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Ballistic InSb nanowires and networks via metal-sown selective area growth Journal: Nano Letters Manuscript ID nl-2019-04265p Manuscript Type: Communication Date Submitted by the 15-Oct-2019 Author: Complete List of Authors: Aseev, Pavel; Microsoft Quantum Lab Delft Wang, Guanzhong; TU Delft Binci, Luca; TU Delft Singh, Amrita; Microsoft Quantum Lab Delft Martí-Sánchez, Sara; Catalan Institute of Nanoscience and Nanotechnology Botifoll, Marc; Catalan Institute of Nanoscience and Nanotechnology Stek, Lieuwe; Microsoft Quantum Lab Delft Bordin, Alberto; TU Delft Watson, John; Microsoft Quantum Lab Delft Boekhout, Frenk; TNO Abel, Daniel; Microsoft Quantum Lab Delft Gamble, John; Microsoft Corp Van Hoogdalem, Kevin; Microsoft Quantum Lab Delft Arbiol, Jordi; ICREA and Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Advanced Electron Nanoscopy Kouwenhoven, Leo; Microsoft Quantum Lab Delft de Lange, Gijs; Microsoft Quantum Lab Delft Caroff, Philippe; Microsoft Quantum Lab Delft ACS Paragon Plus Environment Page 1 of 43 Nano Letters 1 2 3 4 5 Ballistic InSb nanowires and networks via 6 7 8 9 metal-sown selective area growth 10 11 12 13 14 Pavel Aseev1,*,†, Guanzhong Wang2,†, Luca Binci2,†, Amrita Singh2, Sara Martí- 15 16 17 Sánchez3, Marc Botifoll3, Lieuwe J. Stek2, Alberto Bordin2, John D. Watson1, Frenk 18 19 20 21 Boekhout1,4, Daniel Abel1, John Gamble5, Kevin Van Hoogdalem1, Jordi Arbiol3,6, Leo P. 22 23 24 Kouwenhoven1,2, Gijs de Lange1, Philippe Caroff1,* 25 26 27 28 1 Microsoft 29 Quantum Lab Delft, Lorentzweg 1, 2628 CJ Delft, Netherlands. 30 31 32 33 2 QuTech and Kavli Institute of NanoScience, Delft University of Technology, 34 35 36 37 Lorentzweg 1, 2600 GA Delft, The Netherlands. 38 39 40 41 3 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, 42 43 44 45 Campus UAB, 08193 Bellaterra, Barcelona, Catalonia, Spain 46 47 48 49 4 QuTech and Netherlands Organization for Applied Scientific Research (TNO), 50 51 52 53 Stieltjesweg 1, 2628 CK Delft, The Netherlands 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 2 of 43 1 2 3 5 Microsoft Quantum, 1 Redmond Way, Redmond, WA 98052 USA 4 5 6 7 8 6 ICREA, Pg. Lluí s Companys 23, 08010 Barcelona, Catalonia, Spain 9 10 11 12 13 KEYWORDS: InSb, molecular beam epitaxy, selective area growth, droplet epitaxy. 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 3 of 43 Nano Letters 1 2 3 4 Table of content graphic: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ABSTRACT 22 23 24 25 26 Selective area growth is a promising technique to realize semiconductor- 27 28 29 30 superconductor hybrid nanowire networks potentially hosting topologically protected 31 32 33 Majorana-based qubits. In some cases, however, such as molecular beam epitaxy of InSb 34 35 36 37 on InP or GaAs substrates, nucleation and selective growth conditions do not necessarily 38 39 40 overlap. To overcome this challenge we propose Metal-Sown Selective Area Growth (MS 41 42 43 44 SAG) technique which allows decoupling selective deposition and nucleation growth conditions by 45 46 47 temporarily isolating these stages. It consists of three steps: (i) selective deposition of In droplets 48 49 50 only inside the mask openings at relatively high temperatures favoring selectivity, (ii) nucleation of 51 52 InSb under Sb flux from In droplets which act as a reservoir of group III adatoms, done at relatively 53 54 55 low temperatures favoring nucleation of InSb, (iii) homoepitaxy of InSb on top of formed nucleation 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 4 of 43 1 2 3 layer under simultaneous supply of In and Sb fluxes at conditions favoring selectivity and high crystal 4 5 6 quality. We demonstrate that complex InSb nanowire networks of high crystal and 7 8 9 electrical quality can be achieved this way. We extract mobility values of 10,000–25,000 10 11 12 13 cm2 V-1 s-1 consistently from field-effect and Hall mobility measurements across single 14 15 16 nanowire segments as well as wires with junctions. Moreover, we demonstrate ballistic 17 18 19 20 transport in a 440 nm long channel in a single nanowire under magnetic field below 1 T. 21 22 23 We also extract a phase-coherent length of ~8 µm at 50 mK in mesoscopic rings. 24 25 26 27 28 Semiconductor-superconductor hybrid nanowire (NW) networks are promising 29 30 31 32 candidates for hosting topologically protected Majorana-based qubits, which have a 33 34 35 potential to revolutionize the emerging field of quantum computing.1 The III-V 36 37 38 39 semiconductor InSb is of particular interest in this regard owing to its large g-factor, which 40 41 42 enables a relatively small magnetic field to drive a hybrid semiconductor-superconductor 43 44 45 46 NW into the topological regime. Moreover the small effective mass favorably leads to a 47 48 49 large subband spacing.2 So far, mostly single3 or small-scale networks4 of InSb NWs were 50 51 52 53 used in Majorana-related transport experiments. To support further progress in the field, 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 5 of 43 Nano Letters 1 2 3 4 advanced NW networks are needed to fulfill the requirements of recent theoretical 5 6 7 proposals.5–8 Selective area growth (SAG) is a promising technique for realization of in- 8 9 10 11 plane NW networks, where a crystalline III-V substrate is covered with an amorphous 12 13 14 mask and growth proceeds selectively only inside lithographically defined openings. 15 16 17 18 However, early results suggest that in contrast to well-studied III-V materials such as InAs 19 20 21 and GaAs,9–11 the special case of InSb SAG by molecular beam epitaxy (MBE) has 22 23 24 25 selectivity conditions that do not overlap with its preferred nucleation conditions.12,13 This 26 27 28 can be overcome by using hydrogen plasma during the growth of InSb but at the cost of 29 30 31 32 reduced shape uniformity of different NWs and networks.12,13 33 34 35 In this work we implement a Metal-Sown Selective Area Growth (MS SAG) technique 36 37 38 39 which allows to decouple nucleation and selective growth conditions. MS SAG consists 40 41 42 of three steps schematically outlined in Figure 1 a: 43 44 45 46 (i) Selective metal sowing – supplying only In flux at relatively high substrate 47 48 49 temperature favoring selective In droplets (“seeds”) deposition only inside the 50 51 52 53 mask openings, 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 6 of 43 1 2 3 4 (ii) InSb nucleation layer – supplying only Sb flux (”watering”) to convert In 5 6 7 droplets into InSb networks at relatively low temperatures which favor 8 9 10 11 nucleation of InSb; In droplets act as a sole source of group-III element in that 12 13 14 case. 15 16 17 18 (iii) Homoepitaxy of InSb on top of the nucleation layer - growth is continued 19 20 21 under simultaneous supply of In and Sb fluxes at conditions favoring 22 23 24 25 selectivity and high crystal quality; improving faceting and achieving desired 26 27 28 out-of-plane dimensions. 29 30 31 32 The broad applicability of developed technique is confirmed by successful fabrication 33 34 35 of InSb NW networks on InP and GaAs substrates of both <001> and <111>B orientations 36 37 38 39 with InP(111)B case being studied in details. The high crystal quality and composition of 40 41 42 both isolated NW segments and junctions are demonstrated by Aberration Corrected High 43 44 45 46 Angle Annular Dark Field Scanning Transmission Electron Microscopy (AC-HAADF- 47 48 49 STEM) and Electron Energy Loss Spectroscopy (EELS). Consistent mobility values are 50 51 52 53 extracted from field-effect and Hall mobility measurements across single NW segments 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 7 of 43 Nano Letters 1 2 3 4 as well as wires with junctions. Moreover, we demonstrate ballistic and phase-coherent 5 6 7 transport in single NWs and mesoscopic rings, respectively. 8 9 10 11 All samples presented in this work are grown by MBE. Prior to loading in the MBE 12 13 14 chamber, a hard mask is fabricated by covering the substrate with ~14 nm thick 15 16 17 18 amorphous dielectric layer by plasma-enhanced chemical vapor deposition in which the 19 20 21 NW pattern is defined by standard lithography techniques.9,10 The substrate temperature 22 23 24 25 (T) is measured by a calibrated pyrometer for T > 500 °C and by extrapolating pyrometer 26 27 28 values using a thermocouple reading for T < 500 °C. Fluxes of In (FIn) and Sb (FSb) are 29 30 31 32 presented in equivalent planar InSb monolayers per second (MLInSb/s).9,14 A standard 33 34 35 substrate deoxidation procedure is used where it is kept under As flux (4x10-6 torr) for 36 37 38 39 5 min for both GaAs and InP substrates at T = 580 and 500 °C, respectively. Note that 40 41 42 500 °C is the highest temperature used in the entire process of InSb MS SAG on InP 43 44 45 46 substrates which makes it compatible with CMOS technology. In the following text the 47 48 49 case of InSb MS SAG on InP(111)B substrate is described in detail, while similar 50 51 52 53 considerations hold for other substrates as demonstrated by successful growth of InSb 54 55 56 MS SAG on GaAs(001) (see Supporting Information SA). 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 8 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Figure 1. MS SAG of InSb NW networks. (a) Schematics of MS SAG step sequence with SEM images (40° 19 20 21 tilt) illustrating the individual steps on patterned InP(111)B substrates: (b) deoxidized substrate, (c) step (i), 22 23 24 selective sowing of In at T(i) = 465 °C, (d) step (ii), conversion of In into InSb solely under Sb flux at T(ii) = 25 26 27 360 °C, (e) step(iii), continuing in conventional SAG regime with simultaneous supply of In and Sb fluxes 28 29 30 at T(iii) = 430 °C. Insets highlight faceting evolution from (ii) to (iii). 31 32 33 34 In a previous work, we demonstrated selective homoepitaxy of InSb wires on 35 36 37 InSb(111)B and InSb(001) substrates following conventional SAG method.9 However, in 38 39 40 41 case of heteroepitaxy of InSb on InP(111)B the conventional SAG method, in which both 42 43 44 elemental fluxes provided continuously, results in poor filling of the mask openings due 45 46 47 48 to unfavorable nucleation. This is true for SAG at both the relatively high substrate 49 50 51 temperature of T = 430 °C favoring selectivity conditions (Supporting Information Figure 52 53 54 55 S3 a)15 and all the way down to the relatively low substrate temperature of T = 360 °C 56 57 58 59 60 ACS Paragon Plus Environment Page 9 of 43 Nano Letters 1 2 3 4 favoring nucleation of planar InSb layers (Supporting Information Figure S3 b).16 To 5 6 7 overcome this issue, we have turned our attention to an Sb-induced growth technique 8 9 10 11 previously proposed for planar InSb growth for the case when the optimal growth 12 13 14 conditions are not known.14 In that method In is pre-deposited in the absence of Sb flux 15 16 17 18 and then converted into planar InSb via exposure to Sb flux (under no concomitant group 19 20 21 III flux).17 For planar growth on unmasked substrate this process can be monitored by an 22 23 24 25 in situ reflection high-energy electron diffraction (RHEED) method.14 We have observed 26 27 28 clear RHEED signal intensity oscillations on planar InSb(001) surfaces, indicating layer- 29 30 31 32 by-layer growth, for substrate temperatures up to Tcrit = 400 °C, above which no 33 34 35 oscillations were visible (Supporting Information Figure S4). 36 37 38 39 In this work we have adapted the above described Sb-induced growth technique to 40 41 42 substrates with patterned amorphous masks. Here we give a more detailed description 43 44 45 46 of individual steps during MS SAG (Figure 1 a). 47 48 49 After successful deoxidation (Figure 1 b), during step (i), only an In flux is supplied to 50 51 52 53 the sample at elevated substrate temperature T(i) resulting in stochastic positioning of In 54 55 56 droplets selectively inside the mask openings (see Figure 1 c). This becomes possible 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 10 of 43 1 2 3 4 due to the higher desorption rate of In adatoms from the amorphous mask compared to 5 6 7 crystalline substrate surface.9 Note that we have observed the mask dielectric layer being 8 9 10 11 occasionally damaged by the droplet (See Supporting Information SD). 12 13 14 During step (ii) the substrate temperature is decreased to T(ii) ≤ Tcrit for the subsequent 15 16 17 18 conversion of In into InSb under Sb flux (without concomitant In flux) to form the InSb 19 20 21 nucleation layer. Note that despite the fact that only Sb flux is being supplied to the 22 23 24 25 surface the growth proceeds under a local In-rich regime around the droplet because it 26 27 28 acts as a metal source. However, this growth mode is not to be confused with standard 29 30 31 32 in-plane vapour-liquid-solid where the droplet is moving along with growth front.18–21 33 34 35 Resulting InSb NW networks filling the mask openings can be seen in Figure 1 d. Attempts 36 37 38 39 to convert In into InSb above Tcrit result in poor nucleation and highly non-uniform growth, 40 41 42 similarly to conventional SAG, as shown in Supporting Information Figure S3 b. 43 44 45 46 During the last step (iii) the substrate temperature is raised to T(iii) at which InSb growth 47 48 49 can be continued via a conventional SAG method with both In and Sb fluxes supplied 50 51 52 53 simultaneously. Here the importance of previous steps (i)+(ii) is demonstrated when 54 55 56 comparing step (iii) of InSb MS SAG (Figure 1 d) to InSb growth without nucleation layer 57 58 59 60 ACS Paragon Plus Environment Page 11 of 43 Nano Letters 1 2 3 4 (Supporting Information Figure S3 a), performed under the same growth conditions. 5 6 7 Indeed, InSb growth proceeds uniformly only in the regions where it is already nucleated 8 9 10 11 and not on bare InP(111)B surfaces. As can be seen in Figure 1 d (inset) the InSb NW 12 13 14 networks faceting improves at the step (iii), except for the region next to the initial In 15 16 17 18 droplet position, where growth is not uniform. A similar effect was reported for quantum 19 20 21 nanorings obtained via droplet epitaxy and is attributed to droplet induced damage of 22 23 24 25 surrounding III-V surface22. Because of this limitation, the active region of devices should 26 27 28 be carefully selected to be away from the droplet. 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 12 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Figure 2. Schematics of diffusion limited growth during the MS SAG for samples (a) w/o and (b) w/ the 40 41 42 mask. SEM images illustrating InSb MS SAG steps for mask openings comprising of (c) 100 nm-wide 43 44 45 stripes, (d) interconnected networks of 130 nm-wide stripes, (e) large open areas and 2 µm-wide stripes. 46 47 48 49 We emphasize that metal droplets formed during MS SAG step (i) act as a sole source 50 51 52 of group III adatoms during step (ii). Therefore, the maximum characteristic in-plane size 53 54 55 56 of NW network is defined by surface diffusion length (D) of In adatoms on InP surface at 57 58 59 60 ACS Paragon Plus Environment Page 13 of 43 Nano Letters 1 2 3 4 step (ii) as schematically illustrated in Figure 2 a, b. This effect becomes evident when 5 6 7 comparing InSb growth evolution during MS SAG in mask openings of different 8 9 10 11 characteristic sizes and geometries (Figure 2 c, d, e). Following the methodology 12 13 14 proposed for III-V droplet epitaxy23,24 we have estimated D(ii) = 25,8 ± 1,3 µm at T(ii) = 15 16 17 18 360 °C from the diameter of the InSb spread around the initial droplet position on large 19 20 21 open areas of InP surface (Figure 2 e). Note that in case of complex networks D can be 22 23 24 25 significantly reduced due to non-trivial migration paths introduced by mask confinement 26 27 28 (see Figure 2 d panel (ii)). 29 30 31 32 Previously it was demonstrated that D can be improved by increasing the substrate 33 34 35 temperature and/or decreasing group V flux.23,24 However, there is limit to such 36 37 38 39 improvement due to Tcrit and the finite diffusion length of In adatoms under vacuum 40 41 42 conditions, which we determined to be D(i) = 52 ± 14 µm (at T = 465 °C and residual 43 44 45 46 pressure in the chamber of 1x10-10 torr). Future work is required to overcome this limit. 47 48 49 Direct measurements of D(iii) are complicated due to InSb lateral growth being 50 51 52 53 suppressed by non-favorable nucleation conditions in the mask regions which are not 54 55 56 already filled with InSb (e.g. Figure 2 d panels (ii) and (iii)). However, it is reasonable to 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 14 of 43 1 2 3 4 assume that D(iii) ≥ D(ii) because of homogeneous out-of-plane growth of the InSb 5 6 7 segments. 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Figure 3. 5x5 InSb NW network on InP(111)B substrate with its morphology accessed by (a) SEM and (b) 41 42 43 AFM with (c) the section highlighting the steps on its surface. Chemical composition of the similar network 44 45 46 sliced through the 5 junctions (indicated by white arrows) observed by (d) HAADF and (e) EELS elemental 47 48 49 maps. HAADF-STEM of (f) the top section of the InSb network and (g) InSb/InP interface containing partial 50 51 52 twin plane (red arrow) with (h) dilatation and (i) rotation maps obtained through GPA applied to the peaks 53 54 55 circled on a Fast Fourier Transform (FFT) power spectrum in the inset of panel (g). 56 57 58 59 60 ACS Paragon Plus Environment Page 15 of 43 Nano Letters 1 2 3 4 Out-of-plane morphology of a representative 5x5 InSb NW network with characteristic 5 6 7 size of less than 7 µm (Figure 3 a) was accessed by atomic force microscopy (AFM) as 8 9 10 11 shown in Figure 3 b. It reveals that the network’s top facet is almost entirely atomically 12 13 14 flat with only occasional large (>7nm in height) descending steps at the further end from 15 16 17 18 the initial droplet position (Figure 3 c). No additional features were found around the NW 19 20 21 junctions such as thickening or shape distortion previously observed in case of merging 22 23 24 25 of out-of-plane NWs.4 26 27 28 Focused-ion beam (FIB) prepared lamella were cut longitudinally along < 112 > 29 30 31 32 direction through the 5x5 InSb NW network similar to the one shown in Figure 3 a. 33 34 35 Excellent chemical uniformity across the entire cut was confirmed by the Z-contrast of 36 37 38 39 high-angle annular dark-field (HAADF) imaging (Figure 3 d) and electron energy loss 40 41 42 spectroscopy (EELS) elemental composition mapping (Figure 3 e). Atomic resolution 43 44 45 46 HAADF-STEM imaging revealed a B-polar pure zincblende (ZB) crystal structure of InSb 47 48 49 on the InP (111)B substrate (Figure 3 f and S8 e-f).25 At the InSb/InP interface we 50 51 52 53 observed formation of periodic array of in-plane misfit dislocations in both < 112 > 54 55 56 (Figure 3 g, I and S8 c) and < 110 > (Figure S7 b) directions.26 Geometric Phase 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 16 of 43 1 2 3 4 Analysis (GPA) of the interface region (Figure 3 h, i) suggest that these defects are 5 6 7 responsible for a full plastic strain relaxation of ~10.4% lattice mismatch between InSb 8 9 10 11 and InP, as expected for largely mismatched III-V epitaxial systems.9,10,12,27 Moreover, 12 13 14 occasional horizontal single twin boundaries were observed in close (< 10nm) region to 15 16 17 18 the InSb/InP interface (red arrow in Figure 3 g) as well as transverse 70.53° double twin 19 20 21 boundaries (Figure S8), similarly to previously reported InAs SAG on InP(111)B 22 23 24 25 substrate.9 Additionally, we emphasize that we found no significant difference in structural 26 27 28 nor chemical uniformity of NW junction regions compared to junction-free segments. 29 30 31 32 Refer to Supporting Information SE for TEM examination of other wire orientations. 33 34 35 Having verified the structural quality of our InSb NWs and networks we now move to 36 37 38 39 low-temperature electrical measurements to characterize the relevant scattering length 40 41 42 scales in classical and quantum transport. After MBE growth, the wafer is diced into 5 × 43 44 45 46 5 mm chips, each of which contains various semiconducting structures available for 47 48 49 transport characterization devices. Ohmic contacts, dielectrics and gates are fabricated 50 51 52 53 by standard means (Supporting Information SF). Devices are then cooled down in a 54 55 56 dilution refrigerator with a base temperature of 𝑇~20 mK. Measurements are performed 57 58 59 60 ACS Paragon Plus Environment Page 17 of 43 Nano Letters 1 2 3 4 with standard DC + lock-in techniques at frequencies below 100 Hz in either voltage- 5 6 7 biased or current-biased circuits. 8 9 10 11 Initial characterization is done by measuring the electron mobility defined in the Drude 12 13 14 model for diffusive transport. We report on two types of strategies commonly employed 15 16 17 18 in the literature to extract mobility using transport in one and two-dimensional 19 20 21 nanostructures. The first is that of the classical Hall effect (Figure 4a-d) and the second 22 23 24 25 is the long-channel field-effect transistor (FET) measurements (Figure 4e,f). 26 27 28 While Hall effect measurements have been the standard for two-dimensional materials, 29 30 31 32 the planar device geometry required is not as easily achieved for NWs. Although Hall 33 34 35 effect has been measured in InAs NWs by making use of the surface electron 36 37 38 39 accumulation layer in that material,28 electron depletion at InSb surfaces precludes similar 40 41 42 attempts on InSb NWs.29 Thus electron mobility in InSb NWs has been most commonly 43 44 45 46 extracted either by taking the peak transconductance30 or by fitting FET pinch-off 47 48 49 curves.31 Both Hall effect and field-effect methods assume the Drude model of 50 51 52 53 conductance 𝜇 = 𝜎/(𝑛𝑒) (𝜇,𝜎,𝑛,𝑒 are mobility, conductivity, carrier density per volume and 54 55 56 elementary charge, respectively). For both methods 𝜎 is measured directly, but 𝑛 is 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 18 of 43 1 2 3 4 obtained differently for each method. Hall effect measurements give direct access to 𝑛 5 6 7 via the Hall resistance 𝑅H but field-effect measurements rely on estimation of 𝑛 via 𝑄 = 𝑒𝒱 8 9 10 11 𝑛 = 𝐶𝑉g. Here, 𝐶 is the gate-to-device capacitance and 𝑉g the gate voltage (𝒱 and 𝑄 are 12 13 14 the volume of the semiconductor and total charge). A major drawback of this method is 15 16 17 18 that only the product 𝜇𝐶 can be reliably extracted from a fit to the data. Acquiring an 19 20 21 accurate estimation of 𝜇 then relies crucially on a reliable estimation of 𝐶 (or 𝑄), which is 22 23 24 25 not trivial for nanodevices with non-ideal semiconductor-dielectric interfaces. However, 26 27 28 the design flexibility of SAG allows us to easily overcome this drawback in straight NWs 29 30 31 32 by fabricating NW Hall bars and measuring the carrier density via 𝑅H, which does not rely 33 34 35 on any 𝐶 estimation and only requires NW width and length32,33 as input parameters. 36 37 38 39 Below, we first present such junction density and Hall mobility measurements assuming 40 41 42 uniform electron sheet density throughout the Hall bar. The information obtained from this 43 44 45 46 measurement then allows us to tune up a more detailed model of the device capacitance 47 48 49 that includes local electron density variations and can be used for field-effect mobility 50 51 52 53 estimations. Finally, comparison between mobilities obtained by the two methods are 54 55 56 discussed. 57 58 59 60 ACS Paragon Plus Environment Page 19 of 43 Nano Letters 1 2 3 4 Transport measurements in Hall-bar devices are shown in Figure 4 a-d. A ∼ 10 nA AC- 5 6 7 current bias 𝐼bias is applied as depicted in the circuit in Figure 4a. The longitudinal voltage 8 9 10 11 response along the NW 𝑉𝑥𝑥 and the transverse voltage across a junction 𝑉𝑥𝑦 are 12 13 14 measured using two synchronized lock-in amplifiers. Examples of the raw data taken 15 16 17 18 during such a measurement are shown in Supporting Information SG. Using the Hall 19 20 21 effect we extract the density 𝑛j in the NW junction through 𝑉𝑥𝑦 = 𝐼bias𝐵 ⊥ /(𝑛j,2D𝑒), where 22 23 24 25 𝐵 ⊥ is the applied out-of-plane magnetic field and 𝑛j,2D the electron sheet density in the 26 27 28 junction, defined as 𝑛j/𝑡 with 𝑡 being the NW thickness. By measuring 𝑉𝑥𝑦 and fitting it 29 30 31 32 linearly in relation to the applied magnetic field, we obtain directly 𝑛j,2D. This measurement 33 34 35 is repeated on each device at different 𝑛j,2D values by tuning 𝑉g (Figure 4b). Next, we can 36 37 38 𝐼bias 39 use the four-terminal conductivity along the NW 𝜎𝑥𝑥 = 𝑉𝑥𝑥 𝐿𝑥𝑥/(𝑊𝑡), with (𝐿𝑥𝑥) the length of 40 41 42 the channel and (𝑊) the width, to determine the Hall mobility as 𝜇H = 𝜎𝑥𝑥/(𝑛j𝑒) (Figure 43 44 45 46 4c). Strictly speaking, the estimation of mobility requires the channel density 𝑛c in the 47 48 49 straight wire segment instead of 𝑛j. This inadequacy resulting from the uniform density 50 51 52 53 assumption will be addressed below once we calibrate the electrostatic simulations with 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 20 of 43 1 2 3 4 the Hall measurement results and use it to model single NWs. As 𝑉g increases, 𝜇H 5 6 7 increases until it saturates at high positive 𝑉g to value in the range 10,000 ― 25,000 cm2 V- 8 9 10 11 1 s-1. Increased scattering at low 𝑛 points towards a charged scattering,34–36 with defects 12 13 14 residing either in the NW interior or the semiconductor surfaces37 and become better 15 16 17 18 screened as 𝑛 increases. At higher 𝑛, the saturation or slight decrease of 𝜇 is suggestive 19 20 21 of surface roughness being the dominant scattering mechanism.38,39 Such roughness and 22 23 24 25 defects are known to occur in native InSb oxide surfaces40,41 and become more relevant 26 27 28 as the electron distribution gravitates towards the semiconductor-dielectric surface under 29 30 31 32 positive gate voltages, as evidenced by our electrostatic simulations. Other factors 33 34 35 including polar molecule adsorbants on InSb31 and imperfections in the dielectric used 36 37 38 39 may also contribute to the surface scattering. We can also calculate the mean free path, 40 41 42 or the elastic scattering length, as 𝑙e = 𝜇ℏ𝑘F/𝑒, where 𝑘F = 2𝜋𝑛2D is the two-dimensional 43 44 45 46 Fermi wave vector. Assuming typical values of 𝑛2D ≈ 1×1012 cm-2 and 𝜇 ≈ 2×104 cm2/(V 47 48 49 s), we estimate 𝑙e ≈ 330 nm. These results compare favorably with existing literature on 50 51 52 53 InAs or InSb NW crosses produced by either SAG or VLS methods.10,12,32,33 We would 54 55 56 like to stress that as Hall effect measurements probe the transport properties inside the 57 58 59 60 ACS Paragon Plus Environment Page 21 of 43 Nano Letters 1 2 3 4 NW cross junctions, the high mobility demonstrates the promising potential of our planar 5 6 7 SAG approach in realizing advanced multi-terminal NW devices for topological quantum 8 9 10 11 computing.8,7,6 12 13 14 In order to benchmark our MS SAG InSb NWs with their VLS-grown counterparts using 15 16 17 18 the same method31 and to compare transport in single wires and cross structures, we also 19 20 21 measured field-effect mobility 𝜇FE in both single NWs and the Hall bars described above. 22 23 24 25 In the former case, NW FETs (Figure 4d) are fabricated with contact spacing either 𝐿 = 2 26 27 28 or 3 µm and a top gate that wraps around the transport region. For the latter we simply 29 30 31 32 float the four transverse voltage probing arms of the NW Hall bars and perform two- 33 34 35 terminal measurements from the left lead to the right lead. We measure current while 36 37 38 39 varying 𝑉g in both directions and fit the DC-conductance 𝐺 with 40 41 ―1 𝐿2 42 43 [ 𝐺(𝑉g) = 𝑅s + 𝜇FE𝑄𝑐(𝑉g) ] (1) 44 45 46 which takes as fitting parameters 𝜇FE, the total resistance in series with the transistor 𝑅s 47 48 49 50 and any unaccounted-for pinch-off threshold voltage Δ𝑉th by the simulated amount of 51 52 53 charge 𝑄𝑐(𝑉g) accumulated in the transport channel as a function of 𝑉g. Here, theoretical 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 22 of 43 1 2 3 4 modeling of the charge accumulation is achieved via 3D Thomas-Fermi (T-F) finite- 5 6 7 element electrostatic simulations, which takes into account a layer of interface charge at 8 9 10 11 the semiconductor-dielectric interface.42,43 The T-F approximation is well applicable to 12 13 14 high electron density regimes when the electron Fermi wavelength is smaller than the 15 16 17 18 device width 𝜆F < 𝑊.42 The interface charge density 𝐷it is obtained by setting it as a fitting 19 20 21 parameter while calibrating the model of the NW cross on the Hall-bar charge density 22 23 24 25 measurement results shown in Figure 4c. The fitted values of 𝐷it for the 6 Hall bars ranges 26 27 28 from 0.8×1012 cm-2 eV-1 to 6.8×1012 cm-2 eV-1 with the average being 2.9×1012 cm-2 eV-1, 29 30 31 32 similar to experimental findings of the quantity on InAs NW transistors in reference.44 In 33 34 35 the case of linear charge accumulation 𝑄 = 𝐶(𝑉g ― Δ𝑉th) and 𝐷it = 0, this method reduces 36 37 38 39 to the standard literature apporach.31 Due to different surface to volume ratios and the 40 41 42 gate geometry, we observe typically different electron density in the junction (𝑛j) and in 43 44 45 46 the straight channel (𝑛c) for NW Hall bars. The translation from 𝑛j to 𝑛c (and thus 𝑄𝑐 of the 47 48 49 FET devices) and other details of the model are described in the Supporting Information 50 51 52 53 SH. The example of such a pinch-off curve and the device on which it was measured, 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 23 of 43 Nano Letters 1 2 3 4 together with the simulated charge area density by our theoretical model, are shown in 5 6 7 Figure 4e. 8 9 10 11 We have thus measured sixteen FETs and the results are summarized in Figure 4f. The 12 13 14 averaged field-effect mobility 𝜇FE = 1.9 ± 0.6 × 104 cm2 V ―1s ―1 for upward gate sweeps, 15 16 17 18 agreeing roughly with 𝜇H data. The 𝜇FE measured on NW Hall bars are displayed in Figure 19 20 21 4d as horizontal lines spanning the gate range in which they are measured. The difference 22 23 24 25 between 𝜇FE and 𝜇H may be attributed to the fact that they do not reflect transport 26 27 28 properties in the exact same regions in the device. Where 𝜇FE is measured between the 29 30 31 32 normal contacts, 𝜇H is measured only between the voltage probes of the Hall bar. 33 34 35 Furthermore, hysteresis in pinch-off curves and the finite surface charge density required 36 37 38 39 to match simulations with the measured 𝑛 indicate the presence of a dynamic surface 40 41 42 charge density at the semiconductor-dielectric interface, which complicates the 43 44 45 46 comparison. However, we observe that the extracted 𝜇FE of single NWs, of entire Hall 47 48 49 bars and 𝜇H are all in a similar range, which would mean that the cross junctions do not 50 51 52 53 disproportionately add more scattering. Such cross junctions are crucial ingredients for 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 24 of 43 1 2 3 4 integration of parity read out needed for measurement-based braiding of Majorana zero 5 6 7 modes.8,7,6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Figure 4. Diffusive transport properties of NWs and junctions demonstrating high electron mobility in both 53 54 55 Hall effect and field-effect transistor measurements. (a) False-colored SEM image of a Hall bar measured 56 57 58 59 60 ACS Paragon Plus Environment Page 25 of 43 Nano Letters 1 2 3 (Device C) with illustration of the four-terminal circuit used for Hall effect measurements. Blue regions mark 4 5 6 the Cr/Au Ohmic contacts evaporated on top of the sulphur-passivated surface of InSb. The purple region 7 8 9 marks the gate electrode, separated from the NW by a layer of SiN𝑥 dielectric (not visible) sputtered globally 10 11 12 onto the entire chip. Blue is the NW. The scale bar is 1 µm. (b) View of the NW model used for electrostatic 13 14 15 simulation of the Hall bar junctions. The potential profile is simulated for the NW-cross region depicted 16 17 18 assuming appropriate material parameters and with input from the Hall measurements to establish the 19 20 21 surface charge density. The tiled inset shows an example of the calculated electron density profile in the 22 23 24 cross section. (c) Carrier concentration of the 6 NW Hall bars obtained from classical Hall effect 25 26 measurements via 𝑛2D = (𝑒Δ𝑅H/Δ𝐵) , together with the calibrated simulation result of them. (d) Hall ―1 27 28 29 30 mobility calculated from carrier concentration and sample resistivity obtained by Hall measurements 31 32 described above according to 𝜎 = 𝑛𝑒𝜇. Horizontal lines in each color represent the corresponding field- 33 34 35 effect mobility on each device. (e) An example pinch-off curve (orange) of the FET device used for field- 36 37 38 effect mobility extraction and its SEM image shown in the top inset (scale bar is 1). A DC bias voltage 39 40 41 𝑉bias = 10 mV is applied between source and drain contacts (blue). 𝐺 is measured while applying 𝑉g to the 42 43 44 gate (pink). Blue dashed lines are best fits of Eq. (1) to the data from which we extract 𝜇. (f) Field effect 45 46 47 mobility of all NW FETs measured. All curves were taken by sweeping the gate both from below pinch-off 48 49 50 to saturation (upwards) and in the opposite direction (downwards). Horizontal dashed lines indicate the 51 52 53 averaged mobility of all devices in both directions. 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 26 of 43 1 2 3 4 With the mobilities we observed in long channels, we set out to measurement of NW 5 6 7 quantum point contacts (QPCs) and confirm ballistic transport in our InSb MS SAG 8 9 10 11 NWs.4,45–47 Indeed we observe ballistic transport in such a single NW QPC device with 12 13 14 440 ± 20 nm contact spacing (Figure 5a-d), as well as in other devices (Supporting 15 16 17 18 Information SI). We measure the differential conductance of the device shown in Figure 19 20 21 5a as a function of DC-𝑉bias, 𝑉g and 𝐵 ∥ . Figure 5b shows pinch-off traces taken at 𝑉bias 22 23 24 25 = 0 V in DC under increasing 𝐵 ∥ from left to right (offset horizontally for clarity). A 26 27 28 conductance plateau at 𝐺0 = 2𝑒2/ℎ begins to emerge at around 𝐵 ∥ = 1.2 T as cyclotron 29 30 31 32 orbits gradually suppress backscattering.45 More plateaus appear at higher fields and at 33 34 35 other multiples of 0.5𝐺0 as Zeeman splitting lifts the electron spin degeneracy of the 36 37 38 39 subbands. The red linecut at 𝐵 ∥ = 3.9 T show conductance plateaus of the first, third and 40 41 42 fifth spin-split subbands. We attribute slight deviations of the plateaus from half-integer 43 44 45 46 multiples of 𝐺0 to unaccounted-for contact resistance. 47 48 49 We investigate the evolution of the conductance plateaus with 𝐵 ∥ (Figure 5c). For 50 51 52 53 higher 𝐵 ∥ , the plateaus widen and become more clear as spin splitting becomes larger. 54 55 56 At around 𝐵 ∥ = 3.9 T, the higher-energy spin subband of the lowest orbital (𝐸1↑) crosses 57 58 59 60 ACS Paragon Plus Environment Page 27 of 43 Nano Letters 1 2 3 4 the lower-energy spin subband of the second orbital (𝐸2↓), rendering the 1𝐺0 plateau too 5 6 7 narrow to distinguish until 𝐵 ∥ > 5 T when it re-emerges after the crossing. As for 𝐵 ∥ 8 9 10 11 < 1. 2 T, clear plateau features become obscured by mesoscopic conductance 12 13 14 fluctuations which can be attributed to backscattering as a result of uncontrolled potentials 15 16 17 18 induced by non-gated section of the transport channel and/or by the contacts to the 19 20 21 semiconductor. 22 23 24 25 Bias spectroscopy taken at 𝐵 ∥ = 3 T (Figure 5d) further reveals relevant energy scales 26 27 28 via diamond-shaped conductance plateaus of the first few spin-split subbands.45,46 The 29 30 31 32 0.5𝐺0 plateau vanishes at 𝑉bias ≈ 8 mV when the chemical potential difference between 33 34 35 the two leads is equal to the energy splitting between the first two spin-split subbands.48–50 36 37 38 39 The relation 𝑒𝑉bias = 𝐸1↑ ― 𝐸1↓ = 𝑔𝜇B𝐵 ∥ , where 𝜇B is the Bohr magneton, allows us to 40 41 42 extract a Landé 𝑔-factor of 𝑔 ∼ 46, in accordance with previous observations in InSb VLS 43 44 45 46 NWs.45,51,52 The subband spacing between the first two spin-degenerate orbitals is 47 48 49 similarly calculated by summing the width of the first two diamonds to be ∼ 12 meV. We 50 51 52 53 consistently observe ballistic transport on length scales of several hundred nm in multiple 54 55 56 InSb MS SAG QPC devices (Supporting Information SI). 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 28 of 43 1 2 3 4 With ballistic transport established in InSb MS SAG, we finally move to demonstrate 5 6 7 phase coherent transport and extraction of inelastic scattering length, a.k.a. phase 8 9 10 11 coherence length (Figure 5e-g) by a quantum interference experiment. Crucially, this 12 13 14 requires the ability to grow high-quality networks as demonstrated in Figure 2. Such 15 16 17 18 networks are requisite ingredients for implementing proposals for manipulating Majorana 19 20 21 states via electron teleportation8 and for making topological qubits,6,7 provided electrons 22 23 24 25 retain their memory of the quantum mechanical phase throughout the structure. The 26 27 28 canonical experiment for proving phase-coherent transport is by measuring the 29 30 31 32 conductance of a semiconducting loop modulated by Aharonov-Bohm (AB) interference 33 34 35 (Figure 5e).4,53 In such magnetoconductance measurements the two-terminal 36 37 38 39 conductance is probed from one side of the loop, with surface area 𝐴, to the other while 40 41 42 it is threaded by a flux Φ = 𝐵 ⊥ 𝐴. If the transport is phase coherent, the applied flux 43 44 45 46 induces conductance oscillations as a result of the quantum interference between 47 48 49 electron trajectories passing through the two arms of the loop. The periodicity of the 50 51 52 53 oscillations depends on the loop area 𝐴 and the magnetic flux quantum Φ0 = ℎ/𝑒 as Δ𝐵 ⊥ 54 55 56 = Φ0/𝐴. 57 58 59 60 ACS Paragon Plus Environment Page 29 of 43 Nano Letters 1 2 3 4 Figure 5f plots two representative magnetoconductance measurement results in MS 5 6 7 SAG Aharonov-Bohm (AB) loop devices. We observe higher frequency oscillations 8 9 10 11 superimposed on an irregular slow-varying background of mesoscopic conductance 12 13 14 fluctuations. After subtracting the background, the conductance clearly exhibits periodic 15 16 17 18 oscillations as shown in the example in the inset of Figure 5f. Such magnetoconductance 19 20 21 traces are then taken with the device depicted in Figure 5e for several values of 𝑉g and 22 23 24 25 their Fourier spectra are averaged to reveal a clear peak at the expected frequency in 26 27 28 Figure 5f. Its second harmonic is also visible in the spectrum, which results from AB 29 30 31 32 interference between electron paths of opposite directions traversing the entire loop. The 33 34 35 peak broadening can be explained by the finite width of the wire, which sets upper and 36 37 38 39 lower bounds on the periodicity. The expected bounds coincide well with the observed 40 41 42 peak. 43 44 45 46 We can extract the electron phase coherence length 𝑙𝜙 in our devices by measuring the 47 48 49 temperature dependence of the first harmonic peak amplitude. In the case of diffusive 50 51 52 53 transport, the peak amplitude is expected to follow the relation 𝐴ℎ/𝑒 = 𝐴0exp( ―𝑎 𝑇) 54 55 56 where 𝐴0 and 𝑎 are fitting parameters and the phase coherence length is described in 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 30 of 43 1 2 3 𝐿 4 these terms as 𝑙𝜙 = 𝑎 𝑇 with 𝐿 being the loop circumference.54,55 We measure AB 5 6 7 oscillations in the same range of magnetic field at different temperatures on the device 8 9 10 11 shown in Figure 5e and fit the first-harmonic peak in each Fourier spectrum with a 12 13 14 Gaussian envelope. The peak amplitudes thus obtained are then fitted with 𝐴0,𝑎 as 15 16 17 18 parameters and the resulting 𝑙𝜙 dependence on temperature is plotted as the orange 19 20 21 dashed line in Figure 5g. To visualize the standard deviation of the fitting procedure, we 22 23 24 25 translate the oscillation amplitude at each measured temperature back into a 26 27 28 decoherence length scale and plot them in the same panel together with the fitting 29 30 31 32 standard deviation. The phase coherence thus extracted is about 7.5 µm at 50 mK, the 33 34 35 measured electron temperature in our fridge. 36 37 38 39 In summary, we have demonstrated the Metal-Sown Selective Area Growth technique 40 41 42 to overcome the challenge of non-overlapping nucleation and selective growth conditions 43 44 45 46 and applied it to InSb heteroepitaxy. This is achieved by selective group III adatoms pre- 47 48 49 deposition at selectivity favoring conditions and its subsequent conversion into III-V 50 51 52 53 crystal under group V flux at nucleation favoring conditions. We have successfully 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 31 of 43 Nano Letters 1 2 3 4 obtained complex InSb nanowire networks and accessed confirmed their high structural 5 6 7 quality by transmission electron microscopy. Consistently high mobility values are 8 9 10 11 extracted by both Hall and field effect techniques in the presence of cross junctions. The 12 13 14 materials quality was verified by the observation of ballistic transport with conductance 15 16 17 18 plateaus up to the fifth spin-split subband and a long phase coherence length of 7.5 µm. 19 20 21 The results point at promising applications of InSb nanowire networks to advanced 22 23 24 25 topological hybrid semiconducting/ superconducting networks. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 32 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Figure 5. Ballistic transport under finite magnetic field in an InSb quantum point contact and phase coherent 43 44 45 transport in a NW loop. (a) False-colored SEM image of the InSb QPC device. Contacts are in blue, gate 46 47 48 in purple and NW in blue. Scale bar is 500 nm. Magnetic field is applied along the in-plane direction 49 50 51 perpendicular to the NW. (b) Zero-DC-bias pinch-off traces of the device shown in (a), taken at field values 52 53 54 between 0 and 5.5 T with intervals of 0.3 T. Each curve is shifted horizontally from the previous one by 55 56 57 58 59 60 ACS Paragon Plus Environment Page 33 of 43 Nano Letters 1 2 3 +75 mV for clarity. Highlighted curve at 3.9 T shows the first, third and fifth spin-split conductance plateaus. 4 5 6 (c) Plot of zero-DC-bias conductance under different gate and magnetic field showing the evolution of 7 8 9 subband plateaus as increasing B gradually suppresses backscattering and increases the splitting between 10 11 12 the two spin subbands. Dashed lines are guides to the eyes separating conductance plateaus. (d) 13 14 15 Differential conductance measured as a function of 𝑉bias and gate voltages showing the first few spin-split 16 17 18 subbands, taken at a magnetic field of 3 T (indicated in panel (c) by a white line). The diamond shapes in 19 20 21 the color plot provide information on the 𝑔-factor and subband spacing in the NW as indicated by the labels. 22 23 24 (e) Top-view SEM image of one of the InSb NW loops in which Aharanov-Bohm conductance oscillations 25 26 27 were observed. Ohmic contacts are marked in blue and the wrapping gate in purple. The circumference of 28 29 30 the loop measured along the geometrical center of the NW is 4. The scale bar is 800 nm. Magnetic field is 31 32 applied perpendicular to the loop. The area enclosed by the NW center is measured to be 0.69 µm2. (f) 33 34 35 Averaged fast-Fourier-transform spectrum of magnetoconductance traces of the device in (a) among 36 37 38 different gate voltages, after subtraction of a low-frequency background. The red line identifies the peak 39 40 41 corresponding to the magnetic field periodicity given by a flux quantum through the area of the loop. Grey 42 43 44 lines denote the expected widening of the signal peak due to the finite width of the NW. The second 45 46 47 harmonic peak is identified by the orange line. Inset: the magnetoconductance trace of another loop with a 48 49 50 larger size (circumference 8 µm, area 3.25 µm2) after subtraction of background. (g) Temperature 51 52 53 dependence of the extracted phase-coherence length as the orange dashed line, together with the fitting 54 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 34 of 43 1 2 3 errors and the measured oscillation amplitudes translated into length scales according to the fitting formula 4 5 6 as scattered dots. 7 8 9 10 11 12 13 ASSOCIATED CONTENT 14 15 16 17 Supporting Information. 18 19 20 21 22 The supporting information is available free of charge on the website. 23 24 25 26 Additional details and figures on InSb MS SAG on GaAs(001) substrates, 27 28 29 30 demonstration of trials of conventional SAG of InSb, RHEED oscillation during planar 31 32 33 InSb growth, In droplet induced damage to the mask, and strain relaxation in InSb MS 34 35 36 37 SAG on InP(111)B substrates. Device fabrication details, examples of Hall effect 38 39 40 measurements, details on electrostatics simulations, and all other QPC plateaus 41 42 43 44 observed in measurements are given as well (PDF). 45 46 47 48 49 50 51 AUTHOR INFORMATION 52 53 54 †– these authors contributed equally 55 56 57 58 59 60 ACS Paragon Plus Environment Page 35 of 43 Nano Letters 1 2 3 4 Corresponding Authors 5 6 7 * E-mail: Pavel.Aseev@microsoft.com 8 9 10 11 * E-mail: Philippe.Caroff@microsoft.com 12 13 14 15 Author Contributions 16 17 18 P.A. conceived the idea for the research as well as performed the growth, growth kinetic studies, 19 20 morphological analysis and wrote the corresponding part of the manuscript. G. W., and L. B. fabricated 21 22 devices and performed their electronic characterization and analysis and G. W. wrote the corresponding 23 24 25 part of the manuscript. A. S. developed mask preparation procedure and provided patterned substrates for 26 27 the growth. L.J. S., A. B., and J. D. W. assisted with device fabrication and electronic measurements. S. 28 29 M.-S., M. B. and J. A. performed TEM sample preparation and related structural and compositional 30 31 analyses as well as wrote the corresponding section of the manuscript. D. A., J. G., K. v. H. developed 32 33 computational model for mobility curves fitting. F. B. participated in the growth discussion and assisted 34 35 with the growth. P. C., G.d. L., and L. P. K. supervised the work and provided extensive comments to the 36 37 manuscript. All authors commented on the work and provided valuable input throughout the project as well 38 39 as approved the final version of the manuscript. 40 41 42 43 Funding Sources 44 45 46 47 Notes 48 49 50 The authors declare no competing financial interest. 51 52 53 54 ACKNOWLEDGMENT 55 56 57 58 59 60 ACS Paragon Plus Environment Nano Letters Page 36 of 43 1 2 3 4 The project was supported by Microsoft Station Q (Delft). P.A. and P.C. gratefully 5 6 7 acknowledges Emrah Yucelen for fruitful discussions on transmission electron 8 9 10 11 microscopy study. S.M.-S acknowledges funding from "Programa Internacional de Becas 12 13 14 "la Caixa"-Severo Ochoa”. ICN2 members acknowledge funding from Generalitat de 15 16 17 18 Catalunya 2017 SGR 327. ICN2 acknowledges support from the Severo Ochoa 19 20 21 Programme (MINECO, Grant no. SEV-2013-0295) and is funded by the CERCA 22 23 24 25 Programme / Generalitat de Catalunya. Part of the present work has been performed in 26 27 28 the framework of Universitat Autònoma de Barcelona Materials Science PhD program. 29 30 31 32 Part of the HAADF-STEM microscopy was conducted in the Laboratorio de Microscopias 33 34 35 Avanzadas at Instituto de Nanociencia de Aragon-Universidad de Zaragoza. ICN2 36 37 38 39 acknowledge support from CSIC Research Platform on Quantum Technologies PTI-001. 40 41 42 43 REFERENCES 44 45 46 47 (1) Kitaev, A. Yu. 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