Confined Electron and Hole States in Semiconducting Carbon Nanotube sub-10 nm Artificial Quantum Dots

Confined Electron and Hole States in Semiconducting Carbon Nanotube sub-10 nm Artificial Quantum Dots

Abstract

We show that quantum confinement in the valence and conduction bands of semiconducting single-walled carbon nanotubes can be engineered by means of artificial defects. This ability holds potential for designing future nanotube-based quantum devices such as electrically driven room-temperature single-photon sources emitting at telecom-wavelength. Using Ar and N ion-induced defects, intrananotube quantum dots with sub-10 nm lateral sizes are created, giving rise to quantized electronic bound states with level spacings of the order of 100 meV and larger. Using low-temperature scanning tunneling spectroscopy, we resolve the energy and real space properties of the quantized states and compare them with theoretical model calculations. By solving the Schrödinger equation over a one-dimensional piecewise constant potential model, the effects of inhomogeneous defect scattering strength as well as surface variations in the Au(111) substrate on the quantized states structure are remarkably well reproduced. Furthermore, using ab-initio calculations, we demonstrate that defect structures such as vacancies, di-vacancies and chemisorbed nitrogen ad-atoms constitute strong scattering centers able to form quantum dots with clear signatures of discrete bound states as observed experimentally. The ab-initio simulations also allowed to study the scattering strength profile as a function of energy for different defect combinations, supporting the potential of highly stable double vacancies for practical applications at room temperature.

Single-Walled Carbon Nanotubes, Semiconductor, Quantum Dots, Defects, Scanning Tunneling Microscopy/Spectroscopy
\alsoaffiliation

IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain \alsoaffiliationFreiburg Materials Research Center FMF, University of Freiburg, Stefan-Meier-Strasse 21, D-79104 Freiburg, Germany

{tocentry}

Here comes a graphic for the Table of Contents (a thumbnail). A graphic for the Table of Contents must be supplied with each Letter. This graphic, in conjunction with the manuscript title, should give the reader a summary of the research described in the paper. The TOC graphic will also be published in the Abstract of the manuscript. This graphic can be no wider than 8 cm and no taller than 4 cm and should be prepared following the specifications under Artwork. Text should be limited to essential technical labels.

Despite the rise of graphene and other 2D materials, semiconducting single-walled carbon nanotubes (SWNT) are still regarded as strong candidates for the next generation of high-performance ultrascaled transistors [Cao et al.(2015)Cao, Han, Tersoff, Franklin, Zhu, Zhang, Tulevski, Tang, and Haensch, Shulaker et al.(2017)Shulaker, Hills, Park, Howe, Saraswat, Wong, and Mitra] as well as for opto-electronic devices [Avouris et al.(2008)Avouris, Freitag, and Perebeinos, Yamashita et al.(2013)Yamashita, Saito, and Choi] such as chip-scale electronic-photonic platforms [Pyatkov et al.(2016)Pyatkov, Fütterling, Khasminskaya, Flavel, Hennrich, Kappes, Krupke, and Pernice] or low-threshold near-infrared tunable micro-lasers [Grad et al.(2017)Grad, Held, Zakharko, Tropf, Gather, and Zaumseil]. Engineering a quantum dot (QD) along a (suspended) semiconducting SWNT foreshadows promising opportunities in the field of quantum information processing and sensing through recently proposed schemes such as: detection and manipulation of single spins via coupling to vibrational motion [Palyi et al.(2012)Palyi, Struck, Rudner, Flensberg, and Burkard], optomechanical cooling [Wilson-Rae et al.(2012)Wilson-Rae, Galland, Zwerger, and Imamoglu] as well as all optical manipulation of electron spins [Galland and Imamoglu(2008)Galland, and Imamoglu]. Furthermore, the quasi one-dimensional (1D) geometry of SWNTs allows for defining tunable p-n junctions induced by electrostatic doping through local gates [Buchs et al.(2011)Buchs, Barkelid, Bagiante, Steele, and Zwiller, Liu et al.(2011)Liu, C.-C-Wu, and Zhong]. Combining a well-defined QD within such a p-n junction structure could constitute a crucial building-block for the realization of highly desirable electrically driven, on-demand single photon emitters operating at telecom wavelength, based on a turnstile device architecture [Imamoglu and Yamamoto(1994)Imamoglu, and Yamamoto, J.Kim et al.(1999)J.Kim, O.Benson, H.Kan, and Y.Yamamoto]. In practice, QDs in carbon nanotubes have been reported predominantly under two different confinement structures: i) Engineered tunneling barriers at metal-nanotube contacts [Jarillo-Herrero et al.(2004)Jarillo-Herrero, Sapmaz, Dekker, Kouwenhoven, and van der Zant] and/or by gate electrodes, used e.g. to manipulate single electron spins [Laird et al.(2015)Laird, Kuemmeth, Steele, Grove-Rasmussen, Nygård, Flensberg, and Kouwenhoven], ii) Unintentional localization potentials stemming from environmental disorder [Hofmann et al.(2016)Hofmann, Noé, Kneer, Crochet, and Högele], allowing for single-photon emission mediated by localization of band-edge excitons to QD states[Yamashita et al.(2013)Yamashita, Saito, and Choi, Högele et al.(2008)Högele, Galland, Winger, and Imamoglu, Walden-Newman et al.(2012)Walden-Newman, Sarpkaya, and Strauf, Hofmann et al.(2013)Hofmann, Glückert, Noé, Bourjau, Dehmel, and Högele, Khasminskaya et al.(2016)Khasminskaya, Pyatkov, Slowik, Ferrari, Kahl, Kovalyuk, Rath, Vetter, Hennrich, Kappes, Gol’tsman, Korneev, Rockstuhl, Krupke, and Pernice]. Both structures are usually operated at cryogenic temperature due to small energy scales ranging from a few to few tens of millielectronvolts.
Another technique for achieving confinement in SWNTs makes use of artificial defects such as covalently bound oxygen or aryl functionalization groups on the side walls of semiconducting SWNTs, inducing deep exciton trap states allowing for single-photon emission at room temperature [Ma et al.(2015)Ma, Hartmann, Baldwin, Doorn, and Htoon, Zhang et al.(2017)Zhang, Kang, Wang, Tong, Yang, Wang, Qi, Deng, Li, Bai, Ding, and Zhang]. Also, carrier confinement between defect pairs acting as strong scattering centers has been reported for mechanically induced defects [Postma et al.(2001)Postma, Teepen, Yao, Grifoni, and Dekker] as well as for ion-induced defects with reported level spacings up to 200 meV in metallic SWNTs. [Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning]. The latter technique, combined with recent progress in controlling defects structure and localization [Robertson et al.(2012)Robertson, Allen, Wu, He, Olivier, Neethling, Kirkland, and Warner, Yoon et al.(2016)Yoon, Rahnamoun, Swett, Iberi, Cullen, Vlassiouk, adn S. Jesse, Sang, Ovchinnikova, Rondinone, Unocic, and van Duin, Senkovskiy et al.(2017)Senkovskiy, Pfeiffer, Alavi, Bliesener, Zhu, Michel, Fedorov, German, Hertel, Haberer, Petaccia, Fischer, Meerholz, van Loosdrecht, Lindfors, and Grüneis] offers a high potential for engineering a broad set of SWNT-based quantum devices operating at room temperature.
In this letter, we demonstrate confinement of electrons and holes in sub-10 nm QD structures defined by ion-induced defect pairs along the axis of semiconducting SWNTs. Using low temperature scanning tunneling microscopy and spectroscopy (STM/STS), bound states with level spacings of the order of 100 meV and larger are resolved in energy and space. By solving the 1D Schrödinger equation over a piecewise constant potential model, the effects of inhomogeneous defect scattering strength as well as surface variations in the Au(111) substrate on the bound states structure are remarkably well reproduced. By means of ab-initio calculations based on density functional theory and Green’s functions, we find that single (SV) and double vacancies (DV) as well as chemisorbed nitrogen ad-atoms are good candidates in terms of scattering strength to produce QDs with the experimentally observed features. These simulations also allow to study the scattering profile as a function of energy for different defects combination.
The experiments have been performed in a commercial (Omicron) low temperature STM setup operating at  K in ultra high vacuum. Topography images have been recorded in constant current mode with a grounded sample, using mechanically cut Pt/Ir tips. Differential conductance spectra, proportional in first approximation to the local density of states (LDOS) [Tersoff and Hamann(1985)Tersoff, and Hamann] have been recorded using a lock-in amplifier technique. The LDOS spatial evolution along a nanotube axis is obtained by maps built by a series of equidistant spectra. Spatial extent mismatches between topography images and consecutive maps have been systematically corrected [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov], and the metallic nature of the tip has been systematically checked on the gold substrate to prevent any tip artefacts before recording STM or/and STS data sets.
Nanotube samples were made of extremely pure high-pressure CO conversion (HiPCo) SWNTs [Chiang et al.(2001)Chiang, Brinson, Huang, Willis, Bronikowski, Margrave, Smalley, and Hauge] with a diameter distribution centered around 1 nm, FWHM 0.3 nm. The measured intrinsic defect density was below one defect every 200 nm. SWNTs were deposited on atomically flat Au(111) surfaces from a 1,2-dichloroethane suspension, followed by an in-situ annealing process [Buchs et al.(2007)Buchs, Ruffieux, Gröning, and Gröning, Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov].
Local defects in SWNTs have been created in situ by exposure to: (i) Medium energy 200 eV argon ions (Ar) produced by an ion gun [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov, Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning], (ii) Low energy (few eV’s) nitrogen ions (N) produced by a 2.45 GHz ECR plasma source [Buchs et al.(2007)Buchs, Ruffieux, Gröning, and Gröning, Buchs et al.(2007)Buchs, Krasheninnikov, Ruffieux, Gröning, Foster, Nieminen, and Gröning]. In both cases, the exposure parameters have been calibrated to reach an average defect separation along the SWNTs of about 10 nm [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov, Buchs et al.(2007)Buchs, Ruffieux, Gröning, and Gröning].
In Fig. 1 (a)-(b), we show 3D STM images of the same semiconducting SWNT (referred as SWNT I in the following) with Arions-induced defect sites labeled . Panel (d) shows a 3D STM image of a second semiconducting SWNT (referred as SWNT II) with N ions-induced defect sites labeled . In both cases, defect sites typically appear as hillock-like protrusions with an apparent height ranging from 0.5 Å to 4 Å and an apparent lateral extension varying between 5 Å and 30 Å [Buchs et al.(2007)Buchs, Krasheninnikov, Ruffieux, Gröning, Foster, Nieminen, and Gröning, Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov, Buchs(2008)].
The resulting maps recorded along the horizontal dashed line drawn in panel (b) for SWNT I and (d) for SWNT II are displayed in panels (c) and (e) in Fig. 1, respectively. Defect signatures in the LDOS in both cases are characterized by deep in-gap states at the defects positions. This is consistent with the expected defect structures, mainly SVs, DVs and combinations thereof for collisions with Ar ions [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov] and bridgelike N ad-atom for collisions with N ions [Buchs(2008), Lim et al.(2007)Lim, Li, Ji, and Lin]. Note that gap states at energy levels  0.2 eV and  0.05 eV in panels (c) and (e), respectively, are shifted to the right from by about 1 nm and to the right from by about 2 nm. This indicates the presence of intrinsic or ion-induced defects on the lateral or bottom side wall of the SWNTs [Krasheninnikov et al.(2001)Krasheninnikov, Nordlund, Sirviö, Salonen, and Keinonen], not visible in the topographic images. These defects are labelled and , respectively.
Remarkably, the maps in Fig. 1 display several broad discrete states in the conduction bands of SWNT I, II (white dashed boxes in panel (c) and (e), respectively) and in the valence band of SWNT I (white dashed box in panel (c)), characterized by a modulation of the signals in the spatial direction between pairs of consecutive defect sites and . Enlarged plots of these boxed regions are displayed in Fig. 2(a)-(b) and Fig. 3(a) for SWNTs I and II, respectively. In the conduction bands, cross-sectional curves recorded along the black horizontal dashed lines labelled m1–m3 in Fig. 2(a) and m1–m4 in Fig. 3(a) are plotted below the LDOS panels. These clearly reveal one to three and respectively one to four spatially equidistant maxima. The number of maxima increases for increasing and the measured level spacings between consecutive discrete states is of the order of 100 meV and larger for both cases. This indicates that defect sites and , respectively separated by 12.1 nm and 11.2 nm, act as strong scattering centers able to confine carriers in semiconducting SWNTs [Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning, Bercioux et al.(2011)Bercioux, Buchs, Grabert, and Gröning]. Such intrananotube QD structures will be referred as QD I (in SWNT I) and QD II (in SWNT II) in the following. We estimated the level spacings in the conduction band of QD I to 98 meV (m1-m2) and 116 meV (m2-m3). For QD II, we measured about 122 meV (m1-m2), 185 meV (m2-m3) and 210 meV (m3-m4).
In the valence band of SWNT I, discrete states with level spacings in the order of 80-90 meV, with one clear maximum at the level m-1, can also be distinguished between defect sites in Fig. 2(b). The discretization of the states indicates that this QD structure also confines holes. Discrete states starting from m-2 and lower show less well defined structures compared to the conduction band states. In the case of SWNT II, no clear discrete states are observed in the valence band (see supporting information). These observations are most probably the result of an energy dependent scattering strength of the defects, respectively - and -, leading here to a weaker confinement in the valence band. Such energy dependence is well known for metallic SWNTs [Chico et al.(1996)Chico, Benedict, Louie, and Cohen, Neophytou et al.(2007)Neophytou, Ahmed, and Klimeck, Mayrhofer and Bercioux(2011)Mayrhofer, and Bercioux, Bockrath et al.(2001)Bockrath, Liang, Bozovic, Hafner, Lieber, Tinkham, and Park] and is consistent with ab-initio calculations presented further in this work. Note that mixing effects with defect states and substrate-induced effects [Khomyakov et al.(2009)Khomyakov, Giovannetti, Rusu, Brocks, van den Brink, and Kelly] cannot be ruled out.
Another remarkable feature in the LDOS is the strong spatial asymmetry of the lowest energy states m1 and m-1 in QD I and m1 in QD II. In QD I, m1 is shifted to the right side of the dot while m-1 is shifted to the left side. Higher states m2 and m3 show more symmetry in terms of position of the maxima relative to the center of the QD. In QD II, m1 is shifted to the right side of the QD. We attribute the observed lowest energy states asymmetry (for electrons as well as for holes) in part to their strong sensitivity to weak potential modulations within the QD structure (we will corroborate this point in detail when discussing the simulation results). For QD I, this assertion is supported by the observation of a 0.25 nm high Au(111)terrace edge located around the center of the QD, leading to a supported-suspended interface (see white dashed lines in Fig. 1(b) and more topographic details in Fig. S2(a)-(d) in supplementary information). Such configurations have been reported to induce a rigid shift in the SWNT bands [Clair et al.(2011)Clair, Kim, and Kawai], for instance here a down-shift in the right side of QD I corresponding to the “suspended” portion between two terraces. In QD II, we attribute the spatial shift of m1 to a potential modulation induced by a layer of disordered impurities, most probably residua from the 1,2-dichloroethane suspension, lying between the gold substrate and the SWNT (see Fig. 1(d) and Fig. S2(e)-(h) in supplementary information).
Also, the LDOS in QD I and II (Fig. 2(a) and Fig. 3(a), respectively) reveals asymmetric patterns with curved stripes oriented from top left to bottom right for QD I and from bottom left to top right for QD II. These are characteristic signatures for defect pairs with different scattering strengths [Bercioux et al.(2011)Bercioux, Buchs, Grabert, and Gröning, Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning]. For instance here, the left defect in QD I () has a larger scattering strength than the right one (), while the right defect in QD II () has a larger scattering strength than the left one ().
The exact atomic structure of the defects could in principle be determined from a comparison of spectra with simulated first-principle LDOS signatures of expected defect types. In reality, this is hampered by the large number of possible geometries to simulate, including complex multiple defect structures [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov], together with the large unit cells of the semiconducting chiral SWNTs studied here.
To better understand the real space asymmetry of the quantized states in terms of potential modulation and defect scattering strength, we solved the 1D time independent Schrödinger equation over a piecewise constant potential model of QD I and QD II. The scattering centers are approximated by semi-transparent rectangular tunneling barriers leading to a square confinement potential. This is supported by previous results on defect-induced confinement in metallic SWNTs using the same experimental conditions [Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning] and is consistent with ab-initio simulations presented later in this work. The potential modulation within the QD is approximated by a potential step. The resulting potential geometries are illustrated with gray shaded areas in Fig. 2 (c) and (d) and Fig. 3(b). Dispersion relations can be extracted experimentally from the quantized states wavefunctions by measuring the energy and corresponding momenta in the left and right sides of the QDs. The wavevectors are determined using stationary wave-like fitting functions [Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning] displayed with dashed red curves in Figs. 2(a)-(b) and  3(a)). From this procedure, the potential step height and position can be estimated (see supplementary information). The experimental data sets are plotted in the right panels of Figs. 2(a) and 3(a) together with dispersion relations from a third-nearest neighbor tight-binding calculation closely approximating ab-initio results [Reich et al.(2002)Reich, Maultzsch, Thomsen, and Ordejón]. These chirality-dependent tight-binding dispersion relations, calculated within an extended Brillouin zone resulting from the defect-induced breaking of the translation invariance [Bercioux et al.(2011)Bercioux, Buchs, Grabert, and Gröning], are used in the Hamiltonian of our 1D model. Taking into account the measured chiral angle, diameter distribution and measured bandgaps, we find the best match with chiralities for QD I and for QD II (see supplementary information).
Once chiralities together with potential step heights and positions are optimized, one needs to adjust the height and width of the rectangular tunneling barriers in order to reproduce the experimental level spacings and general LDOS patterns. On a qualitative ground, a symmetric double barrier system results in the formation of spatially symmetric discrete bound states. Increasing both barrier heights simultaneously shifts the bound state energy levels up (and at the same time the level spacings). This leads to sharper bound states as the confinement in the QD is made stronger thus increasing the lifetime of the confined electrons. Increasing the barrier thickness (while keeping the QD length, the distance between the barriers edges, constant) does not affect much the level spacings but further sharpens the bound states. Any asymmetry introduced by a change in the width or height of one single barrier leads to broader bound states. The presence of a potential step modifies the LDOS in lifting the levels of the bound states, with a more pronounced effect on the lower states. In QD I and II, the center of each barrier is aligned with the center of the gap states (- for QD I and - in QD II) and the width ratio is kept proportional to the ratio of the spatial extent of the gap states. Thus, by increasing the width of the barriers, we decrease the length of the QD leading to higher level spacings, and vice versa. The experimental level spacings can then be approximated by tuning both widths in the same ratio and the barriers heights individually, knowing that the scattering strength of () is larger than () according to the observed asymmetry in the LDOS described above [T()].
For QD I, we find a good match in the conduction band for the barrier heights eV and eV, widths 3.4 nm, and potential step 60 meV. With these parameters, the spatial profile of the obtained quantized states (see lower subpanels in Fig. 2(a) and (c)) reproduces the experimental modulation features remarkably well. Also, the simulated LDOS displays a pattern with curved stripes oriented from top left to bottom right, as observed experimentally, due to a left barrier with a stronger scattering strength. In the valence band, although modes m-2 and lower do not show a well defined structure in the spatial direction, thinner barriers with dimensions 2.5 nm, eV, leading to a slightly longer QD length (9.6 nm compared to 8.7 nm in the conduction band) can reproduce the measured level spacings very well.
For QD II, we observed that the measured energy levels are overestimated by a factor 1.29, presumably due to a voltage division effect induced by the impurity layer mentioned above (see details in supplementary information). We find a good agreement with the experimental LDOS with the parameters: 0.47 eV, 1.5 nm, 2.6 nm and 47 meV. Note that in Fig. 3(b) the barrier and potential heights are multiplied by to allow a direct comparison with the experimental LDOS. The simulated LDOS shows a pattern with curved stripes oriented from bottom left to top right, as observed experimentally, due to a right barrier exhibiting a stronger scattering strength. Also, the spatial profile of the obtained bound states (see lower subpanels in Fig. 3(a) and (b)) reproduces the experimental features quite well. Note also that one can distinguish an isolated state in the experimental LDOS at an energy level between m1 and m2, about in the middle of the QD. This state that prevented an accurate fit of the state m2 in the right QD part is attributed to a spatial feature visible in the STM topography image in Fig. 2(d) (see also supplementary information, Fig.S2(f)), probably a physisorbed impurity which does not affect the LDOS significantly.
In order to elucidate the physical nature of the electron/hole confining scattering centers, we performed ab-initio simulations based on a combination of density functional theory [Perdew et al.(1996)Perdew, Burke, and Ernzerhof, Blöchl(1994), Kresse and Joubert(1999)Kresse, and Joubert, Kresse and Furthmüller(1996)Kresse, and Furthmüller], maximally localized Wannier orbitals [Mostofi et al.(2008)Mostofi, Yates, Lee, Souza, Vanderbilt, and Marzari] and Green’s functions (see supporting information). Without loss of generality, we have simulated short unit cell semiconducting zigzag SWNTs with different combinations of the most probable defect structures. Results for vacancy defects likely being induced by 200 eV Ar ions, separated by about 11 nm in a SWNT are shown in Fig. 4(a)-(c) with DV-DV, DV-SV and SV-SV pairs, respectively. The LDOS displays midgap states at the defect positions as expected as well as defect states in the valence band [Tolvanen et al.(2009)Tolvanen, Buchs, Ruffieux, Gröning, Gröning, and Krasheninnikov]. Most importantly, clear quantized states with a number of maxima increasing with energy are observed between the defects in the conduction band, emphasizing the ability of SVs and DVs to confine carriers. For the asymmetric configuration DV-SV, one can distinguish faint curved stripe patterns oriented from top left to bottom right, indicating a stronger scattering strength for DVs compared to SVs. This is consistent with observations in transport experiments [Gómez-Navarro et al.(2005)Gómez-Navarro, De Pablo, Gómez-Herrero, Biel, Garcia-Vidal, Rubio, and Flores]. On the other hand, the patterns in the valence band strongly depend on the defect types. Discrete states can be distinguished for the DV-DV case, with m-2 being mixed with defect states. For the DV-SV case, clear curved stripe patterns oriented from bottom left to top right indicate again a stronger scattering strength for DV. Also, broader states are observed, indicating that the scattering strength of DVs and SVs is weaker in the valence band compared to the conduction band.
More insight on the energy dependent scattering strength for each defect pair configurations can be obtained by extracting the wavevector for each resonant state. This data set is plotted in Fig. 4(d) for the conduction and valence bands together with the dispersion relations calculated from the 3rd n.n. TB model and from the ab-initio calculation for the pristine nanotube. A first observation is the excellent agreement between TB and ab-initio results, further validating the method used in Figs. 2(a)-(b) and  3(a). The vertical dashed lines indicate the limiting values corresponding to the closed system (infinite hard walls potential) with nm being the defect-defect distance. In the conduction band, we find that , indicating that the effective lengths of the QD are larger than ( the resonant states wavefunctions are characterized by penetrating evanescent modes inside the defect scattering potential), as expected for an open system. The shortest are obtained for the DV-DV configuration with 12.1 nm (m1), 13.1 nm (m2) and 12.9 nm (m3), which we attribute to wider scattering potential profiles for DVs compared to SVs. In the valence band, we find that , with values between 7.9 nm (DV-DV, m-1) and 9.66 nm (DV-SV, m-2). We attribute this pronounced QD shortening to wider scattering potential profiles of both DVs and SVs in the valence band, probably due to mixing with wide spread defect states in the valence band.
Ab-initio calculations for different defect pairs combinations containing at least one N-adatom, N-DV, N-SV and N-N, are presented in Fig. 4(e)-(h) for a SWNT, along with details on the defects geometries. Remarkably, clear QD states are generated for all three configurations, underlining the potential of N-adatoms to confine carriers in semiconducting SWNTs and thus to generate intrananotube QDs.
Note that the choice of the zigzag SWNT chiralities in the two different ab-initio scenarios is motivated by the different effective masses of both chiralities () which is typical for chirality families and  [Bulusheva et al.(1998)Bulusheva, Okotrub, Romanov, and Tomanek]. Taking advantage of recent reports on SWNT chirality control [Sanchez-Valencia et al.(2014)Sanchez-Valencia, Dienel, Gröning, Shorubalko, Mueller, Jansen, Amsharov, Ruffieux, and Fasel, Zhang et al.(2017)Zhang, Kang, Wang, Tong, Yang, Wang, Qi, Deng, Li, Bai, Ding, and Zhang, Powell et al.(2017)Powell, Kim, and Wang], this property could be used in practice to design QDs with different level spacings for the same QD length. From an application point of view, however, QDs generated by DVs will have far superior stability at room temperature due to their high migration barrier above 5 eV ( 1 eV for single vacancy) [Krasheninnikov et al.(2006)Krasheninnikov, Lehtinen, Foster, and Nieminen]. This value drops down by at least 2 eV for N adatoms depending on their chemisorption configuration [Lim et al.(2007)Lim, Li, Ji, and Lin, Ma et al.(2005)Ma, Foster, Krasheninnikov, and Nieminen].
The above ab-initio simulations do not take into account any substrate effect. In the experimental case, the carriers can decay through the substrate, thus limiting their lifetime. This leads to state broadening, measured between about 60 meV up to 120 meV in QD I and II, while the quantized states widths in ab-initio simulations vary between about 5 meV and 45 meV. This suggests that a better contrast of the experimental quantized states, especially in the valence band, could be achieved by lowering the nanotubes-substrate interaction through the insertion of atomically thin insulating NaCl films [Ruffieux et al.(2016)Ruffieux, Wang, Yang, Sánchez-Sánchez, Liu, Dienel, Talirz, Shinde, Pignedoli, Passerone, Dumslaff, Feng, Mul̈len, and Fasel]. This would allow to gain more insight on the electronic structure of the QDs as well as in the associated scattering physics at the confining defects [Buchs et al.(2009)Buchs, Bercioux, Ruffieux, Gröning, Grabert, and Gröning].
In summary, using low-temperature STM/STS measurements supported by an analytical model and ab-initio simulations, we have demonstrated that intrananotube quantum dots with confined electron and hole states characterized by energy level spacings well above thermal broadening at room temperature can be generated in semiconducting SWNTs by structural defects such as vacancies and di-vacancies, as well as nitrogen adatoms. These results, combined with recent progresses in type and spatial control in the formation of defects [Robertson et al.(2012)Robertson, Allen, Wu, He, Olivier, Neethling, Kirkland, and Warner, Yoon et al.(2016)Yoon, Rahnamoun, Swett, Iberi, Cullen, Vlassiouk, adn S. Jesse, Sang, Ovchinnikova, Rondinone, Unocic, and van Duin, Senkovskiy et al.(2017)Senkovskiy, Pfeiffer, Alavi, Bliesener, Zhu, Michel, Fedorov, German, Hertel, Haberer, Petaccia, Fischer, Meerholz, van Loosdrecht, Lindfors, and Grüneis] as well as chirality control [Zhang et al.(2017)Zhang, Kang, Wang, Tong, Yang, Wang, Qi, Deng, Li, Bai, Ding, and Zhang], hold a high potential for applications in the design of SWNT based quantum devices. These include electrically driven single-photon emitters operating at room temperature and telecom wavelength. In this context, the observation of quantum confinement effects in the emitted light of cut, sub-10 nm, semiconducting SWNTs [Sun et al.(2008)Sun, Zaric, Daranciang, Welsher, Lu, Li, and Dai] shall be seen as an additional motivation for investigating the optical properties of our “QD with leads” building-blocks. These would include studying optical transitions selection rules for different types and configurations of defect pairs [Barros et al.(2006)Barros, Capaz, nad G. G. Samsonidze, Filho, Ismail-Beigi, Spataru, Louie, Dresselhaus, and Dresselhaus] associated with experimental studies such as photoluminescence [Lefebvre et al.(2006)Lefebvre, Austing, Bond, and Finnie] combined to correlation measurements [Hofmann et al.(2013)Hofmann, Glückert, Noé, Bourjau, Dehmel, and Högele] in suspended SWNT devices as well as photocurrent imaging [Buchs et al.(2014)Buchs, Bagiante, and Steele] and spectroscopy [Gabor et al.(2009)Gabor, Zhong, Bosnick, Park, and McEuen].

Supporting information

Supporting information includes atomic resolution STM images for chiral angle determination, detailed 3D topographic images of the QD structures, additional maps as well as detailed descriptions of the analytical 1D piecewise constant potential model and ab-initio simulations.

{acknowledgement}

The authors thank Ethan Minot, Jhon Gonzalez, Andres Ayuela, Omjoti Dutta and Arkady Krasheninnikov for fruitful discussions. The work of DB is supported by Spanish Ministerio de Economía y Competitividad (MINECO) through the project FIS2014-55987-P and by the (LTC) QuantumChemPhys. LM acknowledges support from the BMBF-project WireControl (FKZ16ES0929K) and computing time for the supercomputers JUROPA and JURECA at the Jülich Supercomputer Centre (JSC).

Figures:

Figure 1: (a)-(b) 3D topography images (processed with WSXM [Horcas et al.(2007)Horcas, Fernandez, Gomez-Rodriguez, Colchero, J., and Baro]) of SWNT I with Ar ions-induced defects, with sample-tip bias voltage () 1 V and tunneling current 0.1 nA. (c) Corresponding map recorded along the horizontal dashed lines in (b), with V, nA. Spatial resolution 0.3 nm. (d) 3D topography image of SWNT II with N ions-induced defects, with V, pA. (e) Corresponding map recorded along the horizontal dashed lines in (d), with V, nA. Spatial resolution 0.2 nm.
Figure 2: (a)-(b) QD I detailed maps in conduction and valence bands. Lower subpanels contain QD states linecut profiles and stationary wave-like fits in left and right QD parts. Right subpanels contain experimental energy dispersion relation data sets and tight-binding calculations. (c)-(d) Resulting LDOS calculated from a 1D piecewise constant potential model featuring potential barriers and a potential step (gray area), with position of the potential step: 5.09 nm from the right barrier’s center, potential step heigth: meV, barrier heights: eV, eV, barrier widths: nm. Valence band: eV, nm, eV. stands for bandgap energy.
Figure 3: (a) QD II detailed map. Lower subpanels contain QD states linecut profiles and stationary wave-like fits in the left and right QD parts. Right subpanel contains experimental energy dispersion relation data sets and tight-binding calculations. (b) Resulting LDOS calculated from a 1D piecewise constant potential model featuring potential barriers and a potential step (gray area) with position of the potential step: 4.7 nm from the right barrier’s center, potential step heigth: meV, barrier heights: eV, eV, barrier widths: nm, nm.
Figure 4: (a)-(c) LDOS ab initio simulations of a semiconducting SWNT with combinations of vacancies defects separated by 11.1 nm. Subpanels display QD state linecut profiles. (d) Tight binding (black curve) and ab-initio dispersion relations (green circles) for a pristine SWNT with data sets extracted from (a)-(c). (e)-(g) LDOS ab initio simulations of a semiconducting SWNT with combinations of N-adatoms and vacancies defects separated by 10.7 nm. (h) Tight binding (black curve) and ab-initio dispersion relations (green circles) for a pristine SWNT with data sets extracted from (e)-(g).

References

  1. Cao, Q.; Han, S.-J.; Tersoff, J.; Franklin, A. D.; Zhu, Y.; Zhang, Z.; Tulevski, G. S.; Tang, J.; Haensch, W. Science 2015, 350, 68 – 72.
  2. Shulaker, M. M.; Hills, G.; Park, R. S.; Howe, R. T.; Saraswat, K.; Wong, H.-S. P.; Mitra, S. Nature 2017, 547, 74.
  3. Avouris, P.; Freitag, M.; Perebeinos, V. Nature Photon. 2008, 2, 341 – 350.
  4. Yamashita, S.; Saito, Y.; Choi, J. H. Carbon nanotubes and graphene for photonic applications; Woodhead Publishing: Philadelphia, USA, 2013.
  5. Pyatkov, F.; Fütterling, V.; Khasminskaya, S.; Flavel, B. S.; Hennrich, F.; Kappes, M. M.; Krupke, R.; Pernice, W. H. Nature Photon. 2016, 10, 420.
  6. Grad, A.; Held, M.; Zakharko, Y.; Tropf, L.; Gather, M. C.; Zaumseil, J. Nature Mater. 2017, advance online publication.
  7. Palyi, A.; Struck, P.; Rudner, M.; Flensberg, K.; Burkard, G. Phys. Rev. Lett. 2012, 108, 206811.
  8. Wilson-Rae, I.; Galland, C.; Zwerger, W.; Imamoglu, A. New J. Phys. 2012, 14, 115003.
  9. Galland, C.; Imamoglu, A. Phys. Rev. Lett. 2008, 101, 157404.
  10. Buchs, G.; Barkelid, M.; Bagiante, S.; Steele, G. A.; Zwiller, V. J. Appl. Phys. 2011, 110, 074308.
  11. Liu, C.-H.; C.-C-Wu,; Zhong, Z. Nano Lett. 2011, 11, 1782.
  12. Imamoglu, A.; Yamamoto, Y. Phys. Rev. Lett. 1994, 72, 210–213.
  13. J.Kim,; O.Benson,; H.Kan,; Y.Yamamoto, Nature 1999, 72, 500–503.
  14. Jarillo-Herrero, P.; Sapmaz, S.; Dekker, C.; Kouwenhoven, L. P.; van der Zant, H. S. J. Nature 2004, 429, 389.
  15. Laird, E. A.; Kuemmeth, F.; Steele, G. A.; Grove-Rasmussen, K.; Nygård, J.; Flensberg, K.; Kouwenhoven, L. P. Rev. Mod. Phys. 2015, 87, 703.
  16. Hofmann, M. S.; Noé, J.; Kneer, A.; Crochet, J. J.; Högele, A. Nano Lett. 2016, 16, 2958 –2962.
  17. Högele, A.; Galland, C.; Winger, M.; Imamoglu, A. Phys. Rev. Lett. 2008, 100, 217401.
  18. Walden-Newman, W.; Sarpkaya, I.; Strauf, S. Nano Lett. 2012, 12, 1934 – 1941.
  19. Hofmann, M. S.; Glückert, J. T.; Noé, J.; Bourjau, C.; Dehmel, R.; Högele, A. Nature Nanotech. 2013, 8, 502 – 505.
  20. Khasminskaya, S.; Pyatkov, F.; Slowik, K.; Ferrari, S.; Kahl, O.; Kovalyuk, V.; Rath, P.; Vetter, A.; Hennrich, F.; Kappes, M. M.; Gol’tsman, G.; Korneev, A.; Rockstuhl, C.; Krupke, R.; Pernice, W. H. P. Nature Photon. 2016, 10, 727.
  21. Ma, X.; Hartmann, N. F.; Baldwin, J. K. S.; Doorn, S. K.; Htoon, H. Nature Nanotech. 2015, 10, 671 – 676.
  22. Zhang, S.; Kang, L.; Wang, X.; Tong, L.; Yang, L.; Wang, Z.; Qi, K.; Deng, S.; Li, Q.; Bai, X.; Ding, F.; Zhang, J. Nature Photon. 2017, adv. online.
  23. Postma, H. W. C.; Teepen, T.; Yao, Z.; Grifoni, M.; Dekker, C. Science 2001, 293, 76.
  24. Buchs, G.; Bercioux, D.; Ruffieux, P.; Gröning, P.; Grabert, H.; Gröning, O. Phys. Rev. Lett 2009, 102, 245505.
  25. Robertson, A. W.; Allen, C. S.; Wu, Y. A.; He, K.; Olivier, J.; Neethling, J.; Kirkland, A. I.; Warner, J. H. Nature Comm. 2012, 3:1144.
  26. Yoon, K.; Rahnamoun, A.; Swett, J. L.; Iberi, V.; Cullen, D. A.; Vlassiouk, I. V.; adn S. Jesse, A. B.; Sang, X.; Ovchinnikova, O. S.; Rondinone, A. J.; Unocic, R. R.; van Duin, A. C. T. ACS Nano 2016, 10, 8376–8384.
  27. Senkovskiy, B. V. et al. Nano Lett. 2017, 17, 4029.
  28. Tersoff, J.; Hamann, D. R. Phys. Rev. B 1985, 31, 805–813.
  29. Tolvanen, A.; Buchs, G.; Ruffieux, P.; Gröning, P.; Gröning, O.; Krasheninnikov, A. V. Phys. Rev. B 2009, 79, 125430.
  30. Chiang, I. W.; Brinson, B. E.; Huang, A. Y.; Willis, P. A.; Bronikowski, M. J.; Margrave, J. L.; Smalley, R. E.; Hauge, R. H. J. Phys. Chem. B 2001, 105, 8297–8301.
  31. Buchs, G.; Ruffieux, P.; Gröning, P.; Gröning, O. Appl. Phys. Lett. 2007, 90, 013104.
  32. Buchs, G.; Krasheninnikov, A. V.; Ruffieux, P.; Gröning, P.; Foster, A. S.; Nieminen, R. M.; Gröning, O. New J. Phys. 2007, 9, 275.
  33. Buchs, G. Local modification and characterization of the electronic structure of carbon nanotubes. Ph.D. thesis, University of Basel, 2008.
  34. Lim, S. H.; Li, R.; Ji, W.; Lin, J. Phys. Rev. B 2007, 76, 195406.
  35. Krasheninnikov, A. V.; Nordlund, K.; Sirviö, M.; Salonen, E.; Keinonen, J. Phys. Rev. B 2001, 63, 245405.
  36. Bercioux, D.; Buchs, G.; Grabert, H.; Gröning, O. Phys. Rev. B 2011, 83, 165439.
  37. Chico, L.; Benedict, L. X.; Louie, S. G.; Cohen, M. L. Phys. Rev. B 1996, 54, 2600–2606.
  38. Neophytou, N.; Ahmed, S.; Klimeck, G. Appl. Phys. Lett. 2007, 90, 182119.
  39. Mayrhofer, L.; Bercioux, D. Phys. Rev. B 2011, 84, 115126.
  40. Bockrath, M.; Liang, W.; Bozovic, D.; Hafner, J. H.; Lieber, C. M.; Tinkham, M.; Park, H. Science 2001, 291, 283–285.
  41. Khomyakov, P. A.; Giovannetti, G.; Rusu, P. C.; Brocks, G.; van den Brink, J.; Kelly, P. J. Phys. Rev. B 2009, 79, 195425.
  42. Clair, S.; Kim, Y.; Kawai, M. Phys. Rev. B 2011, 83, 245422.
  43. Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejón, P. Phys. Rev. B 2002, 66, 035412.
  44. Note that for a sufficiently small area under the barrier, it can be shown that the transmission probability is a function of the area such that two rectangular barriers with different geometries but with the same area lead to the same, or very close transmission probability . Indeed, the textbook expression for the transmission probability through a rectangular tunneling barrier is given by , where and are respectively the barrier height and width. For the argument in the sufficently small such that , it can be shown that , with . In our case, this condition is not satisfied and thus the barrier geometries are tuned iteratively on an empirical fashion.
  45. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.
  46. Blöchl, P. E. Phys. Rev. B 1994, 50, 17953–17979.
  47. Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775.
  48. Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169–11186.
  49. Mostofi, A. A.; Yates, J. R.; Lee, Y.-S.; Souza, I.; Vanderbilt, D.; Marzari, N. Comput. Phys. Commun. 2008, 178, 685.
  50. Gómez-Navarro, G.; De Pablo, P. J.; Gómez-Herrero, J.; Biel, B.; Garcia-Vidal, F. J.; Rubio, A.; Flores, F. Nature Mater. 2005, 4, 534–539.
  51. Bulusheva, L. G.; Okotrub, A. V.; Romanov, D. A.; Tomanek, D. J. Phys. Chem. A 1998, 102, 975.
  52. Sanchez-Valencia, J. R.; Dienel, T.; Gröning, O.; Shorubalko, I.; Mueller, A.; Jansen, M.; Amsharov, K.; Ruffieux, P.; Fasel, R. Nature 2014, 512, 61.
  53. Zhang, S.; Kang, L.; Wang, X.; Tong, L.; Yang, L.; Wang, Z.; Qi, K.; Deng, S.; Li, Q.; Bai, X.; Ding, F.; Zhang, J. Nature 2017, 543, 234.
  54. Powell, L. R.; Kim, M.; Wang, Y. J. Am. Chem. Soc. 2017, X, XX.
  55. Krasheninnikov, A. V.; Lehtinen, P. O.; Foster, A. S.; Nieminen, R. M. Chem. Phys. Lett. 2006, 418, 132–136.
  56. Ma, Y.; Foster, A. S.; Krasheninnikov, A. V.; Nieminen, R. M. Phys. Rev. B 2005, 72, 205416.
  57. Ruffieux, P.; Wang, S.; Yang, B.; Sánchez-Sánchez, C.; Liu, J.; Dienel, T.; Talirz, L.; Shinde, P.; Pignedoli, C. A.; Passerone, D.; Dumslaff, T.; Feng, X.; Mul̈len, K.; Fasel, R. Nature 2016, 531, 489.
  58. Sun, X.; Zaric, S.; Daranciang, D.; Welsher, K.; Lu, Y.; Li, X.; Dai, H. J. Am. Chem. Soc. 2008, 130, 6551.
  59. Barros, E. B.; Capaz, R. B.; nad G. G. Samsonidze, A. J.; Filho, A. G. S.; Ismail-Beigi, S.; Spataru, C. D.; Louie, S. G.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rev. B 2006, 73, 241406(R).
  60. Lefebvre, J.; Austing, D. G.; Bond, J.; Finnie, P. Nanolett. 2006, 6, 1603.
  61. Buchs, G.; Bagiante, S.; Steele, G. A. Nature Commun. 2014, 5:4987.
  62. Gabor, N. M.; Zhong, Z.; Bosnick, K.; Park, J.; McEuen, P. L. Science 2009, 325, 1367.
  63. Horcas, I.; Fernandez, R.; Gomez-Rodriguez, J. M.; Colchero, J.; J., G.-H.; Baro, A. M. Rev. Sci. Instrum. 2007, 78, 013705.
100229
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
Edit
-  
Unpublish
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel
Comments 0
Request comment
""
The feedback must be of minumum 40 characters
Add comment
Cancel
Loading ...

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description