Table Of ContentStark shift and field ionization of arsenic donors in 28Si-SOI structures
C. C. Lo,1,2,a) S. Simmons,3 R. Lo Nardo,1,3 C. D. Weis,4 A. M. Tyryshkin,5 J. Meijer,6,b) D. Rogalla,6 S. A.
Lyon,5 J. Bokor,7 T. Schenkel,4 and J. J. L. Morton1,2,c)
1)London Centre for Nanotechnology, University College London, London WC1H 0AH,
U.K.
2)Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE,
U.K.
3)Department of Materials, University of Oxford, Oxford OX1 3PH, U.K.
4)Accelerator and Fusion Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
4 U.S.A.
1 5)Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544,
0 U.S.A.
2 6)RUBION, Ruhr-Universitaet Bochum, Germany
n 7)Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720,
a U.S.A.
J
(Dated: 28 January 2014)
7
2 We develop an efficient back gate for silicon-on-insulator(SOI) devices operating at cryogenic temperatures,
and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified 28Si-
] SOI layers using such structures. The back gate is implemented using MeV ion implantation through the
l
l SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to
a
h ∼2V/µm to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters
- of arsenic donors embedded in the 28Si SOI layer and find a contact hyperfine Stark parameter of ηa =
s −1.9±0.2×10−3 µm2/V2. We also demonstrate electric-field driven dopant ionization in the SOI device
e
m layer, measured by electron spin resonance.
.
t
a
Shallow donors in silicon are promising candidates for derstandingand ability to model the donor energylevels
m
spin-based quantum information processing1. Although accurately when embedded in nano-scale devices where
- it has been known for decades that the coherence times large electric fields are usually present11. In addition,
d
n of donor spins are relatively long at cryogenic tempera- measurementsofionizeddonornuclearspinstodatehave
o tures2–4,recentmeasurementswithimprovedinstrumen- reliedonopticalorthermalionizationprocesses7,12. Itis
c tation, better understanding of the decoherence mecha- thereforedesirabletodevelopamethod, applicabletoan
[
nisms and the availability of ultra high purity isotopi- ensemble,whichachievesmorecontrollabledonorioniza-
1 cally enriched nuclear spin-free 28Si crystals have led to tion and subsequent neutralization.
v dramatic improvements of the measured spin coherence
The first measurement of the Stark shift parameters
5 times, exceeding seconds for phosphorus and bismuth
for shallow donors was reported using electron spin res-
8 donor electron spins5,6. Furthermore, the nuclear spin onance (ESR) of121Sb donorsresiding betweeninterdig-
8
coherence times of ionized phosphorus donors have been
6 itated metallic electrodes evaporated on the silicon sur-
. found to exceed hours at cryogenic temperatures and 39 face13. The geometry resulted in a non-uniform distri-
1 minutesatroomtemperature7. Inadditiontopossessing
bution of the electric field for the donor ensemble. In
0
extraordinarylong spin coherence times, both the donor
4 addition, the maximum electric field that could be ap-
electron and nuclear spins can be read-out in a single
1 plied was below 1V/µm, limited by leakage currents be-
shot8–10 at the single-atom level.
: tween the electrodes in high-field regions. A parallel-
v A number of challenges remain in building on these
plate capacitor-like structure in principle allows the ap-
i
X advancestorealizeascalabledonor-basedquantumcom- plication of uniform electric fields across the silicon and
puting architecture. Some such architectures require lo-
r reducesthe probabilityof havingleakagecurrents. How-
a cal addressability of donors under global microwave ex-
ever, the voltage required to bias across the silicon sub-
citation, achieved, for example, by using electric fields
strate would need to be in the order of 100V to obtain
to tune donor spins in and out of resonance using the
appreciable Stark shifts for typical wafer thicknesses of
Starkshift1. As wellasbeing a prerequisiteforassessing
500µm.
the feasibility of such approaches, precise measurements
of the donor Stark shift are also critical to aid our un- In this work we develop devices for ensemble mea-
surementsutilizing silicon-on-insulator(SOI)substrates,
wherethedonorsofinterestareembeddedinthethinSOI
layer. Weimplementanovelbackgateusinghighenergy
a)Electronicmail: [email protected]. ion implantation into the handle wafer, which allows the
b)Presentaddress: DivisionofNuclearSolidStatePhysics,Univer- efficient application of uniform and large electric fields
sityofLeipzig,Leipzig,Germany across the SOI layer for both Stark shift measurements
c)Electronicmail: [email protected]. and controlled ionization of the dopants. This provides
2
V Ti/Au top gate resulting peak donor concentration is located approxi-
SiO (370nm) mately 60nm away from the dry oxide-SOI layer inter-
2
75As + 28Si (100nm) SOI layer face. 360nm of low temperature oxide was subsequently
natSi (100nm) SiO (200nm) deposited at 450◦ to reduce the probability of gate leak-
2
age in the large-area device required for ensemble mea-
surements. The dopants were then activated by rapid
5μm thermal annealing at 900◦ for 10s in a nitrogen ambi-
m
1m handle wafer ent. We foundsignificantdopantpileuptowardsthedry
2
oxide as measured by secondary ion mass spectroscopy,
<001> which shows an As concentration of 4−5×1016/cm3
E
in the top 50nm of the 28Si epitaxial layer but drops to
B ≈1×1015/cm3 at the natSi-BOX interface, hence 90%
<110>
of the implanted donors reside in the 28Si layer.
2.5mm p+ back gate In order to access the deeply implanted p+ back gate
inthehandlewafer,contactwindowsweremadebyetch-
FIG.1. Schematicofthe28Si-SOIdevicewithap+backgate ing through the oxide layers and SOI layer. A BOSCH
formed byMeV ion implantation. Inset: Cross-section of the etch process was then carried out to etch 5µm down
device. 90%ofthe75Asdonorsresideintheepitaxiallygrown the handle wafer. After native oxide removal by hy-
28Si region of theSOI layer. drofluoric acid, Ti/Au metallic layers were subsequently
deposited to form both the contacts to the p+ back
gate and defining the top gate electrode. The top gate
a platform for ensemble spin resonance measurements electrode covers an area of 21×2.6mm2 with approxi-
on electrically ionized and re-neutralized donor nuclear mately2×1011donorsunderneath. Aforminggasanneal
◦
spins. (90%N2,10%H2)at350 Cfor20minutes wasthencar-
The SOI substrates consisted of 100nm thick p-doped ried out to passivate the silicon-silicondioxide interfaces
(∼10Ωcm) naturalsilicon (natSi) with h100i orientation in the structure. A schematic and the cross section of
(SOITEC), and a similarly p-doped (∼15Ωcm) handle the final device structure are shown in Fig.1.
wafer underneath which normally freezes out at cryo- Capacitance-voltage (CV) measurements at cryogenic
genic temperatures. 100nm thick isotopically purified temperatures reveal a gate capacitance of 1.9 nF/cm2,
99.92%28-silicon(28Si)wasepitaxiallygrownonthenat- in good agreement with the geometry of the device with
uralsiliconSOIwafer(LawrenceSemiconductors),form- the top 5µm of the silicon handle wafer being insulat-
ing the 28Si-SOI device layer. In order to create an ing. The capacitance is essentially constant within the
effective back-gate for realizing a parallel plate geome- gate voltage (≤ 2V) and pulse speed (10 µs) used in
try, a high energy boron (B) implantation of 4MeV at a this study. Frequency dependent CV measurements in-
dose of 2.2×1015/cm2 was performed, with almost all dicate that hole accumulation at the handle wafer-BOX
dopants implanted through the device and the 200nm interfacewasonlyachievedatlowfrequencies (<1kHz),
thick buried oxide (BOX) layers, peaking at 5µm down and on some devices only at temperatures greater than
from the handle wafer-buried oxide interface. The peak the carrier freeze-out temperature. We speculate that
B concentration of 3 × 1019/cm3 is above the metal- this is due to residual lattice defects in the handle wafer
insulator-transition, ensuring that the p+ region in the with sufficient trap density to preventholes fromthe p+
handle wafers remains metallic even at cryogenic tem- back gate migrating to the interface efficiently. Hence,
peratures. The added B concentration in the SOI layer theelectricfieldstrengthiscalculatedassumingametal-
resulting from the high energy implant is expected to be lic parallel-plate capacitor geometry, with dimensions as
less than 1×1015/cm3 from device process simulations, shown in the inset of Fig.1.
andthelatticedamageintheSOIlayerisexpectedtobe All ESR measurements were carriedout with a pulsed
minimal due to ion channeling and most lattice damage X-band (≈ 9.8GHz and B ≈ 0.34T) ESR spectrometer
is expected to be incurred at end-of-range14. A 10nm (BrukerElexsys580). AcontinuouswaveESRlinewidth
silicon dioxide was subsequently grown on the SOI layer of 0.01mT (0.3MHz) for the As donor was measured at
◦
by dryoxidationat900 C.This oxidationstepactivated 20K,afactorof∼40narrowerthantheknownlinewidth
the implanted B and also reduced lattice damage in the in natSi. In addition, an electron spin coherence time
handle wafer induced by the MeV implants. T =0.3ms wasobservedat2K,indicating thatthe spin
2
The 28Si-SOI layer was then implanted with arsenic coherence is limited by the relatively high As concentra-
dopants (75As) at 110keV at a dose of 4 × 1011/cm2 tion instead of natSi in the SOI layer5. Both of these
◦
with 7 tilt. Arsenic was chosen to minimize dopant dif- observations confirm that the signal mostly arises from
fusionfromthe28Silayertothenaturalsiliconlayerdur- dopants residing in the 28Si layerand that the SOI layer
ing thermal activation. In addition, the As nuclear spin has a low defect density. All measurements discussed
of I=3/2 allows the clear elucidation of the contribu- hereafter were performed at 15K, unless stated other-
tionfromthe contacthyperfine inducedStark shift. The wise.
3
(a) e 40
owavulses π2 π echo 30 (d) mI = -3/2
crp time )
Mi 0 τ0=15μs τ0 Hz 20
k
ge es 2 +V -V fΔ ( 10 -1/2
as
Voltpul 0 τ=10μs time hift, 0
S
1 1 y
) (b) (c) c
u. In−phase n−10 +1/2
a. ue
al ( eq−20
n 0 0 Fr
g +3/2
Si −30
R
S Quadrature
E−1 −1 −40
−5 0 5 −5 0 5 0.00 0.05 0.10 0.15 0.20 0.25
Time (μs) Time (μs) Electric Field, E (V/μm)
FIG.2. (a)Synchronizationofthemicrowaveandvoltage(electricfield)pulsesusedintheStarkshiftexperiments. Hahnecho
signal for mI=+3/2 of 75As donors centered at 2τ0: (b) with no applied electric field, and (c) with an applied electric field of
E = 0.23V/µm. The phaseshift from in-phaseto quadratureisduetotheStark effect,with offset for clarity. (d)75Asdonor
frequency shifts for thefour hyperfine-split lines. Solid lines represent fitsto data with Eq1.
Our parallel plate structure permits a uniform elec- hyperfineinteractionstrengthandelectronicg-factor,re-
tric field to be readily applied to the As donors. Under spectively. ForAsdonors,a=819neVandg =1.998373.
small applied voltages the donor remains neutral at low We have neglected linear Stark shift terms (∝ E) which
temperatures, however, the electronic wavefunctions are are much smaller comparedwith the quadratic effects in
distorted,causingachangeinthecontacthyperfineinter- silicon13,15, and linear terms cancel out with the bipo-
action and spin-orbit coupling strengths, hence inducing lar voltages pulses used. With such a frequency shift, a
a Stark shift. We investigate the As Stark shift parame- voltage(electric field) pulse of durationτ then induces a
tersusingaHahnechopulsesequence,andwedetectthe phase shift ∆ϕ =2π∆f τ for the Hahn echo signal.
mI mI
frequencyshiftofthe donorsbyexaminingthe changein
All measurements were carried out with microwave
the Hahn echo signal phase as the applied voltage (elec-
pulsedelaysofτ =15µs,andthe voltagepulsesforeach
tric field) is varied13. In all cases, the static magnetic 0
polarity are 5µs long (total 10µs voltage pulse for each
field B is aligned along the h110i axis, and orthogonal
0 measurement). A two step phase cycling (+X,+X and
to the direction of the applied DC electric field E.
+X,−X)forthe microwavepulses is usedtoremovespu-
We use a bipolar voltage pulse sequence (sequence IV
riousbackgroundsignals. Figure2(b)showsthereference
in Ref [13]), where voltages of opposite sign but equal
echosignalandFig.2(c)showsthephaseshiftedechosig-
amplitude areappliedsuccessivelyduring the defocusing
nal under an applied electric field of E =0.23V/µm for
phaseoftheHahnechosequence. Thesynchronizationof
them =+3/2line. Theechophaseshiftsextractedfrom
I
the microwave and voltage pulses is shown in Fig. 2(a).
theechosignalsforthefourdifferenthyperfine-splitlines
The advantage of using a bipolar pulse sequence over a
areconvertedto frequencyshifts andshowninFig. 2(d).
unipolar pulse sequence (containing only voltage pulses
The solid lines represent quadratic fits to the data as
ofthesamesign)isthatambiguitiesarisingfrombuilt-in
defined by Eq.1. We find the contact hyperfine term
electric fields cancel out. The donor resonant frequency η = −1.9±0.2×10−3µm2/V2 and the spin-orbit term
a
shift∆fmI foragivenESRlinecorrespondingtonuclear η = 3±4×10−6µm2/V2. The spin-orbit shift is very
spin m , due to the applied electric field of magnitude g
I weak compared with the hyperfine shift under our ex-
|E| is given by:
perimentalconditionswithrelativelymoderatemagnetic
fields 13,16, and cannot be determined accurately within
experimental errors. Indeed, fitting the data while ne-
1
∆fmI =(cid:18)h(cid:19)(ηaamI +ηggµBB)E2 (1) glectingthespin-orbittermresultsinvirtuallynochange
to the contact hyperfine value. We summarize the Stark
shiftparametersforvarioussiliconshallowdonorsinTa-
where η is the hyperfine induced Stark parameter, η
a g ble I.
the spin-orbit induced Stark parameter, h Planck’s con-
stant and µ the Bohr magneton, while a and g are the We find that at larger electric fields the ESR signal
B
4
Donor Orientation ηa ηg Experiment/Theory
(10−3µm2/V2) (10−6µm2/V2)
31P – −2.8 – Tight-bindingcalculation.15
B||E – -12 Tight-bindingcalculation.16
B ⊥E – +14 Tight-bindingcalculation16
75As B ⊥E −1.9±0.2 +3±4 ESR with parallel-plate geometry (present work).
121Sb B ⊥E −3.7 −10 ESR with interdigitated electrodes.13a
a NotethatthesignsofthenuclearspinprojectionsinFig.4ofRef[13]weremislabeled,butthesignsandvalues givenfortheStark
shiftparametersarecorrect.
TABLE I. Summary of the experimentally and theoretically determined Stark shift parameters for shallow donorin silicon.
0.08 ing, which is about 0.2MHz in the highest quality 28Si
material,implyinganelectricfieldoftheorderof1V/µm
0.06 isneededforshifting anentireESRlineoutofresonance
as previously noted13. We found that even at 1V/µm
theESRsignalsaresignificantlyreduced,indicatingthat
0.04
u.) E = 2V/μm somedonorsbegintobeionizedbythemoderateelectric
a. fields, which is consistent with theoretical calculations18
al ( 0.02 and electricalmeasurements19. This underlines the diffi-
n culty of Stark tuning of donors relying on the hyperfine
g
Si 0.00 term alone. At higher magnetic fields when the spin-
R orbit term becomes appreciably larger16, or by inducing
ES−0.02 additional strain in the sample20, larger Stark shifts can
E= 0V/μm be induced to circumvent this issue.
Insummary,wehaveinvestigateddonorspindynamics
−0.04
under the influence of applied electric fields with pulsed
electronspinresonance. Arsenicdonorsareembeddedin
−0.06 isotopically purified 28-silicon SOI parallel-plate struc-
336 337 338 339
tures formed between a metallic top gate and MeV im-
Magnetic Field (mT) planted back gate. We measured the Stark shift of the
donors by applying electric fields below the ionization
FIG. 3. Continuous wave ESR signal of the mI=+3/2 sig- thresholdofthedopants,andfindahyperfineStarkshift
nal with constant voltage (lower) E=0V and (upper) E = parameter of ηa =−1.9±0.2×10−3µm2/V2.
2µm/V measured at 18K, offset for clarity.
ACKNOWLEDGMENTS
intensity decayssubstantially due to the onsetof dopant
ionization, and that ∼2V/µm is sufficient to completely This researchis supportedby the EPSRCthroughthe
field-ionizethedonors,asshowninFig.3. Removingthe Materials World Network (EP/I035536/1) and CAESR
electricfieldcausestheelectronspinechotoreappear(i.e. (EP/ D048559/1) as well as by the European Research
re-neutralization of the donors) on a timescale of ∼1µs, Council under the European Community’s Seventh
limited by the RC constant of the device. The results of Framework Programme (FP7/2007-2013)/ERC grant
electric field-controlled dopant ionization on the nuclear agreement No. 279781. Work at Princeton was sup-
spin coherence times will be reported in a subsequent portedbyNSFthroughMaterialsWorldNetwork(DMR-
publication. 1107606) and through the Princeton MRSEC (DMR-
The As dopant density used in this study corresponds 0819860). WorkatLBNLwassupportedbytheU.S.Na-
to a mean donor-donor separation of approximately tional Security Agency (100000080295) and by the U.S.
40nm, which is close to the upper limit of exchange- Department of Energy (DE-AC02-05CH11231, LBNL).
based entanglement schemes for donor qubits. At these C.C.L. is supported by the Royal Commission for the
concentration levels, the spin coherence time is limited Exhibitionof1851. S.S.issupportedbytheVioletteand
by direct dipole-dipole interaction amongst the donors5. Samuel Glasstone Fund and St. Johns College Oxford.
Wenotethatinaperfectlyplanerdevicearchitecturethe J.J.L.M. is supported by the Royal Society.
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