Deterministic Single Ion Implantation with 99.87% Confidence for Scalable Donor-Qubit Arrays in Silicon
Alexander M. Jakob, Simon G. Robson, Vivien Schmitt, Vincent Mourik, Matthias Posselt, Daniel Spemann, Brett C. Johnson, Hannes R. Firgau, Edwin Mayes, Jeffrey C. McCallum, Andrea Morello, David N. Jamieson
DDeterministic Single Ion Implantation with 99.87%Confidence for Scalable Donor-Qubit Arrays inSilicon
Alexander M. Jakob , Simon G. Robson , Vivien Schmitt , Vincent Mourik ,Matthias Posselt , Daniel Spemann , Brett C. Johnson , Hannes R. Firgau , EdwinMayes , Jeffrey C. McCallum , Andrea Morello , and David N. Jamieson ARC Centre for Quantum Computation and Communication Technology (CQC T) School of Physics, University of Melbourne, Parkville, 3010, VIC, Australia School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, 2052, NSW, Australia Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, 01328, Saxony, Germany Leibniz Institute of Surface Engineering (IOM), Leipzig, 04318, Saxony, Germany RMIT Microscopy and Microanalysis Facility, RMIT University, Melbourne, 3001, VIC, Australia * [email protected] ABSTRACT
The attributes of group-V-donor spins implanted in an isotopically purified Si crystal make them attractive qubits for large-scalequantum computer devices. Important features include long nuclear and electron spin lifetimes of P, hyperfine clock transitionsin
Bi and electrically controllable
Sb nuclear spins. However, architectures for scalable quantum devices require theability to fabricate deterministic arrays of individual donor atoms, placed with sufficient precision to enable high-fidelity quantumoperations. Here we employ on-chip electrodes with charge-sensitive electronics to demonstrate the implantation of singlelow-energy (14 keV) P + ions with an unprecedented . ± . % confidence, while operating close to room-temperature.This permits integration with an atomic force microscope equipped with a scanning-probe ion aperture to address the criticalissue of directing the implanted ions to precise locations. These results show that deterministic single-ion implantation can be aviable pathway for manufacturing large-scale donor arrays for quantum computation and other applications. Introduction
The development of quantum computers has reached the stagewhere noisy, intermediate-scale quantum (NISQ) deviceswith ∼ −
100 qubits can surpass classical supercomputersin executing some specific algorithms . Even at the NISQstage, the error budgets for the physical qubits are strict, re-quiring errors well below 1% in order to achieve sufficientcircuit depths. Beyond NISQ, error-corrected, universal quan-tum processors of the kind necessary to run Shor’s factoringalgorithm on a 2,000 bit classical key will require upwardsof 4,000 logical qubits. Using a 2-dimensional surface codearchitecture, this would translate to about 200 million phys-ical qubits with present error rates of around 0.1% . Futuredevices with lower error rates will reduce the required numberof physical qubits. The surface code is also able to tolerate5 −
10% physically non-functional (absent or faulty) qubits inthe architecture .Taking these constraints into account, a scalable universalquantum computing platform requires: (i) manufacturabil-ity at the ∼ physical qubit scale; (ii) physical gate errorrates at or below 0.1%; (iii) no more than a few percent offaulty qubits. Leading technologies including superconduct-ing qubits and ion traps satisfy requirements (ii) and (iii).However, requirement (i) appears extremely challenging forthese technologies where the physical qubits are spaced on a scale of several microns.Classical silicon devices can be manufactured using industry-standard metal-oxide-semiconductor (MOS) methods thatyield billions of transistors on a ∼
30 nm pitch ; their ex-tension to quantum devices can thus naturally address require-ment (i). This has motivated the development of silicon spinqubits , starting from the donor-based proposal of Kane .The electron and the nuclear spin of a single P donor,ion-implanted in a silicon MOS device, have proven to beoutstanding qubits, with coherence times exceeding 0.5 s(electron) or 30 s (nucleus) . Single-qubit error rates are inthe 0.01% - 0.03% range , thus addressing requirement (ii)at the 1-qubit level. Conditional two-qubit operations betweenexchange-coupled donors have been recently demonstrated .In this work, we provide the first experimental evidence thatthe implantation of individual dopants can be detected withsuch high confidence to not constitute a barrier to the fulfil-ment of requirement (iii), i.e. a low density of faulty or absentqubits.All examples of coherent quantum control of single-donorspin qubits in silicon have been so far obtained in deviceswhere a small number of donors, subject to Poisson statistics,were introduced in the chip by ion implantation . Thisfollows the well-established precedent of ion implantation tointroduce dopants in classical MOS devices . However, forthe goal of manufacturing a large-scale quantum computer a r X i v : . [ c ond - m a t . m e s - h a ll ] S e p ith a billion-qubit array of controllable donors in silicon, itwill be essential to precisely and deterministically place theindividual donors within the array.A key benefit of ion implantation is that all group-V donorscan be introduced into the silicon, allowing a diverse rangeof applications. P is the simplest system, offering spin-1/2 nuclear and electron spin qubits . Sb has a nuclearspin 7/2 which can encode error protected logical qubits and can be controlled by local electric fields . Bi has alarge electron-nuclear hyperfine coupling that results in theformation of noise-protected “clock transitions” . Utilizingthese donors for quantum information requires placing them ∼
20 nm under the surface, so they can be addressed andread out with suitable nanoelectronic circuitry. As a conse-quence, the kinetic ion implantation energy lies in the range of ∼ −
35 keV. Achieving both, deterministic ion implantationof individual donors at such low energy, and localisation ofeach implant to high spatial precision, represents an ongoingchallenge.Several alternative strategies that address this challenge arein an advanced stage of development. The cold-ion trap and the fly-by image charge detector are both deterministicion source concepts, where the incidence of a single ion is de-tected prior to implantation. These approaches do not imposeany special requirements on the substrate and can thereforebe used for many materials as well as silicon.An earlier approach, analogous to Scanning Electron Mi-croscopy (SEM), employs the ion-impact-induced burst of sec-ondary electrons escaping from the substrate surface to countdopant atoms implanted into silicon devices . However,the yield of secondary electrons is typically below 10 e − /ionfor the implant energies of interest here which limits thesingle ion detection confidence with conventional secondaryelectron detectors to ≈ .In this work we adopt a method that detects the electron-hole(e-h) pairs generated by an ion impact in a silicon substrate byutilising on-chip detector electrodes. The on-chip electrodesform a reverse-biased p-i-n diode, as developed in solid-statedetector technologies for ionizing radiation . This method,based on the Ion Beam Induced Charge (IBIC) principle ,is well established for high-energy (of order MeV) ions, butdemonstrated here with keV ions. Thanks to a typical ∼ . We address someof the challenges of using this system to build, e.g., a donor-spin qubit architecture that utilises flip-flop qubits . Theseare typically placed on a two-dimensional array with 200 nmpitch and coupled by electric dipole interactions (Fig. 1c).Each donor must be located at a shallow depth, ∼ −
25 nm beneath a thin gate oxide so that it can be tunnel-coupled to areadout device and electrostatically controlled by metallicsurface gates.We further demonstrate that the ion impact signal can also beused to assess the physical characteristics of the ion stoppingtrajectory, which is subject to random collision events calledstraggling. Statistically rare events that result in an undesir-able ion placement location can be identified from the signalcharacteristics. This unique capability distinguishes our IBICprinciple from all other deterministic implantation approaches.Suitable algorithms, capable of signal pulse shape discrimi-nation, could increase the yield of functioning donor qubitsin ultra-scaled dopant arrays by employing active correctionprotocols such as conditional implant-repetition steps and dy-namic array reconfiguration.However, to exploit this capability requires charge-sensitivesignal processing electronics for the ∼ ,
000 e-h pairs typi-cally generated by each ion impact for shallow implantation.Cryogenic operation of the substrate and electronics is com-monly applied to achieve sufficiently low noise thresholds.However, cryogenic systems are not readily compatible withthe integration into ancillary apparatus that must operate atroom temperature and can impose considerable operation com-plexity .Here, we present a reliable, high-fidelity, counted single-ionimplantation system operating near room temperature. Weaccurately benchmark the noise and error budget of the sys-tem and extract a detection confidence approaching 99.9% for P + ions implanted at 14 keV. This system is compatible withsubsequent processing steps required to fabricate multi-qubitdevices. Single-Ion Implant Detection
The devices presented here employ a substrate configuredwith multiple construction sites, which will allow us tofabricate multiple single- or few-qubit devices on a singlechip. Each construction site has a lateral diameter of15 µm. As shown in Figure 1a, the construction sites aresurrounded by a detector top electrode, and each site featuresa pre-fabricated thin gate oxide needed for subsequentintegration of qubit control nano circuitry. The top electrodemakes contact with a boron-doped p-well on the intrinsicsilicon substrate, with a n-type back contact forming the p-i-ndetector. To meet the low noise performance requirements,two important design features are employed: (i) A groundedp-type guard ring surrounds the top electrode and screens theactive detector volume against parasitic free charge carriersfrom outer interface and bulk defects and minimises thereverse bias leakage current, which would otherwise obscureion impact signals; (ii) Minimising the top electrode arealowers the total device capacitance and consequently theparallel white noise contribution in the charge-sensitivepreamplifier.The principle of controlled donor array formation inside aselected construction site is illustrated in Fig. 1b. An AFM Localisation of single ion implants a . Schematic of thesilicon single ion detector die, incorporating a vertical ‘sandwich-type’ p-i-n detector geometry. The detector incorporates an innercircular top electrode and an outer grounded p-type guard ring tominimise leakage current. The inner top electrode comprises sixcircular construction sites each with a uniform 5 nm SiO thickgate oxide above intrinsic (100) silicon. b . Formation of a donorarray by deterministic step-and-repeat single ion implantation in theselected construction site. The AFM cantilever, which incorporates ananostencil aperture, acts as a movable mask for the ion beam. Thesignal from a single ion implant event triggers the AFM nanostencilscanner to step to the next implant site. c . Schematic of a 2 × P-donor array with ≈
200 nm spacing, as appropriate for flip-flopqubit devices . These qubits employ long-range electric dipoleinteractions, so that entangling gate operations can be performedeven beyond the nearest-neighbours, for instance across the diagonalof the array. The control and readout circuitry is fabricated after theimplantation and the rapid thermal anneal for donor activation. nanostencil scanner localises the implant site to high spatialprecision and steps to the next array site when triggered by the detected ion implant signal. The signal can also trigger afast ion beam blanker (typically ∼
100 ns response time) tominimise the probability of further implant events at the samearray site.The gate dielectric is a 5 nm thin high-quality SiO oxide,thermally grown (see Methods) in advance of all otherfabrication steps, because the required thermal budget is notcompatible with subsequent fabrication steps. Moreover,the thermal growth of the gate oxide has the advantage ofpassivating interface charge traps and reducing fixed oxidecharges that would otherwise reduce the ion-induced chargesignal in the detector. The ions traversing the gate oxideduring implantation suffer from some kinetic energy loss thatis not available for the signal generation. However, this effectis tolerable given the low oxide thickness and the excellentsignal detection efficiency enabled by this surface passivation.The critical properties of the gate oxide in the present detectorsare measured from MOSCap devices processed together withthe detector wafers. They amount to ≤ × eV − cm − for the fixed oxide charge density and ≤ × cm − forthe oxide interface trap density. These values are found tobe sufficiently low to ensure signals close to 100% of thecharge created by single ion implant events at implantationenergies of interest. In a broader context, these values alsoindicate that the devices have a sufficiently low density ofcharge defects for high-fidelity operation of the donor spinqubits that will result from this fabrication process. Single-Ion Implant Localisation
The single ion implantation detection system operates in con-junction with an AFM that is equipped with a nanostencilintegrated into the cantilever, as shown in Figure 2. The sam-ple stage of the AFM holds the substrate chip to be implantedand also incorporates the charge-sensitive electronics coupledto the on-chip detectors. The AFM cantilever is controlled byintegrated self-actuating technology instead of conventionallaser-based optical schemes, which are incompatible with theon-chip detectors as they would be swamped by light spillage.Additional benefits include a more compact and sturdy AFMdesign that is less sensitive to thermo-mechanical drift. TheAFM cantilever employs tapping mode to approach andimage the substrate. This approach is benign comparedto more invasive techniques such as electron microscopy,which could inject excess charge and degrade the gate oxidepassivation.The AFM cantilever nanostencil assembly incorporatesa Focused Ion Beam(FIB)-milled collimator for ion-implantation. In the results presented here we employed an8 µ m diameter aperture because we sought to investigatethe physics of the ion-solid interaction from ion impactsignals that are randomly distributed over one constructionsite while avoiding edge effects. Sub-10 nm ion aperturesare readily available for controlled donor array formationexperiments, and will be described in a separate study. The The single ion implanter system a.
The system incor-porates an AFM, where the integrated sample stage also houses thecharge-sensitive preamplifier electronics . The stage incorporatesPeltier cooling to 263 K. b. SEM micrograph of the AFM cantilever(see text). For the present study we equipped the cantilever witha micro-aperture of 8 × µ m , sufficient to localise the ion beamwithin a single construction site. c. In-situ optical camera view ofthe detector, showing the cantilever and the wire bond connectingthe detector top electrode to the charge-sensitive preamplifier circuitboard housed within the sample stage. d. The AFM image from c showing the selected construction site as a 3D topography map.The irradiated region localised by the nanostencil is highlighted bythe dashed circle. Lithographic alignment markers mapped by theAFM (not shown) allow nanometer precision alignment between ionimplant sites and subsequent processing steps. AFM cantilever is operated by a monolithic top stage with anindependently controllable travel range of 18 × × ≈ µ m diameter.The much larger cantilever dimension of 350 × µ m ensures that no unintentional ion strikes occur outside thecollimator.The device for implantation is mounted on a circuit board thatalso contains the charge-sensitive preamplifier electronics.This assembly is mounted on the AFM stage within aFaraday shield containing a thermo-electric Peltier cooler foroperation of the detector at 263 K (-10 ◦ C). An opening in theshield enables access for the AFM cantilever and the stageprovides a 60 × µ m lateral travel range with nominally5 Å repeated positioning accuracy. The entire AFM assemblyis mounted on a positioning stack with ±
15 mm lateral travel.This allows coarse positioning between sample and cantileverwith nominally ∼
50 nm placement accuracy. An AFM imageof a construction site is shown in Fig. 2c, which shows therequired uniformity of the surface needed for ion implantationof the near-surface donors. The AFM micrograph can alsoidentify location markers (not shown) to align the cantileverion aperture with the required implant sites to high precision.
Induction and Detection of Charge Signals
Detecting with high confidence the signal from (cid:46) I tot andcapacitance C tot of the detector and its first-stage amplifier.For ultra-low noise applications, the latter typically consistsof a junction field effect transistor (JFET), whose internal gatedesign and fabrication technology determine I tot and C tot .Our system incorporates several optimisation strategiesdeveloped for different applications. State-of-the-art radiationdetectors for X-rays feature an integrated JFET and exhibita capacitance on the order of C tot ≤
300 fF . Fast-recoveryp-i-n photo diodes can have a full-depletion reversed biasleakage current as low as I tot ≤ .These highly application-optimised detectors provide abenchmark for the performance of our devices optimised fordeterministic doping.Figure 3a illustrates capacitance-voltage (C-V) and current-voltage (I-V) graphs representative of the present devicealongside results from a reference photodiode . By minimis-ing the top electrode area that contains the construction sites,and incorporating a p-guard ring surrounding the top electrodeto suppress leakage current, we obtained a capacitance of80 ±
30 fF (a factor four lower than the reference diode) and aleakage current of approximately 35 ±
10 pA at 10 V reversebias and room temperature operation. Moderate cooling to-10 ◦ C gives the required sub-pA leakage current. Furtherimprovement of these values is possible by optimisation ofthe detector fabrication process.Experimental measurements of the detector noise are obtained
Detector characteristics a.
I-V and C-V data of thedetector die compared to a reference photodiode. The detector hasa comparable low capacitance but a leakage current an order ofmagnitude higher, suggesting further improvements are possible. b. The detector dark noise spectrum n and related rate ˙ n as functionsof the charge-equivalent signal amplitude q . A Rayleigh distributionis used to model the noise spectrum. A threshold q t is delineatedhere where 99.999,999% of the cumulative noise N ( q t ) (pink area)is discarded by a lower-level discriminator in the data acquisitionelectronics. The inset shows the Fe X-ray K-emission lines of a Co radionuclide, acquired with all system components activated,including the AFM system. A resolution of about 200 eV FWHMfor the 6.4 keV K α peak acquired at a substrate temperature of263 K verifies negligible signal degradation from cross-talk from theAFM system. This signal spectrum s ( q ) also allows a quantitativecalibration of the charge-equivalent signal axis q in units of [keV]. using a Co radionuclide, emitting characteristic Fe K α andK β X-ray photons at 6.40 keV and 7.06 keV respectively.Upon absorption inside the active detector volume, an X-rayphoton excites a number of e-h pairs proportional to itsenergy. Drift of the e-h pairs in the bias field results in acharge-equivalent voltage pulse q at the detector electrodeswhose amplitude is in turn proportional to the photon energy E X − ray and commonly expressed in units of keV. The signalspectrum, s X − ray ( q ) , also features Bremsstrahlung anddetector noise. A representative X-ray spectrum from apresent detector, operated at 263 K, is shown in Fig. 3b. Theclosely spaced Fe-K α and K β photon energies are clearly resolved. The K α -peak exhibits an FWHM of about 200 eV,which corresponds to an r.m.s. noise of σ noise ≈
70 eVand thus comparable to state-of the-art silicon detectors forother applications. The detector dark noise spectrum, n ( q ) ,obtained with no radionuclide present is shown in Figure 3b.As demonstrated in the following, the steep noise attenuationas a function of energy of ≈ . Deterministic Ion Implantation
The stopping of an ion as it dissipates kinetic energy in acrystal is caused by nuclear and electronic energy loss inproportions that depend on the ion mass and energy. The elec-tronic stopping fraction f el , i of a single ion generates e-h pairsand thus the energy-equivalent signal amplitude q i utilisedfor the event detection. For an ensemble { i } of consecutiveion implants, each event i contributes to a signal spectrum s ( q ) = { q i } . Electron-hole (e-h) pairs generated within thegate oxide (i.e. outside the silicon crystal) and losses fromcharge recombination reduce the signal amplitude q i . Fur-ther effects like ion channeling and substrate atom recoilsinfluence the electronic fraction f el , i itself. The interactionof these factors leads to characteristic high and low energytails in the spectrum s ( q ) , which consequently reflects boththe stopping physics specific for an ion species as well as thedetector properties.To measure the response of the present detector to ionimplantation, the AFM cantilever with an 8 µ m diameteraperture was used to localize the ion beam to the constructionsites. We first show a spectrum from 14 keV H + ions. Thismolecular ion dissociates instantaneously upon impactingthe surface gate oxide, yielding two 7 keV H + ions, eachhaving ∼
100 nm average penetration depth. The e-h pairsproduced by both ions produce a combined signal pulse in thedetector. The low mass of protons results in ∼
95% of theirkinetic energy dissipating in e-h-pair generation . Thesignal spectrum (Fig. 4a inset) s ( q ) thus exhibits a sharp peakat an energy very close to the 14 keV energy of the incomingH + ions. This result demonstrates the expected detectorperformance and minimal losses due to charge trapping andrecombination. Furthermore, essentially no low energy signalevents are registered outside the main peak body, indicatingnegligible scattering artifacts from the ion aperture.The construction site was subsequently irradiated with 14 keVP + ions for approximately 760 s and a beam current of ∼
80 ions/min. The corresponding signal spectrum consistsof ∼ × µ m , which isvery similar to the density produced with the present implantparameters. It furthermore corresponds to a sufficiently lowion fluence to not cause any measurable charge collectionefficiency deterioration from ion-induced substrate damage . Counted ion implantation - experiments and analysis a.
Experimental signal spectrum s ( q ) + n ( q ) for 14 keV P + ionsimplanted inside the construction site of a single ion detector. The spectrum contains 1000 events in total, with 18 events assigned to noise n ( q ) (light blue) and remaining 982 events s ( q ) (pink) induced by ions with a residual uncertainty below 10 − . The related time-derivatives(rates) ˙ s ( q ) and ˙ n ( q ) can be determined with the known total acquisition time of 760 s. A numerical simulation with optimised parameters(see text) of s ( q ) for 500,000 virtual implants (blue square scatter plot) is overlaid on the experimental spectrum and demonstrates closeagreement. The experimental spectrum for 614 14 keV H + molecule-ion implants appears in the inset. These ions produce signals wellabove the noise threshold and confirm 100% charge collection efficiency of the detector. b. The cumulative "false positives" F Pos and "falsenegatives" F Neg are plotted alongside the ion ensemble detection diffidence 1 − Ξ as a function of the discriminator threshold level q t . Theoptimum value q t0 yields a nominal detection confidence of 99.87%. The inset depicts the final calculated ion placement depths of thesub-threshold signal events F Neg ( q t0 ) below q t . The majority consists of non-critical ion backscatter events and ions stopping inside the gateoxide. The intended application of our system is for near-surfacedoping, including the 14 keV P + -ion implants presented here.The corresponding spectrum, shown in Fig. 4a, exhibits apeak at 3.6 keV, which is significantly less than the incidention kinetic energy, owing to the smaller fraction of electronicenergy loss to generate e-h pairs compared to lighter ions.Also, the straggling from statistical variations in the ionstopping process leads to a more pronounced variation in thefraction of electronic energy loss per ion compared to 7 keVH + ions. Consequently, the spectrum is broader and skewedtowards low energy signals. Ion channeling, mainly along theSi [100] axis, enhances electronic energy loss and leads to ahigh-energy tail in the signal spectrum. Recoiling Si and Oatoms generated by P + -ions within the oxide layer are respon-sible for the low-energy signals near the detection threshold q t . Deterministic Implantation Confidence
We now consider the implications of this experimental spec-trum for the use of deterministic doping in the fabrication oflarge-scale donor arrays, e.g. for donor-based quantum com-puters. We estimate the detection confidence by separatingthe ion-induced signal spectrum s ( q ) from the noise spectrum n ( q ) . This is achieved by combining a computational modelwith realistic experimental parameters. The trajectories ofindividual ions can be modeled to provide insights into thefinal location of the ion in the substrate and the correspondingsignal amplitude from the detector. We consider here a binary collision model for the ion-solidinteraction to compute the associated electronic energy lossand hence the detector signal. The model first uses the TRIMcode to compute the ion trajectory through the surface gateoxide and to determine ion position and velocity vector at theinterface to the silicon substrate (including recoiling Si andO atoms). Then, a modified Crystal-TRIM code is used tocompute the ion trajectory inside the (100) crystalline siliconand determine the total electronic energy loss of the ion andassociated recoils. Details of the simulation procedure areexplained in the Methods section. A set of semi-empiricalparameters (see Methods section) are fitted to match the ex-perimental signal spectrum.Results from this model to compute the signal spectrum of500,000 14 keV P + -ions are shown in Figure 4a. The simu-lation agrees with the experimental spectrum within Poissonstatistics. A sparse set of signals visible in the experimentalspectrum above 6 keV appears to point to physical processesnot included in the model. The model assumes the surfacegate oxide to be homogeneous, whereas the actual oxide hasan amorphous structure leading to inevitable small variationsin the density and thus the scattering dynamics, which areneglected by the model. Nevertheless, the satisfactory match,especially in the low-energy signal regime, justifies the use ofthis simulation procedure to assess the detection confidencefor our experiments with 14 keV P + -ions.For a given experimental data acquisition time, the confidencethat a signal arises from a single ion implantation event is imited by the probability that a noise event occurs within thesame time window. This confidence is in proportion to thenumber of e-h pairs available from the ion impact. A discrim-inator threshold, q t , is used to discard most of the low-energyevents which are dominated by noise signals. The key featureof the experimental spectrum is the near-absence of signals inthe energy window above the discriminator threshold, whichis a testament to the extremely low noise obtained by oursystem. To demonstrate the role of the discriminator thresh-old, the experimental spectrum in Fig. 4a was obtained witha discriminator threshold set to q t = .
42 keV (rose-colouredarea) so that some signals otherwise rejected by the optimumdiscriminator threshold (discussed below) are retained in theexperimental spectrum of Fig. 4a (light-blue events). We nowexamine these signals in detail.First, we consider the noise signals registered immediatelyabove the discriminator threshold. The event rate ˙ n ( q ) for thenoise spectrum can be obtained from the Rayleigh function inFig. 3b and compared with the corresponding ion signal rate˙ s ( q ) extracted from the modelled signal spectrum in Fig. 4a.For the first two energy bins q ∈ ( . , . ] keV (17 counts)and q ∈ ( . , . ] keV (1 count) just above the discrimina-tion threshold q t , the probability ˙ s ( q ) : ˙ n ( q ) that the eventsbinned therein are from ions is about 1 : 100 and 1 : 2, respec-tively. In contrast, the single event registered at q = . (cid:38) − andtherefore has high confidence of being an ion implant event.Consequently, the remaining 982 signal events binned beyond0.9 keV are with near 100% confidence due to ion implantsbecause of the very low noise threshold of the detector. Theresidual uncertainty is mainly determined by rare environmen-tal disturbances not considered here, such as power supplystability fluctuations or natural nuclear decays in the environ-ment.Second, we evaluate the detection confidence for ion implantsignals which relies on the consideration of all relevant sig-nals that are gathered or discarded by the detector system.Due to the partial overlap of the signal ( s ( q ) ) and noise ( n ( q ) )distributions, it is possible to identify the optimum discrim-inator threshold level q t by considering two critical quanti-ties: false-positive signals from retaining noise above q t , andfalse-negative signals from discarding ion implantation eventsbelow q t . The false-positive rate is easily obtained by inte-grating the experimental noise spectrum n ( q ) normalised tothe acquisition time from q t to ∞ , i.e. F Pos ( q t ) : = ˙ N | ∞ q t . Thefalse-negative rate F Neg ( q t ) : = ˙ S | q t is derived via integrationof the model signal spectrum s ( q ) and a normalisation to theaverage ion rate r Ion = ˙ S | ∞ .Figure 4b. illustrates the experimentally obtained F Pos ( q t ) event rate as well as the F Neg ( q t ) event rate for an ion rateof r Ion =
80 min − ≈ . − (as adopted in the experimentreported in Fig. 4a).The ion detection confidence Ξ (normalised as probability) can be then derived as (see Methods): Ξ ( q t0 ) : = (cid:18) − F Neg ( q t0 ) r Ion (cid:19) (cid:18) r Ion r Ion + F Pos ( q t0 ) (cid:19) (1)with the first factor describing the fraction of ions that createdetectable signal events above the threshold level q t0 and thesecond factor stating the probability that the registered eventwas not due to noise. Equation 1 constitutes an optimisationproblem with the threshold level q t0 adjusted to maximise Ξ .The ion detection diffidence 1 − Ξ is illustrated in Fig. 4b. For q t set to a low threshold level, false positives F Pos dominatethe acquired signal and cause the diffidence to saturate closeto 1. At the other extreme, for q t set to a high thresholdlevel, false negatives (rejected real ion implantation signals) F Neg become the main confidence limitation. Noteworthy inFig. 4b is the shallow curve profile of F Neg throughout theentire signal regime, causing Ξ to remain below 99.99% -regardless of the detector noise performance.The optimum threshold level can be determined from thecurves in Fig. 4b to be q t0 ≈ . Ξ ( q t0 ) = . ± . q t (cid:46) .
54 keV), our computational model allows an examinationof the corresponding ion stopping trajectories. As tabulated inthe inset of Fig. 4b, the model shows that most of these ions(0 . .
02% of the 14 keVP + -ions end up in the silicon substrate without producing adetectable signal. Hence, the majority of the sub-thresholdsignal events induced by ions are not detrimental in termsof qubit loss faults, because only ions reaching the siliconsubstrate form electrically active dopants. Conclusion
We have presented a single-ion detector, integrated withan AFM nanostencil and operating near room-temperature,which allows deterministic ion implantation by detecting ion-induced e-h pairs inside the silicon substrate. The system canbe employed with group-V dopant atoms, implanted near thesurface of a silicon device, to form single-atom spin qubitdevices such as the 2D architectures exploiting the flip-flop-qubit . Our single-ion detector technology exhibits an ex-ceptionally low noise background at near-room temperature,as shown with 14 keV P + ions. The system is compatiblewith many standard ion implanters, commonly equipped withstochastic ion sources that cause random ion arrival times atthe substrate. The detector signals from implanted ions pro-vide a characteristic spectrum that allows deeper insight intothe ion-solid interaction. Thanks to an improved model, rareimplantation events that produce sub-threshold ion signalscould be investigated in detail.For the configuration of our system, we conclude that theconfidence of detecting a single ion implantation event takes he promising and unprecedented value of 99.87%. Remark-ably, the residual diffidence can be mainly attributed to thestopping physics of 14 keV P + -ions in silicon, whereas thedetector noise plays only a subordinate role here. Future stud-ies will analyse advanced scalability projections for 2D qubitarray formation and extend Equation 1 to include e.g. thedouble-implant probability as a function of the incident ionbeam current (see Methods section). These considerationswill become important when seeking to increase the ion beamfluence to reduce the total implantation time for large donorarrays. Although the present study employed P donors, weexpect comparable confidence levels for other dopant species,as long as the implantation energy is adjusted to preserve asimilar number of ∼ P-ion,implanted in a silicon device operated at near-room temper-ature and integrated with an AFM nanostencil scanner, canbe detected with extremely high confidence. Therefore, iondetection uncertainties will not constitute an obstacle to theconstruction of a fault-tolerant, large-scale donor-based quan-tum computer in silicon.
Methods
Detector fabrication:
Standard metal-oxide-semiconductor(MOS) processing is employed to fabricate the detectorsstudied in this work. The initial wafer is a <100> UniformHigh Purity Silicon (UHPS) wafer from Topsil. The lowresidual n-doping yields a resistivity of 9250 Ohm-cm. Theon-chip single-ion detectors are fabricated as follow:1. Etching of alignment markers for subsequent opticallithographical steps: The pattern is first defined usingstandard optical lithography and then transferred into apreviously grown wet thermal SiO oxide. Using tetram-ethylammonium hydroxide (TMAH), the pattern is thenetched into the silicon; the oxide is subsequently re-moved using BHF.2. Creation of the detector’s p-doped regions: The area tobe doped is defined using standard optical lithographyand then transferred onto a thermally-grown wet oxide.P-type doping is obtained by thermal diffusion of boron.Lastly, the oxide is removed using BHF.3. Back n-doping of the detector: First, a thermal oxide isgrown in a steam ambient. Using photoresist as a mask,the oxide on the back of the detector is then removedusing BHF. This then serves as the mask for the ther-mal diffusion doping of the rear of the detectors usingphosphorous. The masking oxide is then removed usingBHF.4. Growth of the thick field oxide using a dry oxidationprocess.5. Growth of the thin gate oxide using a dry oxidation pro-cess, in areas defined within the field oxide using optical lithography and etched using BHF.6. Etching of vias for metallisation using a photolitho-graphic mask and BHF.7. Deposition of metallisation: A mask is first defined usingphotolithography and any native oxide that has grownonto exposed silicon is removed using a quick hydroflu-oric acid dip. Using e-beam evaporation, 100 nm ofaluminium is then deposited onto the wafer, directly fol-lowed by 10 nm of Platinum, both on the front and back.Metallisation in undesired regions is removed using a lift-off process using warm N-Methyl-2-pyrrolidone (NMP).8. Annealing of the detectors in a forming gas ambient (5%hydrogen, 95% nitrogen) at 400 ◦ C. I-V/C-V analysis:
Detector chips are mounted on a chip car-rier and placed inside a light-shielded analysis chamber heldunder rough vacuum ( ∼ × − Torr). The chip carrier isattached to a low-noise multiplexed feedthrough that allowsinterconnection to either a Keithley 6487 picoammeter (reso-lution 20 fA) or Boonton 7200 capacitance meter (resolution1 fF) for I-V and C-V measurements, respectively.
FOC/DIT analysis:
The Si/SiO interface trap densities (Dit)were estimated using the Hill-Coleman method and deep leveltransient spectroscopy. Mid-gap values of test devices with a5 nm oxide are found to be in the low 10 cm − eV − range.The fixed oxide charge was estimated by identifying the flatband voltage shift in a CV curve as a function of oxide thick-ness. Values are in the low 10 cm − range Charge-sensitive electronics:
The charge-sensitive pream-plifier is based on the forward-biased FET circuit design ofBertuccio et al. . The preamplified signal pulse is fed into anAmptek PX5 digital pulse processor, which performs trape-zoidal pulse shaping ( τ peak = . µ s) and multi-channel analy-sis to provide the final signal histogram data via USB connec-tion to the Amptek MCA control- and acquisition software.Additionally, the digital signal resolution was set to about60 eV/channel (256 channels ranging from 0 to 15.4 keV) togive about 10% statistical variation in the maximum countsper channel for the total fluence of 1000 ion counts. Thischoice is also consistent with the ion energy straggling whichdoes not justify a higher resolution. Nanostencil fabrication:
The fabrication of the aperture inthe AFM cantilever to form the nanostencil is done with anFEI Scios SEM/FIB system. The aperture can be made with adiameter from microns down to sub-10 nm via in-situ moni-toring with the SEM. After milling the aperture a Pt layer of50 nm thickness is deposited in-situ on both entry and exitopenings of the aperture which reduces the probability of for-ward scattered ions reaching the substrate. The resulting chan-nel length of the aperture in the ion direction is sub-500 nm.This measure lowers the interaction probability between pass-ing ions and aperture walls, and consequently shallow-anglescattering effects. They can be caused by the intrinsic ionbeam divergence of about 9 mrad along the aperture tunnel xis. The aperture position relative to the probe tip apex of thecantilever is measured from SEM imaging at the conclusionof the fabrication process. This lateral offset allows AFMtopographic images to be precisely aligned with the implantsites from ions passing through the aperture.
Ion beamline and detection experiments:
The raw P + -ionbeam is generated in a BIS DCIS-100 DC plasma filamentusing a gas intermix consisting of 5% PF diluted in 95%Argon. A BIS 600-B Wien filter selects the ion species with abeam divergence of typically 9 mrad and about 10 nA beamcurrent. The vacuum pressure inside the ion source chamber is1 × − Torr and about 5 × − Torr in the beam line duringoperation. A commercial double V-slit configuration madeof tantalum membranes and attached to micro-meter screwsis employed for beam current adjustment. Further ion beampurification and removal of scattered vacuum backgroundatoms is realised via an NEC 90 ◦ electrostatic spherical dipoleanalyser located at the target chamber entry. A Tungstenmembrane of 25 µ m thickness and 20 µ m aperture diameterpre-collimates the ion beam onto the AFM nanostencil aper-ture. Precision ion current adjustments to 80 and 150 ions/s,respectively, are done on a sacrificial detector constructionsite by monitoring the ion signal rate.A long working distance optical microscope provides a topview on the substrate via a 45 ◦ mirror with integrated ionaperture. It is used for coarse alignment between AFM nanos-tencil and ion beam spot as well as the detector relative to thenanostencil. The optical resolution is approximately 2 µ m. Theory:
In order to produce a functional qubit via determin-istic ion implantation, the following requirements have to befulfilled: (i) on each location exactly one ion is implanted witha yield defined to be Y DetIon ; (ii) the final location of the ion inthe matrix is compatible with the tolerances of the qubit archi-tecture, which is constrained by the ion straggling and relatedyield Y QCon ; (iii) the implanted ion is successfully activatedupon thermal anneal with the yield Y Act . The overall yield Y toform a functional donor-qubit then is Y = Y DetIon · Y QCon · Y Act .In the following, Y DetIon is addressed for the experimental ap-proach presented here and its derivation may differ for otherapproaches to deterministic ion implantation. In order to suc-cessfully record the implantation of an ion, the signal inducedby the ion must exceed the data acquisition threshold q t0 . With F Neg ( q t0 ) / r Ion as the fraction of ions that create signals below q t0 , the yield for s ( q ) > q t0 is Y s > q t0 ( q t0 ) = − F Neg ( q t0 ) / r Ion .Furthermore, the signal recorded above the threshold q t0 shall not be due to noise events that are erroneously inter-preted as an ion implant event. The probability that thesignal above q t0 is related to noise is given as the fraction F Pos ( q t0 ) / ( F Pos ( q t0 ) + r Ion ) . Hence, the yield Y NoNoise ( q t0 ) that the signal above q t0 is not due to noise is Y NoNoise ( q t0 ) = − F Pos ( q t0 ) / ( F Pos ( q t0 ) + r Ion ) = r Ion / ( F Pos ( q t0 ) + r Ion ) . Theion beam from the nanostencil dwells on an implant site untila signal above q t0 is recorded. Then the beam is blankedoff to protect the implant site from further ion implants andfor the nanostencil to re-position to the next implant site. The beam blanker duty cycle time depends on parametersincluding the signal rise time in the pre-amplifier and relatedblanker trigger electronics as well as the charging time of thebeam electrostatic deflector plates. Realistically achievableblanker times are τ ≈
100 ns. Since the ion source deliv-ers the ions stochastically in time, there is a probability P DI that a second ion is implanted, creating an unwanted dou-ble implant. The probability P DI ( τ , r Ion ) is given by e − τ r Ion .Hence, the yield that no double implant occurs is 1- P DI . Theyield of successful deterministic ion implants is then given by Y DetIon ( q t0 , τ ) = Y s > q t0 ( q t0 ) · Y NoNoise ( q t0 ) · ( − P DI ( τ , r Ion )) .Due to the low ion rate on the order of 1 s − and all ions be-ing implanted in one site (only one blanking cycle at the startand end of experiment) for the experiment presented above,the double implant probability is of the order of P DI ∼ − and has therefore been neglected in equation 1, which thenreduces to Y DetIon ( q t0 ) ≈ Ξ ( q t0 ) = Y s > q t0 ( q t0 ) · Y NoNoise ( q t0 ) . Simulations:
The simulation of the signal spectrum consistsof two steps. At first, the TRIM code is applied to treatthe P + -ion transmission through the thin amorphous siliconoxide layer representing the surface gate oxide on our de-vices. From this it is possible to simulate the energies anddirections of a population of P-ions transmitted through theoxide layer and of the recoiled Si and O atoms which aredirected into the underlying (100) Si. In the second step thecode Crystal-TRIM is employed to obtain the electronicenergy loss per P-ion in the population within the underly-ing Si. This quantity corresponds to the signal measured bythe detector. Finally, detector noise and Fano statistics ofe-h pair generation were taken into account and allow thedirect comparison with the experimental signal spectrum (seeFig. 4a). Crystal-TRIM simulates the trajectories of energeticprojectiles (in the present case: P, Si and O) in single crystalSi and can therefore treat channeling effects that cause largervalues of electronic energy loss per ion than in amorphous Si.Like TRIM, Crystal-TRIM is based on the binary collisionapproximation, which assumes that the motion of an energeticprojectile may be described by a sequence of binary collisionswith target atoms. The trajectory of a projectile between twosubsequent collisions is approximated by a straight line givenby the asymptote to the trajectory of the energetic particle afterthe first collision. The electronic energy loss occurring duringthe collision of a projectile with a target atom is describedusing a semi-empirical expression, depending on an impact-parameter and is similar to the Oen-Robinson model .In the present work, the value 2.8 was chosen for the modelparameter C el in the case of P, Si, and O projectiles. The valueof the second parameter C λ was set to 0.92 for P and Si, andto 0.88 for O. This parameter describes the average electronicenergy loss for random incidence directions of a projectile.Therefore, C λ determines the energy related to the histogrampeak maximum of the electronic energy loss per incident P ion.The shape of the histogram is sensitive to the parameter C el ,which influences the channeling of a projectile. Thermal vibra-tions of lattice atoms affect projectile trajectories, especially or the motion in channels. In Crystal-TRIM a simple modelis used to take into account this effect . Only the motion ofP, Si, and O projectiles in single-crystalline Si is followed.However, the Si recoils formed in the collision cascades ofthese projectiles also contribute to electronic energy loss perincident P ion. This contribution is described by the semi-empirical expression of Funsten et al. , which considersnon-negligible self-trapping mechanisms due to a high densityof low-energy e-h pairs generated closely around the path ofenergetic ion projectiles. For the purpose of the present work,the Crystal-TRIM code was modified by the introduction ofthe Funsten model. This semi-empirial approach replacesearlier models that employed the model of Robinson . Testcalculations showed that the Robinson model is not capableto describe the electronic energy loss of the low-energy Sirecoils to be treated in this work. References Preskill, J. Quantum computing in the nisq era and be-yond.
Quantum , 79 (2018). Arute, F. et al.
Quantum supremacy using a pro-grammable superconducting processor.
Nature , 505–510 (2019). Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cle-land, A. N. Surface codes: Towards practical large-scalequantum computation.
Phys. Rev. A , 032324, DOI:10.1103/PhysRevA.86.032324 (2012). Nagayama, S., Fowler, A. G., Horsman, D., Devitt,S. J. & Meter, R. V. Surface code error correctionon a defective lattice.
New J. Phys. , 023050, DOI:10.1088/1367-2630/aa5918 (2017). Auger, J. M., Anwar, H., Gimeno-Segovia, M., Stace,T. M. & Browne, D. E. Fault-tolerance thresholds forthe surface code with fabrication errors.
Phys. Rev. A ,042316, DOI: 10.1103/PhysRevA.96.042316 (2017). Fischer, K. et al.
Low-k interconnect stack with multi-layer air gap and tri-metal-insulator-metal capacitors for14nm high volume manufacturing. In , 5–8 (IEEE, 2015). Zwanenburg, F. A. et al.
Silicon quantum electronics.
Rev. modern physics , 961 (2013). Kane, B. E. A silicon-based nuclear spin quantum com-puter. nature , 133–137 (1998). Pla, J. J. et al.
A single-atom electron spin qubit in silicon.
Nature , 541–545, DOI: 10.1038/nature11449 (2012).
Pla, J. J. et al.
High-fidelity readout and control of anuclear spin qubit in silicon.
Nature , 334–338, DOI:10.1038/nature12011 (2013).
Muhonen, J. T. et al.
Storing quantum information for 30seconds in a nanoelectronic device.
Nat. nanotechnology , 986–991 (2014). Muhonen, J. T. et al.
Quantifying the quantum gate fi-delity of single-atom spin qubits in silicon by randomizedbenchmarking.
J. Physics: Condens. Matter , 154205,DOI: 10.1088/0953-8984/27/15/154205 (2015). Dehollain, J. P. et al.
Optimization of a solid-state elec-tron spin qubit using gate set tomography.
New J. Phys. , 103018 (2016). M ˛adzik, M. T. et al.
Conditional quantum opera-tion of two exchange-coupled single-donor spin qubitsin a mos-compatible silicon device. arXiv preprintarXiv:2006.04483 (2020).
Jamieson, D. N. et al.
Controlled shallow single-ionimplantation in silicon using an active substrate for sub-20-kev ions.
Appl. Phys. Lett. , 202101, DOI: 10.1063/1.1925320 (2005). https://doi.org/10.1063/1.1925320. van Donkelaar, J. et al. Single atom devices by ion im-plantation.
J. Physics: Condens. Matter , 154204, DOI:10.1088/0953-8984/27/15/154204 (2015). Rubin, L. & Poate, J. Ion implantation in silicon technol-ogy.
Ind. Phys. , 12–15 (2003). Gross, J. A. Encoding a qubit in a spin. arXiv preprintarXiv:2005.10910 (2020).
Asaad, S. et al.
Coherent electrical control of a singlehigh-spin nucleus in silicon.
Nature , 205–209 (2020).
Wolfowicz, G. et al.
Atomic clock transitions in silicon-based spin qubits.
Nat. nanotechnology , 561–564(2013). Meijer, J. et al.
Concept of deterministic single ion dopingwith sub-nm spatial resolution.
Appl. Phys. A , 321–327, DOI: 10.1007/s00339-006-3497-0 (2006). Schnitzler, W. et al.
Deterministic ultracold ion source tar-geting the heisenberg limit.
Phys. Rev. Lett. , 070501,DOI: 10.1103/PhysRevLett.102.070501 (2009).
Groot-Berning, K. et al.
Deterministic single-ion implan-tation of rare-earth ions for nanometer-resolution color-center generation.
Phys. Rev. Lett. , 106802, DOI:10.1103/PhysRevLett.123.106802 (2019).
Räcke, P., Staacke, R., Gerlach, J. W., Meijer, J. & Spe-mann, D. Image charge detection statistics relevant fordeterministic ion implantation.
J. Phys. D: Appl. Phys. , 305103, DOI: 10.1088/1361-6463/ab1d04 (2019). Shinada, T., Ishikawa, A., Fujita, M., Yamashita, K. &Ohdomari, I. Influence of secondary electron detectionefficiency on controllability of dopant ion number in sin-gle ion implantation.
Jpn. J. Appl. Phys. , 3419–3421,DOI: 10.1143/jjap.38.3419 (1999). Schenkel, T. et al.
Single ion implantation for solid statequantum computer development.
J. Vac. Sci. & Technol. : Microelectron. Nanometer Struct. Process. Meas. Phe-nom. , 2819–2823, DOI: 10.1116/1.1518016 (2002).https://avs.scitation.org/doi/pdf/10.1116/1.1518016. Shinada, T., Okamoto, S., Kobayashi, T. & Ohdomari,I. Enhancing semiconductor device performance usingordered dopant arrays.
Nature , 1128–1131, DOI:10.1038/nature04086 (2005).
Wang, Y., Zhao, Y., Qayyum, A. & Xiao, G. Separationof potential and kinetic electron emission from si and winduced by multiply charged neon and argon ions.
Nucl.Instruments Methods Phys. Res. Sect. B: Beam Interac-tions with Mater. Atoms , 474–478 (2007).
Xu, Z. et al.
Charge effect in secondary electronemission from silicon surface induced by slow neonions.
Laser Part. Beams , 319–324, DOI: 10.1017/S0263034612000171 (2012). Jamieson, D. N. et al.
Deterministic atom placementby ion implantation: Few and single atom devices forquantum computer technology. In , 1–6,DOI: 10.1109/IIT.2016.7882858 (2016).
Breese, M. B. H., King, P. J. C., Grime, G. W. & Watt, F.Microcircuit imaging using an ion-beam-induced charge.
J. Appl. Phys. , 2097–2104, DOI: 10.1063/1.351596(1992). https://doi.org/10.1063/1.351596. Kim, G., van den Boogaart, M. & Brugger, J. Fabrica-tion and application of a full wafer size micro/nanostencilfor multiple length-scale surface patterning.
Microelec-tron. Eng. , 609 – 614, DOI: https://doi.org/10.1016/S0167-9317(03)00121-7 (2003). Proceedings ofthe 28th International Conference on Micro- and Nano-Engineering.
Persaud, A. et al.
Ion implantation with scanningprobe alignment.
J. Vac. Sci. & Technol. B: Micro-electron. Nanometer Struct. Process. Meas. Phenom. ,2798–2800, DOI: 10.1116/1.2062628 (2005). https://avs.scitation.org/doi/pdf/10.1116/1.2062628. Meijer, J. et al.
Towards the implanting of ions and posi-tioning of nanoparticles with nm spatial resolution.
Appl.Phys. A , 567–571, DOI: 10.1007/s00339-008-4515-1(2008). Tosi, G. et al.
Silicon quantum processor with robustlong-distance qubit couplings.
Nat. Commun. , 450,DOI: 10.1038/s41467-017-00378-x (2017). Morello, A. et al.
Single-shot readout of an electronspin in silicon.
Nature , 687–691, DOI: 10.1038/nature09392 (2010).
Singh, M. et al.
Electrostatically defined silicon quantumdots with counted antimony donor implants.
Appl. Phys.Lett. , 062101, DOI: 10.1063/1.4940421 (2016). https://doi.org/10.1063/1.4940421.
Evensen, L., Hanneborg, A., Avset, B. S. & Nese, M.Guard ring design for high voltage operation of silicondetectors.
Nucl. Instruments Methods Phys. Res. Sect. A:Accel. Spectrometers, Detect. Assoc. Equip. , 44–52(1993).
Bertuccio, G., Rehak, P. & Xi, D. A novel charge sen-sitive preamplifier without the feedback resistor.
Nucl.Instruments Methods Phys. Res. Sect. A: Accel. Spec-trometers, Detect. Assoc. Equip. , 71 – 76, DOI:https://doi.org/10.1016/0168-9002(93)90334-E (1993).
Majstrzyk, W. et al.
Thermomechanically and electro-magnetically actuated piezoresistive cantilevers for fast-scanning probe microscopy investigations.
Sensors Actu-ators A: Phys. , 237–245 (2018).
Binnig, G., Quate, C. F. & Gerber, C. Atomic forcemicroscope.
Phys. Rev. Lett. , 930–933, DOI: 10.1103/PhysRevLett.56.930 (1986). Watkins, R. E. J., Rockett, P., Thoms, S., Clampitt, R. &Syms, R. Focused ion beam milling.
Vacuum , 961–967(1986). Betta, G. et al.
Development of a detector-compatible jfettechnology on high-resistivity silicon.
Nucl. InstrumentsMethods Phys. Res. Sect. A: Accel. Spectrometers, Detect.Assoc. Equip. , 346–350 (1998).
Betta, G.-F. et al.
Monolithic integration of Si-pin diodesand n-channel double-gate jfet’s for room temperaturex-ray spectroscopy.
Nucl. Instruments Methods Phys. Res.Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. ,275–280 (2001).
Fiorini, C. & Porro, M. Drago chip: a low-noise cmospreamplifier shaper for silicon detectors with integratedfront-end jfet.
IEEE Transactions on Nucl. Sci. , 1647–1653 (2005). Biersack, J. P. & Haggmark, L. G. A monte carlo com-puter program for the transport of energetic ions in amor-phous targets.
Nucl. Instruments Methods , 257–269(1980).
Ziegler, J. F., Ziegler, M. D. & Biersack, J. P. SRIM –the stopping and range of ions in matter (2010).
Nucl. In-struments Methods Phys. Res. Sect. B: Beam Interactionswith Mater. Atoms , 1818–1823 (2010).
Auden, E. C. et al.
Sub-micron resolution of localizedion beam induced charge reduction in silicon detectorsdamaged by heavy ions.
IEEE Transactions on Nucl. Sci. , 2919–2925 (2015). Rossi, A. et al.
Silicon metal-oxide-semiconductor quan-tum dots for single-electron pumping.
JoVE (Journal Vis.Exp. e52852 (2015).
Ziegler, J. F. & Biersack, J. P.
The Stopping and Rangeof Ions in Matter , 93–129 (Springer US, Boston, MA,1985).
Posselt, M., Mäder, M., Grötzschel, R. & Behar, M.Competing influence of damage buildup and lattice vi-brations on ion range profiles in si.
Appl. Phys. Lett. , 545–547, DOI: 10.1063/1.1594281 (2003). https://doi.org/10.1063/1.1594281. Posselt, M., Bischoff, L., Grambole, D. & Herrmann,F. Competition between damage buildup and dynamicannealing in ion implantation into ge.
Appl. Phys. Lett. , 151918, DOI: 10.1063/1.2360238 (2006). https://doi.org/10.1063/1.2360238. Pilz, W. et al.
Dependence of the silicon detector responseto heavy ions on the direction of incidence: Computersimulations versus experimental data.
Nucl. InstrumentsMethods Phys. Res. Sect. A: Accel. Spectrometers, Detect.Assoc. Equip. , 137 – 145, DOI: https://doi.org/10.1016/S0168-9002(98)01151-6 (1998).
Oen, O. S. & Robinson, M. T. Computer studies of thereflection of light ions from solids.
Nucl. InstrumentsMethods , 647 – 653, DOI: https://doi.org/10.1016/0029-554X(76)90806-5 (1976).
Funsten, H. O., Ritzau, S. M., Harper, R. W. & Korde, R.Response of 100collection efficiency silicon photodiodesto low-energy ions.
IEEE Transactions on Nucl. Sci. ,1785–1789 (2001). Funsten, H. O., Ritzau, S. M., Harper, R. W., Borovsky,J. E. & Johnson, R. E. Energy loss by kev ions in silicon.
Phys. Rev. Lett. , 213201, DOI: 10.1103/PhysRevLett.92.213201 (2004). Robinson, M. Nuclear fusion reactors.
Proc. Br. Nucl.Energy Soc., UKAEA, Lond. (1970).
Acknowledgements
We thank F.E. Hudson and A.S. Dzurak for discussions andsupport in the establishment of this research project. The re-search at the University of Melbourne and UNSW was fundedby the Australian Research Council Centre of Excellencefor Quantum Computation and Communication Technology(Grant No. CE170100012) and the US Army Research Of-fice (Contract No. W911NF-17-1-0200). We acknowledge agrant from the University of Melbourne Research and Infras-tructure Fund (RIF) and use of the facilities of the AustralianNational Fabrication Facility (ANFF) at the Melbourne Centrefor Nanofabrication (MCN) and at UNSW. H.R.F. acknowl-edges the support of an Australian Government ResearchTraining Program Scholarship. A.M. Jakob acknowledgesan Australia–Germany Joint Research Cooperation Scheme (UA-DAAD) travel scholarship that supported collaborationwith partner institutions in Germany. We are grateful to D.McCulloch of the RMIT Microscopy and Microanalysis Fa-cility for use of SEM/FIB and TEM equipment. The viewsand conclusions contained in this document are those of theauthors and should not be interpreted as representing the of-ficial policies, either expressed or implied, of the ARO orthe US Government. The US Government is authorized toreproduce and distribute reprints for government purposesnotwithstanding any copyright notation herein.
Author contributions statement
A.M. Jakob designed and constructed the detector preampli-fier electronics and the integration of the ion beam line withthe AFM nanostencil scanner. A.M. Jakob conceived and con-ducted the deterministic implantation experiments with assis-tance from S.G. Robson. A.M. Jakob, V. Schmitt, V. Mourikand B.C. Johnson developed single ion detectors. V. Schmitt,V. Mourik and H.R. Firgau fabricated single ion detectors.S.G. Robson and B.C. Johnson conducted DIT/FOC as well asC-V/I-V analysis for iterative detector performance improve-ment. S.G. Robson performed FIB ion-aperture milling andSEM imaging, with assistance from E. Mayes. A.M. Jakoband D. Spemann developed theoretical groundwork on thedetection confidence. M. Posselt developed the Crystal-TRIMcode. A.M. Jakob and M. Posselt conducted Crystal-TRIMcomputations and analysis. J.C. McCallum contributed to thedesign of the ion implantation experiments. A. Morello pro-vided the design of the flip-flop qubit architecture, the designconstraints on the fabrication of the detectors, and supervisedthe research at UNSW. D.N. Jamieson conceived the deter-ministic ion implantation process and the implementation ofthe apparatus. The manuscript was written by A.M. Jakob andD.N. Jamieson with contributions from the co-authors.
Additional information