Non-adiabatic single-electron pump in a dopant-free GaAs/AlGaAs 2DEG
B. Buonacorsi, F. Sfigakis, A. Shetty, M. C. Tam, H. S. Kim, S.R. Harrigan, F. Hohls, M. E. Reimer, Z. R. Wasilewski, J. Baugh
NNon-adiabatic single-electron pump in a dopant-free GaAs/AlGaAs 2DEG
B. Buonacorsi,
1, 2
F. Sfigakis,
1, 3, 4, a) A. Shetty,
1, 4
M. C. Tam,
5, 6
H. S. Kim,
5, 6
F. Hohls, M. E. Reimer,
1, 3, 5
Z. R. Wasilewski,
1, 2, 3, 5, 6 and J. Baugh
1, 2, 3, 4, 6, b) Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1,Canada Department of Physics, University of Waterloo, Waterloo N2L 3G1, Canada Northern Quantum Lights inc., Waterloo N2B 1N5, Canada Department of Chemistry, University of Waterloo, Waterloo N2L 3G1, Canada Department of Electrical and Computer Engineering, University of Waterloo, Waterloo N2L 3G1,Canada Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo N2L 3G1,Canada Physikalisch-Technische Bundesanstalt (PTB), 38116 Braunschweig, Germany
We demonstrate single-electron pumps in dopant-free GaAs 2DEGs with one-gate pumping, operating in zeromagnetic field at temperatures
T > I = nef , where e is the electron charge, f is the radiofrequency (RF) of an ac signal applied to a local gate(see circuit diagram in Figure 1), and n is the number ofelectrons pumped from source to drain during each RFcycle (see Figure 2). These pumps have been the subjectof several reviews, and have been variously referred toas tunable-barrier pumps, one-parameter pumps, ratchetpumps, or dynamic quantum dots. They do not requirean applied source-drain bias, operate at high frequen-cies ( ∼ GHz), and are distinct from adiabatic turnstilepumps, which require a finite source-drain bias and aminimum of two RF gates to operate (with f <
20 MHz).Following the 2019 re-definition of the ampere in the In-ternational System of Units (SI), non-adiabatic singleelectron pumps have emerged as candidates to serve asprimary standards for accurately measuring a ∼ In that vein, the most commonly used pumparchitectures for metrology involve modulation-doped GaAs/AlGaAs two-dimensional electron gases(2DEG), because of their simple operation (one-gatepumping), relative ease of fabrication, and high perfor-mance. The state-of-the-art relative uncertainty ( ± f > The easeof fabrication allows the positioning of non-invasivedetectors near pumps, thus enabling to individu-ally count pumped electrons and to identify errormechanisms, and allows the integration of pumpsinto more complex circuits, towards a self-referencedquantum current standard. However, challenges withmodulation-doped GaAs devices include cooldown-to-cooldown reproducibility, and the occurrence of random a) corresponding author: francois.sfi[email protected] b) [email protected] telegraph switching (RTS) events, i.e. intermittentshifts in gating characteristics of the device, due tounstable charge traps (dopant-related DX centers). Non-adiabatic pumps have also been realized in othermaterial systems: graphene, InAs nanowires, andsilicon. In some Si-based non-adiabatic pumps, thedynamic quantum dot consists of a charge trap locatednear the transport channel.
Some of these display su-perb pumping characteristics. However, their stochasticfabrication is problematic for integration with other on-chip circuitry ( e.g. , self-referenced standards or electronoptics). Conventional silicon-based pumps suffer lessfrom this particular problem, but it remains an issue tobe aware of. RTS noise is a challenge in Si-CMOS de-vices, due to charge traps in the amorphous SiO layerlocated immediately next to the 2DEG. Finally, one-gate pumping in Si-based devices is not as routine as inGaAs-based pumps, but work is ongoing at resolving thischallenge. The limitations described above could be circumventedby using GaAs-based dopant-free heterostructure-insulator-gate field effect transistor (HIGFET)geometry in the context of single-electron pumps.Dopant-free field effect transistors have already beenused to produce Hall bars, quantum wires, and quantum dots, with demonstrated superiorperformance in terms of low disorder,suppressed RTS noise, and cooldown-to-cooldown(even device-to-device) reproducibility relative to theirmodulation-doped counterparts.
In this Letter, we demonstrate non-adiabatic single-electron pumps in dopant-free GaAs 2DEGs (see Fig. 1)with one-gate pumping, no visible random telegraphswitching, operating in zero magnetic field at temper-atures
T > a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b FIG. 1. Measurement circuit diagram and scanning electronmicroscope (SEM) image of a single-electron pump (“box” de-sign) in a dopant-free 2DEG with gate layout design A, similarto device A1. A one-dimensional channel, defined electrostat-ically by gates V qpc1 and V qpc2 , is connected at both ends toa 2DEG (source and drain ohmic contacts (cid:2) ) induced by aglobal topgate deposited on top of the device (not shown).Entrance and exit barrier gates ( V ent and V exit ) are used toform a dynamically driven quantum dot (white dot); they areisolated from V qpc1 and V qpc2 by 30 nm of SiO . By RF mod-ulation of the entrance barrier voltage, electrons are collectedfrom the source and ejected into the drain, resulting in a time-averaged quantized current I = nef (see Fig. 3) measured bya DC current pre-amplifier at the 2DEG drain ( (cid:53) ). (A1, A2, A3, B1, B2), using two different gate layouts,design A and design B. Samples using design A (design B)were fabricated on heterostructures G371 (G370), whichwere both grown by molecular beam epitaxy (MBE) andhad the following sequence: starting from a 3” semi-insulating (SI) GaAs (100) substrate, a 200 nm GaAsbuffer, a 20-period smoothing superlattice composed of a2.5 nm GaAs layer and 2.5 nm Al . Ga . As layer, a 500nm GaAs layer, a 65 nm (80 nm) Al . Ga . As barrier forsamples A n (B n ), and a 10 nm GaAs cap layer. Therewas no doping anywhere in the structure. Using the fieldeffect from a topgate, a 2DEG is induced (enhancementmode) at the GaAs/AlGaAs interface located 90 nm (75nm) below the surface for wafer G371 (G370). Transportthrough the single-electron pump was oriented along thehigh mobility crystal direction [1¯10]. All data shown herecame from devices A1 and B1, the most studied out ofthe group of samples.Details of fabrication are otherwise identical to andextensively described in Ref. 39. Ti/Au gates ( V qpc inFig. 1), defining a 1D channel, were fabricated by electronbeam lithography directly on the surface of the GaAs cap,followed by 30 nm of SiO . Another set of Ti/Au gates( V exit and V ent in Fig. 1), defining an entrance barrierand exit barrier within the 1D channel, were also fabri-cated by electron beam lithography, followed by 270 nmof SiO . Above these layers, a Ti/Au overall topgate V tg ,overlapping the ohmic contacts, defines where the 2DEGwill form, and linearly varies the electron density n ,from n = 0 at V tg ≈ +0.5 Volts to n ≈ × /cm at V tg = +5.0 Volts. Unlike all other gate voltages, V ent is an RF gate: V ent = V dc + V rf sin(2 πf ), where V dc and FIG. 2. The four stages of operation for a tunable-barrierpump during one RF cycle. (a)
Loading . The entrance bar-rier V ent is brought below the Fermi level E F (dashed blackline) and many electrons (blue dots) load into the dot from thesource 2DEG. (b) Backtunneling . As the entrance barrieris raised, electrons backtunnel into the source 2DEG. Higherenergy electrons have faster backtunneling rates Γ i +1 > Γ i .(c) Capture . A small number of electrons are captured andremain in the quantum dot as the entrance barrier is raised.(d)
Ejection . When the entrance barrier rises above that ofthe exit barrier V exit , the electron is ejected from the quan-tum dot into the drain 2DEG. The entrance barrier is thenlowered back to the loading stage in the next RF cycle. V rf are DC and RF voltages, respectively, combined to-gether using a bias tee. Note the “box” shape of the V qpc gates in Figure 1: its purpose is to exclude the2DEG from forming in the vicinity of the V ent gate, andthus eliminate parasitic coupling between the 2DEG and V ent and the associated RF heating of electrons in thereservoirs. Under the combined actions of the V qpc , V exit , V ent , and V tg gates, a quantum dot forms and dis-solves during every RF cycle, which is why non-adiabaticpumps are sometimes called dynamic quantum dots. Figure 2 shows the operating principles of a non-adiabatic (ratchet) single-electron pump, depicting theenergy versus position profile in a cut along the arrow inFig. 1 at four distinct stages of a single RF cycle: load-ing, backtunneling, capture, and ejection. The number ofpumped electrons per RF cycle depends on the numberof electrons captured and ejected during those respectivestages, and these numbers are controlled by the DC volt-age components of the entrance and exit gates. Thus theaverage number of ejected electron (cid:104) n (cid:105) per RF cycle canbe directly and precisely tuned by V ent and V exit .The accuracy of a single-electron pump is determinedby the backtunneling stage. In an ideal pump ejecting ex-actly one electron per RF cycle, the backtunneling ratesof the last electron and second-to-last electron in thedynamic quantum dot would be Γ = 0 and Γ = ∞ ,respectively. If Γ (cid:54) = 0, then occasionally the last elec-tron will escape the dynamic quantum dot before it is FIG. 3. Quantized current from device A1 (black dots) at T = 1 . V qpc1 = V qpc2 = +0 .
18 V and V tg =+6 . I = nef , and the solid yellow linesare fits of the first quantized current plateau to Equation (1),and the figure of merit δ determined from the fits are stated. ejected, and no electron will be transferred from sourceto drain during that particular RF cycle. If Γ is fi-nite, the pump will occasionally eject two electrons in-stead of just one, because the second-to-last electron willnot have escaped back to the source 2DEG before theejection stage of the RF cycle. Thus, a good real-worldsingle-electron pump design ensures Γ (cid:28) Γ . However,the tunneling rates Γ , Γ are exponentially dependenton the time dependent gate voltage. A figure of merit ofthe pump is given by δ = ln(Γ / Γ ) + E c / ∆ ptb , where E c is the maximum charging energy of the dynamic quan-tum dot and ∆ ptb is the plunger-to-barrier ratio of theentrance gate V ent . The first term in the expression for δ comes from the tunnelling selectivity described above,and the second term accounts for different start times ofbacktunnelling. Furthermore, it can be shown thatln(Γ / Γ ) ∼ E c , so that δ can be expressed in terms ofthe charging energy only. The larger the value of δ ,the better the current quantization (flatter plateau andsteeper plateau steps) and its accuracy. The uni-versal decay cascade model is used to fit the first quan-tized current plateau of a single-electron pump: I = ef (cid:88) n =1 , exp (cid:18) − exp (cid:2) − a ( V exit − V )+ δ ( n − (cid:3)(cid:19) (1)where a and δ are fitting parameters, and V is the posi-tion in gate voltage of the first plateau.Figure 3 demonstrates electron pumping in device A1at different driving frequencies. The current is clearlyquantized at the expected integer average number ofelectrons pumped per RF cycle, (cid:104) n (cid:105) . Quantization isstrongest for the (cid:104) n (cid:105) = 1 plateaus and weakens as (cid:104) n (cid:105) increases, consistent with the charging energy of the dy-namic quantum dot (and hence δ ) decreasing with in-creasing gate voltage. As the driving frequency increasesfrom 500 MHz to 850 MHz, V rf had to be correspond-ingly increased from 1.0 V to 1.6 V to compensate forthe higher transmission line losses in order to maintainthe same effective peak-to-peak RF voltage at the deviceto produce quantized current plateaus, whereas V dc did FIG. 4. Pumping map of device A1, with experimental pa-rameters f = 500 MHz, V qpc1 = V qpc2 = +0.18 V, V tg = +6.0V, V rf = 1.1 V (+11 dBm), and T = 1 . | dI pump /dV ent | . Current plateaus arelabeled according to the number of electrons pumped per RFcycle. Note the absence of random telegraph switching eventsand the wide voltage range over which the (cid:104) n (cid:105) = 1 plateauis flat. The 500 MHz data shown in Figure 3a was taken at V dc = 0 .
87 V and V rf = 1 . i.e. in slightlydifferent conditions than for the pump map shown above. not change significantly, from 0.87 V to 0.94 V.The decay cascade model eqn. (1) is fit to the (cid:104) n (cid:105) = 1quantized current plateaus in Figure 3. The resulting fit(yellow solid line) is overlaid on the experimental data.Using the fit, we can estimate the expected error (cid:15) p, est ofthe pumped current accuracy with (cid:15) p, est = 1 −(cid:104) n fit (cid:105) at thepoint of inflection of the fitted plateau. The estimatederror (cid:15) p, est we obtained is 1.7 ppm (40 ppm) for the f =500 MHz ( f = 850 MHz) trace. While these are onlyestimated values, we expect the true pump error (cid:15) p to bewithin an order of magnitude of (cid:15) p, est . If our estimatederror (1.7 ppm) for the f = 500 MHz data is correct,it would be near in performance to the state-of-the-artGaAs electron pumps found in the literature. This isall the more remarkable since the best performance ofstate-of-the-art GaAs pumps is typically achieved onlyin large magnetic fields ( B = 9 −
16 T), whereas ourmeasurements were performed at B = 0.Figure 4 shows a pump map of device A1, whichconsists of the derivative | dI pump /dV ent | . The pumpedcurrent traces in Figure 3 would appear as horizontalline cuts on the map. When the color is dark blue,the pumped current is either I = 0 or on a quan-tized plateau. The bright yellow lines correspond tocurrent steps between quantized plateaus. The slant inthe plateau boundary lines is attributed to RF couplingbetween the entrance and exit gates, mediated throughthe V qpc gates. The principal feature of this map is theabsence of random telegraph switching, i.e. intermittentshifts in gating characteristics of the device. The fine FIG. 5. Temperature dependence of single-electron pumpingin device B1, with experimental parameters f = 150 MHz, V qpc1 = V qpc2 = +0.15 V, V tg = +5.0 V, V rf = 1.2 V, and V dc = 1.0 V. The upper inset shows a top view of the modifiedgate layout of device B1 relative to device A1. speckle seen in the current steps is most likely electri-cal pick-up noise (each data point was averaged for lessthan 0.3 seconds). Another key feature of Figure 4 isthe wide gate voltage range over which the first quan-tized plateau extends ( ∼
80 mV for V exit and more than400 mV for V ent , along the longest cut of either axis). For comparison, the (cid:104) n (cid:105) = 1 plateau in state-of-the-artGaAs-based pumps is only 20-40 mV long in exit gatevoltage. This suggests dopant-free single-electronpumps could be “robust”, with invariance of the pumpedcurrent against small changes in the experimental con-trol parameters. Robustness is required for any primarymetrological standard.
The main panel of Figure 5 shows four fully quantizedcurrent plateaus at T = 1 . δ = 11 . At T = 1 . At T = 3 . B > most likely by increasingthe sensitivity of the tunnel rates Γ i to the varying po-tential landscape as well as by suppressing non-adiabaticexcitations of the last electron to higher energy states. Single electron pumps have been studied in fields up to30 T, but no further improvement in accuracy was ob-served beyond B = 12 −
15 T. Using an arbitrary wave- form generator, an RF pulse can be shaped to engineerlonger backtunneling and capture times with respect tothe ejection time, improving the pumping accuracy byorders of magnitude. In addition to using high magnetic fields and shapedRF pulses, higher pumping accuracy could be achievedin principle by tuning the confinement potential of thedynamic quantum dot to increase its charging energy. Inpractice, such tuning has allowed GaAs-based single elec-tron pumps in modulation-doped 2DEGs to operate at T = 4 K. Because of their topgate and absence of inten-tional dopants, dopant-free devices can generate strongerelectric fields than their modulation-doped counterparts,and thus potentially increase their accuracy and/or op-erating temperature.Applications for non-adiabatic single electron pumpsextend beyond possible standards for current and evenfor voltage in quantum metrology. Such applicationsinclude the fields of single electronics and single elec-tron optics. In the latter, non-adiabatic single electronpumps have already made an impact on the field, with atrapping/counting scheme for hot electrons, partition-ing of on-demand electron pairs and on-demand emis-sion of electron pairs with deterministically controlled ex-change symmetry. Another possible application wouldbe an electrically-driven single photon source, realized byjuxtaposing a non-adiabatic single electron pump (suchas the one presented here) next to a “lateral” p-i-njunction in the same dopant-free device. A similarsingle photon source based on surface acoustic waves hasrecently been realized. In conclusion, we have demonstrated early prototypesof non-adiabatic single electron pumps in dopant-freeGaAs/AlGaAs 2DEGs operating at near-GHz frequen-cies, high temperature, and zero magnetic field. Giventhe experimental conditions, these pumps have achievedremarkable performance with an estimated error of 1.7ppm within the decay cascade model. To put our re-sults in context, they offer a possible route towards morepractical quantum standards for current by significantlyreducing the complexity of the measurement infrastruc-ture required (dilution refrigerators, large superconduct-ing magnets, and high frequency hardware for shapedRF pulses), and thus expand the user base of GaAs pumptechnology beyond the most-well funded national metrol-ogy institutes and research laboratories.The authors thank Christine Nicoll for useful discus-sions. This research was undertaken thanks in part tofunding from the Canada First Research Excellence Fund(Transformative Quantum Technologies), Defence Re-search and Development Canada (DRDC), and the Natu-ral Sciences and Engineering Research Council (NSERC)of Canada. The University of Waterloo’s QNFCF facilitywas used for this work. 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