Spin selective segregation of oxygen in dislocation cores in 29Si enriched silicon crystals Текст научной статьи по специальности «Физика»

DOI: 10.17277/amt.2018.04.pp.019-024

Spin Selective Segregation of Oxygen in Dislocation Cores in 29Si Enriched Silicon Crystals

O.V. Koplak1'2*, A.N. Tereshchenko3, O.S. Dmitriev2, R.B. Morgunov1' 2

1 Institute of Problems of Chemical Physics of RAS, 1, Acad. Semenov avenue, Chernogolovka, 142432, Russia; 2 Tambov State Technical University, 112, Michurinskaya, Tambov, 392032, Russia; 3 Institute of Solid State Physics of RAS, 2, Acad. Ossipyan St., Chernogolovka, 142432, Russia

* Corresponding author: Tel: +7 911 861 98 10. E-mail: o.koplak@gmail.com

Abstract

29 29 29

Plastic deformation of Fz— Si crystals enriched with Si magnetic isotope causes redistribution of Si atoms and 29Si160 complexes in the surface areas of the crystal. Redistribution of the magnetic isotope correlates well with the density of dislocations introduced by plastic deformation. Oxidization of silicon is forbidden in the absence of the magnetic field due to

29

strict prohibition to change full angular momentum conservation in Si—O electronic pair. The presence of the Si nuclear spin allows conversion of the initial triplet state to the singlet state in the Si—O pair. This transition accelerates formation of the stable SiO oxide. The single event of the oxidization was interpreted in terms of quantum computation accordingly with the CNOT quantum gate equivalent to the transformation of the triplet state to the singlet one. The read out of the stored quantum information corresponds to "1" in stable SiO complex or logic "0" in the decomposed Si—O pair.

Keywords

Dislocations; isotopes; qubit; quantum logic.

© O.V. Koplak, A.N. Tereshchenko, O.S. Dmitriev, R.B. Morgunov, 2018

Introduction

Approaching the sizes of logic devices to atomic size meets quantum effects transferring modern technologies to the area strongly different from classical electronics. Quantum computing based on pure mono isotope silicon crystals [1 - 5] is of interest for researchers investigating spin-dependent phenomena in silicon and methods of pumping of spin polarization [4 - 8]. Although the main advantage of silicon quantum computers is a long coherency time of electron [9, 10] and nuclear [11] spins, this device still requires overcoming multiple difficulties to realize this intriguing idea. Most efforts are spent to propose a method to create topologically isolated ensembles of electronic keys to read nuclear spin states [12], to develop fast optical initialization of spins [13-16] and to organize read out of the quantum information with no disturbance of the information stored in nuclear qubits. In generally, most of the experimental researches ignore the contribution of the crystal surface and structural defects in real crystals. Despite this in

[17 - 19] reading out electronic key was proposed on the basis of chemical reaction between silicon and oxygen dissolved in a crystal lattice. This oxidization reaction and the amount of oxide 29Si160 on crystal surface can be controlled by external magnetic field as well as hyperfine magnetic field of the 29Si magnetic nuclei [17]. Nuclear magnetic and electron spin resonances are the main methods of selective access to qubits. These methods were applied to study spin dynamics in isotope enriched Si crystals containing dislocations [20 - 22]. Paramagnetic defects generated by deformation have low enough concentration (< 1018 cm-3) satisfying to the conditions of spin coherency, that still remain appropriate for quantum computations even in plastically deformed crystals [18]. An accurate and systematical study of energy spectrum of dislocations and extended defects in semiconductors was realized by Yu. Ossipyan and his team by electron spin resonance, microwave conductivity, photoconductivity ant other methods [23]. Fundamental knowledge on electronic properties of dislocations is necessary to resolve the problems of full

silicon quantum computations. A spin state of dislocations controls their mobility in silicon [23], where dangling bonds exist and contribute to dislocation of electrical and optical properties [24 - 26]. The introduction of linear dislocations populated by dangling covalent bonds allows designing linear chains containing electron spins. The population of the electron spin can be controlled by optical irradiation in dislocation core. Low diffusion coefficient limits the oxidization rate in silicon. Thus, elementary oxidization events are very rare. At the same moment, a very low concentration of the nonstable Si—O pairs is in the sample. Detection of the pairs by the ESR or NMR spectrometer is not possible due to their low concentration. The accumulation of successful oxidizations during a few hours or even days causes the emergence of macroscopic amount of the oxide available for observation by different methods. The secondary ion mass spectroscopy (SIMS) allows identifying final products of the spin controlled reaction as well as distinguishing the presence of different isotopes in the final stage of the magnetically driven processes. In this article, we used the SIMS to probe the silicon isotopes presence in the subsurface silicon crystal layers after the deformation of the crystals. Thus, the spin-controlled oxidization was indirectly detected by the SIMS following the ideas developed by E. Frankevich and A. Buchachenko in spin chemistry. They studied chemical reactions by indirect detection of the spin-dependent processes through electrical current or a reaction yield product. The aims of this research are to test the possibility of using deformation defects (dislocations and 29Si160 complexes) to create photo-controlled areas of silicon crystals providing read

out quantum information stored in nuclear spin ensembles (qubits), and to provide the optical monitoring of the reaction between the oxygen atom and silicon in the presence of hyperfine interaction with 29Si nuclei.

Experimental

Single crystals of silicon doped with boron (~ 1013 cm-3) sample No. 1 and sample No. 3 were grown by the floating zone technique and enriched with 29Si isotope. The sample No. 5 of natural isotope concentrations was grown by the Czochralski technique (see Table 1). The samples were 1^4^16 mm3 sizes, long side was along (110) crystallography orientation. The deformation of the samples was performed by the three point bend until dislocation density ~ 108 cm-2 in the sample center was reached. The deformation temperature was 950 °C.

The isotope analysis of silicon crystals was performed by the time-of flight secondary ion mass-spectroscopy by spectrometer TOF.SIMS 5 (ION-TOF Germany). The cleaned initial surfaces as well as the surface formed after the ionic etching until the 30 nm depth were also analyzed. The concentrations of isotopes were determined with the high accuracy of ± 0.01 %. The concentration profiles of three stable Si isotopes 28Si, 29Si, 30Si, as well as 29Si160, 29SiHO,

28Si29Si, 29SiO

29Si2, 29Si3 complexes were recorded.

The ionic etching was performed by bombardment by Ce- ions convenient for oxygen complexes revealing. The estimations of the isotopes concentrations are given in Table 1.

Parameters of samples

Table 1

Sample Active area Isotope concentrations, % 28Si 29Si 30Si Deformation

Surface 0.36 99.58 0.06 Fz—29Si

Sample No. 1 Deformed until ~ 108 cm-2 dislocation

Depth 30 nm 0.045 99.9 0.051 density at the central part of sample

Surface 2.00 97.89 0.11 Fz—29Si

Sample No. 3 Deformed with low dislocation density

Depth 30 nm 0.19 99.77 0.045 (5 x10s cm -2)

Surface 93.49 3.41 3.10 Cz—28Si

Sample No. 5 Deformed until ~ 3x107 cm-2

Depth 30 nm 93.21 3.79 3.00 dislocation density

Photoluminescence (PL) of the samples placed to helium cryostat was excited by GaAs laser (X = 920 nm) and analyzed by the monochromator and cooling Ge photo resistor. At a temperature of 6 K PL the spectra of isotope enriched silicon were compared in crystals with different dislocation density and crystals of natural isotope abundance.

Results and discussion

The main idea of our paper is application of natural chains of paramagnetic centers distributed along dislocations core for creation of the information reading spin keys placed in massive of the nuclear qubits. Dangling bonds along the dislocation core can be labeled by oxygen captured by dislocation paramagnetic centers in the presence of a magnetic field or a hyperfine field. Thus, the silicon-oxygen reaction and the amount of 29Si160 complexes in the dislocation core control the population of the dangling bonds. The SIMS can distinguish 29Si160 complexes because Si emission under ionic bombardment depends on the Si environment [11]. Distribution of 29Si160,

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SiHO, SiO2, Si emission versus the depth of the bombarded layer in the silicon samples are shown in Fig. 1. Deformation of the crystals causes redistribution of the 29Si magnetic isotope as well as oxygen complexes containing this isotope 29Si160, 29SiHO, 29SiO2. This is in good agreement with our previous results manifesting control of the spin-dependent reaction between Si and O by the hyperfine magnetic field of 29Si nuclei [17, 19]. In our previous work, the redistribution of 28Si, 29Si and 30Si isotopes in the surface layers of single Si crystals under plastic deformation was reported [27]. Here, we are going to compare new data on oxide redistribution with the Si atoms depth monitoring. It was shown that oxidization

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0 5 10 15 20 25

Depth, nm

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Depth, nm

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of silicon atoms mainly occurred for those of them that contained 29Si magnetic nucleus. In this work we had confirmed the data concerning the deformation induced migration of 29Si atoms involved in the oxygen complexes. In addition, we determined what oxygen complexes are subjected to the influence of the hyperfine magnetic field of 29Si nuclei (Fig. 1). This fact follows from the distributions of the 28Si29Si complexes different in the deformed Fz—29Si and Cz—29Si crystals containing 3*107 cm-2 dislocations (Fig. 2). In the deformed Cz—28Si samples with low magnetic isotope concentration the profile of 28Si29Si secondary ions was the depth independent in contrast with Fz—29Si crystals. A similar distribution of 28Si in crystal with different concentrations of dislocations independent on 29Si enrichment (Fig. 3) was also a good confirmation of the 29Si importance in oxidization. The profile of 29Si distribution strongly depends on deformation and presence of 29Si, in contrast with 28Si. Atoms 29Si participate in oxidation twice as fast as the atoms containing nonmagnetic

3

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Fig. 1. Profiles of atomic distribution in deformed sample 1 (a) and sample 3 (b) with low dislocation density

10 12 14 16 18 20 22 24

c) Depth, nm

Fig. 2. Profiles of distribution of secondary ions of Si S in three types of crystals:

a - in isotope enriched deformed sample 1;

b - in isotope enriched sample 3 (with low dislocation density (5*105 cm-2)); c - deformed sample 5 with natural abundance of isotopes

10 15 20

9Si

25

10 15

a)

20

25

Depth, nm

9Si

10

15 20

25

10 15

b)

20

25

Depth, nm

9Si

5 10 15

X Axis Title » .

29Si

20

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25

15

c)

90 25

Depth, nm

Si

Fig. 3. Distributions of magnetic 29Si and non magnetic 28 isotopes in three types of crystals:

a - in isotope enriched deformed sample 1; b - with low dislocation density sample 3; c - deformed sample 5 with natural abundance of isotopes

nuclei 28Si, 30Si due to the hyperfine interaction [17, 19]. One can conclude that the change of the elastic constants and the dilatation of the crystal lattice due to the change of the isotope nuclei size can be a reason of the described above effects, because 28Si, 30Si

behaviors are similar, although both of them are different from 29Si.

Oxygen complexes are non-equilibrium structural defects migrating to the dislocation core in the energy profile of the distorted crystal lattice. This migration minimizes free energy of the crystal. The analysis of photoluminescence of dislocation levels D1 - D4 allows monitoring of the spin dependent processes involving magnetic nuclei and reading paramagnetic keys. For this purpose, low temperature measurements of photoluminescence were carried out in the crystals (Fig. 4). The intensities of the D1 - D4 dislocation luminescence bands were strongly different due to different dislocation densities in the studied samples. An increase in the dislocation density leads to the enhancement of the luminescence intensity as well as to the appearance of the long wave shoulder at D1 line caused by the oxygen segregation in the dislocation cores during their movement through the crystal [28]. In [20, 21], a correlation between temperature dependencies of the D1 line intensity and the magnetic moment and the magnetic susceptibility of the plastically deformed crystals was revealed. This fact allows us to verify the interrelation between the centers responsible for D1 luminescence and paramagnetic structural defects in the isotope enriched 29Si : B crystals. It seems to be reasonable to suppose that the early observed magnetic and microwave magnetic field effect on the dislocation mobility [23] has a direct relation to the elementary processes reported in this article. The effect of the external and/or hyperfine magnetic fields on the oxidization of silicon in the areas close to the dislocation cores is able to change the structure and the potential relief of the dislocation obstacles. Thus, the change of the dislocation mobility

Fig. 4. Spectra of dislocation photoluminescence at 6 K in the crystals with different dislocation densities (see legend)

under the magnetic field can be judged as an indicator of spin-dependent processes stimulated in the dislocation core. Direct experimental evidence of this fact was proposed in [30].

The calculation of probability of different states in three spin system (Si = '/2 spin of O, S2 = '/2 spin of Si, I = / spin of Si nucleus) was performed by spin composer instrument, proposed by IBM [31]. The superconductive quantum computer operating at 15.736 mK performed the calculation of probabilities of the 3-qubit states (results see in Fig. 5, 6). Eight eigenstates of the three spin system are 1000), 1001), 1010), 1011), 1100), 1101), 1110), 1111) and probabilities of their mixing during classical random score are shown in Fig. 5 (Bloch sphere) and Fig. 6 (population of the states). One can estimate a very small fraction of 1100) state due to the saving of the system in the initial 1000) state. A small admixture of the I 100) state indicates a negligible role of the decoherency as it takes place in the silicon crystal lattice.

Bo

Bo

Sa

Sa

Sb

a)

T+-

b)

Fig. 7. Scheme of spin-dependent formation of

a - singlet state; b - triplet state

9SiO:

The conventional gate providing transformation of the two electron spin system from a singlet state (Fig. 7a) to a triplet state (Fig. 7b) is the Controlled-NOT, or CNOT. Nuclear spin controls NOT transition. The examples of this transformation are given in [31].

Thus, the photo controlled electronic states of dislocations and other deformation defects allows one to dissolve the main problem of quantum computations, i.e. the suppression of the spin decoherency resulting from the electron-nuclear interaction in the introduced spin "key" by doping atoms. The possibility of the rapid filling of electronic levels on dislocation under the light emission allows creating an optical shutter keeping a nuclear subsystem isolated from thermal fluctuations. This method provides rapid access to the stored information. Thus, a combination of a long storage of the nuclear spin polarization with the photo controlled key based on the optically controlled deformation defect gives advantages in quantum computing due to the combination of microwave readout and the optical population/depopulation of the keys opening for a short time window.

Conclusions

Fig. 5 Results of realization of random score on Bloch sphere with eigenstates marked by points

0.875 0.75 0.625

0.5

13

0.375 P^ 0.25 0.125 0

0.025

Eigenstate

Fig. 6. Results of evaluation of real quantum IBM computer for 3 spin system

The formation of 29Si16O complexes passed through a spin-selective stage. The distribution of these complexes in the near surface layers was determined by the SIMS. In the 29Si enriched crystals the amount of the deformation defects was larger in comparison with the crystals of natural isotope abundance. The dislocation movement caused the redistribution of the isotopes contained in the subsurface layers. The variation of the isotope concentration under the plastic deformation correlated well with the dislocation density.

The work was partially supported by Russian Foundation for Basic Research (Grant 16-02-00420).

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References

1. Kane B.E. A silicon-based nuclear spin quantum computer. Nature, 1998, Vol. 393, pp. 133-137. doi: 10.1038/30156

2. Zwanenburg F.A., Dzurak A.S., Morello A., Simmons M.Y., Hollenberg L.C.L., Klimeck G., Rogge S., Coppersmith S.S.N., Eriksson M.A. Silicon quantum electronics. Reviews of Modern Physics, 2013, vol. 85, pp. 961-1019. doi: 10.1103/RevModPhys.85.961

3. Itoh K.M. An all-silicon linear chain NMR quantum computer. Solid State Commun., 2005, vol. 133, issue 11, pp. 747-752. doi.org/10.1016/j.ssc.2004.12.045

4. Gorman J., Hasko D.G., Williams D.A. Charge-Qubit Operation of an Isolated Double Quantum Dot. Phys. Rev. Lett., 2005, vol. 95, issue 9, pp. 090502. doi/10.1103/PhysRevLett.95.090502

5. Min B.C., Motohashi K., Lodder C., Jansen R. Tunable spin-tunnel contacts to silicon using low-work-function ferromagnets. Nature Mater. 2006, vol. 5, issue 10, pp. 817-822.

6. Huang B., Monsma D.J., Appelbaum I. Coherent Spin Transport through a 350 Micron Thick Silicon Wafer. Phys. Rev. Lett., 2007, vol. 99, issue 17, pp. 177209. doi.org/10.1103/PhysRevLett.99.177209

7. Appelbaum I., Huang B., Monsma D.J. Electronic measurement and control of spin transport in silicon. Nature. 2007, vol. 447, pp. 295-298. doi: 10.1038/nature05803

8. Jonker B.T., Kioseoglou G., Hanbicki A.T., Li C.H., Thompson P.E. Electrical spin-injection into silicon from a ferromagnetic metal/tunnel barrier contact. Nat. Phys., 2007, vol. 3, pp. 542-546. doi.org/10.1038/nphys673

9. Abe E., Itoh K.M., Isoya J., Yamasaki S. Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon. Phys. Rev. B, 2004, vol. 70, pp. 033204. doi: 10.1103/PhysRevB.70.033204

10. Tyryshkin A.M., Lyon S.A., Astashkin A.V., Raitsimring A.M. Electron spin relaxation times of phosphorus donors in silicon. Phys. Rev. B, 2003, vol. 68, pp. 193207. doi.org/10.1103/PhysRevB.68.193207

11. Ladd T. D., Maryenko D., Yamamoto Y., Abe E., Itoh K. M. Coherence time of decoupled nuclear spins in silicon. Phys. Rev. B, 2005, vol. 71, pp. 014401. doi: org/10.1103/PhysRevB.71.014401

12. Sekiguchi T., Yoshida S., Itoh K. M. Self-assembly of parallel atomic wires and periodic clusters of silicon on a vicinal Si(111) surface. Phys. Rev. Lett., 2005, vol. 95, pp. 106101. doi: 10.1103/PhysRevLett.95.106101

13. Verhulst A.S., Rau I.G., Yamamoto Y., Itoh K.M. Optical pumping of 29Si nuclear spins in bulk silicon at high magnetic field and liquid helium temperature. Phys. Rev. B, 2005, vol. 71, pp. 235206. doi: org/10.1103/PhysRevB.71.235206

14. Hayashi H., Ko W., Itahashi T., Sagara A., Itoh K.M., Vlasenko L.S., Vlasenko M.P. Dynamic nuclear polarization of 29Si nuclei in the isotope enriched n-type silicon. Phys. Status Solidi C, 2006, vol. 3, pp. 4388-4391. doi: org/10.1002/pssc.200672823

15. Dementyev A.E., Cory D.G., Ramanathan C. Dynamic Nuclear Polarization in Silicon Microparticles. Phys. Rev. Lett, 2008, vol. 100, issue 12, pp. 127601. doi: 10.1103/PhysRevLett.100.127601

16. McCamey D. R., J. van Tol, Morley G. W., Boehme C. Fast Nuclear Spin Hyperpolarization of Phosphorus in Silicon. Phys. Rev. Lett., 2009, vol. 102, pp. 027601. doi: 10.1103/PhysRevLett.102.027601

17. Koplak O., Morgunov R., Buchachenko A. Magnetic isotope and magnetic field effects on the silicon oxidation. Chemical Phys. Lett., 2013, vol. 560, pp. 29-31. doi: 10.1016/j.cplett.2013.01.003

18. Morgunov R.B., Koplak O.V. Deformation Defects Supporting Quantum Readout of 29Si Nuclear Spins in Si: P Deformed Crystals. Silicon, 2016, vol. 8, pp.331-336. doi: 10.1007/s12633-014-9208-0

19. Koplak O.V., Dmitriev A.I., Morgunov R.B. Kinetics of oxidation of subsurface layers of 29Si-enriched silicon in a magnetic field. Physics of the Solid State, 2014, vol. 56, pp. 1443-1448. doi: 10.1134/S106378341407021X

20. Koplak O.V., Dmitriev A.I., Vasil'ev S.G., Shteinman E.A., Morgunov R.B. Electron and nuclear spin dynamics in plastically deformed silicon crystals enriched in isotope 29Si. Journal of Experimental and Theoretical Physics, 2014, vol. 118, pp. 621-629. doi: 10.1134/S1063776114030133

21. Koplak O.V., Dmitriev A.I., Vasiliev S.G., Shteinmann E.A., Alekseev S.I., Morgunov R.B. Deformation paramagnetic defects in Fz-29Si : P crystals. Semiconductors, 2014, vol. 48, pp. 989-995. doi: 10.1134/S1063782614080144

22. Koplak O.V., Talantsev A.D., Morgunov R.B. Power-law versus exponential relaxation of 29Si nucleus spins in Si:B crystals. Journal of Magnetism and Magnetic Materials, 2015, vol. 400, pp. 145-148. doi: 10.1016/j.jmmm.2015.07.052

23. Ossipyan Yu.A., Morgunov R.B., Baskakov A.A., Orlov A.M., Skvortsov A.A., Inkina E.N., Tanimoto Y. Magnetoresonant Hardening of Silicon Single Crystals. JETP Lett., 2004, vol. 79, pp. 126-130.

24. Grazhulis V.A., Osipyan Yu.A. Electron paramagnetic resonance of dislocation in silicon. Soviet Physics JETP, 1971, vol. 33, pp. 623-628.

25. Bagraev N.T., Gusarov A.I., Mashkov V.A. Spin-dependent processes in one-dimensional disordered dangling-bond systems in semiconductors. Soviet Physics JETP, 1987, vol. 65, issue 3, pp. 548-559.

26. Goltzene A. Electron paramagnetic resonance of plastically deformed semiconductors : a short review. Revue Phys. Appl, 1987, vol. 22, pp. 469-471. doi: 10.1051/rphysap:01987002206046900

27. Koplak O.V., Morgunov R.B. 28Si Distribution of 29Si and 30Si isotopes in subsurface layers of Si:B single crystals under plastic deformation. Chemical Phys. Lett, 2016, vol. 643, pp. 39-42.

28. Steinman E.A. Influence of oxygen on the dislocation related luminescence centers in silicon. Phys. Status Solidi C, 2005, vol. 6, pp. 1837-1841. doi: org/10.1002/pssc.200460513

29. Akhtar W., Filidou V., Sekiguchi T., Kawakami E., Itahashi T., Vlasenko L., Morton J. J. L., Itoh K.M. Coherent storage of photoexcited triplet states using Si29 nuclear spins in silicon. Phys. Rev. Lett., 2012, vol. 108, pp. 097601. doi: 10.1103/PhysRevLett.108.097601

30. Morgunov R.B. Spin micromechanics in the physics of plasticity. Phys. Usp, 2004, vol. 47, pp. 125-147. doi: org/10.1070/PU2004v047n02ABEH001683

31. https://quantumexperience.ng.bluemix.net