Article https://doi.org/10.1038/s41467-023-36951-w Reducing charge noise in quantum dots by using thin silicon quantum wells Received: 30 September 2022 Brian Paquelet Wuetz1, Davide Degli Esposti1, Anne-Marije J. Zwerver1, Sergey V. Amitonov1,2, Marc Botifoll 3, Jordi Arbiol 3,4, Amir Sammak2, Accepted: 25 February 2023 Lieven M. K. Vandersypen 1, Maximilian Russ 1 & Giordano Scappucci 1 Published online: 13 March 2023 Check for updates Charge noise in the host semiconductor degrades the performance of spin- qubits and poses an obstacle to control large quantum processors. However, it 1234567890():,; is challenging to engineer the heterogeneous material stack of gate-defined 1234567890():,; quantum dots to improve charge noise systematically. Here, we address the semiconductor-dielectric interface and the buried quantum well of a 28Si/SiGe heterostructure and show the connection between charge noise, measured locally in quantum dots, and global disorder in the host semiconductor, measured with macroscopic Hall bars. In 5 nm thick 28Si quantum wells, we find that improvements in the scattering properties and uniformity of the two- dimensional electron gas over a 100 mm wafer correspond to a significant reduction in charge noise, with a minimum value of 0.29 ± 0.02 μeV/Hz½ at 1 Hz averaged over several quantum dots. We extrapolate the measured charge noise to simulated dephasing times to CZ-gate fidelities that improve nearly one order of magnitude. These results point to a clean and quiet crystalline environment for integrating long-lived and high-fidelity spin qubits into a larger system. Spin-qubits in silicon quantum dots are a promising platform for Charge noise is commonly associated with two-level fluctuators building a scalable quantum processor because they have a small (TLF)19 in the semiconductor host. In gated heterostructures with footprint1, long coherence times2,3, and are compatible with advanced buried quantum wells, TLF may arise from impurities in several semiconductor manufacturing4. Furthermore, rudimentary quantum locations: within the quantum well, the semiconductor barrier, the algorithms have been executed5 and quantum logic at high-fidelity semiconductor/dielectric interface, and the dielectrics layers performed6–9. As the qubit count is increasing, with a six-qubit pro- above20–26. Furthermore, previous work on strained-Si MOSFETs27–29, cessor demonstrated10, significant steps have been taken to couple with strained-Si channels deposited on SiGe strain relaxed buffers, silicon spin qubits at a distance, via microwave photons or spin has associated charge noise with dislocations arising from strain shuttling11–16, towards networked spin-qubit tiles17. However, electrical relaxation, either deep in the SiGe buffer or at the quantum well/ fluctuations associated with charge noise in the host semiconductor buffer interface. Since these impurities and dislocations are ran- can decrease qubit readout and control fidelity18. Reducing charge domly distributed over the wafer and are also a main scattering noise independently of the device location on a wafer is pivotal to source for electron transport in buried quantum wells30, a holistic achieving the ubiquitous high-fidelity of quantum operations, within approach to materials engineering should be taken to address dis- and across qubit tiles, necessary to execute more complex quantum order in two-dimensional electron gases and charge noise in algorithms. quantum dots. 1 QuTech and Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands. 2QuTech and Netherlands Organisation for Applied Scientific Research (TNO), Delft, The Netherlands. 3Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Catalonia, Spain. 4ICREA, Pg. Lluís Companys 23, 08020 Barcelona, Catalonia, Spain. e-mail: g.scappucci@tudelft.nl Nature Communications | (2023)14:1385 1 Article https://doi.org/10.1038/s41467-023-36951-w In this work, we demonstrate thin quantum wells in 28Si/SiGe Heterostructure A has an ≃9 nm thick quantum well and is terminated heterostructures with low and uniform charge noise, measured over with an epitaxial Si cap grown by dichlorosilane at 675 °C. This kind of several gate-defined quantum dot devices. By linking charge noise heterostructure has already produced high performance spin- measurements to the scattering properties of the two-dimensional qubits6,10,31. Heterostructure B misses a final epitaxial Si cap but fea- electron gas, we show that a quiet environment for quantum dots is tures an amorphous Si-rich layer obtained by exposing the SiGe barrier obtained by improving the semiconductor/dielectric interface and to dichlorosilane at 500 °C. Compared to A, heterostructure B sup- the crystalline quality of the quantum well. We feed the measured ports a two-dimensional electron gas with enhanced and more uniform charge noise into a theoretical model, benchmark the model against transport properties across a 100 mm wafer, owing to a more uniform recent experimental results6,10, and predict that these optimized SiOx layer with less scattering centers32. Finally, we introduce here heterostructures may support long-lived and high-fidelity spin heterostructure C, having the same amorphous Si-rich termination as qubits. in heterostructure B, but a thinner quantum well of ≃5 nm (Supple- mentary Fig. 1). This is much thinner than the Matthews-Blakeslee Results critical thickness33,34, which is ≃10 nm35 for the relaxation of tensile Si Description of 28Si/SiGe heterostructures on Si0.7Ge0.3 via the formation of misfit dislocation at the bottom Figure 1a illustrates the undoped 28Si/SiGe heterostructures, grown interface of the quantum well. In light of recent morphological char- by reduced-pressure chemical vapor deposition, and the gate-stack acterization by electron channeling constrast imaging of Si/SiGe het- above. From bottom to top, the material stack comprises a 100 mm Si erostructures with similar quantum well thickness and SiGe chemical substrate, a strain-relaxed SiGe buffer layer, a strained 28Si quantum composition36, we expect misfit dislocation segments in hetero- well, a 30 nm thick SiGe barrier, a Si cap oxidized in air to form a SiOx structure B because the quantum well approaches the Matthews- layer, an AlOx layer formed by atomic layer deposition, and metallic Blakeslee critical thickness. Due to the much thinner quantum well, gates. The SiGe layers above and below the quantum well have a Ge instead, the epitaxial planes may adapt to the SiGe buffer much better concentration of ≃0.3 (Methods). in heterostructure C than in heterostructure B, meaning that misfit We consider three 28Si/SiGe heterostructures (A, B, C) to improve, dislocations are, in principle, suppressed. in sequence, the semiconductor/dielectric interface (from A to B) and Figure 1b, c shows bright-field scanning transmission electron the crystalline quality of the quantum well (from B to C). microscopy (BF-STEM) images from heterostructure C after a b AlOx AlOx SiOx SiOx z SiGe 10 nm SiGe c SiGe 28 Si 28 Si SiGe SiGe 10 nm d e 2 2.5 10 2.0 μ (105 cm2/Vs) σxx (e2/h) 1.5 1.0 1 0.5 10 0.0 0 2 4 6 1 2 n (1011 cm-2) n (1011 cm-2) Fig. 1 | Material stack and heterostructure field effect transistor characteriza- strain relaxation. b, c BF-STEM images from heterostructure C highlighting the tion. a Schematics of the 28Si/SiGe heterostructure and dielectric stack above. z semiconductor/dielectric interface and the 5 nm thick 28Si quantum well, respec- indicates the heterostructure growth direction. Circles represent remote impurities tively. d Mobility μ and e conductivity σxx measured as a function of density n at a at the semiconductor/dielectric interface and perpendicular symbols represent temperature of 1.6 K in a Hall bar H-FET from heterostructure C. The red curve in e is misfit dislocations that might arise at the quantum well/buffer interface due to a fit to percolation theory. Nature Communications | (2023)14:1385 2 Article https://doi.org/10.1038/s41467-023-36951-w a b 200 1e−12 dI/dV (nA/mV) 2.5 VSD (μV) 150 500 0.0 ISD (pA) P SDRAcc 0 −2.5 100 340 345 350 355 360 SD RB VP (mV) SD 50 SD LB 200 nm LA cc z 260 280 300 320 340 360 380 VP (mV) c d e −11 10 −11 10 −12 10 10 − 10 Sε (eV2/Hz) Sε (eV2/Hz) Sε (eV /Hz) 10 − 11 −12 10 2 −13 10 10 − 12 10 − 13 −14 10 ∝1/f 10 − 14 −13 250 10 10 − 1 10 −1 10 0 10 1 300 10 0 300 350 V ( P m z) f (Hz) V ) 350 10 1 f (H VP (mV) Fig. 2 | Quantum dots and charge noise measurements. a False colored SEM- VP and the source drain bias VSD. c Charge noise spectrum Sϵ measured at the image of a double quantum dot system with a nearby charge sensor. Charge noise is Coulomb peak at VP ≃ 360.3 mV in b and extracted using the lever arm from the measured in the multi-electron quantum dot defined by accumulation gates corresponding Coulomb diamond. The black trendline is proportional to 1/f. d Sϵ SDLAcc and SDRAcc (blue), plunger P (blue), with the current going along the black for the same device in b, plotted in 3D as a function of f and VP. The dark gray plane arrow. In these experiments, the gates defining the double quantum dot (red) are is a fit through the datasets, i.e. the collection of noise spectra as in c measured at used as screening gates. There is an additional global top gate (not shown) to different VP and each obtained using a unique lever arm from the corresponding facilitate charge accumulation when needed. b Source-drain current ISD through a Coulomb diamond. e Line cut through the data in d at f = 1 Hz, showing the charge sensor device fabricated on heterostructure C against the plunger gate experimental noise Sϵ (colored dots) and fit (dark gray line). The black circled data voltage VP. Colored dots mark the position of the flank of the Coulomb peak where point (also in d) marks the minimum charge noise measured for this specific device charge noise measurements are performed. The inset shows Coulomb diamonds (Sϵ,min) at f = 1 Hz. from the same device, plotted as the differential of the current dI/dV as a function of fabrication of a Hall bar shaped heterostructure field effect transistors above 99% were demonstrated6, silicon quantum circuits were con- (H-FET). We observe a sharp SiGe/SiOx semiconductor/dielectric trolled by CMOS-based cryogenic electronics31, and energy splittings in 28 interface (Fig. 1b), characterized by a minor Ge pile up (dark line) in line Si/SiGe heterostructures were studied with statistical significance40. with ref. 32. The ≃5 nm thick quantum well (Fig. 1c, Supplementary Here, we electrostatically define a multi-electron quantum dot Fig. 1) is uniform, has sharp interfaces to the nearby SiGe, and appears in the charge sensor by applying gate voltages to the accumulation of high crystalline quality. gates SDRAcc and SDLAcc, the barriers SDLB and SDRB, and the plunger gate P. All other gates (red in Fig. 2a) are set to 0 V for Electrical characterization of heterostructure field effect measurements of heterostructure B and C, whereas they are posi- transistors tively biased in heterostructure A to facilitate charge accumulation We evaluate the scattering properties of the two-dimensional electron in the sensor (Methods). Figure 2b shows typical Coulomb blockade gases by wafer-scale electrical transport measured on Hall-bar shaped oscillations of the source-drain current ISD for a charge sensor from H-FETs operated in accumulation mode (Methods). For each hetero- heterostructure C measured at a dilution refrigerator base tem- structure, multiple H-FETs over a wafer are measured in the same cool- perature of 50 mK. We follow the same tune-up procedure (Meth- down at a temperature of 1.7 K in refrigerators equipped with cryo- ods) consistently for all devices and we measure charge noise at the multiplexers37. Figure 1d, e shows typical mobility-density and flank of each Coulomb peak within the VP range defined by the first conductivity-density curves for heterostructure C, from which we peak observable in transport and the last one before onset of a extract the mobility measured at high density (n = 6 × 1011 cm−2) and the background channel (Supplementary Figs. 2–4). For example, in percolation density (np)38. The mobility rises steeply at low density due Fig. 2b we consider Coulomb peaks within the VP range from 260 mV to progressive screening of scattering from remote impurities and to 370 mV. The data collected in this systematic way is taken as a flattens at higher density (n > 5 × 1011 cm−2), limited by scattering from basis for comparison between the three different heterostructures impurities within or nearby the quantum well, for example uniform in this study. background charges, surface roughness, or crystalline defects such as For each charge noise measurement at a given VP we acquire threading or misfit dislocations30,39. 60 s (heterostructure A) or 600 s (heterostructures B, C) long traces of ISD and split them into 10 (heterostructure A) or 15 windows Charge noise measurements in quantum dots (heterostructures B, C). We obtain the current noise spectrum SI by For charge noise measurements, we use devices comprising a double averaging over the 10 (15) windows the discrete Fourier transform of quantum dot and a charge sensor quantum dot nearby, illustrated in the segments (Methods). We convert SI to a charge noise spectrum Fig. 2a. Using the same device design, two-qubit gates with fidelity Sϵ using, for each measurement at a given VP, the unique lever arm Nature Communications | (2023)14:1385 3 Article https://doi.org/10.1038/s41467-023-36951-w a b 3 1.6 1.4 μ (105 cm2 /Vs) n p (1011 cm− 2 ) 2 1.2 1 1.0 0.8 0 A B C A B C c d e 1.8 Sε1/2 m in (1 Hz) (μeV/Hz1/2 ) 1.6 0 0 10 β (mV-1) 1.4 −20 α 1.2 −40 1.0 −1 10 0.8 A B C A B C A B C Fig. 3 | Distribution of transport properties and charge noise. a, b Distributions indicating the change in noise spectrum with increasing VP, and minimum charge 1=2 of mobility μ measured at n = 6 × 1011 cm−2 and percolation density np for hetero- noise Sϵ,min within the range of VP investigated for heterostructure A (red, 4 devices structure A (red, 20 H-FETs measured, of which 16 reported in ref. 32), B (blue, 16 measured), B (blue, 7 devices measured), and C (green, 5 devices measured). H-FETs measured of which 14 reported in ref. 32), and C (green, 22 H-FETs mea- Quartile box plots, mode (horizontal line), means (diamonds), 99% confidence sured). c–e Distributions of noise spectrum power law exponent α, coefficient β intervals of the mean (dashed whiskers), and outliers (circles) are shown. from the corresponding Coulomb diamonds and slope of the Cou- Distribution of transport properties and charge noise lomb peak to take into account a possible deformation of the charge We have introduced key metrics for 2D electrical transport (μ, np) and sensor with the increasing electron number (inset Fig. 2b, Methods, charge noise (α, β and Sϵ,min) from Hall bar and quantum dot mea- and Supplementary Fig. 5). A representative charge noise spectrum surements, respectively. In Fig. 3a–e we compare the distributions of Sϵ measured at VP = 360.3 mV is shown in Fig. 2c. We observe an all these metrics for the three heterostructures A, B, C. Each box-plot is approximate 1/f trend at low frequency, pointing towards an obtained from the analysis of measurements in Figs. 1d, e, and 2d ensemble of TLF with a broad range of activation energies affecting repeated on multiple H-FETs or quantum dots, on dies randomly charge noise around the charge sensor41,42. Figure 2e shows the selected from different locations across the 100 mm wafers (Methods). charge noise Sϵ at 1 Hz as a function of VP. The charge noise To facilitate a comparison with previous studies, the minimum charge 1=2 decreases, with a linear trend, with increasing VP, suggesting that, noise at 1 Hz is plotted in Fig. 3e as Sϵ,min and therefore in units of similar to scattering in 2D, screening by an increased electron den- μeV/Hz½. sity shields the electronically active region from noise arising from As reported earlier in ref. 32, the improvement in both mean values the heterostructure and the gate stack43. From this measurement we and spread for μ and np was associated with a reduction of remote extract, for a given device, the minimum measured charge noise at 1 impurities when replacing the epitaxial Si cap in heterostructure A Hz (Sϵ,min circled data point in Fig. 2e) upon variation of VP in our with a Si-rich passivation layer in heterostructure B. Moving to experimental range. We use Sϵ,min as an informative metric to com- heterostructure C, we measure a high mean mobility of pare charge noise levels from device to device in a given hetero- (2.10 ± 0.08) × 105 cm2/Vs and a low mean percolation density of structure. For a given device, all charge noise spectra Sϵ are plotted (7.68 ± 0.37) × 1010 cm−2, representing an improvement by a factor ≃1.4 in 3D as a function of f and VP (Fig. 2d). To quantify our observations, and ≃1.3, respectively (compared to heterostructure A). Most strik- we fit the data to the plane log Sϵ =  α log f + βV P + γ (Supplemen- ingly, the 99% confidence intervals of the mean for μ and np are dras- tary Note 4). Coefficient α = 0.84 ± 0.01 indicates the spectrum tically reduced by a factor ≃9.8 and ≃4.8, respectively. We speculate power law exponent and coefficient β = − 15.6 ± 0.1 mV−1 quantifies that these improvements in heterostructure C are associated with the the change in noise spectrum with increasing plunger gate and, suppression of misfit dislocations at the quantum well/buffer inter- consequently, the susceptibility of charge noise to the increasing face, thereby reducing short range scattering and increasing uni- electron number in the sensor. formity on a wafer-scale. This interpretation is supported by previous Nature Communications | (2023)14:1385 4 Article https://doi.org/10.1038/s41467-023-36951-w studies of mobility limiting mechanisms as a function of the quantum dislocations at the quantum well/buffer interface, further reduces the well thickness in strained Si/SiGe heterostructures39. We speculate that charge noise picked up by quantum dots. This explanation is based on further reducing the quantum well thickness could increase surface earlier studies of charge noise in strained Si-MOSFETs27–29, which roughness scattering from the bottom interface, and therefore dis- showed a correlation between low-frequency noise spectral density order. Instead, fine-tuning the quantum well thickness between 5 nm and static device parameters. Dislocations at the bottom of the and 9 nm might minimize surface roughness scattering whilst still strained channel may act as scattering centers that degrade mobility avoiding the formation of misfit dislocations. and as traps for the capture and release of carriers, which causes noise We now shift our attention to the results of charge noise mea- similarly to traps at the dielectric interface. surements. First, the power law exponent α (Fig. 3c) shows a mean value ≃1, however the 99% confidence interval and interquartile range Calculated dephasing time and infidelity increase when moving from heterostructure A to B and C. Next, we To emphasize the improvement of the electrical environment in the observe a decreasing trend for the absolute mean value of coefficient β semiconductor host, we calculate the dephasing time T ?2 of charge and (Fig. 3d), meaning that the noise spectrum is less susceptible to changes spin qubits assuming these qubits experience the same fluctuations as 1=2 in VP. Finally, Fig. 3e shows the distributions for Sϵ,min , the minimum our 28Si/SiGe quantum dots. The dephasing time of a qubit (in the charge noise at 1 Hz upon varying VP. We find in heterostructure C quasistatic limit and far-off from a sweet spot) is given by51,52 1=2 an almost order of magnitude reduction in mean Sϵ,min to 0.29 ± 0.02 μeV/Hz . This trend is confirmed by plotting the distributions of max- ½ h T ?2 = pffiffiffi ð1Þ imum charge noise at 1 Hz upon varying VP (Supplementary Fig. 4). 2πσ 1=2 Furthermore, within the distribution of Sϵ,min for heterostructure C, the minimum value of the measured charge noise as a function of VP and with the Planck constant h and the standard deviation across quantum dots is 0.15 μeV/Hz½. These charge noise values are on  2 Z f high 2 par or compare favorably to the best values reported previously at 1 Hz ∂E  Sϵ in gate defined quantum dots. In multi-electron quantum dots, charge σ 2 =   × 2 α df : ð2Þ ∂μ f low f noise of 0.47 μeV/Hz½ was reported for Si/SiGe44, 0.6 μeV/Hz½ (average value, with a minimum of ≤0.2 μeV/Hz½) for Ge/SiGe45, Importantly, both the charge noise amplitude S2ϵ ðf Þ and the 0.49 ± 0.1 μeV/Hz½ for Si/SiO246, and 1 μeV/Hz½ for InSb47. In single- noise exponent α have a strong impact on the dephasing time while electron quantum dots, charge noise of 0.33 μeV/Hz½ was reported for the low and high frequency cut-off, flow and fhigh, given by the Si/SiGe48 and 7.5 μeV/Hz½ for GaAs49. duration of the experiment have a weaker impact. The prefactor ∣ ∂E ∂μ∣ We understand the charge noise trends in Fig. 3c–e by relating translates shifts in chemical potential of the charge sensor into them to the evolution of the disorder landscape moving from het- energy shifts of the qubit and depends on many parameters such as ∂E erostructures A to B and C, as inferred by the electrical transport the type of qubit and the device itself. We find ∣ ∂μ ∣ = 1 for a charge 5 measurements in Fig. 3a, b. The narrow distribution of α in hetero- qubit53 and ∣ ∂E∂μ ∣≈10 for an uncoupled spin- qubit 44 (see Supple- structure A points to charge noise being dominated from many TLFs mentary Note 7 for a derivation of these numbers and the used possibly located at the low quality semiconductor/dielectric interface frequency bandwidths). and above, albeit other sources of charge noise in the surrounding Figure 4a shows the computed dephasing times of charge qubits environment of the quantum dot may be present, such as highly (circle) and spin qubits (star) for all three heterostructures. These localized misfit dislocations arising from partial strain relaxation in the calculations represent a best case scenario, since we use the distribu- quantum well or other nearby fluctuators. With a better semi- tion of measured Sϵ,min from Fig. 3 as input parameter for each het- conductor/dielectric interface, the effect of these other nearby fluc- erostructure. The improvements in our material can be best seen by tuators emerges in heterostructure B and C as a larger spread of the investigating T ?2 of the charge qubit since it is directly affected by frequency exponent α, indicating a nonuniform distribution of acti- charge noise. Our theoretical extrapolation shows two orders of vation energies according to the Dutta-Horn model50. Yet, the noise magnitude improvement in T ?2 by switching from heterostructures A spectra still follow a 1/f-like behavior (Supplementary Fig. 3), sug- to heterostructures B and C. One order is gained from the reduced gesting that TLFs also experience slow temperature fluctuations42. The charge noise amplitude and another order is gained through a more electrical transport measurements support this interpretation: scat- beneficial noise exponent α > 1. Note, that the integration regimes tering from many remote impurities is dominant in heterostructure A, differ for spin and charge qubits due to the different experimental whereas with a better semiconductor/dielectric interface remote setups and operation speeds44,53. For potential spin qubits in hetero- ? scattering has less impact in the transport metrics of hetero- structure A the calculated T ?2 shows an average T 2 = 8:4 ± 5:6 μs. This ? structures B and C. distribution compares well with the distribution T 2 = 6:7 ± 5:6 μs of ? The decreasing trend in ∣β∣ is in line with the observation from experimental T 2 data from state-of-the-art semiconductor spin qubits electrical transport. As the impurity density decreases from hetero- in materials with similar stacks as in heterostructure A6,10. Note that structure A to B and C, charge noise is less affected by an increasing VP, while such comparisons oversimplify actual semiconductor spin-qubit since screening of electrical noise through adding electrons to the devices by reducing them to a single number, they fulfill two aims. charge sensor becomes less effective. While we are not able to measure They allow us to benchmark the computed performance of hetero- directly the electron number in the charge sensor, we deem unlikely structure A to past experiments and provide a prognosis on the qubit the hypothesis that charge sensors in heterostructure A are operated quality in novel material stacks. Heterostructures B and C, in this case, ? with considerably fewer electrons than in heterostructure C. This is may support average dephasing times of T 2 = 24:3 ± 12:5 μs and ? because all operation gate voltages in heterostructure A are con- T 2 = 36:7 ± 18 μs, respectively. The highest values T ?2 = 70:1 μs hints sistently larger than in heterostructure C (Supplementary Fig. 4), due towards a possible long dephasing time for spin qubits, previously only to the higher disorder. reported in ref. 2. 1=2 Finally, the drastic reduction in mean value and spread of Sϵ,min Figure 4b shows the simulated infidelity, a metric to measure mirrors the evolution of mean value and spread of np and μ. From the closeness to the ideal operation, of a universal CZ-gate between heterostructure A to B, a reduction in scattering from remote impu- two spin qubits following ref. 6 and Supplementary Note 7. Note that rities is likely to result in less charge noise from long-range TLFs. From the device used in ref. 6 has the same architecture as our test devices. heterostructure B to C, the reduction in the possible number of In the CZ-gate simulation, noise couples in dominantly via barrier Nature Communications | (2023)14:1385 5 Article https://doi.org/10.1038/s41467-023-36951-w a 2 b −2 10 10 1 10 0 10 −1 10 T2* (μs) spin qubit 1-FCZ spin qubit literature −3 10 charge qubit −2 10 −3 10 −4 10 −5 −4 10 10 A B C A B C Fig. 4 | Calculated dephasing times and infidelity. a Computed dephasing times (fmin, fmax) = (1.6 mHz, 10 kHz). Literature values (squares) are taken from refs. 6,10. T ?2 of a charge qubit (circle) and of a spin-qubit (star) using Sϵ,min from hetero- b Simulated infidelity of a CZ-gate between two spin qubits following the ref. 6 using structure A (red), B (blue), C (green). Eq. (1) was used to compute T ?2 as a function of Sϵ and α from heterostructure A (red), B (blue), C (green) in Fig. 3 as input for barrier Sϵ and α from Fig. 3 with frequency cutoffs (fmin, fmax) = (1.6 mHz, 33 GHz) and fluctuations. voltage fluctuations which affects the interaction between the against published spin-qubit data, we predict that our optimized electron spins. Again, we use the charge noise amplitude Sϵ,min and semiconductor host could support long-lived and high-fidelity spin exponent α from the quantum dot experiments in Fig. 3 as input for qubits. We envisage that further materials improvements in the the simulations. The simulations show an averaged average gate structural quality of the quantum well, in addition to the commonly infidelity 1  F CZ = 0:02 ± 0:01% which means on average a single considered semiconductor/dielectric interface, may lead system- error every 5000 runs. We also observe a saturation value close to atically to quantum dots with less noise and to better qubit 1 − F = 10−4 which arises from single-qubit dephasing T ?2 = 20 μs used performance. in the simulations estimated from nuclear spin noise due to a 800 ppm concentration of the 29Si silicon isotope which has a non-zero Methods nuclear spin44. Si/SiGe heterostructure growth The 28Si/SiGe heterostructures are grown on a 100-mm n-type Discussion Si(001) substrate using an Epsilon 2000 (ASMI) reduced pressure In summary, we have measured electron transport and charge noise in chemical vapor deposition reactor. The reactor is equipped with a 28 28 Si/SiGe heterostructures where we improve the semiconductor/ SiH4 gas cylinder (1% dilution in H2) for the growth of isotopically dielectric interface, by adopting an amorphous Si-rich passivation, and enriched 28Si. The 28SiH4 gas was obtained by reducing 28SiF4 with a the structural quality of the quantum well, by reducing the quantum residual 29Si concentration of 0.08%54. Starting from the Si substrate, well thickness significantly below the Matthew-Blakeslee critical the layer sequence of all heterostructures comprises a 3 μm step- thickness for strain relaxation. We relate disorder in 2D to charge noise graded Si(1−x)Gex layer with a final Ge concentration of x = 0.3 in quantum dots by following a statistical approach to measurements. achieved in four grading steps (x = 0.07, 0.14, 0.21, and 0.3), fol- A reduction of remote impurities and dislocations nearby the quantum lowed by a 2.4 μm Si0.7Ge0.3 strain-relaxed buffer. The hetero- well is connected with the key improvements in the scattering prop- structures differ for the active layers on top of the strain-relaxed erties of the 2D electron gas, such as mobility and percolation density, buffer. Heterostructure A has a 9 nm tensile strained 28Si quantum and their uniformity across a 100 mm wafer. The trend observed from well, a 30 nm Si0.7Ge0.3 barrier, and a sacrificial 1 nm epitaxial Si cap. electron transport in 2D is compatible with the observations from Heterostructure B has an 9 nm tensile strained 28Si quantum well, a measurements of charge noise in quantum dots. As remote impurities 30 nm Si0.7Ge0.3 barrier, and a sacrificial passivated Si cap grown at are reduced, charge noise becomes more sensitive to local fluctuators 500 °C. Heterostructure C has a 5 nm tensile strained 28Si quantum nearby the quantum well and less subject to screening by an increased well, a 30 nm Si0.7Ge0.3 barrier, and a sacrificial passivated Si cap number of electrons in the dot. Furthermore, with this materials grown at 500 °C. A typical secondary ions mass spectrometry of our optimization, we achieve a statistical improvement of nearly one order heterostructures is reported in Supplementary Fig. S13 of ref. 40 and of magnitude in the charge noise supported by quantum dots. Using the Ge concentration in the SiGe layers is confirmed by quantitative the charge noise distribution as input parameter and benchmarking electron energy loss spectroscopy (EELS). Nature Communications | (2023)14:1385 6 Article https://doi.org/10.1038/s41467-023-36951-w Device fabrication across the screening gates. We measure the current ISD and the current The fabrication process for Hall-bar shaped heterostructure field effect noise spectrum SI on the left side of the Coulomb peak where ∣dI/dVP∣ is transistors (H-FETs) involves: reactive ion etching of mesa-trench to largest. We use a sampling rate of 1 kHz for 1 min using a Keithley isolate the two-dimensional electron gas; P-ion implantation and acti- DMM6500 multimeter. The spectra are then divided into 10 segments vation by rapid thermal annealing at 700 °C; atomic layer deposition of of equal length and we use a Fourier transform to convert from time- a 10-nm-thick Al2O3 gate oxide; deposition of thick dielectric pads to domain to frequency-domain for a frequency range of protect gate oxide during subsequent wire bonding step; sputtering of 167 mHz–500 Hz. We set the upper limit of the frequency spectra at Al gate; electron beam evaporation of Ti:Pt to create ohmic contacts to 10 Hz, to avoid influences from a broad peak at around 150 Hz coming the two-dimensional electron gas via doped areas. All patterning is from the setup (Supplementary Fig. 3). A peak in the power spectral done by optical lithography. Double quantum dot devices are fabri- density at 9 Hz is removed from the analysis since it is an artifact of the cated on wafer coupons from the same H-FET fabrication run and share pre-amplifier. To convert the current noise spectrum to a charge noise the process steps listed above. Double-quantum dot devices feature a spectrum, we use the formula20 single layer gate metallization and further require electron beam lithography, evaporation of Al (27 nm) or Ti:Pd (3:17 nm) thin film a2 SI Sϵ = ð3Þ metal gate, lift-off, ALD of a 5 nm thick Al2O3 insulating layer, and a ∣dI=dV P ∣2 global top-gate. where a is the lever arm and ∣dI/dVP∣ is the slope of the Coulomb peak Electrical characterization of H-FETs at the plunger voltage used to acquire the time trace. Hall-bar H-FETs measurements are performed in an attoDRY2100 The charge noise measurements conditions have been slightly variable temperature insert refrigerator at a base temperature of modified from sample A to sample B, C to extend the probed fre- 1.7 K32. We apply a source-drain bias of 100 μV and measure the source- quency range from 100 μHz to 10 μHz. For heterostructures B and C drain current ISD, the longitudinal voltage Vxx, and the transverse Hall we apply a source drain bias of 150 μV across the quantum dot, finite voltage Vxy as function of the top gate voltage Vg and the external gate voltages across the operation gates of the quantum dot, and we perpendicular magnetic field B. From here we calculate the long- apply 0 V to all other gates. We measure the current ISD and the current itudinal resistivity ρxx and transverse Hall resistivity ρxy. The Hall noise spectrum SI on the left side of the Coulomb peak where ∣dI/dVP∣ is electron density n is obtained from the linear relationship ρxy = B/en at largest. We use a sampling rate of 1 kHz for 10 min using a Keithley low magnetic fields. The carrier mobility μ is extracted from the rela- DMM6500 multimeter. The spectra are then divided into 15 segments tionship σxx = neμ, where e is the electron charge. The percolation of equal length and we use a Fourier transform to convert from time- density np is extracted by fitting the longitudinal conductivity σxx to domain to frequency-domain for a frequency range of 25 mHz–500 Hz. the relation σ xx / ðn  np Þ1:31 . Here σxx is obtained via tensor inversion We set the upper limit of the frequency spectra at 10 Hz, to avoid of ρxx at B = 0. The box plots in Fig. 3a, b for heterostructure A (red) and influences from a broad peak at around 150 Hz coming from the setup. B (blue) expand previously published data in Fig. 2f, e of ref. 32 by We use Eq. (3) to convert the current noise spectrum to a charge noise considering measurements of 4 additional H-FETs for heterostructure spectrum. A (20 H-FETs in total) and of 2 additional H-FETs for heterostructure B (16 H-FETs in total). (Scanning) Transmission Electron Microscopy For structural characterization with (S)TEM, we prepared cross- Electrical characterization of quantum dots sections of the quantum well heterostructures by using a Focused Measurements of the multi-electron quantum dots defined in the Ion Beam (Helios 600 dual beam microscope). Atomically resolved charge sensor are performed in a Leiden cryogenic dilution refrig- HAADF STEM data was acquired in a probe corrected TITAN micro- erator with a mixing chamber base temperature TMC = 50 mK40. The scope operated at 300 kV. Quantitative EELS was carried out in a devices are tuned systematically with the following procedure. We TECNAI F20 microscope operated at 200 kV with approximately 2 eV sweep all gate voltages (VSDRAcc, VSDRB, VP, VSDLB, and VSDLAcc) from 0 V energy resolution and 1 eV energy dispersion. Principal Component towards more positive bias, until a source-drain current ISD of ≈1 nA is Analysis (PCA) was applied to the spectrum images to enhance measured, indicating that a conductive channel has formed in the S/N ratio. device. We then reduce the barrier voltages to find the pinch-off voltages for each barrier. Subsequently, we measure ISD as a function Data availability of VSDLB and VSDRB and from this 2D map we find a set of gate voltage All data included in this work are available from the 4TU.ResearchData parameters so that Coulomb blockade peaks are visible. We then fix international data repository at https://doi.org/10.4121/20418579. the barrier voltages and sweep VP to count how many clearly defined Coulomb peaks are observed before onset of a background current. References The quantum dot is tuned to show at least 9 Coulomb peaks, so that 1. Vandersypen, L. M. K. & Eriksson, M. A. 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No. W911NF-17-1-0274). The views and conclusions contained in this Nature Communications | (2023)14:1385 8 Article https://doi.org/10.1038/s41467-023-36951-w document are those of the authors and should not be interpreted as Additional information representing the official policies, either expressed or implied, of the Supplementary information The online version contains Army Research Office (ARO), or the U.S. Government. The U.S. Gov- supplementary material available at ernment is authorized to reproduce and distribute reprints for Gov- https://doi.org/10.1038/s41467-023-36951-w. ernment purposes notwithstanding any copyright notation herein. M.R. acknowledges support from the Netherlands Organization of Correspondence and requests for materials should be addressed to Scientific Research (NWO) under Veni grant VI.Veni.212.223. ICN2 Giordano Scappucci. acknowledges funding from Generalitat de Catalunya 2021SGR00457. 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M.B. acknowledges support from SUR Generalitat de Catalunya isdictional claims in published maps and institutional affiliations. and the EU Social Fund; project ref. 2020 FI 00103. We acknowledge support from CSIC Interdisciplinary Thematic Platform (PTI+) on Open Access This article is licensed under a Creative Commons Quantum Technologies (PTI-QTEP+). Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as Author contributions long as you give appropriate credit to the original author(s) and the A.S. grew and designed the 28Si/SiGe heterostructures with B.P.W. and source, provide a link to the Creative Commons license, and indicate if G.S.. M.R. developed the theory. A.S. and D.D.E. fabricated hetero- changes were made. The images or other third party material in this structure field effect transistors measured by B.P.W. and D.D.E.. M.B and article are included in the article’s Creative Commons license, unless J.A. performed TEM characterization. S.A and D.D.E. fabricated quantum indicated otherwise in a credit line to the material. If material is not dot devices. B.P.W. and D.D.E. measured the quantum dot devices with included in the article’s Creative Commons license and your intended contributions from A.M.J.Z.. G.S. conceived and supervised the project. use is not permitted by statutory regulation or exceeds the permitted B.P.W, D.D.E, M.R, and G.S. wrote the manuscript with input from all use, you will need to obtain permission directly from the copyright authors. holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. Competing interests The authors declare no competing interests. © The Author(s) 2023, corrected publication 2023 Nature Communications | (2023)14:1385 9