Electron paramagnetic resonance and dynamic nuclear polarization of 29si nuclei in lithium-doped silicon
Electron paramagnetic resonance and dynamic nuclear polarization of29Si nuclei in lithium-doped silicon
M.R. Rahman a, L.S. Vlasenko b, E.E. Haller c, K.M. Itoh a,Ã
a School of Fundamental Science and Technology, Keio University, Yokohama 223-8522, Japanb A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russiac Lawrence Berkeley National Laboratory and UC Berkeley, 1 Cyclotron Rd., Berkeley, CA 94720, USA
Electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) experiments with Li-
doped FZ silicon wafers are reported. The Li related EPR spectrum of tetrahedral symmetry was detected
clearly without external stress even at low temperatures (To5 K) implying that the Li electron spin-
lattice relaxation time is much shorter than that of other shallow donors, e.g. phosphorus. The solid-
effect was found to be responsible for the DNP and the polarization was enhanced by a factor of 87 at
& 2009 Elsevier B.V. All rights reserved.
microwave ﬁeld of 9 GHz at 4.2 K . Such low efﬁciency of DNPwith phosphorus-doped silicon at low temperatures (To10 K) is
Recently silicon-based quantum computing utilizing 29Si
due to the long electron spin-lattice relaxation time T1e$1–10 s
nuclear spins as qubits has been proposed . While 29Si
The maximum value of the nuclear polarization PNmax that can
nuclear spins have been shown to have more than 25 s of
be achieved by complete saturation of EPR transitions is;
coherence time, even at room temperature, it is not
straightforward to polarize all the nuclear spin qubits in the same
orientation because of the small magnetic moment of the nuclear
spins. Since application of a large magnetic ﬁeld and lowering of
temperature (e.g., B410 T, To1 K) alone cannot lead to 5%
polarization needed for the initialization step of quantum
Here Nn is the number of nuclei interacting with one
computation, it is necessary to control the average distance
paramagnetic center, Ne is the number of paramagnetic centers,
between 29Si nuclear spin qubits through isotope engineering
and Tp1 is the nuclear polarization time ranging from a few
and utilized photons and/or electron spin to
minutes to a few hours depending on the concentration of
polarize nuclear spin qubits dynamically.
paramagnetic centers. When the electron relaxation time is short,
The DNP process transfers the equilibrium Boltzmann electron
1eoNeT1/Ne, the maximum nuclear polarization can be achieved
spin polarization Pe0 at temperature T and magnetic ﬁeld B to the
when fo1. In this regard, lithium donors in silicon some of the
nuclear spin by electron paramagnetic resonance (EPR) of
most attractive candidates for effective DNP of 29Si nuclear spins.
paramagnetic centers that are in hyperﬁne contact with nuclear
In contrast to a phosphorus donor that has a non-degenerate
spins. The largest nuclear spin polarization enhancement obtain-
singlet ground A1 state, the ﬁve-fold degenerate ground state
able is given by Emax ¼ PN/PN0 ¼ ge/gN where PN0 is equilibrium
(doublet E+triplet T2) of Li in Si leads to shorter electron
Boltzmann nuclear polarization and ge and gN are the electron and
spin-lattice relaxation time than that for phosphorus. EPR
nuclear gyromagnetic ratios, respectively For silicon the
investigations of Li in Si with externally applied stress have
shown that Li prefers to occupy interstitial tetrahedral sites
The ﬁrst experiments on DNP of 29Si nuclei were performed by
leading to an EPR spectrum with axial symmetry about the
Abragam et al. using phosphorus-doped silicon. A DNP
enhancement of E ¼ 30 and a nuclear polarization of 0.048% wereobtained under saturation of the phosphorus EPR lines in a
Ã Correspondence to: Department of Applied Physics and Physico-Informatics,
Experiments were performed with FZ silicon doped with Li by
Keio University, 3-14-1, Hiyoshi, Kohoku-Ku, Yokohama 223-8522, Japan.
diffusion at 420 1C in vacuum for 15 min. The sample was
Tel.: +81 45 566 1594; fax: +81 45 566 1587.
quenched in alcohol immediately after annealing to prevent
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M.R. Rahman et al. / Physica B 404 (2009) 5060–5062
oxidation of Li. The concentration of shallow donors after
angular dependence of this EPR spectrum ((b)) shows
axially symmetric g-tensors about /10 0S with g ¼ g
A X-band EPR spectrometer was used for the detection and
1.999670.0001 and g? ¼ 1.998670.0001 and they agree very
saturation of the Li EPR lines. The temperature of the samples was
well with previously reported values for Li atoms occupying
controlled by an Oxford Instruments He gas ﬂow cryostat in the range
of 3.2–50 K. In order to determine the g-values of the observed EPR
Strong enhancement of 29Si NMR nuclei was observed after
lines precisely, the EPR measurements were performed together with
saturation of the Li EPR transitions. The dependence of the NMR
a Si:P reference sample having the well known isotropic g-value of
signal amplitude on the magnetic ﬁeld Bsat that has been used for
1.998570.0001. The DNP of the 29Si nuclei were performed using the
the saturation in the EPR spectrometer is shown in (a)
EPR spectrometer for saturation of the EPR lines at the microwave
together with the ﬁrst derivative shape of the EPR spectrum. The
power of 1–200 mW. The time of saturation, t, was varied between
shape of the enhanced NMR signal represented by ﬁlled square in
10 min and 15 h. The long nuclear spin-lattice relaxation time
resembles that of the EPR curve shown by the solid curve.
T1430 min for all investigated samples at room temperature allows
This shows that the ‘‘differential’’ solid-effect is respon-
us to transfer the sample from EPR to the pulse nuclear magnetic
resonance (NMR) spectrometers to evaluate the polarization of
Temperature dependences of the Li EPR intensity and 29Si DNP
degree are shown in In contrast to the phosphorus EPRspectrum , the intensity of the Li EPR spectrum increases withdecreasing temperature even below TE12 K. This suggests that
isolated interstitial Li atoms have a much shorter electron spin-lattice relaxation time than that of phosphorus. The temperature
An EPR spectrum recorded without any externally applied
dependence of the 29Si DNP degree correlates with the
stress at 3.2 K with BJ/10 0S is shown in It agrees very
temperature dependence of the Li EPR spectrum.
well with previously reported spectra for isolated Li . The
The dependence of the DNP degree on the duration of the EPR
saturation measured at T ¼ 3.2 K and B0 ¼ 323.16 mT is shown in(b). The DNP degree extrapolated to inﬁnite saturation time
reaches the NMR signal enhancement of 87 corresponding to thepolarization of 0.17% that is three orders better than that of
thermal equilibrium. The nuclear polarization time (Tp1) of 29Si
and normalized NMR signal intensity -1.0
Fig. 1. (a) Solid curve shows the EPR signal of isolated Li measured with BJ/10 0S.
Here Bsat is the saturation magnetic ﬁeld and B0 is the center magnetic ﬁeld. Solidsquares represent the normalized 29Si NMR intensity after saturation of isolated-Li
Fig. 2. (a) The temperature dependence of the Li EPR intensity (open circle) and
at Bsat–B0. (b) The angular dependence of EPR signals position where y is the angle
the degree of polarization of 29Si nuclei (square). (b) Dependence of the DNP
between the symmetry axis /1 0 0S and applied magnetic ﬁeld direction.
degree on the time of EPR saturation. Solid line is the single exponential ﬁt.
M.R. Rahman et al. / Physica B 404 (2009) 5060–5062
nuclei is 24 min, which is signiﬁcantly shorter than 82 min
part by Special Coordination Funds for Promoting Science and
obtained for DNP of 29Si via phosphorus donors for the same
Technology, in part by JST-DFG Strategic Cooperative Program on
concentration of paramagnetic centers. Inhomogeneous broad-
Nanoelectronics, and in part by a Grant-in-Aid for the Global
ening of the EPR line in the present sample does not allow for an
Center of Excellence at Keio University.
efﬁcient DNP through the pure solid effect. It is important toidentify the origin of the inhomogeneous broadening to improvethe efﬁciency of DNP via Li in Si.
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This work was supported in part by Grant-in-Aid for Scientiﬁc
Research by MEXT Specially Promoted Research #18001002, in
Nursing Pharmacology Pretest – Part 1 Section 1: Fractions Section 2: Decimals Round the number to the place value indicated. Section 3: Ratio & Proportion 37. – 38. Each nurse can care for 7 patients. How many nurses will be needed for 42 patients? 39 – 40. Each Xanax tablet is equal to 0.25 mg. If the doctor ordered 0.75 mg of Xa
ﺍﺭـــــﺘﺒﻝﺍ ﺔـــﻌﻤﺎﺠ (ﺓﺩﻤﺘﻌﻤ ﺔﺼﺎﺨ ﺔﻌﻤﺎﺠ ) Faculty of Pharmacy &Medical Sciences. ﺔﻴﺒﻁﻝﺍ ﻡﻭﻠﻌﻝﺍﻭ ﺔﻝﺩﻴﺼﻝﺍ ﺔﻴﻠﻜ CURRICULUM VITAE (CV) TAWFIQ ARAFAT PERSONAL DATA 2012 Nationality : Jordanian Marital Status: Married with three children Address: Petra Univ