Microscopic metallic air-bridge arrays for connecting quantum devices
Y. Jin, M. Moreno, P. M. T. Vianez, W. K. Tan, J. P. Griffiths, I. Farrer, D. A. Ritchie, C. J. B. Ford
MMicroscopic metallic air-bridge arrays for connecting quantum devices
Y. Jin, M. Moreno, a) P. M. T. Vianez, a) W. K. Tan, J. P. Griffiths, I. Farrer, D. A. Ritchie, and C. J. B.Ford b) Semiconductor Physics Group, Department of Physics, Cavendish Laboratory, University of Cambridge, Cambridge,CB3 0HE, UK Departamento de F´ısica Aplicada, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca,Spain Department of Electronic & Electrical Engineering, University of Sheffield, Sheffield, S1 3JD,UK (Dated: 12 February 2021)
We present a single-exposure fabrication technique for a very large array of microscopic air-bridges using atri-layer resist process with electron-beam lithography. The technique is capable of forming air-bridges withstrong metal-metal or metal-substrate connections. This was demonstrated by its application in an electrontunnelling device consisting of 400 identical surface gates for defining quantum wires, where the air-bridgesare used as suspended connections for the surface gates. This technique enables us to create a large array ofuniform one-dimensional channels that are open at both ends. In this article, we outline the details of thefabrication process, together with a study and the solution of the challenges present in the development ofthe technique, which includes the use of water-IPA developer, calibration of resist thickness and numericalsimulation of the development.The successful interconnection of conducting layers iskey to the performance of printed or integrated circuits.When fabricating ultra-small specialised research deviceshowever, the process for depositing and patterning aninsulating layer to keep regions apart, or to space gatesaway from the surface in places, is complex and often af-fects operation. A straightforward and reliable methodfor bridging between regions is therefore highly desirableand can make possible much more complicated devicearchitectures for physics research. This is particularlyneeded in areas such as quantum computing, where in-terconnecting qubits can often prove challenging.Normal and cross-linked polymer resist (PMMA)has been used as a patterned insulator under metalbridges for studying quantum ring structures and anti-dots. Air-bridges have also been used in quantum-dot in-terference devices. In all these cases, the bridge playeda crucial role in connecting a central gate while leavingthe interference path undisturbed. Various methods havebeen employed for the fabrication of these bridges: Li,Chen, and Chou , for example, demonstrated a processwith nanoimprint lithography (NIL) for monolithic mi-crowave integrated circuits with air-bridges. While NILsimplifies repeated fabrication, its complexity is unsuit-able for rapid iteration of research prototypes. Instead,resist exposure is preferable. Photo-resist can be par-tially cross-linked and later removed to form an air gapbelow the bridge. One drawback of cross-linking, how-ever, is that it is susceptible to pattern distortion dueto swelling of the resist, hence making it unsuitable fordense sub-micron patterns. a) These authors have contributed equally to this work. b) Author to whom correspondence should be addressed:[email protected]
An alternative approach is variable exposure: theelectron-beam penetration depth into the resist can becontrolled by varying the acceleration voltage and dose ona single layer of PMMA resist in a one-stage exposure, and polyimide and double-layer PMMA can be combinedin a two-stage technique. In the former method, varyingthe acceleration voltage has the undesirable consequenceof changing the focus and alignment and the low accel-eration voltage limits the electron-beam resolution. Thelatter method does not suffer from these drawbacks butdoes involve the use of two lithography stages.In this letter, we present a process with the combinedadvantages of the single-stage exposure and multiple-resist methods, in order to fabricate large numbers offine-feature air-bridges with very high yield. We haveoptimized the process by using a water/IPA mixture todevelop the PMMA. This minimizes residual resist andgives good exposure contrast. We show results from aset of 1D wires defined using an array of gates linked by ∼
400 air-bridges. We note however that we have regu-larly used this technique to fabricate devices with up to ∼ µ m in length and thereforeshould be useful in a wide range of nanodevices made forresearch purposes.The development of our air-bridge technique was mo-tivated by the need to fabricate arrays of 1D chan-nels in order to study the exotic properties of electron-electron interactions. Figure 1a demonstrates the ge-ometry of the array under scanning electron microscopy(SEM). The substrate is a GaAs/AlGaAs heterostructurethat contains two parallel quantum wells separated bya 14 nm-thick tunnel barrier, which allows electron tun-nelling. A 1D electron channel is formed underneath thenarrow region between each pair of metallic gates whenthey are negatively biased. Each device consists of a largenumber of identical channels organized into multiple sets a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b (b)(a) Co-polymerPMMA 100kPMMA 950k Bridge dosePedestal doseGate metal (c)(d) (e)
FIG. 1. (a) SEM images of a 1D tunnelling device. 1D channels are formed beneath the narrow regions between two depletiongates. The tunnel device contains multiple columns of identical depletion gates that are inter-connected by air-bridges withoutclosing the channels, as well as crossing over other device structures. Inset: SEM micrograph of a bridge 10 µ m long. (b)–(e)Air-bridge fabrication by our three-layer PMMA single-exposure process: (b) Triple-layer resist spin-coated on sample surface.(c) Selective exposure by electron beam and development. Regions exposed to pedestal dose are completely cleared afterdevelopment while regions exposed to bridge dose have the 950k layer intact. (d) Gate metallization by thermal evaporation.(e) Lift-off leaves just the air-bridge pattern. of parallel wires to enhance the tunnelling current. Werequire the gates to be electrically connected while keep-ing the potential in the 1D channel as uniform as possiblealong its whole length. Consequently, bridges are neces-sary. An air gap, instead of a solid dielectric, providesminimal capacitive coupling between the bridge and the2D electron gas (2DEG) in the quantum well underneath,for a given gap height. Approximating the structure toa parallel-plate capacitor, the capacitance is given by C = ε A/ ( d sp /ε sp + d sub /ε sub ), where A is the area ofthe bridge, ε sp , ε sub are the dielectric constants of thespacer below the bridge and of the substrate above the2DEG, respectively, and d sp , d sub are their thicknesses.Therefore, C is minimized by minimizing ε sp (using anair gap), and maximizing d sp .Figure 1b-1e outlines the steps of our multilayer-resist/single-exposure air-bridge process. It begins withthe spin coating of the sample with three different re-sist layers, firstly PMMA with molecular weight 950k,then MMA(8.5)MAA copolymer and finally 100k PMMA(Figure 1b). Next, the sample is patterned by electron-beam lithography (EBL) using two well calibrated doses D p and D b , referred to as the pedestal dose and thebridge dose, respectively. D p is capable of fully exposingall three resist layers, while D b is only able to expose thetop two and leaves the bottom layer unaffected, because 950k PMMA has much lower sensitivity than the otherresists. The resist profile after development is shown inFigure 1c, where areas exposed by D p have been com-pletely cleared and those exposed by D b are still coveredin 950k PMMA. The copolymer is far more sensitive thanthe PMMA and so the middle layer is undercut relativeto the top layer, which aids with the removal of residualmetal during lift-off. An air-bridge structure is formedwhen gate metal is evaporated on top (Figure 1d) andremains on the sample after the resists are stripped off(lift-off, Figure 1e). Metal over the D p region is in di-rect contact with the substrate, and is referred to as thepedestal. ‘Bridge‘ regions exposed at D b are covered inmetal separated from the substrate by an air gap but an-chored to the substrate via pedestals. The thickness ofthe bottom layer of resist after development correspondsto the height of the air gap below the bridge, which inour samples is approximately ∼
100 nm.In order to achieve a reliable process, it is necessaryto precisely control the thickness and uniformity of theresists. Using ellipsometry, we calibrated the thicknessas a function of spinner rotation speed for each type ofresist using test wafers. Additionally, after each layer wasspin-coated on the actual sample, an ellipsometry mea-surement was performed to confirm that the resist waswithin ±
10 nm of the target thickness. For the reported
FIG. 2. Differentiated AFM images of resists treated by var-ious development methods: (a) Three layers of resist (100k,copolymer, 950k) developed at room temperature ( ∼ ° C)for 30 seconds in 3:1 IPA/MIBK. (b) The same sample asin (a) after 15 seconds of plasma ashing at 50 W. (c, d)Two layers of resist (copolymer, 950k) developed at roomtemperature for 5 seconds in (c) 3:7 water-IPA and (d)3:1:1.5% IPA/MIBK/MEK (methyl ethyl ketone). Corre-sponding cross-sections of the resist height along lines 1 and2 are shown above or below each image. sample, we applied 133 nm of 950k, 297 nm of copolymerand 128 nm of 100k resists using 60-second spins at 5700,4500 and 6000 RPM, respectively. The target thicknesseswere 130, 300 and 130 nm. We note, however, that thethickness can be changed and successful samples havebeen obtained within ±
20 % of these values after ad-justing for the e-beam dose. The dilution ratios of theresist solutions were: 4% (w/w) 950k PMMA in anisolediluted with methyl isobutyl ketone (MIBK) in 2:1 vol-ume ratio, 9% (w/w) copolymer in ethyl lactate and 100kPMMA (undiluted). The base doses received by the re-sist for the exposure of the pedestals and bridges were 880and 600 µ C/cm , respectively Prior to the resists beingapplied, the sample was baked on a 150 ° C hotplate for10 minutes to eliminate moisture. After each layer wasapplied, the sample was also further baked on a 110 ° Chotplate for 10 minutes to dry off solvents in the resist.Finally, we note that when spinning, particularly for the100k resist, significantly better uniformity was obtainedwhen using a metal as opposed to a PTFE stage.The most significant challenge of the air-bridge pro-cess is achieving good adhesion between the pedestals and the underlying material. For our device this meantthe metal-to-metal contact between the pedestals and the1D channel gates. The standard development techniquewith 3 : 1 MIBK:IPA (isopropanol) developer was foundto be unreliable as the resulting air-bridges often brokeaway from the sample during lift-off. Atomic force mi-croscopy (AFM) showed the cause of this type of fail-ure to be trace amounts of residual resist after devel-opment. Figure 2 shows a comparison of AFM scansof the same exposure pattern on 950k PMMA treatedby different developers. The EBL doses and develop-ment times used in these results were such that the sub-strate was expected to be fully exposed after develop-ment. The images demonstrate that the choice of devel-oper has substantial impact on the surface roughness ofthe developed region. As is shown in Figure 2(b), thesurface roughness can be reduced by RF plasma ashing,suggesting these are resist residues. Since plasma ash-ing attacks both the residue and the unexposed resist, itmay also cause damage to the ultra-fine resist patterns.The safer option is therefore to adopt the developer thatleaves the least amount of resist residue after develop-ment. The use of water/IPA mixture to develop PMMAwas studied by Yasin.
Owing to the high sensitivityof the water/IPA developer at room temperature, we con-ducted the development at (5 . ± . ° C with the use oftemperature-controlled water bath, in order to limit therate of development and increase the tolerance to timingerror in the process. The lower temperature also resultsin higher contrast. The samples were immersed in pre-cooled beakers of water/IPA mixture with manual agita-tion. No rinse was used at the end of development, asimmersing the sample in pure water or IPA after devel-opment can increase the development rate and was alsofound to deposit precipitates on the sample surface. Thebest result was produced when the samples were removedimmediately from the developer and dried with nitrogengas.In order to calibrate D p and D b for the triple-layerprocess, we determined the sensitivity curves of the threetypes of EBL resist by measuring the depths of developedresist as functions of electron-beam dose. Measurementswere made on 200 × µ m rectangular test patterns,as well as fine gratings with 2 µ m width and 2 µ m sepa-rations. Both types of patterns were exposed with 100 kVacceleration voltage on a Vistec VB6 system over a rangeof doses. The development depth was measured both bya Dektak surface profiler and an AFM, with the formermethod applied to the rectangular patterns and the lat-ter to the fine gratings. Figure 3 shows the normalizeddevelopment depth of different types of resist as func-tions of EBL dose. When dose is plotted on logarithmicscale, the negative of the gradient of the linear part of thecurve is the contrast γ . We note that the contrast mea-sured in our calibration is similar to the values reportedby Rooks. A polynomial fit to each of these curves wasused to estimate the rate of development at any arbitrarydose. To give insight into the development process, we
100 200 300 400 500 600 700
E-beam dose ( C/cm ) N o r m a li s ed dep t h o f de v e l op m en t =5.91=6.39=7.34=4.52=5.91=6.39=7.34=4.52=5.91=6.39=7.34=4.52 Copolymer AFMCopolymer Dektak100k AFM100k Dektak495k AFM495k Dektak950k AFM950k Dektak
FIG. 3. Contrast curves of different EBL resists based ondevelopment depth after 30 seconds of immersion at 5 ° C in 3:7water/IPA. Each data series is normalized to the undevelopedthickness of the corresponding type of resist (here, 146 nm for950k, 313 nm for copolymer and 105 nm for 100k resists). Thecontrast γ refers to the gradient of the linear region of thecurve. have developed a numerical model of the process withthe electron-beam dose and development time as input.Our calculation assumes: 1. the development is a time-limited process, meaning development depth is alwaysproportional to time; 2. the development has a uniformrate as a function of dose, and is estimated from the con-trast curve; 3. the direction of development at each pointis normal to the surface there. Figure 4 shows the resultof this numerical calculation by displaying the evolutionof the resist profile in 5-second increments. The calcu-lation gives a similar hump of copolymer as seen in anunder-developed sample shown in the SEM image in theinset.Calculations performed using the average developmentrates from the measurements in Figure 3 imply that theoptimum development time should be around 35 s. How-ever, we found empirically that 60 s–70 s was required tofully develop the combined layers, with poor metal ad-hesion for development times at or below 55 s. This dis-crepancy is likely caused by variations in the rate as de-velopment progresses: solute builds up in the developer,slowing down the dissolution. Hence different structuresor depths may require different development times. Prac-tically however, this can be managed by dividing samplesinto multiple development batches and using an iterativescheme to home in on the optimum time for a particularsample or type of device.After development, we evaporated approximately 110–130 nm (i.e. roughly equal to the thickness of the baseresist) of gold at a rate of ∼ ° C for approximately 90min before finallift-off. Use of ultrasonication is not recommended at this
D=600 -200 0 200 400 600 800 1000 1200
Lateral position (nm) D ep t h ( n m ) G=1563 G=1045 G=1563
D=880D=880
FIG. 4. Results of a numerical model estimating the evolutionof resist profile as a function of electron-beam dose and time.Each contour differs from its closest neighbour by 5 secondsin development time. The figures at the top of each region arethe average EBL dose D required there, and the actual dose G given by the EBL machine after correcting for proximity-effect. The same spreading parameters were used in both themodel calculation and the proximity correction. Inset: SEMmicrograph of an under-developed sample showing a similarhump of copolymer as predicted by our model. stage as this was found to often result in damage to thebridges.We checked the integrity of the newly-fabricated air-bridge arrays by inspecting the sample under an opti-cal microscope. Except for sacrificial trial samples, werefrained from analysing any experimental device underSEM, so as to avoid potential contamination by electron-beam-induced deposition. Although individual elementsof the array cannot be clearly resolved under an opticalmicroscope, the large number of repeating units producesa uniform and iridescent appearance of the entire struc-ture. In practice, optical inspection can therefore easilyreveal defects in the two EBL layers, with the most com-mon modes of failure being incomplete lift-off after thebase layer metallisation, and poor adhesion between theair-bridge pedestals and the underlying base-layer metal.Both types of failure lead to defects that distort the uni-form appearance of the array and are easily visible un-der optical microscopy. After optical inspection, sampleswere tested further for electrical continuity between con-tacts. We also checked that the air-bridge-connected wiregates did not short to other nearby control gates.Finally, we present some typical measurements of oneof our air-bridge devices. Details of the sample layoutand experimental setup can be found elsewhere. Fig-
Magnetic fi eld B (T) -0.20 1 2 3 4 5-505 -0.400.20.4 V D C ( m V ) d G/ d V DC ( μ S/mV)(a) (b)-15-10Magnetic fi eld B (T)0 1 2 3 4 5-0.6-0.55-0.5-0.45-0.4-0.35-0.3 -5051015 W i r e g a t e v o l t a g e V W G ( V ) dG/dV WG ( μ S/V)
FIG. 5. (a) Derivative of the equilibrium tunneling conductance G of the resonance device with respect to the 1D wire-gatevoltage V WG vs magnetic field B and V WG , at T = 0 . B . The black dashed curves mark the 2D bandand the 1D subbands. Three 1D subbands can be resolved, with the last subband cutting off at V WG ∼ − .
55 V. (b) Tunnellingdifferential d G/ d V DC vs B and the DC bias V DC between the two quantum wells, with V WG held at − .
515 V. The parabolaeindicate the positions of the calculated dispersions of the 1D subbands. At this wire-gate voltage, only a single 1D subband isobserved. The magenta/blue parabolae mark the observed dispersions resulting from 1D-2D tunnelling. The black parabolaecorrespond to the dispersions of the background ‘parasitic‘ tunnelling region. ure 5a shows an intensity map of the equilibrium tun-nelling conductance (i. e. at zero DC bias V DC betweenthe wells) between the two quantum wells of the deviceas a function of the in-plane magnetic field B and the1D wire-gate voltage V WG . The dashed lines highlightthe positions of the local maxima of the tunnelling con-ductance. Figure 5b shows the tunnelling conductancedifferential d G/ d V DC measured in terms of B and V DC between the wells, while the 1D wire gates are held at − .
515 V. For an electron to tunnel between the quan-tum wells, the difference in energy between its initial andfinal states must be provided by eV DC , and the canoni-cal momentum boosted by the Lorentz force, ∝ B . Themaximum conductance is therefore observed when theFermi energy and wavevector of one (2D) system tracksthe dispersion of the other (1D) system, revealing the dis-persions of the electron subbands, which are found to beessentially parabolic. Detailed fitting of these dispersionsreveals the existence of strong electron-electron interac-tions in the 1D wires, including separate spin and chargemodes. Since G is summed over the ∼
400 1D channels ina single device, the fact that that we are able to resolvethe 1D subband structure clearly (Fig. 5a) demonstratesthe high degree of uniformity of the wire-gate array, andthat the air-bridge structure connecting the gate arrayperforms reliably.In conclusion, we have demonstrated a process that iscapable of reliably fabricating large arrays of air-bridges in a single step of EBL exposure. The essential stepsto the process are: 1. Careful control of the thickness ofdeposited resist; 2. Accurate calibration of the dose curve;3. Use of a water/IPA developer to improve the adhesionof the air-bridge pedestals. The process is suitable forfast iteration of prototype or research devices and can begeneralised to other substrate materials and metals.Acknowledgements: The authors would like to thankYunchul Chung (Pusan National University, SouthKorea) for advice on air-bridge fabrication. Thiswork was supported by the UK EPSRC [Grant Nos.EP/J01690X/1 and EP/J016888/1]. P.M.T.V. ac-knowledges financial support from EPSRC Interna-tional Doctoral Scholars studentship via grant numberEP/N509620/1.
DATA AVAILABILITY
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