [10] L.P. Biro, P. Lambin, Carbon 48 (2010) 2677. [11] S. Masubuchi, M. Ono, K. Yoshida, K. Hirakawa, T. Machida, Appl. Phys. Lett. 94 (2009) 082107. [12] S. Neubeck, F. Freitag, R. Yang, K.S. Novoselov, Phys. Status Solidi (b) 247 (2010) 2904. [13] C. Stampfer, J. Guettinger, S. Hellmueller, F. Molitor, K. Ensslin, T. Ihn, Phys. Rev. Lett. 102 (2009) 056403. [14] K. Todd, H.-T. Chou, S. Amasha, D. Goldhaber-Gordon, Nano Lett. 9 (2009) 416. [15] X. Liu, J.B. Oostinga, A.F. Morpurgo, L.M.K. Vandersypen, Phys. Rev. B 80 (2009) 121407. ¨ [16] S. Schnez, J. Guttinger, M. Huefner, C. Stampfer, K. Ensslin, T. Ihn, 2010, /arXiv:1005.2024v1S. [17] M.R. Connolly, K.L. Chiu, A. Lombardo, A. Fasoli, A.C. Ferrari, D. Anderson, G.A.C. Jones, C.G. Smith, 2010, /arXiv:1009.1103v2S. [18] B. Oezyilmaz, P. Jarillo-Herrero, D. Efetov, P. Kim, Appl. Phys. Lett. 91 (2007) 192107. [19] R. Jalilian, L.A. Jauregui, G. Lopez, J. Tian, C. Roecker, M.M. Yazdanpanah, R.W. Cohn, I. Jovanovic, Y.P. Chen, 2010 /arXiv:1003.5404S. [20] M.R. Connolly, K.L. Chiou, C.G. Smith, D. Anderson, G.A.C. Jones, A. Lombardo, A. Fasoli, A.C. Ferrari, Appl. Phys. Lett. 96 (2010) 113501. [21] J. Berezovsky, M.F. Borunda, E.J. Heller, R.M. Westervelt, Nanotechnology 21 (2010) 274013. [22] P. Blake, E.W. Hill, A.H. Castro Neto, K.S. Novoselov, D. Jiang, R. Yang, T.J. Booth, A.K. Geim, Appl. Phys. Lett. 91 (2007) 063124. [23] A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, A.K. Geim, Phys. Rev. Lett. 97 (2006) 187401.