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 à 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 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved.
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.
[1] T.D. Ladd, et al., Phys. Rev. Lett. 89 (2002) 017901.
[2] K.M. Itoh, Solid State Commun. 135 (2005) 747.
[3] T.D. Ladd, et al., Phys. Rev. B 71 (2005) 014401.
The EPR spectrum observed in FZ silicon without external [4] K. Takyu, et al., Jpn. J. Appl. Phys. 38 (1999) L1493.
stress after diffusion of Li atoms was found to agree with the EPR [5] K.M. Itoh, et al., Jpn. J. Appl. Phys. Pt. 1 42 (2003) 6248.
spectrum observed earlier under uniaxial stress . Temperature [6] T. Kojima, et al., Appl. Phys. Lett. 83 (2003) 2318.
dependence of EPR and field dependence of NMR intensity shows [7] A.S. Verhulst, et al., Phys. Rev. B 71 (2005) 235206.
[8] H. Hayashi, et al., Phys. Status Solidi (c) 3 (2006) 4388.
that Li has a short enough electron spin relaxation time for [9] L.S. Vlasenko, et al., Phys. Status Solidi (c) 3 (2006) 4376.
efficient DNP at liquid helium temperature. It was shown that [10] A.W. Overhauser, Phys. Rev. 92 (1953) 411.
DNP is a result of the differential solid-effect. 29Si nuclear [11] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, polarization of 0.17% has been achieved via saturation of electron [12] A. Abragam, et al., Compt. Rend. 247 (1958) 2337.
paramagnetic resonance transitions related to isolated lithium [13] O.S. Leifson, et al., Phys. Rev. 122 (1961) 1781.
[14] R.L. Aggarwal, et al., Phys. Rev. 138 (1965) A882.
[15] G.D. Watkins, et al., Phys. Rev. B 1 (1970) 4071.
[16] H. Hayashi, et al., Phys. Rev. B 78 (2008) 153201.
This work was supported in part by Grant-in-Aid for Scientific Research by MEXT Specially Promoted Research #18001002, in

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