Reducing charge noise in quantum dots by using thin silicon quantum wells

Abstract

Charge noise in the host semiconductor degrades the performance of spin-qubits and poses an obstacle to control large quantum processors. However, it is challenging to engineer the heterogeneous material stack of gate-defined 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.

Full text

Article https://doi.org/10.1038/s41467-023-36951-w
Reducing charge noise in quantum dots by
using thin silicon quantum wells
Brian Paquelet Wuetz
1
, Davide Degli Esposti
1
, Anne-Marije J. Zwerver
1
,
Sergey V. Amitonov
1,2
, Marc Botifoll
3
, Jordi Arbiol
3,4
, Amir Sammak
2
,
Lieven M. K. Vandersypen
1
, Maximilian Russ
1
& Giordano Scappucci
1
Charge noise in the host semiconductor degrades the performance of spin-
qubits and poses an obstacle to control large quantum processors. However, it
is challenging to engineer the heterogeneous material stack of gate-defined
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
reductioninchargenoise,withaminimumvalueof0.29±0.02μeV/Hz½at
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
building a scalable quantum processor because they have a small
footprint1, long coherence times2,3, and are compatible with advanced
semiconductor manufacturing4. Furthermore, rudimentary quantum
algorithms have been executed5and quantum logic at high-fidelity
performed6–9. As the qubit count is increasing, with a six-qubit pro-
cessor demonstrated10,significant steps have been taken to couple
silicon spin qubits at a distance, via microwave photons or spin
shuttling11–16, towards networked spin-qubit tiles17. However, electrical
fluctuations associated with charge noise in the host semiconductor
can decrease qubit readout and control fidelity18.Reducingcharge
noise independently of the device location on a wafer is pivotal to
achieving the ubiquitous high-fidelity of quantum operations, within
and across qubit tiles, necessary to execute more complex quantum
algorithms.
Charge noise is commonly associated with two-level fluctuators
(TLF)19 in the semiconductor host. In gated heterostructures with
buried quantum wells, TLF may arise from impurities in several
locations: within the quantum well, the semiconductor barrier, the
semiconductor/dielectric interface, and the dielectrics layers
above20–26. Furthermore, previous work on strained-Si MOSFETs27–29,
with strained-Si channels deposited on SiGe strain relaxed buffers,
has associated charge noise with dislocations arising from strain
relaxation, either deep in the SiGe buffer or at the quantum well/
buffer interface. Since these impurities and dislocations are ran-
domly distributed over the wafer and are also a main scattering
source for electron transport in buried quantum wells30, a holistic
approach to materials engineering should be taken to address dis-
order in two-dimensional electron gases and charge noise in
quantum dots.
Received: 30 September 2022
Accepted: 25 February 2023
Published online: 13 March 2023
Check for updates
1
QuTech and Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
2
QuTech and Netherlands
Organisation for Applied Scientific Research (TNO), Delft, The Netherlands.
3
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST,
Campus UAB, Bellaterra, 08193 Barcelona, Catalonia, Spain.
4
ICREA, Pg. Lluís Companys 23, 08020 Barcelona, Catalonia, Spain.
e-mail: g.scappucci@tudelft.nl
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In this work, we demonstrate thin quantum wells in 28Si/SiGe
heterostructures with low and uniform charge noise, measured over
several gate-defined quantum dot devices. By linking charge noise
measurements to the scattering properties of the two-dimensional
electron gas, we show that a quiet environment for quantum dots is
obtained by improving the semiconductor/dielectric interface and
the crystalline quality of the quantum well. We feed the measured
charge noise into a theoretical model, benchmark the model against
recent experimental results6,10, and predict that these optimized
heterostructures may support long-lived and high-fidelity spin
qubits.
Results
Description of 28Si/SiGe heterostructures
Figure 1a illustrates the undoped 28Si/SiGe heterostructures, grown
by reduced-pressure chemical vapor deposition, and the gate-stack
above. From bottom to top, the material stack comprises a 100 mm Si
substrate, a strain-relaxed SiGe buffer layer, a strained 28Si quantum
well, a 30 nm thick SiGe barrier, a Si cap oxidized in air to form a SiO
x
layer, an AlO
x
layer formed by atomic layer deposition, and metallic
gates.TheSiGelayersaboveandbelowthequantumwellhaveaGe
concentration of ≃0.3 (Methods).
We consider three 28Si/SiGe heterostructures (A, B, C) to improve,
in sequence, the semiconductor/dielectric interface (from A to B) and
the crystalline quality of the quantum well (from B to C).
Heterostructure A has an ≃9 nm thick quantum well and is terminated
with an epitaxial Si cap grown by dichlorosilane at 675°C. This kind of
heterostructure has already produced high performance spin-
qubits6,10,31. Heterostructure B misses a final epitaxial Si cap but fea-
tures an amorphous Si-rich layer obtainedby exposing the SiGe barrier
to dichlorosilane at 500°C. Compared to A, heterostructure B sup-
ports a two-dimensionalelectron gaswith enhancedand more uniform
transport properties across a 100 mm wafer, owing to a more uniform
SiO
x
layer with less scattering centers32. Finally, we introduce here
heterostructure C, having the same amorphous Si-rich termination as
in heterostructure B, but a thinner quantum well of ≃5 nm (Supple-
mentary Fig. 1). This is much thinner than the Matthews-Blakeslee
critical thickness33,34, which is ≃10 nm35 for the relaxation of tensile Si
on Si
0.7
Ge
0.3
via the formation of misfit dislocation at the bottom
interface of the quantum well. In light of recent morphological char-
acterization by electron channeling constrast imaging of Si/SiGe het-
erostructures with similar quantum well thickness and SiGe chemical
composition36,weexpectmisfit dislocation segments in hetero-
structure B because the quantum well approaches the Matthews-
Blakeslee critical thickness. Due to the much thinner quantum well,
instead, the epitaxial planes may adapt to the SiGe buffer much better
in heterostructure C than in heterostructure B, meaning that misfit
dislocations are, in principle, suppressed.
Figure 1b, c shows bright-field scanning transmission electron
microscopy (BF-STEM) images from heterostructure C after
a
28Si
SiOx
SiGe
SiGe
AlOx
z
b
c
10 nm
28Si
SiOx
SiGe
SiGe
SiGe
AlOx
10 nm
0 2 4 6
0.0
0.5
1.0
1.5
2.0
2.5
1 2
10
1
10
2
n (1011 cm-2)n (1011 cm-2)
µ (105 cm2/Vs)
σxx (e2/h)
de
Fig. 1 | Material stack and heterostructure field effect transistor characteriza-
tion. a Schematics of the 28Si/SiGe heterostructure and dielectric stack above. z
indicates the heterostructure growth direction. Circles represent remoteimpurities
at the semiconductor/dielectric interface and perpendicular symbols represent
misfit dislocations that might arise at the quantum well/buffer interface due to
strain relaxation. b,cBF-STEM images from heterostructure C highlighting the
semiconductor/dielectric interface and the 5nm thick 28Si quantum well, respec-
tively. dMobility μand econductivity σ
xx
measured as a function of density nat a
temperature of1.6 K in a Hall bar H-FET from heterostructure C.The red curve in eis
afit to percolation theory.
Article https://doi.org/10.1038/s41467-023-36951-w
Nature Communications |(2023)14:1385 2
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fabrication of a Hall bar shaped heterostructure field effect transistors
(H-FET). We observe a sharp SiGe/SiO
x
semiconductor/dielectric
interface (Fig. 1b), characterized by a minor Ge pile up (dark line) in line
with ref. 32.The≃5nmthickquantumwell(Fig.1c, Supplementary
Fig. 1) is uniform, has sharp interfaces to the nearby SiGe, and appears
of high crystalline quality.
Electrical characterization of heterostructure field effect
transistors
We evaluate the scattering properties of the two-dimensional electron
gases by wafer-scale electrical transport measured on Hall-bar shaped
H-FETs operated in accumulation mode (Methods). For each hetero-
structure, multiple H-FETs over a wafer are measured in the same cool-
down at a temperature of 1.7 K in refrigerators equipped with cryo-
multiplexers37. Figure 1d, e shows typical mobility-density and
conductivity-density curves for heterostructure C, from which we
extract the mobility measured athigh density (n=6×10
11 cm−2)andthe
percolation density (n
p
)38. The mobility rises steeply at low density due
to progressive screening of scattering from remote impurities and
flattens at higher density (n>5×10
11 cm−2), limited by scattering from
impurities within or nearby the quantum well, for example uniform
background charges, surface roughness, or crystalline defects such as
threading or misfit dislocations30,39.
Charge noise measurements in quantum dots
For charge noise measurements, we use devices comprising a double
quantum dot and a charge sensor quantum dot nearby, illustrated in
Fig. 2a. Using the same device design, two-qubit gates with fidelity
above 99% were demonstrated6, silicon quantum circuits were con-
trolled by CMOS-based cryogenic electronics31, and energy splittings in
28Si/SiGe heterostructures were studied with statistical significance40.
Here, we electrostatically define a multi-electron quantum dot
in the charge sensor by applying gate voltages to the accumulation
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
measurements of heterostructure B and C, whereas they are posi-
tively biased in heterostructure A to facilitate charge accumulation
in the sensor (Methods). Figure 2b shows typical Coulomb blockade
oscillations of the source-drain current I
SD
for a charge sensor from
heterostructure C measured at a dilution refrigerator base tem-
perature of 50 mK. We follow the same tune-up procedure (Meth-
ods) consistently for all devices and we measure charge noise at the
flank of each Coulomb peak within the V
P
range defined by the first
peak observable in transport and the last one before onset of a
background channel (Supplementary Figs. 2–4). For example, in
Fig. 2b we consider Coulomb peaks within the V
P
range from 260 mV
to 370 mV. The data collected in this systematic way is taken as a
basis for comparison between the three different heterostructures
in this study.
For each charge noise measurement at a given V
P
we acquire
60 s (heterostructure A) or 600 s (heterostructures B, C) long traces
of I
SD
and split them into 10 (heterostructure A) or 15 windows
(heterostructures B, C). We obtain the current noise spectrum S
I
by
averaging over the 10 (15) windows the discrete Fourier transform of
the segments (Methods). We convert S
I
to a charge noise spectrum
S
ϵ
using, for each measurement at a given V
P
, the unique lever arm
c
a
d
SDLB
SDRB
SDLAcc
SDRAcc
P
b
200 nm
z260 280 300 320 340 360 380
50
100
150
200
260 280 300 320 340 360 380
50
100
150
200
VP (mV)
ISD (pA)
340 345 350 355 360
0
500
−2.5
0.0
2.5
1e−12
VP (mV)
VSD (µV)
dI/dV (nA/mV)
10−1 100101
10−14
10−13
10−12
10−11
f (Hz)
Sε (eV2/Hz)
∝1/f
10−1
100
101
250
300
350
10−14
10−13
10−12
10−11
10−10
V
P
(mV)
f (Hz)
Sε (eV2/Hz)
300 350
10
−13
10
−12
10
−11
Sε (eV2/Hz)
V
P
(mV)
e
Fig. 2 | Quantum dots and charge noise measurements. a False colored SEM-
imageof a double quantumdot system with a nearby chargesensor. Chargenoise is
measured in the multi-electron quantum dot defined by accumulation gates
SDLAccand SDRAcc (blue), plunger P (blue),with the current goingalong the black
arrow. In these experiments, the gates defining the double quantum dot (red) are
used as screening gates. There is an additional global top gate (not shown) to
facilitate charge accumulation when needed. bSource-drain current I
SD
through a
charge sensor device fabricated on heterostructure C against the plunger gate
voltage V
P
. Colored dots mark theposition of the flank of the Coulomb peak where
charge noise measurements are performed. The inset shows Coulomb diamonds
from thesame device, plotted asthe differentialof the currentdI/dV as a functionof
V
P
and the source drain bias V
SD
.cCharge noise spectrum S
ϵ
measured at the
Coulomb peak at V
P
≃360.3 mV in band extracted using the lever arm from the
corresponding Coulomb diamond. The black trendline is proportional to 1/f.dS
ϵ
for the same device in b, plotted in 3D as a function of fand V
P
. The dark gray plane
is a fit through the datasets, i.e. the collection of noise spectra as in cmeasured at
different V
P
and each obtained using a unique lever arm from the corresponding
Coulomb diamond. eLine cut through the data in dat f= 1 Hz, showing the
experimental noise S
ϵ
(colored dots) and fit (dark grayline). Theblack circled data
point (also in d) marks the minimumcharge noise measured for this specificdevice
(S
ϵ,min
)atf= 1 Hz.
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from the corresponding Coulomb diamonds and slope of the Cou-
lomb peak to take into account a possible deformation of the charge
sensor with the increasing electron number (inset Fig. 2b, Methods,
and Supplementary Fig. 5). A representative charge noise spectrum
S
ϵ
measured at V
P
= 360.3 mV is shown in Fig. 2c. We observe an
approximate 1/ftrend at low frequency, pointing towards an
ensemble of TLF with a broad range of activation energies affecting
charge noise around the charge sensor41,42. Figure 2e shows the
charge noise S
ϵ
at 1 Hz as a function of V
P
. The charge noise
decreases, with a linear trend, with increasing V
P
, suggesting that,
similar to scattering in 2D, screening by an increased electron den-
sity shields the electronically active region from noise arising from
the heterostructure and the gate stack43. From this measurement we
extract, for a given device, the minimum measured charge noise at 1
Hz (S
ϵ,min
circled data point in Fig. 2e) upon variation of V
P
in our
experimental range. We use S
ϵ,min
as an informative metric to com-
pare charge noise levels from device to device in a given hetero-
structure. For a given device, all charge noise spectra S
ϵ
are plotted
in 3D as a function of fand V
P
(Fig. 2d). To quantify our observations,
we fit the data to the plane log Sϵ=αlog f+βVP+γ(Supplemen-
tary Note 4). Coefficient α= 0.84 ± 0.01 indicates the spectrum
power law exponent and coefficient β=−15.6 ± 0.1 mV−1quantifies
the change in noise spectrum with increasing plunger gate and,
consequently, the susceptibility of charge noise to the increasing
electron number in the sensor.
Distribution of transport properties and charge noise
We have introduced key metrics for 2D electrical transport (μ,n
p
)and
charge noise (α,βand S
ϵ,min
) from Hall bar and quantum dot mea-
surements, respectively. In Fig. 3a–e we compare the distributions of
all thesemetrics for the three heterostructures A, B, C. Each box-plot is
obtained from the analysis of measurements in Figs. 1d, e, and 2d
repeated on multiple H-FETs or quantum dots, on dies randomly
selected from different locationsacross the 100 mm wafers(Methods).
To facilitate a comparison with previous studies, the minimum charge
noise at 1 Hz is plotted in Fig. 3easS1=2
ϵ,min and therefore in units of
μeV/Hz½.
As reported earlier in ref. 32, the improvement in both mean values
and spread for μand n
p
was associated with a reduction of remote
impurities when replacing the epitaxial Si cap in heterostructure A
with a Si-rich passivation layer in heterostructure B. Moving to
heterostructure C, we measure a high mean mobility of
(2.10 ± 0.08) × 105cm2/Vs and a low mean percolation density of
(7.68 ± 0.37) × 1010 cm−2, representing an improvement by a factor ≃1.4
and ≃1.3, respectively (compared to heterostructure A). Most strik-
ingly, the 99% confidence intervals of the mean for μand n
p
are dras-
tically reduced by a factor ≃9.8 and ≃4.8, respectively. We speculate
that these improvements in heterostructure C are associated with the
suppression of misfit dislocations at the quantum well/buffer inter-
face, thereby reducing short range scattering and increasing uni-
formity on a wafer-scale. This interpretation is supported by previous
ba
μ(105cm2/Vs)
n
p
(10
11
cm
−2
)
β(mV
-1
)
S
1/2
εmin
(1 Hz) (μ eV/Hz
1/2
)
ce
α
A B C
0
1
2
3
A B C
0.8
1.0
1.2
1.4
1.6
A B C
0.8
1.0
1.2
1.4
1.6
1.8
A B C
−40
−20
0
A B C
10 −1
10
0
d
Fig. 3 | Distribution oftransport properties and charge noise. a,bDistributions
of mobility μmeasured at n=6×10
11 cm−2and percolation density n
p
for hetero-
structure A (red, 20 H-FETs measured, of which 16 reported in ref. 32), B (blue, 16
H-FETs measured of which 14 reported in ref. 32), and C (green, 22 H-FETs mea-
sured). c–eDistributions of noise spectrum power law exponent α, coefficient β
indicating the change in noise spectrum with increasing V
P
, and minimum charge
noise S1=2
ϵ,min within therange of V
P
investigated for heterostructure A (red, 4 devices
measured), B (blue, 7 devices measured), and C (green, 5 devices measured).
Quartile box plots, mode (horizontal line), means (diamonds), 99% confidence
intervals of the mean (dashed whiskers), and outliers (circles) are shown.
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studies of mobility limiting mechanisms as a function of the quantum
well thickness in strained Si/SiG e heterostructures39. We speculate that
further reducing the quantum well thickness could increase surface
roughness scattering from the bottom interface, and therefore dis-
order. Instead, fine-tuning the quantum well thickness between 5 nm
and 9 nm might minimize surface roughness scattering whilst still
avoiding the formation of misfit dislocations.
We now shift our attention to the results of charge noise mea-
surements. First, the power law exponent α(Fig. 3c) shows a mean value
≃1, however the 99% confidence interval and interquartile range
increase when moving from heterostructure A to B and C. Next, we
observe a decreasing trend for the absolute mean value of coefficient β
(Fig. 3d), meaning that the noise spectrum is less susceptible to changes
in V
P
. Finally, Fig. 3e shows the distributions for S1=2
ϵ,min, the minimum
charge noise at 1 Hz upon varying V
P
.Wefind in heterostructure C
an almost order of magnitude reduction in mean S1=2
ϵ,min to 0.29 ± 0.02
μeV/Hz½.Thistrendisconfirmed by plotting the distributions of max-
imum charge noise at 1 Hz upon varying V
P
(Supplementary Fig. 4).
Furthermore, within the distribution of S1=2
ϵ,min for heterostructure C, the
minimum value of the measured charge noise as a function of V
P
and
across quantum dots is 0.15 μeV/Hz½. These charge noise values are on
par or compare favorably to the best values reported previously at 1 Hz
in gate defined quantum dots. In multi-electron quantum dots, charge
noise of 0.47 μeV/Hz½was reported for Si/SiGe44,0.6μeV/Hz½
(average value, with a minimum of ≤0.2 μeV/Hz½)forGe/SiGe
45,
0.49 ± 0.1 μeV/Hz½for Si/SiO
2
46,and1μeV/Hz½for InSb47.Insingle-
electron quantum dots, charge noise of 0.33 μeV/Hz½was reported for
Si/SiGe48 and 7.5 μeV/Hz½for GaAs49.
We understand the charge noise trends in Fig. 3c–e by relating
them to the evolution of the disorder landscape moving from het-
erostructures A to B and C, as inferred by the electrical transport
measurements in Fig. 3a, b. The narrow distribution of αin hetero-
structure A points to charge noise being dominated from many TLFs
possibly located at the low quality semiconductor/dielectric interface
and above, albeit other sources of charge noise in the surrounding
environment of the quantum dot may be present, such as highly
localized misfit dislocations arising from partial strain relaxation in the
quantum well or other nearby fluctuators. With a better semi-
conductor/dielectric interface, the effect of these other nearby fluc-
tuators emerges in heterostructure B and C as a larger spread of the
frequency exponent α, indicating a nonuniform distribution of acti-
vation energies according to the Dutta-Horn model50. Yet, the noise
spectra still follow a 1/f-like behavior (Supplementary Fig. 3), sug-
gesting that TLFs also experience slow temperature fluctuations42.The
electrical transport measurements support this interpretation: scat-
tering from many remote impurities is dominant in heterostructureA,
whereas with a better semiconductor/dielectric interface remote
scattering has less impact in the transport metrics of hetero-
structures B and C.
The decreasing trend in ∣β∣is in line with the observation from
electrical transport. As the impurity density decreases from hetero-
structure A to B and C, charge noise is less affected by an increasing V
P
,
since screening of electrical noise through adding electrons to the
chargesensor becomes less effective. While we are notable to measure
directly the electron number in the charge sensor, we deem unlikely
the hypothesis that charge sensors in heterostructure A are operated
with considerably fewer electrons than in heterostructure C. This is
because all operation gate voltages in heterostructure A are con-
sistently larger than in heterostructure C (Supplementary Fig. 4), due
to the higher disorder.
Finally, the drastic reduction in mean value and spread of S1=2
ϵ,min
mirrors the evolution of mean value and spread of n
p
and μ. From
heterostructure A to B, a reduction in scattering from remote impu-
rities is likely to result inless charge noise from long-range TLFs. From
heterostructure B to C, the reduction in the possible number of
dislocations at the quantum well/buffer interface, further reduces the
charge noise picked up by quantum dots. This explanation is based on
earlier studies of charge noise in strained Si-MOSFETs27–29,which
showed a correlation between low-frequency noise spectral density
and static device parameters. Dislocations at the bottom of the
strained channel may act as scattering centers that degrade mobility
and as traps for the capture and release of carriers, which causes noise
similarly to traps at the dielectric interface.
Calculated dephasing time and infidelity
To emphasize the improvement of the electrical environment in the
semiconductor host, we calculate the dephasing time T?
2of charge and
spin qubits assuming these qubits experience the same fluctuations as
our 28Si/SiGe quantum dots. The dephasing time of a qubit (in the
quasistatic limit and far-off from a sweet spot) is given by51,52
T?
2=h
ffiffiffi
2
pπσ ð1Þ
with the Planck constant hand the standard deviation
σ2=∂E
∂μ







2
×2Zfhigh
flow
S2
ϵ
fαdf :ð2Þ
Importantly, both the charge noise amplitude S2
ϵðfÞand the
noise exponent αhave a strong impact on the dephasing time while
the low and high frequency cut-off, f
low
and f
high
, given by the
duration of the experiment have a weaker impact. The prefactor ∣∂E
∂μ∣
translates shifts in chemical potential of the charge sensor into
energy shifts of the qubit and depends on many parameters such as
the type of qubit and the device itself. We find ∣∂E
∂μ∣= 1 for a charge
qubit53 and ∣∂E
∂μ∣≈105for an uncoupled spin- qubit44 (see Supple-
mentary Note 7 for a derivation of these numbers and the used
frequency bandwidths).
Figure 4a shows the computed dephasing times of charge qubits
(circle) and spin qubits (star) for all three heterostructures. These
calculations represent a best case scenario, since we use the distribu-
tion of measured S
ϵ,min
from Fig. 3as input parameter for each het-
erostructure. The improvements in our material can be best seen by
investigating T?
2of the charge qubit since it is directly affected by
charge noise. Our theoretical extrapolation shows two orders of
magnitude improvement in T?
2by switching from heterostructures A
to heterostructures B and C. One order is gained from the reduced
charge noise amplitude and another order is gained through a more
beneficial noise exponent α> 1. Note, that the integration regimes
differ for spin and charge qubits due to the different experimental
setups and operation speeds44,53. For potential spin qubits in hetero-
structure A the calculated T?
2shows an average T?
2=8:4±5:6μs. This
distribution compares well with the distribution T?
2=6:7±5:6μsof
experimental T?
2data from state-of-the-art semiconductor spin qubits
in materials with similar stacks as in heterostructure A6,10.Notethat
while such comparisons oversimplify actual semiconductor spin-qubit
devices by reducing them to a single number, they fulfill two aims.
They allow us to benchmark the computed performance of hetero-
structure A to past experiments and provide a prognosis on the qubit
quality in novel material stacks. Heterostructures B and C, in this case,
may support average dephasing times of T?
2=24:3±12:5μsand
T?
2=36:7±18 μs, respectively. The highest values T?
2=70:1μshints
towards a possible longdephasing time for spin qubits, previously only
reported in ref. 2.
Figure 4b shows the simulated infidelity, a metric to measure
the closeness to the ideal operation, of a universal CZ-gate between
two spin qubits following ref. 6and Supplementary Note 7. Note that
the device used in ref. 6has the same architecture as our test devices.
In the CZ-gate simulation, noise couples in dominantly via barrier
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Nature Communications |(2023)14:1385 5
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voltage fluctuations which affects the interaction between the
electron spins. Again, we use the charge noise amplitude S
ϵ,min
and
exponent αfrom the quantum dot experiments in Fig. 3as input for
the simulations. The simulations show an averaged average gate
infidelity 1 FCZ =0:02 ± 0:01% which means on average a single
error every 5000 runs. We also observe a saturation value close to
1−F=10
−4which arises from single-qubit dephasing T?
2=20 μs used
in the simulations estimated from nuclear spin noise due to a 800
ppm concentration of the 29Si silicon isotope which has a non-zero
nuclear spin44.
Discussion
In summary, we have measured electron transport and charge noise in
28Si/SiGe heterostructures where we improve the semiconductor/
dielectric interface, by adopting an amorphous Si-rich passivation, and
the structural quality of the quantum well, by reducing the quantum
well thickness significantly below the Matthew-Blakeslee critical
thickness for strain relaxation. We relate disorder in 2D to charge noise
in quantum dots by following a statistical approach to measurements.
A reduction of remote impurities and dislocations nearby the quantum
well is connected with the key improvements in the scattering prop-
erties of the 2D electron gas, such as mobility and percolation density,
and their uniformity across a 100 mm wafer. The trend observed from
electron transport in 2D is compatible with the observations from
measurements of charge noise in quantum dots. As remote impurities
are reduced, charge noise becomes more sensitive to local fluctuators
nearby the quantum well and less subject to screening by an increased
number of electrons in the dot. Furthermore, with this materials
optimization, we achieve a statistical improvement of nearly one order
of magnitude in the charge noise supported by quantum dots. Using
the charge noise distribution as input parameter and benchmarking
against published spin-qubit data, we predict that our optimized
semiconductor host could support long-lived and high-fidelity spin
qubits. We envisage that further materials improvements in the
structural quality of the quantum well, in addition to the commonly
considered semiconductor/dielectric interface, may lead system-
atically to quantum dots with less noise and to better qubit
performance.
Methods
Si/SiGe heterostructure growth
The 28Si/SiGe heterostructures are grown on a 100-mm n-type
Si(001) substrate using an Epsilon 2000 (ASMI) reduced pressure
chemical vapor deposition reactor. The reactor is equipped with a
28SiH
4
gas cylinder (1% dilution in H
2
) for the growth of isotopically
enriched 28Si. The 28SiH
4
gas was obtained by reducing 28SiF
4
with a
residual 29Si concentration of 0.08%54. Starting from the Si substrate,
the layer sequence of all heterostructures comprises a 3 μm step-
graded Si
(1−x)
Ge
x
layer with a final Ge concentration of x= 0.3
achieved in four grading steps (x= 0.07, 0.14, 0.21, and 0.3), fol-
lowed by a 2.4 μmSi
0.7
Ge
0.3
strain-relaxed buffer. The hetero-
structures differ for the active layers on top of the strain-relaxed
buffer. Heterostructure A has a 9 nm tensile strained 28Si quantum
well, a 30 nm Si
0.7
Ge
0.3
barrier, and a sacrificial 1 nm epitaxial Si cap.
Heterostructure B has an 9 nm tensile strained 28Si quantum well, a
30 nm Si
0.7
Ge
0.3
barrier, and a sacrificial passivated Si cap grown at
500 °C. Heterostructure C has a 5 nm tensile strained 28Si quantum
well, a 30 nm Si
0.7
Ge
0.3
barrier, and a sacrificial passivated Si cap
grown at 500 °C. A typical secondary ions mass spectrometry of our
heterostructures is reported in Supplementary Fig. S13 of ref. 40 and
the Ge concentration in the SiGe layers is confirmed by quantitative
electron energy loss spectroscopy (EELS).
ab
T2
(μs)
1-FCZ
A B C
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
10
1
10
2
spin qubit
spin qubit literature
charge qubit
A B C
10
−4
10
−3
10
−2
*
Fig. 4 | Calculated dephasing times and infidelity. a Computed dephasing times
T?
2of a charge qubit (circle) and of a spin-qubit (star) using S
ϵ,min
from hetero-
structure A (red), B (blue), C (green).Eq. (1) was used to computeT?
2as a functionof
S
ϵ
and αfrom Fig. 3with frequency cutoffs (f
min
,f
max
) = (1.6 mHz, 33 GHz) and
(f
min
,f
max
) = (1.6 mHz,10 kHz). Literature values (squares) are taken from refs. 6,10.
bSimulated infidelity of a CZ-gate between two spin qubi ts following the ref. 6using
S
ϵ
and αfromheterostructure A (red), B (blue),C (green) in Fig. 3as inputfor barrier
fluctuations.
Article https://doi.org/10.1038/s41467-023-36951-w
Nature Communications |(2023)14:1385 6
Content courtesy of Springer Nature, terms of use apply. Rights reserved

Device fabrication
The fabricationprocess for Hall-bar shaped heterostructure field effect
transistors (H-FETs) involves: reactive ion etching of mesa-trench to
isolate the two-dimensional electron gas; P-ion implantation and acti-
vationby rapid thermal annealing at 700 °C; atomiclayer deposition of
a 10-nm-thick Al
2
O
3
gate oxide; deposition of thick dielectric pads to
protect gate oxide during subsequent wire bonding step; sputtering of
Al gate; electron beam evaporation of Ti:Pt to create ohmic contacts to
the two-dimensional electron gas via doped areas. All patterning is
done by optical lithography. Double quantum dot devices are fabri-
cated on wafer coupons from the same H-FET fabrication run and share
the process steps listed above. Double-quantum dot devices feature a
single layer gate metallization and further require electron beam
lithography, evaporation of Al (27 nm) or Ti:Pd (3:17 nm) thin film
metal gate, lift-off, ALD of a 5 nm thick Al
2
O
3
insulating layer, and a
global top-gate.
Electrical characterization of H-FETs
Hall-bar H-FETs measurements are performed in an attoDRY2100
variable temperature insert refrigerator at a base temperature of
1.7 K32. We apply a source-drain bias of 100 μV and measure the source-
drain current I
SD
, the longitudinal voltage V
xx
, and the transverse Hall
voltage V
xy
as function of the top gate voltage V
g
and the external
perpendicular magnetic field B. From here we calculate the long-
itudinal resistivity ρ
xx
and transverse Hall resistivity ρ
xy
.TheHall
electron density nis obtained from the linear relationship ρ
xy
=B/en at
low magnetic fields. The carrier mobility μis extracted from the rela-
tionship σ
xx
=neμ,whereeis the electron charge. The percolation
density n
p
is extracted by fitting the longitudinal conductivity σ
xx
to
the relation σxx /ðnnpÞ1:31 .Hereσ
xx
is obtained via tensor inversion
of ρ
xx
at B= 0. The box plots in Fig. 3a, b for heterostructure A (red) and
B (blue) expand previously published data in Fig. 2f, e of ref. 32 by
considering measurements of 4 additional H-FETs for heterostructure
A (20 H-FETs in total) and of 2 additional H-FETs for heterostructure B
(16 H-FETs in total).
Electrical characterization of quantum dots
Measurements of the multi-electron quantum dots defined in the
charge sensor are performed in a Leiden cryogenic dilution refrig-
erator with a mixing chamber base temperature T
MC
=50mK
40. The
devices are tuned systematically with the following procedure. We
sweep all gate voltages (V
SDRAcc
,V
SDRB
,V
P
,V
SDLB
, and V
SDLAcc
) from 0 V
towards more positive bias, until a source-drain current I
SD
of ≈1nAis
measured, indicating that a conductive channel has formed in the
device. We then reduce the barrier voltages to find the pinch-off
voltages for each barrier. Subsequently, we measure I
SD
as a function
of V
SDLB
and V
SDRB
and from this 2D map we find a set of gate voltage
parameters so that Coulomb blockade peaks are visible. We then fix
the barrier voltages and sweep V
P
to count how many clearly defined
Coulomb peaks are observed before onset of a background current.
The quantum dot is tuned to show at least 9 Coulomb peaks, so that
noise spectra may be fitted as in Fig. 2d with meaningful error bars. If
we see less than 9 Coulomb peaks we readjust the accumulation gate
voltages V
SDRAcc
, and V
SDLAcc
, and repeat the 2D scan of V
SDLB
against
V
SDRB
. In one case (device 2 of heterostructure A), we tuned device to
show past 5 Coulomb peaks and still performed the fit of the charge
noise spectra similar to the one shown in Fig. 2d. Further details on
the extraction of the lever arms and operation gate voltages of the
devices are provided in Supplementary Figs 4 and 5. We estimate an
electron temperature of 190 mK by fitting Coulomb blockade peaks
(see Supplementary Fig. 2 in ref. 32) measured on quantum dot
devices.
For heterostructure A we apply a source drain bias of 100 μV(1
device) or 150 μV (3 devices) across the quantum dot, finite gate vol-
tages across the operation gates of the dot, and finite gate voltages
across the screening gates. We measure the currentI
SD
and the current
noise spectrum S
I
ontheleftsideoftheCoulombpeakwhere∣dI/dV
P
∣is
largest. We use a sampling rate of 1 kHz for 1 min using a Keithley
DMM6500 multimeter. The spectraare then divided into 10 segments
of equal length and we use a Fourier transform to convert from time-
domain to frequency-domain for a frequency range of
167 mHz–500Hz. We set the upper limit of the frequency spectra at
10 Hz, to avoid influences from a broad peak at around 150 Hz coming
from the setup (Supplementary Fig. 3). A peak in the power spectral
density at 9 Hz is removed from the analysis since it is an artifact of the
pre-amplifier. To convert the current noise spectrum to a charge noise
spectrum, we use the formula20
Sϵ=a2SI
∣dI=dVP∣2ð3Þ
where ais the lever arm and ∣dI/dV
P
∣is the slope of the Coulomb peak
at the plunger voltage used to acquire the time trace.
The charge noise measurements conditions have been slightly
modified from sample A to sample B, C to extend the probed fre-
quency range from 100 μHz to 10 μHz. For heterostructures B and C
we apply a source drain bias of 150 μV across the quantum dot, finite
gate voltages across the operation gates of the quantum dot, and we
apply 0 V to all other gates. We measure the current I
SD
and the current
noise spectrum S
I
ontheleftsideoftheCoulombpeakwhere∣dI/dV
P
∣is
largest. We use a sampling rate of 1 kHz for 10 min using a Keithley
DMM6500 multimeter. The spectra are then divided into 15 segments
of equal length and we use a Fourier transform to convert from time-
domain to frequency-domain for a frequency range of 25 mHz–500 Hz.
We set the upper limit of the frequency spectra at 10 Hz, to avoid
influences from a broad peak at around 150 Hz coming from the setup.
We use Eq. (3) to convert the current noise spectrum to a charge noise
spectrum.
(Scanning) Transmission Electron Microscopy
For structural characterization with (S)TEM, we prepared cross-
sections of the quantum well heterostructures by using a Focused
Ion Beam (Helios 600 dual beam microscope). Atomically resolved
HAADF STEM data was acquired in a probe corrected TITAN micro-
scope operated at 300kV. Quantitative EELS was carried out in a
TECNAI F20 microscope operated at 200 kV with approximately 2 eV
energy resolution and 1 eV energy dispersion. Principal Component
Analysis (PCA) was applied to the spectrum images to enhance
S/N ratio.
Data availability
All data included in this work are available from the 4TU.ResearchData
international data repository at https://doi.org/10.4121/20418579.
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Acknowledgements
We acknowledge helpful discussions with G. Isella, D. Paul, M. Meh-
mandoost, the Scappucci group and the Vandersypen group. This
research was supported by the European Union’s Horizon 2020
research and innovation programme under the Grant Agreement No.
951852 (QLSI project) and in part by the Army Research Office (Grant
No. W911NF-17-1-0274). The views and conclusions contained in this
Article https://doi.org/10.1038/s41467-023-36951-w
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document are those of the authors and should not be interpreted as
representing the official policies, either expressed or implied, of the
Army Research Office (ARO), or the U.S. Government. The U.S. Gov-
ernment is authorized to reproduce and distribute reprints for Gov-
ernment purposes notwithstanding any copyright notation herein.
M.R. acknowledges support from the Netherlands Organization of
Scientific Research (NWO) under Veni grant VI.Veni.212.223. ICN2
acknowledges funding from Generalitat de Catalunya
2021SGR00457. ICN2 is supported by the Severo Ochoa program
from Spanish MCIN / AEI (Grant No.: CEX2021-001214-S) and is funded
by the CERCA Programme / Generalitat de Catalunya and ERDF funds
from EU. Part of the present work has been performed in the frame-
work of Universitat Autònoma de Barcelona Materials Science PhD
program. Authors acknowledge the use of instrumentation as well as
the technical advice provided by the National Facility ELECMI ICTS,
node “Laboratorio de Microscopias Avanzadas" at University of Zar-
agoza. M.B. acknowledges support from SUR Generalitat de Catalunya
and the EU Social Fund; project ref. 2020 FI 00103. We acknowledge
support from CSIC Interdisciplinary Thematic Platform (PTI+) on
Quantum Technologies (PTI-QTEP+).
Author contributions
A.S. grew and designed the 28Si/SiGe heterostructures with B.P.W. and
G.S.. M.R. developed the theory. A.S. and D.D.E. fabricated hetero-
structure field effect transistors measured by B.P.W. and D.D.E.. M.B and
J.A. performed TEM characterization. S.A and D.D.E. fabricated quantum
dot devices. B.P.W. and D.D.E. measured the quantum dot devices with
contributions from A.M.J.Z.. G.S. conceived and supervised the project.
B.P.W, D.D.E, M.R, and G.S. wrote the manuscript with input from all
authors.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s41467-023-36951-w.
Correspondence and requests for materials should be addressed to
Giordano Scappucci.
Peer review information Nature Communications thanks Yujia Liu and
the other anonymous reviewer(s) for their contribution to the peer
review of this work. Peer reviewer reports are available.
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