quantum grade silicon - nist
TRANSCRIPT
Use of quantum effects as potential qualifying metrics for “quantum grade1
silicon”2
A. N. Ramanayaka,1, 2 Ke Tang,1, 2 J. A. Hagmann,1 Hyun-Soo Kim,1, 2 D. S. Simons,1 C. A. Richter,1 and J. M.3
Pomeroy1, a)4
1)National Institute of Standards & Technology, Gaithersburg, Maryland 20899,5
USA6
2)Joint Quantum Institute, University of Maryland, College Park, Maryland 20742,7
USA8
(Dated: 10 December 2019)9
Across solid state quantum information, materials deficiencies limit performance through enhanced relaxation,10
charge defect motion or isotopic spin noise. While classical measurements of device performance provide cur-11
sory guidance, specific qualifying metrics and measurements applicable to quantum devices are needed. For12
quantum applications, new materials metrics, e.g., enrichment, are needed, while existing, classical metrics13
like mobility might be relaxed compared to conventional electronics. In this work, we examine locally grown14
silicon superior in enrichment, but inferior in chemical purity compared to commercial-silicon, as part of15
an effort to underpin the materials standards needed for quantum grade silicon and establish a standard16
approach for intercomparison of these materials. We use a custom, mass-selected ion beam deposition tech-17
nique, which has produced isotopic enrichment levels up to 99.99998 % 28Si, to isotopically enrich 28Si, but18
with chemical purity > 99.97% due the MBE techniques used. From this epitaxial silicon, we fabricate19
top-gated Hall bar devices simultaneously on the 28Si and on the adjacent natural abundance Si substrate20
for intercomparison. Using standard-methods, we measure maximum mobilities of ≈ (1740± 2) cm2/(V · s)21
at an electron density of (2.7× 1012 ± 3× 108) cm−2 and ≈ (6040± 3) cm2/(V · s) at an electron density of22
(1.2× 1012 ± 5× 108) cm−2 at T = 1.9 K for devices fabricated on 28Si and natSi, respectively. For magnetic23
fields B > 2 T, both devices demonstrate well developed Shubnikov-de Haas (SdH) oscillations in the longitu-24
dinal magnetoresistance. This provides transport characteristics of isotopically enriched 28Si, and will serve25
as a benchmark for classical transport of 28Si at its current state, and low temperature, epitaxially grown Si26
for quantum devices more generally.27
Conventional electronics have been industrialized for28
decades; consequently, precise metrics based on macro-29
scopic properties, such as chemical purity, charge car-30
rier mobility, defect density, are established for qualify-31
ing a material, e.g., silicon, for conventional electronics.32
While silicon has been the work horse of conventional33
electronics, it also is becoming a promising host for spin34
based quantum information processing devices.1,2 Specif-35
ically, spin qubits have already shown promising advance-36
ments with regard to long coherence times,3,4 manipula-37
tion with high gate fidelity,3,4 and scalability.5,638
Even though silicon has improved tremendously over39
the decades to meet demands of today’s state-of-the-40
art transistors, this excellent material is still not suf-41
ficient to support quantum information. For example,42
in spin-based quantum information systems, the pres-43
ence of the 29Si isotope in natural abundance silicon re-44
duces coherence times dues to the non-zero nuclear spin45
of I = 1/2. Nuclei with non-zero spin in the host lattice46
act as a source of decoherence for spin based qubits,747
as they interact with the electron spin through hyper-48
fine interactions.8,9 However, by placing a spin qubit in49
an isotopically enriched 99.995 % 28Si environment,10 de-50
velopment of silicon based quantum devices have gained51
a)Correspondence to [email protected]
considerable momentum, with reports of exceptionally52
long quantum coherence times.11,1253
The need for some level of enrichment provides an ex-54
ample of how “semiconductor grade” silicon quality may55
be necessary, but is not sufficient to meet the needs of56
quantum. Further, the metrics for conventional silicon57
may not always be relevant for quantum, e.g., the ease58
of carrier motion as quantified by mobility may not be59
directly relevant to quantum device performance where60
confinement and coherence in the absence of motion are61
critical. Additionally, as we establish properties and their62
numerical thresholds that are sufficient for quantum, rel-63
atively simple qualifying metrics that act as general prox-64
ies for properties more challenging to measure are invalu-65
able. So, it may be that mobility in and of itself is not66
important, but it could be a good proxy for estimating67
spin-qubit relaxation or coherence.68
As part of a larger program to identify and quantify69
“quantum grade” silicon, we are identifying 1) proper-70
ties beyond those considered for semiconductor grade sil-71
icon critical to quantum; 2) the relevance and priority of72
properties currently considered critical for semiconduc-73
tors; and 3) standard methods that may be used for new74
properties, or provide a general indicator for challenging75
properties, e.g., coherence time; as three main goals that76
are paramount for development of metrics for “quantum77
grade” silicon. This work is part of a broader effort to78
find ways besides making and measuring qubits to pro-79
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vide diagnostics that will indicate the likely performance80
of qubits early in a fabrication stream.81
This paper presents devices, methods and results for82
a comparative study of magnetotransport properties be-83
tween 1) high isotopic enrichment, low chemical purity84
and 2) high chemical purity, natural abundance (low iso-85
topic enrichement) silicon. This characterization sets the86
stage for determining whether coherence properties in87
quantum dot devices correlate with the trends in these88
simpler measurements, since the benefit of enrichment on89
coherence may outpace the liability of some additional90
contaminants. In a detailed theoretical study, Witzel et91
al.,13 illustrate that the coherence of a spin qubit can,92
in principle, be increased by an order of magnitude for93
every order of magnitude increase in the isotopic enrich-94
ment of 28Si in the qubit’s Si environment. A comprehen-95
sive experimental investigation of this prediction, how-96
ever, is hindered due to the discreteness of the available97
isotopic enrichment levels. Among the four different en-98
richment levels have been reported10,14–16 only 99.98%99
28Si14 and 99.995% 28Si10 have been utilized for quantum100
electronic device fabrication.11,17,18 Moreover, contem-101
porary methods for producing isotopically enriched 28Si102
material are based on chemical vapor deposition (CVD)103
techniques and are not compatible with qubit architec-104
tures requiring low temperature processing, e.g. STM105
fabricated single dopant atom qubits.19 In contrast, the106
method used for producing 28Si reported here is compat-107
ible with all the contemporary qubit architectures, and108
represents molecular beam epitaxy (MBE) grown Si more109
generally. While the coherence of a spin qubit is pre-110
dicted to improve at higher isotopic enrichment levels,13111
how other material properties will limit the expected en-112
hancement of qubit coherence is unclear. To the best of113
our knowledge, no study yet has attempted to correlate114
macroscopic electrical characteristics to the performance115
of quantum devices. Yet such a study will be an essen-116
tial component for defining metrics for “quantum grade”117
silicon within the three main goals identified earlier.118
Starting from natural abundance SiH4 gas, we have119
developed a method to grow isotopically purified silicon120
reaching isotopic enrichments up to 99.99998 % 28Si.20,21121
This method provides the unique advantage of targeting122
a desired enrichment level anywhere from natural abun-123
dance to the highest possible enrichment.22 As a first124
step towards correlating macroscopic electrical charac-125
teristics with the performance of quantum devices, we126
report here on characterization of gated Hall bar de-127
vices fabricated on isotopically enriched 28Si, and con-128
trol devices on the same natural abundance Si (natSi)129
substrate but outside the isotopically enriched 28Si spot130
using macroscopic manifestations of quantum effects such131
as Shubnikov-de Haas (SdH) effect and weak-localization132
effect. We compare the devices fabricated on natSi (float-133
zone grown) and 28Si (MBE grown) during the same fab-134
rication process, eliminating possible differences due to135
imperfect fabrication conditions. We present results of136
28Si devices to serve as a benchmark for MBE grown iso-137
0 50 100 150 200
10-4
10-3
10-2
10-1
Isoto
pic
ratio 2
9S
i/2
8S
i
Natural Si
1
2
3
Depth (nm)
(a)
natSi substrate
Enriched 28Si
Gate oxide(60 nm SiO2)
P implant
Ohmic contact
Top gate
200 μm
(c)
Top gate
P implants
Ohmic contacts
(d)
12
3
(b)
natSi
Deposited 28Si spot
Si handle (4 × 10) mm Devices
FIG. 1. (a) A schematic illustrating the device layout of agiven sample. Reduced coverage of the 28Si spot allows to fab-ricate devices on 28Si and natSi simultaneously. (b) Schematicrepresentation of the gated Hall bar device fabricated on 28Siis shown. (c) An optical micrograph of a gated multi-terminalHall bar device fabricated on 28Si is shown.(d) The isotopicratios of 29Si/28Si at positions 1 (4), 2 (©), and 3 (�) in (c)are shown. The shift in the rising edge at different positionscorresponds to the thickness variation in the deposited 28Sifilm. Measured 29Si isotopic ratios at locations 1, 2, and 3 are(149± 18)× 10−6 mol/mol, (128± 14)× 10−6 mol/mol, and(45± 2)× 10−6 mol/mol, respectively.
topically enriched 28Si, and a basis for comparing macro-138
scopic electrical characteristics within silicon quantum139
electronics.140
Starting with 99.999 % pure, commercially available,141
natural isotopic abundance SiH4 gas, isotopically en-142
riched 28Si is grown using a hyperthermal energy ion143
beam deposition system20. Gated Hall bar devices are144
fabricated on isotopically enriched 28Si epilayers in or-145
der to electrically characterize the material. Typically,146
the isotopically purified 28Si spot is ≈ 2 mm2 to 3 mm2147
in area and covers only a small fraction of the starting148
float-zone grown, natural abundance, intrinsic Si sub-149
strate (4 mm× 10 mm), see Fig. 1(a). Due to the re-150
duced coverage of the 28Si spot, devices on isotopically151
enriched and natural abundance Si can be fabricated on152
the same Si chip [see Fig. 1(a)] at the same time. This153
eliminates the effect of imperfections in the fabrication154
process (e.g., oxide growth) when comparing the electri-155
cal properties of the devices. A schematic cross section156
of a device fabricated on 28Si spot is shown in Fig. 1(b).157
The structure of the devices fabricated on natSi, i.e. out-158
side the 28Si spot, is identical except without the 28Si159
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TABLE I. Macroscopic materials and electrical properties ofnatural abundance, natSi, and isotopically enriched, 28Si, sil-icon.
PropertyMaterial
natSi 28Si
Avg. 28Siconcentration 92.23 % 99.983 %
Impurities (cm−3)C
≤ 10162× 1019
N 3× 1017
O 3× 1018
Max. mobilityµ (cm2/(V · s)) (6040± 3) (1740± 2)Percolation densitynp (1011 cm−2) (2.3± 2) (4.2± 2)
layer. An optical micrograph of the gated multi-terminal160
Hall bar device is shown in Fig. 1(c).161
The isotopic enrichment of the 28Si epilayers is162
measured by using Secondary Ion Mass Spectrometry163
(SIMS). In Fig. 1(d), the SIMS-derived isotopic ratio164
of 29Si/28Si is shown as a function of depth at several165
locations near the fabricated Hall bar device. For the de-166
vice reported here, the level of isotopic enrichment mea-167
sured at locations 1, 2, and 3 corresponds to ≈ 99.976 %,168
≈ 99.980 %, and ≈ 99.993 % 28Si, respectively. Figure169
1(d) also reveals the thickness non-uniformity of the170
deposited 28Si epilayer, i.e., the thickness of the 28Si171
epilayer at location 3 is greater than that of locations172
1 and 2. Moreover, separate SIMS measurements on173
these isotopically enriched 28Si epilayers reveals that the174
films contain adventitious chemical impurities, namely175
C, N, O, with approximate atomic concentrations of176
2× 1019 cm−3, 3× 1017 cm−3, and 3× 1018 cm−3. How-177
ever, the atomic concentrations of these chemical impu-178
rities on the handle wafer were below the SIMS detection179
limit (≤ 1016 cm−3). We believe that these chemical im-180
purities are being introduced by the ion beam as result181
of non-UHV compatible ionization source that is used182
to create the ion beams during the 28Si deposition, and183
since been upgraded.184
The magnetoresistance (Rxx) and the Hall resistance185
(Rxy) at 1.9 K for isotopically enriched 28Si and natural186
abundance Si are shown in Fig. 2(a) and Fig. 2(b), re-187
spectively. Using low field magnetotransport data, we188
find maximum mobilities at T = 1.9 K for 28Si and189
natSi are, respectively, µ28Si = (1740± 2) cm2/(V · s)190
at an electron density n of (2.7× 1012 ± 3× 108) cm−2191
and µnatSi = (6040± 3) cm2/(V · s) at an electron den-192
sity of (1.2× 1012 ± 5× 108) cm−2. Charge carrier mo-193
bilities for these devices are within the typical range194
of mobilities for Si-MOS (Metal Oxide Semiconduc-195
tor) devices fabricated using non-MBE (e.g. CVD)196
growth techniques,23,24 the maximum mobility for a Si-197
MOS device to date being > 4× 104 cm2/(V · s)25. In198
contrast, mobilities reported for Si-MOS devices fabri-199
-10 -5 0 5 10-6000
-4000
-2000
0
2000
4000
6000
0
200
400
600
800
1000
1200
Rxx (
)
On chip natural abundance Si
Rxy (
)
B (T)
T=1.9 K, Vg=8 V
=
-10 -5 0 5 10-3000
-2000
-1000
0
1000
2000
3000
1100
1200
1300
1400
T=1.9 K, Vg=8 V
Isotopically enriched 28Si
Rxx (
)
=
Rxy (
)
B (T)
(a)
(b)
FIG. 2. The magnetoresistance Rxx (right-axis) and the Hallresistance Rxy (left-axis) measured for the devices fabricatedon (a) isotopically enriched 28Si epi-layer, and (b) naturalSi substrate are shown. For both devices, the correspondingfilling factors (ν) are shown at the minima of Shubnikov-deHass oscillations. In contrast to the device on isotopicallyenriched 28Si epi-layer, the device on natSi demonstrates spin-splitting for B > 3 T. Both devices are fabricated on thesame Si chip, see main text for more information. The relativeuncertainty associated with Rxx and Rxy is typically less than0.1 % and is mostly due to the uncertainty of the measuredcurrent.
cated on MBE grown Si ranges from 900 cm2/(V · s) to200
1250 cm2/(V · s)26,27.201
In order to estimate the percolation electron density202
np, we extrapolate the electron density as a function of203
gate voltage (as determined from Hall measurements)204
back to the threshold voltage (as determined from the205
channel current Isd vs. Vg), i.e., np = ne(Vth). Using206
this method, we find percolation densities of (2.3± 2)×207
1011 cm−2 for natSi and (4.2 ± 2) × 1011 cm−2 for 28Si.208
While the relative uncertainties are large due to the ex-209
trapolation, we think the ≈ 2× larger value for 28Si is210
significant. A summary of these macroscopic materials211
and electrical properties for the on-chip natSi and 28Si is212
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provided in table I.213
Both devices show well developed SdH oscillations in214
Rxx with accompanying plateaus in Rxy. The slight215
asymmetry in Rxx in Fig. 2(a) could be due to sev-216
eral reasons, e.g., magnetic impurities or inhomogeneity217
of the magnetic field.28,29 The SIMS of a similar 28Si epi-218
layer found no measurable magnetic impurities. The Hall219
resistance shows non-idealities particularly in the natSi220
device [Fig. 2(b)] where Rxy is non-monotonic. These221
non-idealities could be due to scattering between discrete222
degenerate states at the tails due to level broadening.30,31223
However, a detailed discussion of the asymmetry of Rxx224
and the flatness of the Hall plateaus is outside the scope225
of this article. We also see a lifting of the four-fold de-226
generacy at B > 5 T for natSi, which is likely due to the227
spin degree of freedom, but, at this time we are unable228
to determine whether this is due to spin or valley degree229
of freedom, due to limitations in the experimental setup.230
Near zero magnetic field, both devices demonstrate231
a peak in the sample resistance, see Fig. 2. This in-232
crease in resistance near zero magnetic field is known as233
weak localization (WL). Weak localization is a quantum234
mechanical phenomenon that can be observed in two-235
dimensional (2D) electron systems at low temperatures236
where the phase coherence length (lφ) is greater than237
the mean free path (l)32,33. Relative to the zero field238
resistance, the weak-localization is larger for the device239
fabricated on isotopically enriched 28Si.240
To further investigate the WL behavior of these de-241
vices, we plot the change in conductivity ∆σxx as a func-242
tion of magnetic field B applied perpendicular to the 2D243
electron system [see Fig. 3]. The change in conduc-244
tivity due to WL ∆σxx = σxx(B)− σxx(B = 0), where245
σxx = ρxx/(ρ2xx + ρ2
xy). For non-zero B, the change246
in conductivity due to WL in a 2D electron system247
can be modeled by the Hikami-Larkin-Nagaoka (HLN)248
equation,34249
∆σxx(B) =α( e2
2π2~
)[Ψ(1
2+
~4el2φB
)−Ψ(1
2+
~2el2B
)− ln
( l
2lφ
)], (1)
where Ψ is the digamma function, l is the mean free250
path, lΦ is the phase coherence length, and α is a con-251
stant close to unity. In Fig. 3, the solid lines are the252
fits to experimental data (symbols) using the HLN equa-253
tion. For these fits, we use the calculated values of l254
TABLE II. Parameters extracted from the least-squares-fitsof Eq. 2 to the data in Fig. 3 inset.
Devicea b c Adjusted
(1010 s−1) (1010 K−1s−1) (1010 K−2s−1) R-square
28Si 6.6± 2 3.1± 0.7 0.60± 0.08 0.997natSi 5.1± 0.4 - 1.5± 0.1 0.989
0.0 0.1 0.2 0.30
2
4
6
8
10
12
14
16
18
28Si
natSi
HLN fits
xx (
S)
B (T)
T = 3 K 2 4 6 8 10
2
4
6
8
10
12 28Si
natSi
fit
1/ (
10
11/s
)
T (K)
FIG. 3. The change in conductivity (∆σxx) vs external mag-netic field (B) for devices fabricated on 28Si (�) and natSi(©) measured at 3 K. Solid lines are the least-square-fits toHLN equation (Eq. 1). Estimated uncertainty for ∆σxx is< 0.3 %. Inset: The inelastic scattering rates (1/τφ) for 28Siand natSi vs the measurement temperature are shown. Herethe solid lines are the least-squares-fit to a quadratic equa-tion, see main text details. Error bars in the inset representthe fit uncertainty associated with the values extracted for1/τφ at each temperature.
using the relation l =√
2Dτ . Here D is the diffusion co-255
efficient defined as D = v2F τ/2, where the Fermi velocity256
vF = ~kF /m∗, and τ is the elastic scattering time, also257
known as transport lifetime, defined as τ = µm∗/e. The258
effective mass m∗ is defined as m∗/m0 = 0.19, where m0259
is the rest mass of an electron.35,36 The Fermi wavelength260
kF can be calculated for a 2D electron system in Si as261
kF = (4πn2D/gsgv)1/2, where n2D, gs, gv are the charge262
carrier density, spin degeneracy and valley degeneracy,263
respectively. We leave α and lφ as free fitting param-264
eters, constraining the value of α to be close to unity.265
From the fit-extracted values of lφ, we calculate 1/τφ,266
where inelastic scattering time τφ = l2φ/D. The fit de-267
rived values of 1/τφ as a function of T are plotted in268
Fig.3 inset for devices fabricated on isotopically enriched269
28Si and natural abundance Si, respectively. The solid270
lines in Fig. 3 inset are the least-squares-fit to the data271
using the equation272
1
τφ= a+ bT + cT 2. (2)
The linear in T term captures the scattering from im-273
purities, and the quadratic in T term is related to the274
electron-electron scattering.37 Table II shows the param-275
eters extracted from the least-squares-fit to the data, the276
fit uncertainties for both devices, and the adjusted R-277
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(a)
(b) (c)
2 4 60.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(p
s)
q (28Si)
(28Si)
q (natSi)
(natSi)
T (K)
0.1 0.2 0.30
1
2
3
4
5 28Si
fit
ln(A
SdH/X
(T))
1/B (1/T)
T = 3 K
0.1 0.2 0.3
1200
1250
1300
T = 3 K
Rxx (
)
1/B (1/T)
Amplitude (ASdH)
Isotopically enriched 28Si
FIG. 4. (a) The background subtracted (see text) Rxx,i.e., ∆Rxx, vs the inverse of the external magnetic field(1/B) for the 28Si device is shown. (b) A “Dingle plot” ofln(ASdH/X(T )) versus 1/B. Error bars represent the uncer-tainty associated with extracting ASdH from ∆Rxx vs. 1/Bplot. (c) The single particle lifetimes, τq, extracted from theDingle plots and transport lifetimes, τ , at different temper-atures for devices on 28Si and natSi. Error bars representthe uncertainty associated with calculating the values of τq(τ) using the Dingle plots (charge carrier mobilities) at eachtemperature.
square. For the natural abundance Si, the best fit is278
achieved when the linear term is set to zero, i.e., b = 0.279
Consequently, for natural abundance Si the dominant280
scattering mechanism appears to be the electron-electron281
(long-range) scattering. In contrast, for isotopically en-282
riched 28Si, the best fit is achieved with a significant283
linear in T term. This large linear term implies that284
impurity (short-range) scattering is a significant contri-285
bution in 28Si. The temperature independent parameter286
a is similar (within the uncertainties) for both the de-287
vices indicating the processes (e.g., interface roughness)288
contributing to a are likely the same.289
Line shape analysis of the SdH oscillations as a290
function of temperature is also used to investigate291
the underlying scattering mechanisms in 2D electron292
systems. The amplitude of the SdH oscillations can293
be written as ASdH = X(T )R0exp(−π/ωcτq)38,39,294
where R0 is the zero field resistance,295
X(T ) = (2π2kBT/~ωc)/ sinh(2π2kBT/~ωc) is the296
temperature damping factor, and ωc = eB/m∗ is the297
cyclotron frequency. Here, kB is Boltzmann’s constant,298
and τq is the single particle (quantum) lifetime.38–40299
To extract the amplitude of SdH oscillations, we first300
subtract a slow varying background from Rxx41 to isolate301
the oscillatory part of Rxx. The Rxx after background302
subtraction (∆Rxx) is plotted against 1/B in Fig. 4(a).303
Then we extract the amplitude ASdH as schematically304
defined in Fig. 4(a) at each minima of ∆Rxx and305
calculate ln(ASdH/X(T )). Figure 4(b) is a plot of306
ln(ASdH/X(T )) versus 1/B, also known as the “Dingle307
plot”38,39 for the device fabricated on 28Si measured308
at T = 3 K. The approximately linear dependence of309
ln(ASdH/X(T )) on 1/B [see Fig. 4 (b)] indicates a310
magnetic field independent quantum lifetime, τq. In311
Fig. 4 (c), we plot the quantum lifetimes, τq, for devices312
fabricated on 28Si and natSi extracted from a linear313
least-squares-fit to Dingle plots at each temperature.314
The calculated values of the transport lifetimes, where315
τ = µm∗/e, using the magnetotransport measurement316
at low magnetic fields for both devices, are also plotted317
in Fig. 4 (c).318
For the device fabricated on 28Si, the ratio of τ/τq ≈ 1,319
and for the device on natSi the ratio of τ/τq ≈ 1.4. The320
transport lifetime τ is primarily affected by the large an-321
gle scattering events that cause large momentum change,322
whereas τq is affected by all of the scattering events42.323
When the background impurities dominate the scattering324
the ratio τ/τq is less than or equal to 10, whereas it is ≈ 1325
when the scattering is dominated by short-range isotropic326
scattering42, e.g. surface roughness scattering43. The327
thickness of the gate oxide for the devices reported here328
is ≈ 60 nm. We therefore neglect the scattering due to re-329
mote interface roughness (i.e., the interface between the330
gate oxide and the gate metal) as a dominant scatter-331
ing mechanism for these devices.44 Therefore, the ratio332
τ/τq implies that the charge carrier mobility is limited by333
the background impurity scattering. Furthermore, the334
charge carrier mobility of the device on isotopically en-335
riched 28Si may also be limited by the interface roughness336
scattering.337
The analysis of the weak-localization, SdH oscilla-338
tions, and low-field magnetotransport data indicate that339
the shortest scattering length scale to be the elastic340
(transport) scattering length l calculated, ≈ 33 nm and341
≈ 71 nm for 28Si and natSi, respectively. Capacitance342
voltage (CV) measurements of MOS capacitors fabri-343
cated on natural abundance silicon (data not shown) with344
gate oxides grown using similar conditions to the devices345
reported here reveals a fixed charge density of approxi-346
mately 3× 1010 cm−2 corresponding to a nearest neigh-347
bor distance of ≈ 58 nm. This nearest neighbor distance348
is in close agreement with the transport scattering length349
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l. Considering SIMS measured chemical impurity con-350
centrations of C, N, and O and assuming these impurities351
acting as isolated scatters, for 28Si where l ≈ 33 nm, we352
estimate the fraction of C, N, and O impurities contribut-353
ing to scattering to be ≈ 0.2 %, ≈ 9.3 % and ≈ 1.0 %,354
respectively.355
In conclusion, we have reported on the first low tem-356
perature electrical measurements of MBE grown isotopi-357
cally enriched 28Si. For this report we fabricated and358
characterized the low temperature magnetotransport of359
gated Hall bar devices fabricated on highly enriched 28Si.360
In comparison to control devices fabricated on float-zone361
grown, intrinsic, natural abundance Si on the same sub-362
strate, the charge carrier mobility on isotopically en-363
riched 28Si is approximately a factor of 3 lower. Neverthe-364
less, the magnetotransport measurements of devices fab-365
ricated on isotopically enriched 28 Si demonstrate strong366
manifestations of quantum effects. Based on the analysis367
of temperature dependence of the weak localization and368
SdH oscillations, we believe that the dominant scatter-369
ing mechanism is short-range scattering (impurity scat-370
tering). We believe adventitious chemical impurities de-371
tected in the 28Si epilayers act as the impurity scatters in372
the devices fabricated on 28Si. However, higher levels of373
adventitious chemical impurities detected in the 28Si epi-374
layers are too high to be considered as isolated scattering375
centers, since the nearest neighbor distance is consider-376
ably shorter than the scattering lengths extracted from377
the transport data. Further, for these impurity levels,378
the dipolar interactions between randomly distributed379
electron spins associated with impurities and the central380
spin of a potential qubit is considered to be the domi-381
nant decoherence mechanism at high enrichments.13 For382
the worst case analysis, if all of the N and O chemical383
impurities are considered as randomly distributed single384
electron spins, the influence of these dipolar interactions385
on the central spin could result in qubit coherence times386
poorer than high purity natural abundance Si. However,387
we are confident that the recent and planned improve-388
ments, as well as techniques for depleting impurities near389
the surfaces, will allow us to move forward and study the390
tension between chemical impurites and enrichement on391
quantum coherence.392
Next we plan to fabricate quantum dot devices on con-393
trol (natural abundance) and isotopically enriched 28Si394
to more rigorously assess the impact of purity and en-395
richment, e.g. charge offset drift, as the chemical purity396
of these MBE grown 28Si films is improved. Therefore,397
macroscopic transport and material characteristics of the398
devices reported here will serve as a benchmark for find-399
ing the correlations between macroscopic properties and400
the performance of future nanoscale devices, e.g. quan-401
tum dots, and lead to identifying qualifying metrics for402
“quantum grade” silicon.403
ACKNOWLEDGMENTS404
The authors acknowledge stimulating discussions with405
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Stein, Binhui Hu, and Peihao Huang.407
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0 50 100 150 200
10-4
10-3
10-2
10-1
Isoto
pic
ratio 2
9S
i/2
8S
i
Natural Si
1
2
3
Depth (nm)
(a)
natSi substrate
Enriched 28Si
Gate oxide(60 nm SiO2)
P implant
Ohmic contact
Top gate
200 μm
(c)
Top gate
P implants
Ohmic contacts
(d)
12
3
(b)
natSi
Deposited 28Si spot
Si handle (4 × 10) mm Devices
-10 -5 0 5 10-6000
-4000
-2000
0
2000
4000
6000
0
200
400
600
800
1000
1200
Rxx (
)
On chip natural abundance Si
Rxy (
)
B (T)
T=1.9 K, Vg=8 V
=
-10 -5 0 5 10-3000
-2000
-1000
0
1000
2000
3000
1100
1200
1300
1400
T=1.9 K, Vg=8 V
Isotopically enriched 28Si
Rxx (
)
=
Rxy (
)
B (T)
(a)
(b)
0.0 0.1 0.2 0.30
2
4
6
8
10
12
14
16
18
28Si
natSi
HLN fits
xx (
S)
B (T)
T = 3 K 2 4 6 8 10
2
4
6
8
10
12 28Si
natSi
fit
1/ (
10
11/s
)
T (K)
(a)
(b) (c)
2 4 60.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(p
s)
q (28Si)
(28Si)
q (natSi)
(natSi)
T (K)
0.1 0.2 0.30
1
2
3
4
5 28Si
fit
ln(A
SdH/X
(T))
1/B (1/T)
T = 3 K
0.1 0.2 0.3
1200
1250
1300
T = 3 K
Rxx (
)
1/B (1/T)
Amplitude (ASdH)
Isotopically enriched 28Si