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Quantum dots in InAs nanowires induced by surface potential fluctuations
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 135203 (http://iopscience.iop.org/0957-4484/25/13/135203) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.64.11.153 This content was downloaded on 18/06/2017 at 17:58 Please note that terms and conditions apply.
You may also be interested in: Electronic properties of quantum dot systems realized in semiconductor nanowires J Salfi, S Roddaro, D Ercolani et al. Excited states and quantum confinement in room temperature few nanometre scale silicon single electron transistors Zahid A K Durrani, Mervyn E Jones, Chen Wang et al. Tunable few-electron quantum dots in InAs nanowires I Shorubalko, A Pfund, R Leturcq et al. Gate-induced transition between metal-type and thermally activated transport in self-catalyzed MBE-grown InAs nanowires C Blömers, T Rieger, T Grap et al. Single-molecule transport in three-terminal devices E A Osorio, T Bjørnholm, J-M Lehn et al. Control of charging energy in chemically assembled nanoparticle single-electron transistors Shinya Kano, Daisuke Tanaka, Masanori Sakamoto et al. Single donor electronics and quantum functionalities with advanced CMOS technology Xavier Jehl, Yann-Michel Niquet and Marc Sanquer Short-channel effect and single-electron transport in individual indium oxide nanowires Minkyung Jung, Hyoyoung Lee, Sunkyung Moon et al. Tunable single hole regime of a silicon field effect transistor in standard CMOS technology Marco Turchetti, Harald Homulle, Fabio Sebastiano et al.
Nanotechnology Nanotechnology 25 (2014) 135203 (5pp)
doi:10.1088/0957-4484/25/13/135203
Quantum dots in InAs nanowires induced by surface potential fluctuations Karl Weis, Stephan Wirths, Andreas Winden, Kamil Sladek, Hilde Hardtdegen, Hans Lüth, Detlev Grützmacher and Thomas Schäpers Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany Jülich Aachen Research Alliance, Fundamentals of Future Information Technology (JARA-FIT), Germany E-mail: [email protected] and [email protected] Received 8 December 2013, revised 14 January 2014 Accepted for publication 29 January 2014 Published 4 March 2014
Abstract
Back-gated InAs nanowire field-effect transistors are studied focusing on the formation of intrinsic quantum dots, i.e. dots not intentionally defined by electrodes. Such dots have been studied before, but the suggested explanations for their origin leave some open questions, which are addressed here. Stability diagrams of samples with different doping levels are recorded at electron temperatures below 200 mK, allowing us to estimate the number and size of the dots as well as the type of connection, i.e. in series or in parallel. We discuss several potential physical origins of the dots and conclude that they are most probably induced by potential fluctuations at the nanowire surface. Additionally, we show that via gate voltage and doping, the samples can be tuned to different regimes of Coulomb blockade. Keywords: indium arsenide, quantum dot, nanowire, low-temperature transport, doping S Online supplementary data available from stacks.iop.org/Nano/25/135203/mmedia (Some figures may appear in colour only in the online journal)
1. Introduction
were shown to depend sensitively on surface potential fluctuations. Most importantly, several samples exhibited nonlinear current–voltage curves at zero gate voltage for temperatures below 50 K. A question of particular interest is how the transport properties are affected by doping. Recently, this issue was addressed by Wirths et al [5] for NWs grown by selectivearea metalorganic vapour phase epitaxy (SA-MOVPE). It was shown that the transport properties are tunable by Si doping. Furthermore, for sufficiently low doping levels and temperatures, the current–voltage curves recorded at zero gate voltage showed a nonlinear behaviour similar to the one [8] observed by Bl¨omers et al. This was attributed to the onset of single-electron tunnelling. In order to corroborate this assumption, stability diagrams, i.e. the dependence of the differential conductance on the gate voltage VG and the source–drain bias VSD , of such NWs with two different doping levels are discussed in this paper. The
Single-electron transistors [1, 2] based on quantum dots (QDs) are especially interesting for future logic device applications due to their power efficiency. Among the numerous approaches for fabricating QDs, semiconductor nanowires (NWs) stand out as they are a natural step on the way to zero-dimensional systems and as their preparation [3] is well established. Using InAs is favourable as first, it usually features a surface accumulation layer [4] and thus enables straightforward preparation of ohmic contacts. At the same time, the carrier concentration is highly tunable by electrostatic gating [5]. Moreover, the large electron mobility allows high frequency operation [6]. For fabricating QDs in InAs NWs, a thorough knowledge of their transport properties is required. Recently, selfcatalysed, nominally undoped InAs NWs grown by molecular beam epitaxy were studied by Bl¨omers et al [7, 8]. Back-gated field-effect transistors were fabricated and characterized from room temperature down to 4 K. The transport properties 0957-4484/14/135203+05$33.00
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c 2014 IOP Publishing Ltd
Printed in the UK
Nanotechnology 25 (2014) 135203
K Weis et al
presence of Coulomb diamonds is an unambiguous proof for intrinsic QDs, i.e. dots not intentionally defined by electrodes. Such dots have to be taken into account when attempting to fabricate single-electron transistors. Intrinsic QDs in InAs NWs have been studied before by other groups [9–11], but the suggested explanations for their origin leave some open questions. For example, Kretinin et al [10] examine a back-gated NW (contact separation L = 470 nm, diameter D = 50 nm) and estimate the charging energy E C = e2 /C = 3 meV, where C is the total QD capacitance. They claim that the barriers are formed by the contacts. However, this is not consistent with a simple model proposed by Shorubalko et al [12] treating the QD as a conductive sphere (radius r ) embedded in InAs (εr = 15) and yielding a much smaller QD size r = C/(4π ε0 εr ) = 32 nm. Schroer and Petta [11] investigate back-gated NWs (L = 1.5 µm, D = 65 nm) with an axial defect density larger than 1 nm−1 and attribute the formation of QDs to these defects. They assume the QD sizes to be at least 50 nm, which is however much larger than the mean defect separation. It remains unclear what kind and number of defects are required to form a barrier. In this paper, we show that surface potential fluctuations, originating e.g. from adsorbates, are the most probable reason for the formation of intrinsic QDs. We investigate the number, size and type of connection (i.e. in series or in parallel) of the QDs. Additionally, in the works cited above, the question how doping affects the transport properties of the QDs has not been addressed. Here, we show that the QDs can be tuned to different regimes of Coulomb blockade via doping and also via the gate voltage.
Figure 1. (a) Typical transmission electron micrograph of a NW.
The growth direction is marked by an arrow. A wurtzite and a zinc blende segment are highlighted. At the NW edge, the native oxide layer can be seen. (b) Scanning electron micrograph of sample L1. The contacts marked S and D are used as source and drain, respectively.
the preparation method used in this study (including exposure to an electron beam and to atmosphere), the NWs are expected to feature a surface accumulation layer at least for the low doping level [5, 7]. In this case, electronic transport mainly takes place near the NW surface. 3. Results and discussion 3.1. Lower doping level
In figure 2, the stability diagram of a nearly undoped wire (sample L1, L = 1.5 µm, D = 100 nm) is shown. Its most important feature is a strong overlap of the Coulomb diamonds. Only few Coulomb resonances are present near zero bias, which is indicative [13] of QDs connected in series (figure 3). This is supported by the fact that facing borders of some ‘diamonds’ (e.g. the one at VG = −0.1 V) are not parallel [14]1 . The lines of enhanced conductance at some diamond edges, e.g. at (VG = −3.1 V, VSD = −3 mV), are a signature of excited states contributing to transport [15]. From the vertical distance between the two lines, we determine the excitation energy, and thus the single-particle level spacing, to be about 1 meV. Using this result, we gain a first rough estimate of the QD size by modelling it as a three-dimensional box [16]: With 1E box = 3π 2 h¯ 2 /(2m ∗InAs L 2box ), where m ∗InAs = 0.023 m e is the effective electron mass [6] and 1E box = 1 meV the lowest energy level spacing, we get a box length L box ≈ 220 nm. If facing borders of a diamond have approximately the same slope, this indicates that its origin is only one dot (and not multiple ones connected in series). We call such a diamond an undisturbed one. Its width δVG and height2 δVSD yield the gate lever arm αG = δVSD /(2δVG ). A gate voltage shift 1VG changes the chemical potential of the QD by 1µ = −eαG 1VG [15]. The two smallest3 undisturbed diamonds
2. Experimental details
Our NWs were grown by SA-MOVPE using trimethylindium (TMIn) and arsine (AsH3 ) as well as disilane (Si2 H6 , n-type dopant). Since Si is preferentially incorporated at In lattice sites, the doping level is quantified by a doping factor which is proportional to the partial pressure ratio p(Si2 H6 )/ p(TMIn) and which is set to 1 for p(Si2 H6 )/ p(TMIn) = 7.5 × 10−5 . In this study, wires with doping factors of 1 and 100 are examined. Their typical length and diameter are 4 µm and 100 nm, respectively. Details on NW growth can be found in [5]. The NWs feature a polytypic structure with wurtzite (WZ) and zinc blende (ZB) segments which are just a few nanometres long [5]. Overall, the WZ and ZB fraction is on the same order of magnitude and depends only weakly on the doping level. A typical transmission electron micrograph is shown in figure 1. For transport measurements, the NWs were transferred onto a degenerately n-doped Si(100) wafer covered by a 100-nm-thick SiO2 layer and thus acting as a back gate. The NWs were contacted individually by a set of Ti/Au electrodes using electron beam lithography. Prior to metal deposition, the wire surface was cleaned using Ar+ sputtering. The transport properties of a low-doped sample (L1) and another one with a higher doping level (H1) are investigated in a dilution refrigerator at a bath temperature of 70 mK. All measurements are performed in a two-terminal configuration. A scanning electron micrograph of sample L1 is shown in figure 1. Due to
1
See supplementary material (available at stacks.iop.org/Nano/25/ 135203/mmedia) for a stability diagram of another nearly undoped sample. 2 Disturbed diamonds feature a greater height than undisturbed ones because the voltage drops on multiple dots add up. 3 The physical reason for the variation of δV SD is the fact that the single-particle energy of a QD varies with the number of electrons on it. The height variation of the disturbed diamonds can be explained in the same way. 2
Nanotechnology 25 (2014) 135203
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Figure 2. Sample L1 (lower doping level), stability diagram, i.e. differential conductance map. It indicates the presence of at least two QDs A and B (see figure 3). Some ‘undisturbed’ diamonds originating from these dots are marked; one of them is magnified in the right inset. Lines of enhanced conductance at a diamond edge are highlighted (magnification in the left inset).
characteristics of the NW field-effect transistor, we get a carrier concentration n ∼ 2 × 1017 cm−3 [5] and thus [18] √ rTF = ( aB /2) × [π/(3 n)]1/6 ≈ 10 nm. For a nominally undoped wire (doping factor 0), the known background doping (ND ∼ 1015 cm−3 ) yields a mean impurity distance ∼100 nm. As the transport properties of NWs with doping factors 0 and 1 do not differ significantly [5], this should also hold for the low-doped NWs examined here. In contrast, if there are surface defects with a sufficiently low distance, the effective screening length can become large enough for the formation of barriers. Such defects may originate from trapped charges at the dielectric/NW interface, adsorbates or locally extended surface reconstruction [19] variations. The existence of such defects is consistent with the fact that we observe a significant change of the stability diagram, especially of αG , with thermal cycling (not shown here). To sum up, the kind of defects which can form barriers are most probably potential fluctuations at the NW surface as the electronic transport mainly takes place just there. By tuning VG to more positive values, the Fermi energy E F is shifted upwards and thus the effective barrier heights are lowered. Consequently, it should be possible to suppress Coulomb blockade by applying a sufficiently high VG . In order to check this, we do another VG sweep (not shown here). Due to a charge rearrangement, which could be induced by an uncontrolled change [20] in the occupation of surface states, Coulomb blockade now disappears already at VG = 0. Starting there, another stability diagram is recorded (figure 4), in which three different transport regimes can be identified. For VG < −0.28 V, no Coulomb resonances are found near zero bias (classical Coulomb blockade, multiple QDs connected in series). For VG > −0.28 V, only one dot survives as four undisturbed diamonds can be seen. Obviously, some barriers have vanished due to the higher position of E F . Coulomb resonances4 appear near zero bias and δVSD decreases with increasing VG , indicating a higher value of the dot–lead coupling 0. This can be explained [23] by mesoscopic Coulomb blockade (MCB), for which phase coherence is a necessary condition. The latter is indeed fulfilled, as shown by measurements [24] of universal conductance fluctuations which yield a phase coherence length lϕ ≥ 300 nm. For VG > −0.03 V, no
Figure 3. Simple model of sample L1 as a series connection of QDs (A, B) coupled to source, drain and gate by tunnel barriers and capacitors. The size of the circles is a measure for the QD size. Interactions between the QDs and additional QDs connected in series with A and B are neglected.
are located at VG = −3.2 V and VG = −0.2 V. They yield αG values of 0.02 and 0.07, respectively, and thus belong to different dots, the second one (dot B) being coupled to the gate more strongly than the first one (dot A). The diamond heights give an upper estimate for E C of 1 meV and 2 meV for dots A and B, respectively. Using the model presented by Shorubalko et al ([12], see above), we get a minimal QD size r of 100 nm and 50 nm for dots A and B, respectively. These results differ from the box model considered above by a factor not exceeding 2.2. One expects αG to increase [14] with increasing r , contrary to our findings. This discrepancy might be related to potential fluctuations at the NW surface, which will be discussed below. As all QD sizes estimated above are at least one order of magnitude smaller than the distance of source and drain (L = 1.5 µm), the QDs only fill a small fraction of the NW volume. The remaining parts of the NW serve as leads to the dots. Obviously, the source and drain contacts cannot be an exclusive reason for QD formation. More probably, the barriers are formed by defects. At first sight, several kinds of defects are conceivable to this end, i.e. polytypism, ionized impurities or surface potential fluctuations. However, at a closer look, the polytypism of the NWs is an unlikely explanation at least for the largest QDs as they are ten times longer than the longest WZ or ZB segments. Furthermore, potential barriers are also observed [8] in pure ZB NWs. Ionized impurities cannot induce barriers as the Thomas–Fermi screening length rTF of a single impurity is smaller than both the Bohr radius of InAs (aB = 35 nm [17]) and the wire diameter (D = 100 nm). In addition, adjacent impurities do not ‘see’ each other. This can be understood as follows: from the transfer
4
A fit to the Coulomb peak at VG = −0.27 V (according to [21, 22], assuming the sample is in the regime of quantum Coulomb blockade) yields an electron temperature below 200 mK. 3
Nanotechnology 25 (2014) 135203
K Weis et al
Figure 4. Sample L1, another stability diagram. Three different transport regimes can be identified: classical and mesoscopic Coulomb blockade (CCB, MCB) as well as the Fabry–Perot regime (FP). The arrows highlight some Coulomb resonances near zero bias. Two VSD sweeps marked I and II are shown in the left panel. The solid lines are guides to the eyes.
Figure 5. Sample H1 (higher doping level), stability diagram. The
sample is in the mesoscopic Coulomb blockade regime.
In the future, the interplay of sample structure and electronic properties could be studied in a more detailed way using a setup which allows performing transmission electron microscopy and transport measurements on one and the same sample [25]. Additionally, such a design eliminates the interaction between the substrate and the NW [10]. Further information on the size and position of the intrinsic QDs could be gained by direct imaging methods, e.g. by using a scanning probe microscope tip as a movable gate [26, 27]. An obvious question is what happens if controlled QDs are defined in the NWs using top gates (see e.g. [12]), i.e. how intrinsic and controlled QDs interact with each other. Finally, for the fabrication of reliable devices, the NW surface states have to be passivated, e.g. using 1-octadecanethiol [28] or an InP cap [29] layer.
Coulomb diamonds exist any more, but a pattern [10] appears which is similar to Fabry–Perot oscillations. The conductance peak near (VG = 0, VSD = 0) is consistent with this effect. 3.2. Higher doping level
So far, we have shown that 0 is tunable by VG . We now investigate if this can also be achieved by doping. In figure 5, a stability diagram of a wire with a higher doping level (sample H1, L = 700 nm, D = 70 nm) is shown. As the stability diagram has a simple structure with non-overlapping diamonds, probably a single QD is present in the entire VG region. From the smallest diamond (at VG = −1.9 V), one gets αG = 0.002, E C ≤ 0.6 meV and r ≈ 200 nm. The sample is in the MCB regime, which is more pronounced than in figure 4, as the diamonds are considerably distorted [23] and clearly separated by conductive regions. Compared to figure 4, the conductance inside the diamonds is two orders of magnitude larger, indicating a higher value of 0. The larger conductance leads to a stronger screening of the gate field, which is consistent with the observation of a lower αG . All these effects can be explained by the higher doping level, again leading to a higher value of E F and thus lower and fewer barriers [5]. Summing up, intrinsic quantum dots become less pronounced if the doping level is increased. In other words, the effect of defects on electronic transport decreases. Similar to sample L1, it should be possible to tune sample H1 to the CCB or FP regime by tuning VG to sufficiently large negative or positive values, respectively. Unfortunately, we are not able to check this due to the low value of αG and the limited dielectric strength of the back-gate oxide.
Acknowledgments
We thank H Kertz and K Wirtz for measurement and growth support, respectively, as well as St Trellenkamp for electron beam lithography. In addition, we are indebted to N Demarina, R Frielinghaus, F Haas, S Heedt and P Zellekens for fruitful discussions. References [1] Fulton T A and Dolan G J 1987 Observation of single-electron charging effects in small tunnel junctions Phys. Rev. Lett. 59 109 [2] Barreiro A, van der Zant H S J and Vandersypen L M K 2012 Quantum dots at room temperature carved out from few-layer graphene Nano Lett. 12 6096 [3] Thelander C et al 2006 Nanowire-based one-dimensional electronics Mater. Today 9 28 [4] Weber J R, Janotti A and Van de Walle C G 2010 Intrinsic and extrinsic causes of electron accumulation layers on InAs surfaces Appl. Phys. Lett. 97 192106 [5] Wirths S et al 2011 Effect of Si-doping on InAs nanowire transport and morphology J. Appl. Phys. 110 053709 [6] Ioffe Physico-Technical Institute Characteristics and Properties of New Semiconductor Materials (http://www.io ffe.ru/SVA/)
4. Conclusions
Our NW devices feature QD networks of varying complexity, among them a single dot and multiple ones connected in series. However, in all cases, typical dot sizes on the order of 10–100 nm can be extracted. Most probably, the barriers are formed by potential fluctuations at the NW surface. Our measurements show that the NWs can be tuned to different regimes of Coulomb blockade via gate voltage and doping. 4
Nanotechnology 25 (2014) 135203
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[7] Bl¨omers C, Grap T, Lepsa M I, Moers J, Trellenkamp St, Gr¨utzmacher D, L¨uth H and Sch¨apers Th 2012 Hall effect measurements on InAs nanowires Appl. Phys. Lett. 101 152106 [8] Bl¨omers C, Rieger T, Grap T, Raux M, Lepsa M I, L¨uth H, Gr¨utzmacher D and Sch¨apers Th 2013 Gate-induced transition between metal-type and thermally activated transport in self-catalyzed MBE-grown InAs nanowires Nanotechnology 24 325201 [9] Jespersen T S, Aagesen M, Sørensen C, Lindelof P E and Nyg˚ard J 2006 Kondo physics in tunable semiconductor nanowire quantum dots Phys. Rev. B 74 233304 [10] Kretinin A V, Popovitz-Biro R, Mahalu D and Shtrikman H 2010 Multimode Fabry–P´erot conductance oscillations in suspended stacking-faults-free InAs nanowires Nano Lett. 10 3439 [11] Schroer M D and Petta J R 2010 Correlating the nanostructure and electronic properties of InAs nanowires Nano Lett. 10 1618 [12] Shorubalko I, Pfund A, Leturcq R, Borgstr¨om M T, Gramm F, M¨uller E, Gini E and Ensslin K 2007 Tunable few-electron quantum dots in InAs nanowires Nanotechnology 18 044014 [13] De Franceschi S, van Dam J A, Bakkers E P A M, Feiner L F, Gurevich L and Kouwenhoven L P 2003 Single-electron tunneling in InP nanowires Appl. Phys. Lett. 83 344 [14] Fuhrer A, Fr¨oberg L E, Pedersen J N, Larsson M W, Wacker A, Pistol M-E and Samuelson L 2007 Few electron double quantum dots in InAs/InP nanowire heterostructures Nano Lett. 7 243 [15] Ihn T 2010 Semiconductor Nanostructures (New York: Oxford University Press) [16] L¨uth H 2013 Quantum Physics in the Nanoworld (Berlin: Springer) [17] Scheffler M, Nadj-Perge S, Kouwenhoven L P, Borgstr¨om M T and Bakkers E P A M 2009 Diameterdependent conductance of InAs nanowires J. Appl. Phys. 106 124303 [18] Ibach H and L¨uth H 2009 Solid-State Physics 4th edn (Berlin: Springer)
[19] L¨uth H 2010 Solid Surfaces, Interfaces and Thin Films 5th edn (Berlin: Springer) [20] Hasegawa H and Akazawa M 2008 Surface passivation technology for III–V semiconductor nanoelectronics Appl. Surf. Sci. 255 628 [21] Beenakker C W J 1991 Theory of Coulomb-blockade oscillations in the conductance of a quantum dot Phys. Rev. B 44 1646 [22] Heinzel T 2007 Mesoscopic Electronics in Solid State Nanostructures 2nd edn (Weinheim: Wiley–VCH) [23] Amasha S, Rau I G, Grobis M, Potok R M, Shtrikman H and Goldhaber-Gordon D 2011 Coulomb blockade in an open quantum dot Phys. Rev. Lett. 107 216804 [24] Est´evez Hern´andez S, Akabori M, Sladek K, Volk Ch, Alagha S, Hardtdegen H, Pala M G, Demarina N, Gr¨utzmacher D and Sch¨apers Th 2010 Spin–orbit coupling and phase coherence in InAs nanowires Phys. Rev. B 82 235303 [25] Frielinghaus R, Fl¨ohr K, Sladek K, Weirich T E, Trellenkamp S, Hardtdegen H, Sch¨apers Th, Schneider C M and Meyer C 2012 Monitoring structural influences on quantum transport in InAs nanowires Appl. Phys. Lett. 101 062104 [26] Bleszynski A C, Zwanenburg F A, Westervelt R M, Roest A L, Bakkers E P A M and Kouwenhoven L P 2007 Scanned probe imaging of quantum dots inside InAs nanowires Nano Lett. 7 2559 [27] Zhukov A A, Volk Ch, Winden A, Hardtdegen H and Sch¨apers Th 2011 Low-temperature conductance of the weak junction in InAs nanowire in the field of AFM scanning gate JETP Lett. 93 13 [28] Hang Q, Wang F, Carpenter P D, Zemlyanov D, Zakharov D, Stach E A, Buhro W E and Janes D B 2008 Role of molecular surface passivation in electrical transport properties of InAs nanowires Nano Lett. 8 49 [29] van Tilburg J W W, Algra R E, Immink W G G, Verheijen M, Bakkers E P A M and Kouwenhoven L P 2010 Surface passivated InAs/InP core/shell nanowires Semicond. Sci. Technol. 25 024011
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Quantum dots in InAs nanowires induced by surface potential fluctuations
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 135203 (http://iopscience.iop.org/0957-4484/25/13/135203) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.64.11.153 This content was downloaded on 18/06/2017 at 17:58 Please note that terms and conditions apply.
You may also be interested in: Electronic properties of quantum dot systems realized in semiconductor nanowires J Salfi, S Roddaro, D Ercolani et al. Excited states and quantum confinement in room temperature few nanometre scale silicon single electron transistors Zahid A K Durrani, Mervyn E Jones, Chen Wang et al. Tunable few-electron quantum dots in InAs nanowires I Shorubalko, A Pfund, R Leturcq et al. Gate-induced transition between metal-type and thermally activated transport in self-catalyzed MBE-grown InAs nanowires C Blömers, T Rieger, T Grap et al. Single-molecule transport in three-terminal devices E A Osorio, T Bjørnholm, J-M Lehn et al. Control of charging energy in chemically assembled nanoparticle single-electron transistors Shinya Kano, Daisuke Tanaka, Masanori Sakamoto et al. Single donor electronics and quantum functionalities with advanced CMOS technology Xavier Jehl, Yann-Michel Niquet and Marc Sanquer Short-channel effect and single-electron transport in individual indium oxide nanowires Minkyung Jung, Hyoyoung Lee, Sunkyung Moon et al. Tunable single hole regime of a silicon field effect transistor in standard CMOS technology Marco Turchetti, Harald Homulle, Fabio Sebastiano et al.
Nanotechnology Nanotechnology 25 (2014) 135203 (5pp)
doi:10.1088/0957-4484/25/13/135203
Quantum dots in InAs nanowires induced by surface potential fluctuations Karl Weis, Stephan Wirths, Andreas Winden, Kamil Sladek, Hilde Hardtdegen, Hans Lüth, Detlev Grützmacher and Thomas Schäpers Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany Jülich Aachen Research Alliance, Fundamentals of Future Information Technology (JARA-FIT), Germany E-mail: [email protected] and [email protected] Received 8 December 2013, revised 14 January 2014 Accepted for publication 29 January 2014 Published 4 March 2014
Abstract
Back-gated InAs nanowire field-effect transistors are studied focusing on the formation of intrinsic quantum dots, i.e. dots not intentionally defined by electrodes. Such dots have been studied before, but the suggested explanations for their origin leave some open questions, which are addressed here. Stability diagrams of samples with different doping levels are recorded at electron temperatures below 200 mK, allowing us to estimate the number and size of the dots as well as the type of connection, i.e. in series or in parallel. We discuss several potential physical origins of the dots and conclude that they are most probably induced by potential fluctuations at the nanowire surface. Additionally, we show that via gate voltage and doping, the samples can be tuned to different regimes of Coulomb blockade. Keywords: indium arsenide, quantum dot, nanowire, low-temperature transport, doping S Online supplementary data available from stacks.iop.org/Nano/25/135203/mmedia (Some figures may appear in colour only in the online journal)
1. Introduction
were shown to depend sensitively on surface potential fluctuations. Most importantly, several samples exhibited nonlinear current–voltage curves at zero gate voltage for temperatures below 50 K. A question of particular interest is how the transport properties are affected by doping. Recently, this issue was addressed by Wirths et al [5] for NWs grown by selectivearea metalorganic vapour phase epitaxy (SA-MOVPE). It was shown that the transport properties are tunable by Si doping. Furthermore, for sufficiently low doping levels and temperatures, the current–voltage curves recorded at zero gate voltage showed a nonlinear behaviour similar to the one [8] observed by Bl¨omers et al. This was attributed to the onset of single-electron tunnelling. In order to corroborate this assumption, stability diagrams, i.e. the dependence of the differential conductance on the gate voltage VG and the source–drain bias VSD , of such NWs with two different doping levels are discussed in this paper. The
Single-electron transistors [1, 2] based on quantum dots (QDs) are especially interesting for future logic device applications due to their power efficiency. Among the numerous approaches for fabricating QDs, semiconductor nanowires (NWs) stand out as they are a natural step on the way to zero-dimensional systems and as their preparation [3] is well established. Using InAs is favourable as first, it usually features a surface accumulation layer [4] and thus enables straightforward preparation of ohmic contacts. At the same time, the carrier concentration is highly tunable by electrostatic gating [5]. Moreover, the large electron mobility allows high frequency operation [6]. For fabricating QDs in InAs NWs, a thorough knowledge of their transport properties is required. Recently, selfcatalysed, nominally undoped InAs NWs grown by molecular beam epitaxy were studied by Bl¨omers et al [7, 8]. Back-gated field-effect transistors were fabricated and characterized from room temperature down to 4 K. The transport properties 0957-4484/14/135203+05$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
Nanotechnology 25 (2014) 135203
K Weis et al
presence of Coulomb diamonds is an unambiguous proof for intrinsic QDs, i.e. dots not intentionally defined by electrodes. Such dots have to be taken into account when attempting to fabricate single-electron transistors. Intrinsic QDs in InAs NWs have been studied before by other groups [9–11], but the suggested explanations for their origin leave some open questions. For example, Kretinin et al [10] examine a back-gated NW (contact separation L = 470 nm, diameter D = 50 nm) and estimate the charging energy E C = e2 /C = 3 meV, where C is the total QD capacitance. They claim that the barriers are formed by the contacts. However, this is not consistent with a simple model proposed by Shorubalko et al [12] treating the QD as a conductive sphere (radius r ) embedded in InAs (εr = 15) and yielding a much smaller QD size r = C/(4π ε0 εr ) = 32 nm. Schroer and Petta [11] investigate back-gated NWs (L = 1.5 µm, D = 65 nm) with an axial defect density larger than 1 nm−1 and attribute the formation of QDs to these defects. They assume the QD sizes to be at least 50 nm, which is however much larger than the mean defect separation. It remains unclear what kind and number of defects are required to form a barrier. In this paper, we show that surface potential fluctuations, originating e.g. from adsorbates, are the most probable reason for the formation of intrinsic QDs. We investigate the number, size and type of connection (i.e. in series or in parallel) of the QDs. Additionally, in the works cited above, the question how doping affects the transport properties of the QDs has not been addressed. Here, we show that the QDs can be tuned to different regimes of Coulomb blockade via doping and also via the gate voltage.
Figure 1. (a) Typical transmission electron micrograph of a NW.
The growth direction is marked by an arrow. A wurtzite and a zinc blende segment are highlighted. At the NW edge, the native oxide layer can be seen. (b) Scanning electron micrograph of sample L1. The contacts marked S and D are used as source and drain, respectively.
the preparation method used in this study (including exposure to an electron beam and to atmosphere), the NWs are expected to feature a surface accumulation layer at least for the low doping level [5, 7]. In this case, electronic transport mainly takes place near the NW surface. 3. Results and discussion 3.1. Lower doping level
In figure 2, the stability diagram of a nearly undoped wire (sample L1, L = 1.5 µm, D = 100 nm) is shown. Its most important feature is a strong overlap of the Coulomb diamonds. Only few Coulomb resonances are present near zero bias, which is indicative [13] of QDs connected in series (figure 3). This is supported by the fact that facing borders of some ‘diamonds’ (e.g. the one at VG = −0.1 V) are not parallel [14]1 . The lines of enhanced conductance at some diamond edges, e.g. at (VG = −3.1 V, VSD = −3 mV), are a signature of excited states contributing to transport [15]. From the vertical distance between the two lines, we determine the excitation energy, and thus the single-particle level spacing, to be about 1 meV. Using this result, we gain a first rough estimate of the QD size by modelling it as a three-dimensional box [16]: With 1E box = 3π 2 h¯ 2 /(2m ∗InAs L 2box ), where m ∗InAs = 0.023 m e is the effective electron mass [6] and 1E box = 1 meV the lowest energy level spacing, we get a box length L box ≈ 220 nm. If facing borders of a diamond have approximately the same slope, this indicates that its origin is only one dot (and not multiple ones connected in series). We call such a diamond an undisturbed one. Its width δVG and height2 δVSD yield the gate lever arm αG = δVSD /(2δVG ). A gate voltage shift 1VG changes the chemical potential of the QD by 1µ = −eαG 1VG [15]. The two smallest3 undisturbed diamonds
2. Experimental details
Our NWs were grown by SA-MOVPE using trimethylindium (TMIn) and arsine (AsH3 ) as well as disilane (Si2 H6 , n-type dopant). Since Si is preferentially incorporated at In lattice sites, the doping level is quantified by a doping factor which is proportional to the partial pressure ratio p(Si2 H6 )/ p(TMIn) and which is set to 1 for p(Si2 H6 )/ p(TMIn) = 7.5 × 10−5 . In this study, wires with doping factors of 1 and 100 are examined. Their typical length and diameter are 4 µm and 100 nm, respectively. Details on NW growth can be found in [5]. The NWs feature a polytypic structure with wurtzite (WZ) and zinc blende (ZB) segments which are just a few nanometres long [5]. Overall, the WZ and ZB fraction is on the same order of magnitude and depends only weakly on the doping level. A typical transmission electron micrograph is shown in figure 1. For transport measurements, the NWs were transferred onto a degenerately n-doped Si(100) wafer covered by a 100-nm-thick SiO2 layer and thus acting as a back gate. The NWs were contacted individually by a set of Ti/Au electrodes using electron beam lithography. Prior to metal deposition, the wire surface was cleaned using Ar+ sputtering. The transport properties of a low-doped sample (L1) and another one with a higher doping level (H1) are investigated in a dilution refrigerator at a bath temperature of 70 mK. All measurements are performed in a two-terminal configuration. A scanning electron micrograph of sample L1 is shown in figure 1. Due to
1
See supplementary material (available at stacks.iop.org/Nano/25/ 135203/mmedia) for a stability diagram of another nearly undoped sample. 2 Disturbed diamonds feature a greater height than undisturbed ones because the voltage drops on multiple dots add up. 3 The physical reason for the variation of δV SD is the fact that the single-particle energy of a QD varies with the number of electrons on it. The height variation of the disturbed diamonds can be explained in the same way. 2
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Figure 2. Sample L1 (lower doping level), stability diagram, i.e. differential conductance map. It indicates the presence of at least two QDs A and B (see figure 3). Some ‘undisturbed’ diamonds originating from these dots are marked; one of them is magnified in the right inset. Lines of enhanced conductance at a diamond edge are highlighted (magnification in the left inset).
characteristics of the NW field-effect transistor, we get a carrier concentration n ∼ 2 × 1017 cm−3 [5] and thus [18] √ rTF = ( aB /2) × [π/(3 n)]1/6 ≈ 10 nm. For a nominally undoped wire (doping factor 0), the known background doping (ND ∼ 1015 cm−3 ) yields a mean impurity distance ∼100 nm. As the transport properties of NWs with doping factors 0 and 1 do not differ significantly [5], this should also hold for the low-doped NWs examined here. In contrast, if there are surface defects with a sufficiently low distance, the effective screening length can become large enough for the formation of barriers. Such defects may originate from trapped charges at the dielectric/NW interface, adsorbates or locally extended surface reconstruction [19] variations. The existence of such defects is consistent with the fact that we observe a significant change of the stability diagram, especially of αG , with thermal cycling (not shown here). To sum up, the kind of defects which can form barriers are most probably potential fluctuations at the NW surface as the electronic transport mainly takes place just there. By tuning VG to more positive values, the Fermi energy E F is shifted upwards and thus the effective barrier heights are lowered. Consequently, it should be possible to suppress Coulomb blockade by applying a sufficiently high VG . In order to check this, we do another VG sweep (not shown here). Due to a charge rearrangement, which could be induced by an uncontrolled change [20] in the occupation of surface states, Coulomb blockade now disappears already at VG = 0. Starting there, another stability diagram is recorded (figure 4), in which three different transport regimes can be identified. For VG < −0.28 V, no Coulomb resonances are found near zero bias (classical Coulomb blockade, multiple QDs connected in series). For VG > −0.28 V, only one dot survives as four undisturbed diamonds can be seen. Obviously, some barriers have vanished due to the higher position of E F . Coulomb resonances4 appear near zero bias and δVSD decreases with increasing VG , indicating a higher value of the dot–lead coupling 0. This can be explained [23] by mesoscopic Coulomb blockade (MCB), for which phase coherence is a necessary condition. The latter is indeed fulfilled, as shown by measurements [24] of universal conductance fluctuations which yield a phase coherence length lϕ ≥ 300 nm. For VG > −0.03 V, no
Figure 3. Simple model of sample L1 as a series connection of QDs (A, B) coupled to source, drain and gate by tunnel barriers and capacitors. The size of the circles is a measure for the QD size. Interactions between the QDs and additional QDs connected in series with A and B are neglected.
are located at VG = −3.2 V and VG = −0.2 V. They yield αG values of 0.02 and 0.07, respectively, and thus belong to different dots, the second one (dot B) being coupled to the gate more strongly than the first one (dot A). The diamond heights give an upper estimate for E C of 1 meV and 2 meV for dots A and B, respectively. Using the model presented by Shorubalko et al ([12], see above), we get a minimal QD size r of 100 nm and 50 nm for dots A and B, respectively. These results differ from the box model considered above by a factor not exceeding 2.2. One expects αG to increase [14] with increasing r , contrary to our findings. This discrepancy might be related to potential fluctuations at the NW surface, which will be discussed below. As all QD sizes estimated above are at least one order of magnitude smaller than the distance of source and drain (L = 1.5 µm), the QDs only fill a small fraction of the NW volume. The remaining parts of the NW serve as leads to the dots. Obviously, the source and drain contacts cannot be an exclusive reason for QD formation. More probably, the barriers are formed by defects. At first sight, several kinds of defects are conceivable to this end, i.e. polytypism, ionized impurities or surface potential fluctuations. However, at a closer look, the polytypism of the NWs is an unlikely explanation at least for the largest QDs as they are ten times longer than the longest WZ or ZB segments. Furthermore, potential barriers are also observed [8] in pure ZB NWs. Ionized impurities cannot induce barriers as the Thomas–Fermi screening length rTF of a single impurity is smaller than both the Bohr radius of InAs (aB = 35 nm [17]) and the wire diameter (D = 100 nm). In addition, adjacent impurities do not ‘see’ each other. This can be understood as follows: from the transfer
4
A fit to the Coulomb peak at VG = −0.27 V (according to [21, 22], assuming the sample is in the regime of quantum Coulomb blockade) yields an electron temperature below 200 mK. 3
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Figure 4. Sample L1, another stability diagram. Three different transport regimes can be identified: classical and mesoscopic Coulomb blockade (CCB, MCB) as well as the Fabry–Perot regime (FP). The arrows highlight some Coulomb resonances near zero bias. Two VSD sweeps marked I and II are shown in the left panel. The solid lines are guides to the eyes.
Figure 5. Sample H1 (higher doping level), stability diagram. The
sample is in the mesoscopic Coulomb blockade regime.
In the future, the interplay of sample structure and electronic properties could be studied in a more detailed way using a setup which allows performing transmission electron microscopy and transport measurements on one and the same sample [25]. Additionally, such a design eliminates the interaction between the substrate and the NW [10]. Further information on the size and position of the intrinsic QDs could be gained by direct imaging methods, e.g. by using a scanning probe microscope tip as a movable gate [26, 27]. An obvious question is what happens if controlled QDs are defined in the NWs using top gates (see e.g. [12]), i.e. how intrinsic and controlled QDs interact with each other. Finally, for the fabrication of reliable devices, the NW surface states have to be passivated, e.g. using 1-octadecanethiol [28] or an InP cap [29] layer.
Coulomb diamonds exist any more, but a pattern [10] appears which is similar to Fabry–Perot oscillations. The conductance peak near (VG = 0, VSD = 0) is consistent with this effect. 3.2. Higher doping level
So far, we have shown that 0 is tunable by VG . We now investigate if this can also be achieved by doping. In figure 5, a stability diagram of a wire with a higher doping level (sample H1, L = 700 nm, D = 70 nm) is shown. As the stability diagram has a simple structure with non-overlapping diamonds, probably a single QD is present in the entire VG region. From the smallest diamond (at VG = −1.9 V), one gets αG = 0.002, E C ≤ 0.6 meV and r ≈ 200 nm. The sample is in the MCB regime, which is more pronounced than in figure 4, as the diamonds are considerably distorted [23] and clearly separated by conductive regions. Compared to figure 4, the conductance inside the diamonds is two orders of magnitude larger, indicating a higher value of 0. The larger conductance leads to a stronger screening of the gate field, which is consistent with the observation of a lower αG . All these effects can be explained by the higher doping level, again leading to a higher value of E F and thus lower and fewer barriers [5]. Summing up, intrinsic quantum dots become less pronounced if the doping level is increased. In other words, the effect of defects on electronic transport decreases. Similar to sample L1, it should be possible to tune sample H1 to the CCB or FP regime by tuning VG to sufficiently large negative or positive values, respectively. Unfortunately, we are not able to check this due to the low value of αG and the limited dielectric strength of the back-gate oxide.
Acknowledgments
We thank H Kertz and K Wirtz for measurement and growth support, respectively, as well as St Trellenkamp for electron beam lithography. In addition, we are indebted to N Demarina, R Frielinghaus, F Haas, S Heedt and P Zellekens for fruitful discussions. References [1] Fulton T A and Dolan G J 1987 Observation of single-electron charging effects in small tunnel junctions Phys. Rev. Lett. 59 109 [2] Barreiro A, van der Zant H S J and Vandersypen L M K 2012 Quantum dots at room temperature carved out from few-layer graphene Nano Lett. 12 6096 [3] Thelander C et al 2006 Nanowire-based one-dimensional electronics Mater. Today 9 28 [4] Weber J R, Janotti A and Van de Walle C G 2010 Intrinsic and extrinsic causes of electron accumulation layers on InAs surfaces Appl. Phys. Lett. 97 192106 [5] Wirths S et al 2011 Effect of Si-doping on InAs nanowire transport and morphology J. Appl. Phys. 110 053709 [6] Ioffe Physico-Technical Institute Characteristics and Properties of New Semiconductor Materials (http://www.io ffe.ru/SVA/)
4. Conclusions
Our NW devices feature QD networks of varying complexity, among them a single dot and multiple ones connected in series. However, in all cases, typical dot sizes on the order of 10–100 nm can be extracted. Most probably, the barriers are formed by potential fluctuations at the NW surface. Our measurements show that the NWs can be tuned to different regimes of Coulomb blockade via gate voltage and doping. 4
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[7] Bl¨omers C, Grap T, Lepsa M I, Moers J, Trellenkamp St, Gr¨utzmacher D, L¨uth H and Sch¨apers Th 2012 Hall effect measurements on InAs nanowires Appl. Phys. Lett. 101 152106 [8] Bl¨omers C, Rieger T, Grap T, Raux M, Lepsa M I, L¨uth H, Gr¨utzmacher D and Sch¨apers Th 2013 Gate-induced transition between metal-type and thermally activated transport in self-catalyzed MBE-grown InAs nanowires Nanotechnology 24 325201 [9] Jespersen T S, Aagesen M, Sørensen C, Lindelof P E and Nyg˚ard J 2006 Kondo physics in tunable semiconductor nanowire quantum dots Phys. Rev. B 74 233304 [10] Kretinin A V, Popovitz-Biro R, Mahalu D and Shtrikman H 2010 Multimode Fabry–P´erot conductance oscillations in suspended stacking-faults-free InAs nanowires Nano Lett. 10 3439 [11] Schroer M D and Petta J R 2010 Correlating the nanostructure and electronic properties of InAs nanowires Nano Lett. 10 1618 [12] Shorubalko I, Pfund A, Leturcq R, Borgstr¨om M T, Gramm F, M¨uller E, Gini E and Ensslin K 2007 Tunable few-electron quantum dots in InAs nanowires Nanotechnology 18 044014 [13] De Franceschi S, van Dam J A, Bakkers E P A M, Feiner L F, Gurevich L and Kouwenhoven L P 2003 Single-electron tunneling in InP nanowires Appl. Phys. Lett. 83 344 [14] Fuhrer A, Fr¨oberg L E, Pedersen J N, Larsson M W, Wacker A, Pistol M-E and Samuelson L 2007 Few electron double quantum dots in InAs/InP nanowire heterostructures Nano Lett. 7 243 [15] Ihn T 2010 Semiconductor Nanostructures (New York: Oxford University Press) [16] L¨uth H 2013 Quantum Physics in the Nanoworld (Berlin: Springer) [17] Scheffler M, Nadj-Perge S, Kouwenhoven L P, Borgstr¨om M T and Bakkers E P A M 2009 Diameterdependent conductance of InAs nanowires J. Appl. Phys. 106 124303 [18] Ibach H and L¨uth H 2009 Solid-State Physics 4th edn (Berlin: Springer)
[19] L¨uth H 2010 Solid Surfaces, Interfaces and Thin Films 5th edn (Berlin: Springer) [20] Hasegawa H and Akazawa M 2008 Surface passivation technology for III–V semiconductor nanoelectronics Appl. Surf. Sci. 255 628 [21] Beenakker C W J 1991 Theory of Coulomb-blockade oscillations in the conductance of a quantum dot Phys. Rev. B 44 1646 [22] Heinzel T 2007 Mesoscopic Electronics in Solid State Nanostructures 2nd edn (Weinheim: Wiley–VCH) [23] Amasha S, Rau I G, Grobis M, Potok R M, Shtrikman H and Goldhaber-Gordon D 2011 Coulomb blockade in an open quantum dot Phys. Rev. Lett. 107 216804 [24] Est´evez Hern´andez S, Akabori M, Sladek K, Volk Ch, Alagha S, Hardtdegen H, Pala M G, Demarina N, Gr¨utzmacher D and Sch¨apers Th 2010 Spin–orbit coupling and phase coherence in InAs nanowires Phys. Rev. B 82 235303 [25] Frielinghaus R, Fl¨ohr K, Sladek K, Weirich T E, Trellenkamp S, Hardtdegen H, Sch¨apers Th, Schneider C M and Meyer C 2012 Monitoring structural influences on quantum transport in InAs nanowires Appl. Phys. Lett. 101 062104 [26] Bleszynski A C, Zwanenburg F A, Westervelt R M, Roest A L, Bakkers E P A M and Kouwenhoven L P 2007 Scanned probe imaging of quantum dots inside InAs nanowires Nano Lett. 7 2559 [27] Zhukov A A, Volk Ch, Winden A, Hardtdegen H and Sch¨apers Th 2011 Low-temperature conductance of the weak junction in InAs nanowire in the field of AFM scanning gate JETP Lett. 93 13 [28] Hang Q, Wang F, Carpenter P D, Zemlyanov D, Zakharov D, Stach E A, Buhro W E and Janes D B 2008 Role of molecular surface passivation in electrical transport properties of InAs nanowires Nano Lett. 8 49 [29] van Tilburg J W W, Algra R E, Immink W G G, Verheijen M, Bakkers E P A M and Kouwenhoven L P 2010 Surface passivated InAs/InP core/shell nanowires Semicond. Sci. Technol. 25 024011
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