Ultraclean Single, Double, and Triple Carbon Nanotube Quantum

Aug 20, 2013 - The sputter deposited Re bottom gates in the trench are 40 nm thick, 70 nm ... The total channel length of the device between source an...
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Letter pubs.acs.org/NanoLett

Ultraclean Single, Double, and Triple Carbon Nanotube Quantum Dots with Recessed Re Bottom Gates Minkyung Jung,* Jens Schindele, Stefan Nau, Markus Weiss, Andreas Baumgartner, and Christian Schönenberger* Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland S Supporting Information *

ABSTRACT: We demonstrate that ultraclean single, double, and triple quantum dots (QDs) can be formed reliably in a carbon nanotube (CNT) by a straightforward fabrication technique. The QDs are electrostatically defined in the CNT by closely spaced metallic bottom gates deposited in trenches in SiO2 by sputter deposition of Re. The carbon nanotubes are then grown by chemical vapor deposition (CVD) across the trenches and contacted using conventional resist-based electron beam lithography. Unlike in previous work, the devices exhibit reproducibly the characteristics of ultraclean QDs behavior even after the subsequent electron beam lithography and chemical processing steps. We specifically demonstrate the high quality using CNT devices with two narrow bottom gates and one global back gate. Tunable by the gate voltages, the device can be operated in four different regimes: (i) fully p-type with ballistic transport between the outermost contacts (over a length of 700 nm), (ii) clean n-type single QD behavior where a QD can be induced by either the left or the right bottom gate, (iii) n-type double QD, and (iv) triple bipolar QD where the middle QD has opposite doping (p-type). Our simple fabrication scheme opens up a route to more complex devices based on ultraclean CNTs, since it allows for postgrowth processing. KEYWORDS: electron transport, nanoelectronics, nanodevice, carbon nanotube, quantum dot

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ultraclean characteristics. We have found ultraclean CNTs of a quality that compares favorably with the best known devices, even if a conventional resist-based lithography step is used after placing the CNT. Since the device quality is not reduced significantly after conventional microfabrication, the yield is significantly higher than with other techniques and more complex structures become conceivable. Our devices are fabricated on highly doped p++ Si wafers covered by a 300 nm thermally grown SiO2 layer. The p++-Si is used as a global back gate. QDs are electrostatically defined in CNTs using narrow bottom gates made of sputtered rhenium (Re) and formed in trenches in the SiO2 layer (Figure 1a). The trenches are fabricated by electron beam lithography and anisotropic reactive ion etching with CF4, followed by a wet etch step using buffered HF. After etching, both the depth and width of the trenches are ∼100 nm. The subsequent isotropic wet etch step creates an undercut in the trenches, preventing flags on the bottom gates during the Re sputtering process. The sputter deposited Re bottom gates in the trench are 40 nm thick, 70 nm wide, and spaced at a 200 nm pitch as shown in scanning electron microscope (SEM) image of Figure 1b. No

ltraclean carbon nanotubes (CNTs) that are free from disorder provide a promising platform to manipulate single electron or hole spins for quantum information.1−4 However, the device perfomance is often strongly limited by disorder and contaminations, for example, induced by the substrate or the fabrication process of electrical gates after the CNT growth.5 It is commonly believed that ultraclean CNT quantum dots (QDs) can only be obtained if the CNT is placed in the final step of the whole fabrication chain. All lithography and chemical processing that define source and drain contacts and gate electrodes are carried out first before the CNTs are either grown directly over a predefined contact pattern by chemical vapor deposition2,3,5−9 or transferred onto the contact structure by stamping.4,10−12 These two approaches have provided ultraclean and stable QDs and allowed for the investigation of interesting fundamental physical effects, such as spin−orbit interaction,2 tunable QDs in the few electron regime,3,4,9 Fabry−Perot interference, 6 and Klein tunneling.3 Both approaches are, however, of limited use due to the large processing time. The later is related to the low yield of obtaining exactly one CNT bridging the contacts and to a very demanding alignment procedure, respectively. In this work, we demonstrate that it is not a necessity to place the CNT in the last process step in order to obtain © 2013 American Chemical Society

Received: July 4, 2013 Revised: August 14, 2013 Published: August 20, 2013 4522

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Figure 1. (a) Schematics of the recessed Re bottom gates. Trenches in the SiO2 are fabricated by anisotropic reactive ion etching followed by wet chemical etching. The 40 nm thick Re bottom gates are deposited in the trenches by sputtering. The Re bottom gates are 70 nm wide and have a pitch of 200 nm. (b) Scanning electron microscope (SEM) image of the bottom gate contact area in (d) taken at 80° tilting angle. (c) Schematics of the carbon nanotube (CNT) device with source and drain contacts. CNTs are grown over the predefined bottom gates using chemical vapor deposition (CVD). Unlike in previous work, the CNT growth is not the last step but is followed by a conventional resist-based electron beam lithography step to define the source and drain contacts made of Ti/Au bilayer. (d) SEM image after the carbon CNT growth. A CNT crosses the Re bottom gates. The blue dashed lines indicates where the source and drain contacts were placed afterward.

Figure 2. Main graph: differential electrical conductance g in units of e2/h measured as a function of the gate voltages VR and VL at a sourcedrain voltage VSD = 10 mV. The back gate voltage VB is set to a negative value VB = −7.5 V to prevent the formation of unintentional quantum dots (QDs). This yields a p-type predoping in most areas of the CNT denoted as p*, in particular in the CNT segments connecting the QDs to the source and drain contacts. Depending on the gate voltages VR and VL, the device shows four different transport regimes labeled as (1)−(4). The corresponding energy band diagrams are schematically shown in each corner. CB, VB, and EF denote the conductance and valence band edge and the Fermi energy, respectively. (1) and (3) correspond to a single QD regime, (2) to the ballistic limit, and (4) to a regime with two or even three QDs. White dashed lines in the conductance plot indicate the band gap of the CNT.

adhesive layer is used. The width of the SiO2 pillar separating the two gates is ∼20 nm. As shown in Figure 1c,d, CNTs are then grown across the predefined Re bottom gates by chemical vapor deposition (CVD). The CNT growth is carried out in a tube furnace with a flow of 1000 sccm of CH4 and 500 sccm of H2 during 10 min at 950 °C. Re surface diffusion and changes in the gate geometry are not observed after the high temperature CVD growth as shown in Figure 1b,d. Finally, source-drain contacts of 5/65 nm thick Ti/Au are defined by electron beam lithography in a postgrowth fabrication step using standard PMMA resist. The total channel length of the device between source and drain contacts is ∼700 nm. All ultraclean CNT devices in our work show semiconducting behavior with a CNT band gap of ∼100 − 300 meV. Here, we focus on one particular device, but similar features have been observed in three other devices that were processed in the same way. All electrical measurements were done at 4.2 K in a He-4 transport dewar. The devices were not current annealed or cleaned by any other means before or during measurements. In the measurements, the entire CNT is tuned to p-doping by applying a negative back gate voltage VB = −7.5 V to prevent the unintentional formation of QDs in the CNT segments connecting the QDs to the source and drain contacts. In the following, we denote this lead doping by p*. Figure 2 displays a plot of the differential electrical conductance g measured as a function of left and right bottom gate voltages, VL and VR, at a constant source-drain voltage VSD = 10 mV. Depending on VL and VR, an n-type QD can be formed over the left or right bottom gate. This yields four different regimes labeled (1)−(4) that we denote by the doping state as (1) p*-n-p-p* (single QD over the left bottom gate), (3) p*-p-n-p* (single QD over the

right bottom gate), (2) p*-p-p-p* (ballistic transport without QDs in between the contacts), and (4) p*-n-p-n-p* (double and bipolar triple QD, see below). The respective energy band diagrams with the conductance (CB) and valence (VB) band edges and the Fermi energy EF are shown in each corner of the figure. The white dashed lines in the main plot indicate the energy band gap of the CNT. We first argue how a single quantum dot can be formed over, for example, the left bottom gate by tuning the left gate to a positive and the right gate to a negative voltage (regime (1) of Figure 2). This gate voltage setting lowers the potential in the CNT over the left gate and raises it over the right. On the right side no QD can form, because the raised potential corresponds to a p-doped region that merges smoothly into the p* lead of the drain contact. In contrast, the region over the left gate is ndoped, yielding a single QD (p*-n-p-p* configuration) with a confinement formed by two Esaki tunneling junctions13 (p-n junctions) localized in the CNT at the edges of the bottom gate. The tunnel barrier within the Esaki junction between the p and n regions are formed by the regions with the Fermi energy in the CNT band gap. Note that a band gap is essential, because Klein tunneling would otherwise inhibit the strong confinement needed to define a QD.14 Figure 3a shows the charge stability diagram of a single QD defined over the left gate measured as a function of VL and VSD at VR = −1.5 V. The band gap of the CNT appears between VL 4523

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Figure 3. Differential conductance g in units of e2/h measurement as a function of gate VL or VR and source-drain voltage VSD (a so-called charge stability diagram) of a single QD, which is either defined over the left (a) or the right (b) bottom gate. In (a) VR is fixed and in (b) VL, both to a value of −1.5 V. A clean QD behavior is observed in the few electron regime displaying sequential electron filling starting from the empty QD (0) with the first electron (1e). In the upper row the evolution of the energy band diagrams of the left QD as a function of VL is schematically given. The QD is n-type, while the leads are p-type. Quantum confinement is only possible with semiconducting CNTs with a band gap.

The ultraclean electron transport is further confirmed by the observation of a clean Fabry−Perot interference pattern in the same device when the doping is uniform p-type in all segments (Figure 4). This is achieved by applying negative voltages to the back gate and to both bottom gates, VL and VR (p*-p-p-p* configuration in the lower left corner of Figure 2). Figure 4a displays the linear (small bias) conductance g of the CNT measured as a function of VL and VR in this regime. With increasing negative gate voltages, the device exhibits very regular periodic oscillations on a large conductance background that increases from 1.5 to 3.4 e2/h. The measured maximum conductance is slightly smaller than the theoretical value of 4e2/ h, which one can only obtain when electrons pass through the CNT-metal interfaces without reflection.16 The high conductance shows that the interfaces have a transmission probability T > 0.8, close to the perfect transmission T = 1. The periodic pattern superimposed on the high conductance is a result of Fabry−Perot interferences due to the impinging electron wave interfering with the reflected wave between the source and drain contacts. This interpretation is supported by measuring the finite energy dependence of the oscillation pattern shown in Figure 4b, where the conductance is plotted as a function of the bias VSD and the gate voltage VR, with the left gate voltage VL = −2 V. The zero-bias periodic pattern shows a pronounced phase shift of π at a characteristic voltage VC from which the effective channel length L of the Fabry− Perot resonator can be deduced: L = νFh/2eVC,17 where νF = 8.1 × 105 m/s18,19 is the Fermi velocity in the CNT and h is the Planck constant. The bias voltage VC ∼ 3 mV obtained from Figure 4b (dashed lines) yields an effective resonator length L of ∼700 nm, close to the full device length measured by SEM.

= 0.5 and 1 V (middle inset of Figure 3a). When the gate voltage is increased to ≳1 V a clean QD is formed (right inset of Figure 3a), which is sequentially filled with single electrons starting from the state N = 1 with one electron in the QD. Below VL = 0.5 V, all segments of the nanotube become p-type, yielding an open system (left inset of Figure 3 (a)). The observation in Figure 2 that the QD lever arm of VL is ∼10 times larger than of VR confirms the position of this QD above the left bottom gate. In the same way, an n-type single QD can be formed over the right bottom gate by inverting the gate voltages (lower right corner of Figure 2, region 3). The charge stability diagram of the right QD is displayed in Figure 3b, exhibiting a similar behavior and charging energy as the left dot. The clear single QD behavior indicates that no unintentional QD is formed between the trench segments and the source-drain contacts. A large single QD charging energy (>50 meV) indicates that a very small dot is formed above the narrow bottom gate. We roughly estimate the effective length of the QDs using EC ∼ 8 meV/Leff (μm), which describes the charging energy of suspended CNT QDs.5 The charging energy of ∼100 meV obtained for the first electron yields a dot length of 80 nm, which is comparable to the bottom gate width of 70 nm. From this effective QD length, we estimate an energy level spacing of ΔE = 1 meV/Leff (μm) ∼ 12.5 meV,15 which approximately matches the observed excited state energy in the Coulomb diamond of Figure 3a (see also Supporting Information, Figure S1). The energy level spacing can also further be deduced from the 4-fold shell filling in another device (Supporting Information, Figure S2), yielding a similar value of 10−11 meV. 4524

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Figure 4. (a) Linear electrical conductance g in units of e2/h measured in the unipolar p*-p-p-p* configuration (lower left corner of Figure 2) as a function of VR and VL. Periodic oscillations superimposed on a high conductance value are observed over a wide gate voltage range. (b) Differential conductance g as a function of bias voltage VSD and gate voltage VR in the unipolar regime displaying. The dependence of the periodic oscillation pattern measured as a function of VR at VL = −2 V reveals its origin as Fabry−Perot resonances. VC is a characteristic voltage discussed in the text. (c) Linear conductance g in units of e2/h measured as a function of VR at VL = −2 V at three temperatures 4.2, 8, and 12 K. Inset: Schematic of the corresponding energy diagram. Fabry−Perot interferences occur between the source (S) and drain (D) contacts, as indicated by solid red curves.

Figure 5. (a) Charge stability diagram of the n-p-n triple QD regime measured as a function of VR and VL with a source-drain voltage VSD = 15 mV. Three different slopes can be identified: L, R, and C, corresponding to charge transition in the left, right, and center dots, respectively. (b) Magnification of (a). (c) Schematics of the energy diagram for the triple (upper graph) and double QD (lower graph) regimes. If the voltage of both bottom gates is increased, the middle ptype QD is depleted. Eventually, this QD disappears and only a tunneling barrier is formed in between the two n-type QDs (double QD regime). (d) Charge stability diagram within the double QD regime for a larger source-drain voltage of VSD = 25 mV measured as a function of VR and VL. Almost equidistant lines appear in all conductance triangles that are suggestive of excited QD states due to excited longitudinal vibrations. The energy spacing between successive excitations amounts to ∼2−3 meV.

This supports the view of ballistic transport through the entire CNT. We also note that the effect of both gates on the observed pattern is similar (diagonal lines in Figure 4a), which supports the interpretation of extended Fabry−Perot resonances. The Fabry−Perot interference has a strong temperature dependence. The conductance as a function of VR recorded at VL = −2 V and VSD = 3 mV is plotted for three different temperatures, 4.2, 8, and 12 K in Figure 4c. With increasing temperature, the oscillation amplitude is suppressed, showing no oscillations at 12 K, consistent with phonon scattering. An even more interesting situation arises when both bottom gate voltages, VL and VR, are tuned to positive values, defining two QDs (upper right corner of Figure 2). Detailed measurements of the conductance in this regime as a function of VL and VR are shown in Figure 5 (a,b) for a source-drain bias of VSD = 15 mV. As is common for a double QD, sequential charge transport is only possible if an eigenstate in each of the QDs lies within the bias window. Because of the finite bias a nonvanishing conductance appears only in so-called conductance triangles. These characteristic triangles line up along two lines denoted as L and R in Figure 5a. They define the gate dependence of the eigenstates in each QD. Remarkably, there is another set of triangles appearing at intermediate gate voltages. These triangles are fainter and align along a third line denoted as C. While the lines L and R have a steep slope, the slope of C is in-between suggesting that both gates tune this feature symmetrically. The observed characteristics point to a triple QD20−23 with a third QD formed nearly symmetrically in the middle between the two QDs. The triple QD configuration corresponds to the doping state p*-n-p-n-p*, in which quantum confinement of holes is realized in the central QD. The energy level diagram of the triple QD is shown in the upper diagram of

Figure 5c. The electron tunneling in the n-p-n triple dot takes place between the conduction and valence band, indicative of Klein tunneling between quantum confined electron and hole states.3,14,24 With increasing bottom gate voltages, the middle p-type QD will be depleted due to the energy band bending, as shown in the lower energy diagram of Figure 5c. In this regime, a clean double QD (DQD) characteristics is obtained.25 In Figure 5d, we display the differential conductance of the DQD as a function of the bottom gates VL and VR for an even larger bias voltage of VSD = 25 mV. The conductance triangles (dashed triangle line) are pronounced and repeat very regularly. Inside the triangles sharp conductance peaks run in parallel to the base lines of the bias triangles. These modulations are caused by electron tunneling through excited states. Since the lines are spaced almost equidistantly a harmonic excitation is expected. The energy difference between the lines amounts to 2−3 meV (see also Supporting Information, Figure S3). This energy scale is markedly smaller than the electronic excitation of a single QD (the energy level spacing of an individual QD was determined to be 10−12.5 meV before). In contrast to electronic excitations, vibrational modes can be of a similar energy scale. Assuming that the effective length of a suspended QD is 100 nm, the phonon energy of the CNT stretching mode is expected at ∼1 meV.26 Hence, electron−phonon interaction is a possible mechanism for the resonant transport characteristics inside the finite bias triangles. 4525

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(6) Cao, J.; Wang, Q.; Rolandi, M.; Dai, H. Phys. Rev. Lett. 2004, 93 (21), 216803−216803. (7) LeRoy, B. J.; Lemay, S. G.; Kong, J.; Dekker, C. Nature 2004, 432 (18), 371−374. (8) Cao, J.; Wang, Q.; Dai, H. Nat. Mater. 2005, 4, 745−749. (9) Steele, G. A.; Pei, F.; Laird, E. A.; Jol, J. M.; Meerwaldt, H. B.; Kouwenhoven, L. P. Nat. Commun. 2013, 4, 1573−1579. (10) Wu, C. C.; Liu, C. H.; Zhong, Z. Nano Lett. 2009, 10, 1032− 1036. (11) Waissman, J.; Honig, M.; Pecker, S.; Benyamini, A.; Hamo, A.; Ilani, S. arXiv:1302.2921. (12) Laird, E. A.; Pei, F.; Kouwenhoven, L. P. arXiv:1210.3085. (13) Esaki, L. Phys. Rev. 1958, 109, 603−604. (14) Katsnelson, M. I.; Novoselov, K. S.; Geim, A. K. Nat. Phys. 2006, 2, 620−625. (15) Nygard, J.; Cobden, D. H.; Bockrath, M.; McEuen, P. L.; Lindelof, P. E. Appl. Phys. A 1999, 69, 297−304. (16) White, C. T.; Todorov, T. N. Nature 1998, 393, 240−242. (17) Liang, W.; Bockrath, M.; Bozovic, D.; Hafner, J. H.; Tinkham, M.; Park, H. Nature 2001, 411, 665−669. (18) Wallace, P. R. Phys. Rev. 1947, 71, 622−634. (19) Lemay, S. G.; Janssen, J. W.; van den Hout, M.; Mooij, M.; Bronikowski, J. M.; Willis, P. A.; Smalley, R. E.; Kouwenhoven, L. P.; van der Zand, H. Nature 2001, 412, 617−620. (20) Gaudreau, L.; Studenikin, S. A.; Sachrajda, A. S.; Zawadzki, P.; Kam, A.; Lapointe, J.; Korkusinski, M.; Hawrylak, P. Phys. Rev. Lett. 2006, 97 (3), 036807−036810. (21) Gaudreau, L.; Kam, A.; Granger, G.; Studenikin, S. A.; Zawadzki, P.; Sachrajda, A. S. Appl. Phys. Lett. 2009, 95 (19), 193101−193104. (22) Grove−Rasmussen, K.; Jorfensen, H. I.; Hayashi, T.; Lindelof, P. E.; Fujisawa, T. Nano Lett. 2009, 8 (4), 1055−1060. (23) Schröer, D.; Greentree, A. D.; Gaudreau, L.; Eberl, K.; Hollenberg, L. C. L.; Kotthaus, J. P.; Ludwig, S. Phys. Rev. B 2007, 76 (23), 075306−075316. (24) Klein, O. Z. Phys. 1929, 53, 157−165. (25) van der Wiel, W. G.; De Franceschi, S.; Elzerman, J. M.; Fujisawa, T.; Tarucha, S.; Kouwenhoven, L. P. Rev. Mod. Phys. 2002, 75, 1−22. (26) Sapmaz, S.; Jarillo−Herrero, P.; Blanter, Ya. M.; Dekker, C.; van der Zant, H. S. J. Phys. Rev. Lett. 2006, 96 (2), 026801−026804.

In conclusion, we have demonstrated ultraclean single, double, and triple CNT QDs obtained with a straightforward fabrication technique. We find that it is not a necessity to place the CNT in the last fabrication step to create ultraclean QDs. Our devices show ultraclean QD behavior with a quality that compares well with the best known devices, even if conventional resist-based lithography is used after placing the CNTs. In one single CNT, we demonstrate single QDs that can be fully emptied and sequentially charged starting from the empty dot, double QDs and triple QDs, as well as ballistic transport through the whole CNT from source to drain contacts. The different regimes are tuned solely by electrostatic gating. The most intriguing regime is the triple QD, where the three QDs correspond to the n-p-n state. This triple QD may be viewed as bipolar QD transistor. All observed features appear in a regular fashion, suggesting a clean disorder free CNT QD system. The fact that ultraclean CNT-QD characteristics can be obtained after a resist-based microfabrication process will greatly increase the versatility of CNT quantum devices for applications, for example, for spin-based quantum bits. One may wonder why the devices do not show any sign of impurity or disorder due to the processing. A possible reason is that the characteristic energies of our QDs are much larger than typical disorder potentials leaving the device immune to remaining inhomogeneities due to resist residues and adsorbates.

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ASSOCIATED CONTENT

S Supporting Information *

Figure S1: details of the excited state spectra of the left QDs. Figure S2: charge stability diagram of a single QD measured in another device and the estimation of the energy level spacing. Figure S3: The excited states in a bias triangle of the double quantum dot. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Julia Samm and Romain Maurand for helpful discussions and technical supports. The presented work was supported by the Swiss National Science Foundation (SNF) through various grants including the NCCR-Nano and NCCR-QSIT, by the ERC project QUEST, the FP7 project SE2ND, and through ESF Eurographene.

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REFERENCES

(1) Bulaev, D. V.; Trauzettel, B.; Loss, D. Phys. Rev. B 2008, 77 (23), 235301−235313. (2) Kuemmeth, F.; Ilani, S.; Ralph, D. C.; McEuen, P. L. Nature 2008, 452, 448−452. (3) Steele, G. A.; Gotz, G.; Kouwenhoven, L. P. Nat. Nanotechnol. 2009, 4, 363−367. (4) Pei, F.; Laird, E. A.; Steele, G. A.; Kouwenhoven, L. P. Nat. Nanotechnol. 2012, 7, 630−634. (5) Cao, J.; Wang, Q.; Wang, D.; Dai, H. Small 2005, 1 (1), 138− 141. 4526

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