Top-gate defined double quantum dots in InAs nanowiresA. Pfund, I. Shorubalko, R. Leturcq, and K. Ensslin Citation: Applied Physics Letters 89, 252106 (2006); doi: 10.1063/1.2409625 View online: http://dx.doi.org/10.1063/1.2409625 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/89/25?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Morphological and temperature-dependent optical properties of InAs quantum dots on GaAs nanowires withdifferent InAs coverage Appl. Phys. Lett. 103, 172102 (2013); 10.1063/1.4826612 Site-controlled formation of InAs/GaAs quantum-dot-in-nanowires for single photon emitters Appl. Phys. Lett. 100, 263101 (2012); 10.1063/1.4731208 Tunable double dots and Kondo enhanced Andreev transport in InAs nanowires J. Vac. Sci. Technol. B 26, 1609 (2008); 10.1116/1.2839634 Single electron pumping in InAs nanowire double quantum dots Appl. Phys. Lett. 91, 052109 (2007); 10.1063/1.2767197 Scanning gate microscopy of InAs nanowires Appl. Phys. Lett. 90, 233118 (2007); 10.1063/1.2746422

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Top-gate defined double quantum dots in InAs nanowiresA. Pfund, I. Shorubalko, R. Leturcq, and K. Ensslina�

Solid State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland

�Received 30 August 2006; accepted 9 October 2006; published online 19 December 2006�

The authors present low temperature transport measurements on double quantum dots in InAsnanowires grown by metal-organic vapor phase epitaxy. Two dots in series are created bylithographically defined top gates with a procedure involving no extra insulating layer. The authorsdemonstrate the full tunability from strong to weak coupling between the dots. The quantummechanical nature of the coupling leads to the formation of a molecular state extending over bothdots. The excitation spectra of the individual dots are observable by their signatures in the nonlineartransport. © 2006 American Institute of Physics. �DOI: 10.1063/1.2409625�

Semiconductor nanowires �NWs� are gaining interest aspossible building blocks in new bottom-up nanoelectronicsand as versatile systems for transport studies in reduced di-mensions. Self-assembled or catalyzed epitaxial growth hasbeen realized with large control over structural parameterssuch as diameter, length, crystal structure, and position of thenanowires.1,2 Among the III-V semiconductors, InAs is char-acterized by a small effective mass, a large effective g* fac-tor, and strong spin-orbit interaction. InAs is therefore con-sidered as a promising material for the investigation ofquantum mechanical and spin related phenomena in elec-tronic transport. Single charges and spins can be studied inquantum dots3–5 and are envisioned as candidates for quan-tum bits �qubits� in solid-state-based quantum computers.6

Coupled systems such as double quantum dots appear to beespecially promising in this context due to the possibility tocontrol the entanglement of spins by tuning the exchangecoupling between the dots.7,8 Reliable readout and manipu-lation schemes for qubit states in dots have beendemonstrated.9,10 A crucial prerequisite for these schemes isa good tunability of the tunnel barriers, energy levels, andparticularly the quantum mechanical coupling of the twodots.

Here we describe a technologically simple and reliableprocess to create top-gate-defined double quantum dots inInAs NWs. We present transport measurements demonstrat-ing the full tunability of the interdot coupling, ranging froman artificial “quantum-dot molecule” to weakly capacitivelycoupled quantum dots. Beyond that, nonlinear transport mea-surements at finite bias clearly reveal the excitation spectrumof the individual dots.

Following the pioneering experiments published in Refs.11 and 12, we grow InAs NWs on �111�B oriented GaAssubstrates by metal-organic vapor phase epitaxy. The growthprocess is catalyzed by monodisperse Au particles with di-ameters of 40 nm. The resulting NWs are between 5 and10 �m long and have diameters around 100 nm. Theyemerge with crystalline facets and hexagonal cross section.After growth, the NWs are transferred to a highly doped Sisubstrate covered by 300 nm of SiO2. No predefined markersare needed, since the NWs can be located optically and con-tacts are defined by a single optical lithography step. Beforemetallization with subsequent layers of Ti �20 nm� and Au�180 nm�, the contact areas are simultaneously etched and

passivated with a diluted solution of �NH4�2Sx.13 The result-

ing contacts are of good quality with contact resistances be-low 100 �. Finally, top-gate fingers are created by electronbeam lithography, followed by deposition of 6 nm Cr, 66 nmAu, and standard lift-off. Note that, for this step, no etchingand passivation are done, keeping a native surface oxidelayer of 1–3 nm thickness formed after our growthprocess.14 We find that this oxide is suitable to electricallyisolate the top gates for voltages in the range of at least±1 V. As a result, “half wraparound gates” are created withno additional deposition of an insulating layer between theNW and the top gates.15 Details of the fabrication processcan be found elsewhere.14 This approach is technologicallysimple compared to previously demonstrated methods, wherethe NW is locally gated with predefined back-gate fingers,16

or for carbon nanotubes where the isolating oxide is obtainedby deposition.17,18 A scanning electron microscope image ofthe device and a schematic of the gates is shown in Figs. 1�a�and 1�b�.

We performed electrical measurements on two indepen-dent devices showing comparable behaviors. Data of onesample measured in a dilution refrigerator at a base tempera-ture of 30 mK are presented. Ungated pieces of the NW

a�Electronic mail: ensslin@phys.ethz.ch

FIG. 1. �Color online� �a� Scanning electron micrograph of a device similarto the one measured. Source �S� and drain �D� Ohmic contacts to the nano-wire �NW� are defined by optical lithography. Top gates GL, GR, and GChave width and spacing of about 70 nm. �b� Schematic showing the NWwith hexagonal cross section. The top gates are isolated by a native surfaceoxide layer �ox�. �c� Model for the analysis of the double dot system. CGL

and CGR are the capacitances coupling the gate voltages to the electrochemi-cal potential in the left �L� and right �R� dots, respectively. CS and CD

represent the electrostatic action of source and drain potential. Cm is themutual capacitive coupling between the two dots. A tunnel coupling t be-tween the two dots is also taken into account.

APPLIED PHYSICS LETTERS 89, 252106 �2006�

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show a resistance of around 10 k� per micrometer length.By measuring the conductance of ungated wires as a functionof the back-gate voltage, we determine an electron density of1018 cm−3 and an elastic mean free path of about 100 nm atzero back-gate voltage. With all top gates set to 0 V, theresistance between source �S� and drain �D� is above 1 M�.Applying +0.5 V to all top gates compensates for the pres-ence of the gate fingers and recovers the resistance of theungated device. Two quantum dots in series can be formedby reducing the voltages on gates GL, GC, and GR. Figure 2shows plots of the source-drain current ISD at VSD=140 �Vas a function of the voltages on left �VGL� and right �VGR� topgates for three different values of the center gate voltage�VGC�. In Fig. 2�a� no significant barrier is induced by GCand a single quantum dot is formed between GL and GR.The current exhibits Coulomb oscillations: peaks occur when

the electrochemical potential for the transition of an N elec-tron state to the N+1 electron state is aligned with the elec-trochemical potentials �S and �D in the contacts. ReducingVGC leads to the formation of a double-well potential andinduces a redistribution of the N electrons between the twovalleys �Fig. 2�b��. The electron numbers in the left and rightdots are denoted as n and m, respectively. For even smallerVGC, we obtain the characteristic honeycomb pattern for thecharge stability diagram of the double dot.19 Within eachhexagon of Fig. 2�c�, the charge configuration �n ,m� of thedouble dot is fixed. Elastic electron transport leading to highcurrent is only possible at the corners of the hexagons mark-ing the so-called triple points. Here, the electrochemical po-tentials of the n→n+1 electron transition in the left dot andthe m→m+1 electron transition in the right dot are alignedwith �S and �D. The series shown in Fig. 2 demonstrates thetunability from one large single dot to two mainly capaci-tively coupled dots.

At finite bias, the degeneracy points between differentcharge configurations develop into triangular regions of in-creased conductance �Fig. 3; Ref. 20�. Inside these triangles,current flows due to inelastic tunneling processes. With amodel of purely capacitively coupled dots,19 we can extractall capacitances �as defined in Fig. 1�c�� of the double dotsystem. From the dimensions of the honeycomb cells��VGL,�VGR�, we obtain the capacitances of GL on the leftdot �GR on the right dot� as CGL= �e� /�VGL=13.7 aF �CGR

=12.7 aF�. Equating the sizes of the triangles ��VGL,�VGL�to the applied bias VSD, the lever arms for conversion of gatevoltages into energies follow to be �L=0.46 and �R=0.41.The corresponding total capacitances of the left �right� dot,CL=CGL/�L=29.7 aF �CR=30.7 aF� imply single dot charg-ing energies EC

L =e2CR / �CLCR−Cm2 ��e2 /CL=5.4 meV �EC

R

�5.2 meV�. These values are consistent with Coulombblockade measurements on the individual dots between twoneighboring gates �not shown here�. Assuming spherical dotsembedded in InAs ��r=15�, the capacitances imply radii R=CL,R /4��0�r�18 nm, which are consistent with the litho-graphic dimensions. Considering electron densities of around1018 cm−3 in the NWs,14 we estimate the number of electronsto be less than 20 in the dots. The mutual capacitance be-tween the dots is related to the splittings of the triple points

FIG. 2. �Color online� Source-drain current ISD as a function of left andright gate voltages for different center gate voltages at fixed bias VSD

=140 �V. �a� At VGC= +200 mV, an effective single dot is formed. Thetotal number of electrons between the Coulomb peaks is fixed �N ,N+1, . . . �. �b� VGC=0 mV. Electrons are redistributed in the double well po-tential. �c� VGC=−120 mV yields the charge-stability diagram for two ca-pacitively coupled dots. �d� Zoom around one pair of degeneracy points. Thedeviation from the capacitive model �dashed lines� is clearly visible �seearrow�.

FIG. 3. �Color online� �a� Measurement of ISD as in Fig.2, but at finite bias VSD=1.2 mV. VGC=−120 mV. Fromthe dimensions of the honeycombs and bias triangles,all capacitances of the system can be extracted �seetext�. �b� Zoom into one pair of degeneracy points.Lines starting at points X and X� are explained by ex-cited states. �c� Possible scenario for the level align-ment at points A, B, C, and X.

252106-2 Pfund et al. Appl. Phys. Lett. 89, 252106 �2006�

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�VGL,Rm by �VGL,R

m = �e�Cm /CLCR, which leads to Cm�2.8 aF.

Quantum mechanical tunnel coupling between the statesin both dots induces the formation of molecular states whichare extended over the whole double dot system.21 The pres-ence of tunneling is clearly indicated by the rounded cornersof the honeycombs in the vicinity of the triple points �Figs.2�c� and 2�d��. A Heitler-London picture for two degeneratequantum levels has proven to give a good qualitative andquantitative description for the curvature around the degen-eracy points.22,23 In this model, the spacing of two neighbor-ing triple points is approximately given by �m+2t, wheret is the tunnel coupling between the levels and �m=2e2Cm / �CLCR−Cm

2 � is the total capacitive splitting of thetriple points.22 Neglecting the tunnel coupling therefore leadsto an overestimation of the capacitive coupling energy. Azoom around one pair of triple points is shown in Fig. 2�d�.The deviation from the purely capacitive model �dashedlines� is clearly visible. From the magnitude of the anticross-ing, we estimate a tunnel coupling of t=0.27 meV. The ex-tracted capacitive interdot coupling �m=0.87 meV impliesCm�2.5 aF. This is consistent with the capacitive analysisdescribed above, considering the expected overestimation inthe latter case. The strong tunnel coupling can also explainthe shape of the upper triangles in Fig. 3�a�: large current canflow out of the triangles defined by the bias voltage due tosequential tunneling through superposed double dot states ofthe form �E�=c1�n+1,m�+c2�n ,m+1� with complex coeffi-cients c1 and c2.24

Another impact of quantum mechanics on transportthrough the double dot appears in the fine structure of thefinite bias triangles. As can be seen in Fig. 3�b�, stripes ofhigh current emerge on the background of inelastic transport.These lines arise due to elastic transport when levels origi-nating from excited dot states are in resonance with �S.19

Note that in this case, the features are explained with excitedorbital states in the two individual dots rather than by mo-lecular states. These states give rise to different electro-chemical potentials for a transition �n ,m�→ �n+1,m�. A pos-sible scenario is described by the scheme in Fig. 3�c�. At thelower left corner �A� of the triangles, the ground state levelsare aligned with each other and with �S. Tuning the top gatesalong the line from point A to B, the potential in the right dotis lowered until the ground state is in resonance with �D.Varying the gates along the connection from A to C pullsdown the levels in both dots simultaneously. At the pointslabeled with X �and similarly for X��, chemical potentials fortransitions involving excited states �dashed lines in Fig. 3�c��enter the bias window, giving rise to an increased current.

In conclusion, we have realized top-gate-defined doublequantum dots in InAs nanowires. The full tunability of theinterdot coupling could be demonstrated. We analyzed allcharacteristic capacitances of the system in a classical elec-trostatic model and quantified the tunnel coupling leading tothe formation of a molecular state in the double dot. Thepresence of excited quantum states is observed in the trans-

port at finite bias. This system therefore appears to be suit-able for further experiments on controlling entanglement bytuning the exchange coupling between single spins.

The authors thank M. T. Borgström and E. Gini for ad-vises in the growth. They also acknowledge financial supportfrom the ETH Zurich. One of the authors �I.S.� thanks theEuropean Commission for a Marie-Curie fellowship.

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