pubs.acs.org/NanoLett
Multimode Fabry-Pe´rot Conductance Oscillations in Suspended Stacking-Faults-Free InAs Nanowires Andrey V. Kretinin,*,† Ronit Popovitz-Biro,‡ Diana Mahalu,† and Hadas Shtrikman† †
Braun Center for Submicrometer Research, Department of Condensed Matter Physics and ‡ Electron Microscopy Unit, Weizmann Institute of Science, Israel ABSTRACT We report on observation of coherent electron transport in suspended high-quality InAs nanowire-based devices. The InAs nanowires were grown by low-temperature gold-assisted vapor-liquid-solid molecular-beam-epitaxy. The high quality of the nanowires was achieved by removing the typically found stacking faults and reducing possibility of Au incorporation. Minimizing substrate-induced scattering in the device was achieved by suspending the nanowires over predefined grooves. Coherent transport involving more than a single one-dimensional mode transport was observed in the experiment and manifested by Fabry-Pe´rot conductance oscillations. The length of the Fabry-Pe´rot interferometer, deduced from the period of the conductance oscillations, was found to be close to the physical length of the device. The high oscillations visibility imply nearly ballistic electron transport through the nanowire. KEYWORDS Molecular-beam epitaxy, InAs nanowires, coherent electron transport, Fabry-Perot oscillations
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emiconductor nanowires (NWs), grown by the vaporliquid-solid (VLS) method, gained their popularity for transport and optics applications due to their nanometer scale diameter and large aspect ratio.1 These characteristic properties make NWs ideal for bottom-up nanofabrication, as well as enabling the study of a wide variety of quantum phenomena. Nanowire-based quantum dots were used to directly measure the spin-orbit coupling;2 the gate voltage-dependent g-factor3,4 and investigate spin dynamics.5-7 The combination of a semiconductor NW and superconducting contacts allowed a demonstration of a Cooper pair field-effect transistor8,9 an interplay between Andreev reflections and the Coulomb blockade;10 as well as coexistence of superconductivity and the Kondo effect in a quantum dot.11 Anomalous Andreev reflections were also found12 in a shortchannel Ge/Si core/shell NWs. Using similar nanowiresuperconductor hybrid structure the first step toward implementing a Cooper pair beam splitter was made.13 Despite the significant progress made in growing nanowires, the overwhelming majority suffer from the same problem, a short mean free path (less than 100 nm),8 which limits the application of nanowire-based devices to shortchannel structures.14,15 There are few possible sources of disorder that are responsible for the short mean free path in nanowires. First, disorder is likely to originate from the crystallographic imperfections in the NW, namely stacking faults (SF).16
Normally, InAs nanowires grown by VLS-assisted molecularbeam-epitaxy (MBE) have a wurtzite (WZ) crystal structure, which occasionally changes to the zinc-blende (ZB) structure for one or more monolayers, along the NW growth axis. These two distinct forms of InAs are expected to have a band gap difference of about 30%, with a low-temperature band gap of 0.54 eV for WZ InAs17 and 0.42 eV for ZB InAs. Such abrupt and random changes in the band gap inevitably produce a random disorder potential for electrons in the conduction band. Recent experiments18 showed that the presence of SFs in an InAs nanowire channel significantly decreases the drift mobility, emphasizing the importance of crystallographic perfection for electron transport. Second, disorder is due to unintentional incorporation of contaminating elements present in the growth chamber during nanowires synthesis19 and possible incorporation of gold atoms segregating from the catalyst.20,21 Third, disorder is due to oxidation and possible adherence of impurities to the unprotected NW surface. Further contamination of the NW surface can occur during device fabrication. Transport through the NW takes place close to the NW surface and thus is very sensitive to contamination adsorbed on the surface or trapped on the substrate. The best example of such disorder is water molecules trapped between the nanotube and the SiO2 substrate22 in carbon nanotube-based field-effect-transistors, causing large gate voltage hysteresis and device instability. To extend, the mean free path measures must be taken to eliminate or minimize the above sources of disorder. In this letter we report on improved quality InAs nanowire devices via an optimized growth process by VLS-MBE and the use of a new suspended NW device geometry. Charac-
* To whom correspondence should be addressed: E-mail: andrey.kretinin@ weizmann.ac.il. Received for review: 04/29/2010 Published on Web: 08/09/2010 © 2010 American Chemical Society
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terization of the nanowire-based devices was done by studying coherent electron transport by means of the Fabry-Pe´rot conductance oscillations. The InAs nanowires used in this work were grown in Riber 32 solid-source molecular beam epitaxy (MBE) system using the Au-assisted VLS method.16,23-26 A Knudsen cell was used for in situ evaporation of a thin (∼0.5 nm) layer of gold on to an InAs substrate, which was later heated to form the catalyst particles. InAs NW growth was done at a substrate temperature of 400 °C and As4/In flux ratio of about 100. The arsenic overpressure was set low to decrease the growth rate and avoid the appearance of SFs. The relatively low-growth temperature was chosen to enhance the NW growth relative to the bulk growth. At this low temperature Au-assisted growth is thought to take place via the vapor-solid-solid (VSS) mechanism rather than via the VLS unless the gold droplets are subjected to savior super cooling due to their nanometer-scale size.16,24 At a substrate temperature of 400 °C, which is well below the In-Au eutectic temperature of 454 °C,27 the gold catalyst is assumed to be solid. It is reasonable to believe that under these conditions gold incorporation is minimal or is completely eliminated. Since the substrate surface morphology has an effect on the aggregation of gold droplets we looked into the growth on three different InAs substrate orientations, (111)B, (311)B, and (011). We found that the (011)-oriented substrates gave the best result in terms of eliminating SFs. Namely, comparatively the NWs grown on the (311)B substrate contain SFs mostly along the top half of their length (full length 5-7 µm); under the same growth conditions the commonly used (111)B substrates produced NWs with SFs only along the top third of the length (full length 5 µm) and the most of 4-5 µm-long NWs grown on the (011) substrates were found to be free of SFs under the same growth conditions. As a result of the above optimization process, we were able to grow WZ InAs NWs mostly free of SFs with a diameter of 50-60 nm and an average length of 4-5 µm. As can be seen in Figure 1a, the NW diameter is determined by the Au particle size and has an excellent uniformity (e10%) over the entire length. Figure 1b shows an SEM image of the cross-section of the (011) sample with NWs grown on it. Since the NWs grow in the [111] direction they appear at an angle to (011) substrate surface. The highresolution TEM images, presented in Figure 1c, show three sections (taken from top, middle and bottom of the NW) of a SF-free InAs NW. Careful TEM study of a few tens of such NWs revealed the presence of only a single SF once in several NWs. Figure 1c also demonstrates the surface of the NW being remarkably flat and covered by thin (∼2 nm) native oxide. The WZ crystal structure was confirmed by the electron diffraction taken from the middle of the NW (Figure 1d). We developed a new nanofabrication technique28 to suspend the NWs over the substrate in a similar way to that © 2010 American Chemical Society
FIGURE 1. Electron microscope images of WZ InAs NWs. (a) Lowresolution TEM image of a single NW. (b) SEM cross-section image of InAs (011) substrate with NWs grown in [111] direction. (c) Highresolution TEM image taken from the top (Au particle is also seen), middle, and bottom of the NW. Insets exhibit a higher magnification of the crystal lattice as well as the sharp and uniform interface between the NW and oxide. (d) Electron diffraction taken from the center of the NW. The arrow indicates the direction of the NW growth.
of suspended carbon nanotubes.29 The device platform was a p+-Si wafer with 150 nm thick SiO2 grown on top. First, an array of narrow (200-500 nm) and 20 µm long grooves were chemically etched in SiO2 down to the Si substrate. This was followed by evaporation of the local metal backgate on the bottom of the grooves. Then NWs were spread out across the prefabricated grooves so that a small segment of a NW 3440
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FIGURE 2. (a) Schematic diagram of the experimental NW device. (b) SEM image of the NW device used in the experiment (scale bar is 1 µm). (c) Linear differential conductance G as a function of backgate voltage Vg at two temperatures 0.35 and 1.5 K.
value of the charging energy εc ) e2/Ctot ≈ 3 meV, and the 31 gate capacitance Cg ) e/∆VCB respectively, where g ≈ 1.6 aF, Ctot is the total capacitance of the Coulomb island and ∆VgCB is the period of Coulomb blockade oscillations. The Coulomb diamond at Vg ≈ -8.7 V has a well-pronounced zero-bias anomaly (ZBA) pointed at by the arrow in Figure 3a. This ZBA is a clear sign of the Kondo effect32 that was previously seen in InAs3,23 and InSb4 NW quantum dots. Observation of the Kondo effect, which requires strong coupling to the leads, with relatively high amplitude of conductance peaks (approaching e2/h) leads to the important conclusion that the QD is coupled directly to the device contacts and is not broken by disorder into a few smaller dots connected in series.33 This means that we are dealing with a single NW QD which extends over the entire NW device length. At Vg larger than -5 V, transport through the NW becomes delocalized and G increases nonmonotonically with quasi-periodic oscillations. Under positive gate voltage, the conductance exceeds 2e2/h, indicating transport through the second 1D subband, while exhibiting quasi-periodic oscillations appearing as a chess-board pattern in the grayscale nonequilibrium conductance plot in a wide range of Vg (Figure 3d). For better clarity, a close-up view of two different regions is shown in Figure 4. Seemingly, the quasi-periodic conductance oscillations in the Vg - Vsd plane rule out the universal conductance oscillations (UCF)23,34,35 as a possible explanation. Indeed, the UCF in InAs NWs reported previously appear to be random in Vg23 with no regular pattern in the Vg - Vsd plane,35 which reflects the essence of the UCF originating from electrons being multiply scattered by randomly distributed disorder. On the contrary, in our NW devices electrons are reflected only from the precontact areas and travel between them without scattering. Coulomb blockade oscillations seem also to be unlikely because of the observed high value of the total conductance.36 Hence, a
is suspended over the groove. Using e-beam lithography two Ni/Au contacts (5/100 nm thick) were patterned on top of the parts of the NW supported by the remaining SiO2 leaving the suspended segment untouched. To ensure low contact resistance (NH4)2Sx oxide removal procedure30 was used prior to evaporation of the contacts. Schematic representation and an SEM image of the NW device are shown in Figure 2a,b, respectively. The NW used in this device was 470 nm long with a diameter of about 50 nm. All measurements were done in a 0.35 K in He3 refrigerator. The sample was placed inside the sample space of the refrigerator and pumped to 10-5 Torr. We found that placing the NW device in high vacuum leads to significant increase in conductance (up to a factor of 10), which is most likely explained by desorption of molecules trapped on the nanowire surface. The backgate voltage Vg was applied directly to the local backgate. The differential conductance G was measured using AC lock-in technique with an excitation voltage Vac ) 10 µV and frequency ∼2 kHz using a wideband current preamplifier (see Figure 2a). The typical linear conductance G as a function of backgate voltage is shown in Figure 2c. Close to the pinch-off voltage (Vg ) -10 to -5 V) the device exhibited Coulomb blockade oscillations. Figure 3a presents the grayscale plot of the conductance at finite DC-bias Vsd close to the pinch-off. The observed diamond-shape structure is typical of nonequilibrium transport through a quantum dot (QD) in the Coulomb blockade regime. The pair of tunneling barriers required to confine a QD, must originate from the nonuniform distribution of the electric field induced by the gate (Figure 3b). In the vicinity of the source and drain contacts the lines of the electric field, E¯gate, tend to terminate in the large metal contacts rather than in the NW itself, thus resulting in a reduced carrier density at the edges, effectively acting as a pair of barriers (Figure 3c). The vertical and horizontal dimensions of the Coulomb diamonds provide the © 2010 American Chemical Society
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FIGURE 3. Transport through the NW device. (a) Vg - Vsd grayscale conductance plot of the Coulomb Blockade region. The dimensions of the Coulomb diamond provide values of gate capacitance Cg ) e/∆Vg and charging energy εc ) e/Ctot. Arrow points to the zero-bias anomaly originated from the Kondo effect. (b) Schematic cross-section of the NW device illustrating the nonhomogenous distribution of electric field E¯gate. (c) Schematic conduction band diagram and representation of the Fabry-Pe´rot process. z-axis directed along the nanowire. (d) The Vg Vsd grayscale conductance plot of the delocalized region showing the chess-board pattern typical for Fabry-Pe´rot oscillations. (e) Energy dispersion of two 1D subbands E1 and E2 for electrons moving along the z-axis. Here EF is the Fermi level of the system. Circles depicting the energy quantization due to quantized value of kF with corresponding energy spacing ∆Ez. Solid and empty circles relate to occupied and unoccupied states, respectively.
feasible reason for these oscillations is Fabry-Pe´rot-type interference of electrons, in a similar fashion to that observed in ballistic carbon nanotubes.37-39 Note that despite the fact that the Fermi level lies above the barriers, electrons experience weak reflections40 allowing Fabry-Pe´rot interference (schematically depicted in Figure 3c). Constructive interference is observed for kF2L ) 2πn, where n is integer and L is the length of the NW channel, setting the condition for the wavenumber kF ) nπ/L at which the constructive interference is expected. Combining this condition with the parabolic electron dispersion gives (Figure 3e)
µ ) EF - Ei )
why it is relatively easy to form ohmic contacts to InAs NWs and why the intentionally undoped NWs, grown in the cleanest MBE environment, have intrinsic n-type conductivity. It is, thus, reasonable to assume that the carriers in our NW devices are located near the surface and not in the bulk. At higher Vg, due to the asymmetric geometry of the backgate, the carriers are more likely concentrated at the bottom of the NW where the gate electric E¯gate is stronger, forming a crescent-like conductive channel. Near the pinch-off the carrier distribution seems to be reversed, namely the bottom of the NW is depleted and the carriers are concentrated at the top of the NW where the depleting E¯gate is weaker. In this case, the transverse confinement of the carriers necessary for 1D quantization arises from the combination of radial confinement in the accumulation layer and confinement along the arch of the crescent-like channel at the bottom of NW. At some particular value of Vg one would expect the carrier density to be uniformly distributed along the NW circumference, which results in 1D quantization on the NW circumference. This leads to the appearance of an additional degeneracy of 1D subbands due to either orbital movement42 or localization in the edges of the hexagonal NW.43 Unfortunately, we could not find any definite proof of additional degeneracy in our transport experiments, which does not necessarily exclude its existence. Considering what was said above we can conclude that unlike in the case of carbon nanotubes,37-39 where transport takes place only through the first 4-fold degenerate (spin and orbital movement) 1D subband the transport in our NWs occurs through two 2-fold degenerate (spin only) 1D subbands (in the range of G larger than 2e2/ h). Each of the subbands is characterized by its own value of Fermi wavenumber, having different accumulated electron phase. In accordance with the Landauer-Buttiker
p2kF2 p2π2n2 ) 2m* 2m*L2
where EF is the Fermi level, Ei is the bottom of the corresponding 1D subband and m* is the effective mass. Here the chemical potential µ is proportional to the gate voltage, µ ∝ RVg. Thus, the system can be tuned in and out of the constructive interference modulating the electron transmission through the NW, giving thus rise to conductance oscillations. These oscillations can also be interpreted as resonant transmission via virtual states with energy spacing ∆Ez, as schematically shown in Figure 3e. The experimental value of the level spacing ∆Ez can be estimated by the spacing in Vsd in the nonequilibrium conductance chess-board pattern (Figure 4a), changing with gate voltage from 0.5 to 0.7 meV. One important remark should be made on the details of the InAs NW band structure. It is widely accepted that the Fermi level at the surface of InAs NWs is pinned in the conduction band resulting in the surface accumulation layer.15,41 The presence of the accumulation layer explains © 2010 American Chemical Society
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FIGURE 4. Two zoomed-up regions of the Vg - Vsd grayscale conductance plot for Vg from 1 to 3 V (a) and from 6.5 to 8.5 V (b) clearly show the chess-board pattern of Fabry-Pe´rot oscillations. Conductance in the linear regime (Vsd ) 0 mV) is presented in the top insets. The period of oscillations ∆Vg ranges from approximately 0.2 to 0.3 V. The energy spacing ∆Ez ) 0.5-0.7 meV originates from the quantized values of kF.
formalism the total conductance is the sum of two independent 1D modes
G)
modes. Hence, for the estimation of the length L we used an averaged value ∆Vg ) 0.25 V. Using the value of the gate capacitance Cg ) 1.6 aF, estimated from the period of the Coulomb oscillations ∆VgCB, we determined Cg(L) ≈ 3 pF/m under the assumption that the quantum dot extends over the entire NW (length approximately 470 nm). By substituting the above values into eq 1, we found L ≈ 400 nm, which is close to the physical length of the NW device. This agreement and the fact that the Fabry-Pe´rot oscillations are well-developed, led us to suggest that the transport in our NW is also likely to be ballistic. If not, the carrier’s path length would have been randomized by scattering leading to the randomization of the phase and smearing of FabryPe´rot oscillations. These conclusions were verified by testing few other devices with different channel lengths measured at different temperatures. The Kondo effect at large negative gate voltage was commonly seen in our devices as well. Some examples of the data taken from other NW devices can be found in the Supporting Information. Despite the claim of observing ballistic transport, we make here, more technological effort is needed to eliminate the nonhomogeneous carrier density distribution in order to demonstrate a definite proof of ballistic transport, namely by observing clear 1D conductance quantization.45 At the end, we address some important technical issues. First, the significance of the suspended NW device geometry must be emphasized. We found that regardless of the crystalline quality of the NWs the conductance as a function of Vg of devices contacted in the conventional unsuspended geometry exhibited random switchings and hysteresis over the whole range of Vg regardless of the stabilization time allowed. On the contrary, the suspended NW devices showed excellent weeks-long stability of the conductance over the entire range of Vg. Second, extra care should be taken to ensure the cleanness of the NW surface from resist residue and adsorbed molecules. Our observations suggest that the resist residue promotes surface absorption, resulting in a decrease in the conductance at Vg ) 0. In addition to the thorough cleaning
2e2 [T (V ) + T2(Vg)] h 1 g
where T1(Vg) and T2(Vg) are the gate voltage-dependent transmissions probabilities through the first and second 1D subbands, respectively. We believe that the slowly changing background of the conductance is largely due to the beating between two independently oscillating transmissions probabilities T1(Vg) and T2(Vg). A simple model illustrating this beating behavior is given in the Supporting Information. Nevertheless, we cannot disregard the possible presence of impurities adsorbed on the NW surface, potentially leading to weak backscattering, which may be strongly dependent on the gate voltage causing similar changing of the background. The above model provides only a qualitative explanation of the oscillations. More accurate description of the energy spectrum and transmission requires detailed knowledge of the band structure of WZ InAs and the potential distribution along the wire. Although little is known about the energy spectrum of the NW some simple considerations allowed the following conclusion. The period of the Fabry-Pe´rot oscillations in Vg is directly related to the length L. The change of the Fermi wave vector over one period of the Fabry-Pe´rot oscillations is δkF ) π/L and the corresponding change in the carrier density is δn1D ) 2δkF/π ) Cg(L)∆VgFP/e, where Cg(L) is the gate capacitance per unit length and ∆VgFP is the oscillations period. Therefore, the length of the NW is44
L)
2e FP C(L) g ∆Vg
(1)
From Figure 3b ∆Vg ranges from about 0.2 to 0.3 V with the range likely to be related to the beating between two © 2010 American Chemical Society
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vacuum desorption of surface molecules should be performed. Normally, after few hours of pumping at room temperature and a pressure of about 10-5 Torr the sample conductance at Vg ) 0 rises by at least an order of magnitude, which clearly illustrates the distractive effect of the adsorbed molecules on the conductivity. Often the pumping procedure renders the sample from being insulating-type to metallic-type by increasing its conductance at room temperature to above 2e2/h. Fortunately, the suspended NW geometry makes the entire NW surface accessible for cleaning and avoids the problem of trapping of molecules and resist residue between the NW and the substrate. Third, we would like to point out that observation of the Fabry-Pe´rot oscillations was possible only with NWs in which the SFs were eliminated. From our experience the suspended NW devices bearing some SFs along the conducting channel (for example those made of NWs grown on conventional (111)B substrates) exhibit conductance behavior typical of UCF and similar to the one reported by Jespersen et al.,35 testifying that SFs are responsible for additional disorder. This is consistent with the correlation between the carriers mobility and density of SFs in InAs NWs recently demonstrated by Schroer and Petta.18 It is our believe that the combination of the improvements described above is essential for the observation of the Fabry-Pe´rot oscillations. To the best of our knowledge, no reliable data exists as yet on how the presence of Au atoms from the catalyst could affect the transport properties of InAs NWs. Detection of Au atoms in InAs NWs is a big technological challenge, unfortunately the reported results are so far inconclusive.20,21 We took all possible precautious in order to prevent the incorporation of Au atoms in our InAs NWs, thus minimizing its effect on conductance. Another important issue is related to the device gate capacitance. We noticed that the gate capacitance per unit length in our devices as expected from a cylinder-on-plate model46 is significantly larger than the value we found from the Coulomb blockade period (Figure 2a), 21 pF/m instead of 3 pF/m. This can be explained from the fact that the width and length of the ohmic contacts is much larger than the length of the NW and the distance to the backgate. This in turn, results in strong screening of the gate electric field, causing reduction of the gate capacitance. We carried out a 3D, finite element method simulation of a realistic NW device similar to the one used in the experiment and found that for a 50 nm diameter metallic NW with large contacts Cg(L) decreases from 21 pF/m for an infinite NW to about 8 pF/m for a 490 nm long NW, and to about 5 pF/m for a 280 nm long NW (see Supporting Information for more details). It was also pointed out previously19,47 that further reduction of gate capacitance is expected when the finite density-ofstates of the semiconductor NW is taken into account. In conclusion, we used suspended stacking-faults-free wurtzite InAs NWs grown by gold-assisted low-temperature VLS-MBE process to demonstrate multimode coherent elec© 2010 American Chemical Society
tron transport through Fabry-Pe´rot conductance oscillations at low-temperature. The length of the nanowire deduced from the period of the oscillations was in agreement with the physical length of the device, meaning that coherent transport takes place along its entire length. Good visibility of the Fabry-Pe´rot oscillations and their regularity over a wide range of gate voltage imply ballistic nature of the observed electron transport. We pointed out the possible causes for conductance oscillations and that more technological effort is needed to demonstrate clear conductance quantization. Acknowledgment. Authors are grateful to Moty Heiblum for making this work possible and for suggestions and critical remarks made during our work. We also acknowledge Michele Zaffalon and Sandra Foletti for sharing their experience and help on the early stage of the project, Anna Keselman for the help in GPE programming, Yunchul Chang, Yuval Oreg, David Goldhaber-Gordon, Shahal Ilani, Aveek Bid, and Anindya Das for fruitful discussions and useful suggestions made throughout the entire experiment and manuscript preparation. This work was partially supported by the EU FP6 Program Grant 506095 and Israeli Science Foundation Grant 530-08. Supporting Information Available. Supporting Information consists of three sections. In the first section some additional conductance oscillations data for two different devices is given (Supporting Information, Figure 1). The second section describes the simple model of multimode 1D transport and illustrates slowly changing conductance background observed in the experiment (Supporting Information, Figure 2). The third section discusses the three-dimensional electrostatic simulations made to estimate the gate capacitance of a realistic NW device (Supporting Information, Figure 3). This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2)
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DOI: 10.1021/nl101522j | Nano Lett. 2010, 10, 3439-–3445
