Quantum Supercurrent Transistors in Silicon Quantum Wells Confined by Superconductor Barriers

Nikolay T. Bagraev, Edward Yu. Danilovsky, Leonid E. Klyachkin, Andrei A. Kudryavtsev, Roman V. Kuzmin, Anna M. Malyarenko, Wolfgang Gehlhoff, Vladimir V. Romanov

.

DOI: 10.4236/jmp.2011.24035                

Abstract

We present the findings of spin-dependent single-hole and pair-hole transport in plane and across the p-type high mobility silicon quantum wells (Si-QW), 2 nm, confined by the superconductor δ-barriers on the n-type Si (100) surface. The oscillations of the conductance in normal state and the zero-resistance supercurrent in superconductor state as a function of the top gate voltage are found to be correlated by on- and off-resonance tuning the two-dimensional levels of holes in Si-QW with the Fermi energy in the superconductor δ-barriers. The SIMS and STM studies have shown that the δ-barriers heavily doped with boron, 5 × 1021 cm–3, represent really alternating arrays of silicon empty and doped dots, with dimensions restricted to 2 nm. This concentration of boron seems to indicate that each doped dot located between empty dots contains two impurity atoms of boron. The EPR studies show that these boron pairs are the trigonal dipole centres, B+ - B–, that contain the pairs of holes, which result from the negative -U reconstruction of the shallow boron acceptors, 2B0 => B+ - B–. The electrical resistivity, magnetic susceptibility and specific heat measurements demonstrate that the high density of holes in the Si-QW (> 1011 cm–2) gives rise to the high temperature superconductor properties for the δ-barriers. The value of the superconductor energy gap obtained is in a good agreement with the data derived from the oscillations of the conductance in normal state and of the zero-resistance supercurrent in superconductor state as a function of the bias voltage. These oscillations appear to be correlated by on- and off-resonance tuning the two-dimensional subbands of holes with the Fermi energy in the superconductor δ-barriers. Finally, the proximity effect in the S-Si-QW-S structure is revealed by the findings of the quantization of the supercurrent and the multiple Andreev reflection (MAR) observed both across and along the Si-QW plane thereby identifying the spin transistor effect.

Keywords

Silicon Quantum Well, Superconductor δ-barrier, ESR, Dipole Boron Center, Multiple Andreev Reflection, Supercurrent Conductance, EDESR, Silicon Microcavity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. Macilwain, “Computer Hardware: Silicon Down to the Wire,” Nature, Vol. 436, No. 22-23, 2005, pp. 22-23.
[2]	L. Ozyuzer, A. E. Koshelev, C. Kurter, N. Gopalsami, Q. Li, M. Tachiki, K. Kadowaki, T. Yamamoto, H. Minami, H. Yamaguchi, T. Tachiki, K. E. Gray, W.-K. Kwok and U. Welp, “Emission of Coherent THz Radiation from Superconductors,” Science, Vol. 318, No. 5854, 2007, pp. 1291-1293. doi:10.1126/science.1149802
[3]	N. T. Bagraev, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko, V. V. Romanov and S. A. Rykov, “Superconductivity in Silicon Nanostructures,” Physica C, Vol. 437-438, 2006, pp. 21-24. doi:10.1016/j.physc.2005.12.011
[4]	E. A. Ekimov, V. A. Sidorov, E. D. Bauer, N. N. Mel’nik, N. J. Curro, J. D. Thompson and S. M. Stishov, “Superconductivity in Diamond,” Nature, Vol. 428, 2004, pp. 542-545. doi:10.1038/nature02449
[5]	N. T. Bagraev, A. D. Bouravleuv, L. E. Klyachkin, A. M. Malyarenko, W. Gehlhoff, V. K. Ivanov and I. A. Shelykh, “Quantized Conductance in Silicon Quantum Wires,” Semiconductors, Vol. 36, No. 4, 2002, pp. 439- 460. doi:10.1134/1.1469195
[6]	N. T. Bagraev, A. D. Bouravleuv, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko, V. V. Romanov and S. A. Rykov, “Fractal Self-Assembled Nanostructures on Monocrystalline Silicon Surface,” Proceedings of the 6th International Conference on Diffusion in Materials, Cracow, 2005; pp. 1049-1054.
[7]	N. T. Bagraev, V. K. Ivanov, L. E. Klyachkin and I. A. Shelykh, “Spin Depolarization in Quantum Wires Polarized Spontaneously in a Zero Magnetic Field,” Physical Revive B, Vol. 70, No. 15, 2004, pp. 155315-1-9.
[8]	N. T. Bagraev, A. D. Bouravleuv, L. E. Klyachkin, A. M. Malyarenko, W. Gehlhoff, Y. I. Romanov and S.A. Rykov, “Local Tunneling Spectroscopy of Silicon Nanostructures,” Semiconductors, Vol. 39, No. 6, 2005, pp. 716-728.
[9]	J. Robertson, “Electronic Structure of Amorphous Semiconductors,” Advances in Physics, Vol. 32, No. 3, 1983, pp. 361-452. doi:10.1080/00018738300101571
[10]	G. J. Gerardi, E. H. Poindexter, P. J. Caplan and N. M. Johnson, “Interface Traps and Pb Centers in Oxidized Silicon Wafers,” Applied Physics Letterrs, Vol. 49, No. 6, 1986, pp. 348-351. doi:10.1063/1.97611
[11]	N. T. Bagraev, W. Gehlhoff and L. E. Klyachkin, “Cyclotron Resonance in Heavily Doped Silicon Quantum Wells,” Solid State Phenomena, Vol. 47-48, 1995, pp. 589-594.
[12]	W. Gehlhoff, N. T. Bagraev and L. E. Klyachkin, “Shallow and Deep Centres in Heavily Doped Silicon Quantum Wells,” Materials Science Forum, Vol. 196-201, 1995, pp. 467-472.
[13]	N. T. Bagraev, N. G. Galkin, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko and I. A. Shelykh, “Spin Interference in Silicon One-Dimensional Rings,” Journal of Physics: Conference Series, Vol. 61, 2007, pp. 56-60. doi:10.1088/1742-6596/61/1/012
[14]	J. P. Kotthaus and R. Ranvaud, “Cyclotron Resonance of Holes in Surface Space Charge Layers on Si,” Physical Review. B, Vol. 15, No. 12, 1977, pp. 5758-5761. doi:10.1103/PhysRevB.15.5758
[15]	N. T. Bagraev, A. D. Bouravleuv, L. E. Klyachkin, A. M. Malyarenko, S. A. Rykov, “Self-Ordered Microcavities Embedded in Ultra-shallow Silicon p-n Junctions,” Semiconductors, Vol. 34, No. 6, 2000, pp. 700-711. doi:10.1134/1.1188058
[16]	B. X. Li, P. L. Cao and D. L. Que, “Distorted Icosahedral Cage Structure of Si60 Clusters,” Physical Review B, Vol. 61, No. 3, 2000, pp.1685-1687. doi:10.1103/PhysRevB.61.1685
[17]	A. Slaoui, E. Fogarassy, J. C. Muller and P. Siffert, “Study of Some Optical and Electrical Properties of Heavily Doped Silicon Layers,” J. de Physique Colloq., Vol. 44, No. C5 44, 1983, pp. 65-71.
[18]	P. W. Anderson, “Model for the Electronic Structure of Amorphous Semiconductors,” Physical Review Letters, Vol. 34, No. 15, 1975, pp. 953-955. doi:10.1103/PhysRevLett.34.953
[19]	G. D. Watkins, “Negative-U Properties for Defects in Solids,” Festkoerperprobleme, Vol. 24, 1984, pp. 163- 184.
[20]	R. A. Street and N. F. Mott, “States in the Gap in Glassy Semiconductors,” Physical Review Letters, Vol. 35, No. 19, 1975, pp. 1293-1296. doi:10.1103/PhysRevLett.35.1293
[21]	M. Kastner, D. Adler and H. Fritzsche, “Valence-Alternation Model for Localized Gap States in Lone-Pair Semiconductors,” Physical Review Letters, Vol. 37, No. 22, 1976, pp. 1504-1507. doi:10.1103/PhysRevLett.37.1504
[22]	G. A. Baraff, E. O. Kane and M. Schlüter, “Theory of the Silicon Vacancy: an Anderson Negative-U System,” Physical Review B, Vol. 21, No. 12, 1980, pp. 5662- 5686. doi:10.1103/PhysRevB.21.5662
[23]	N. T. Bagraev and V. A. Mashkov, “Tunneling Negative-U Centers and Photo-Induced Reactions in Solids,” Solid State Communications, Vol. 51, No 7, 1984, pp. 515-521. doi:10.1016/0038-1098(84)91024-X
[24]	N. T. Bagraev, V. A. Mashkov, “A Mechanism for Two-Electron Capture at Deep Level Defects in Semiconductors, Solid State Communications,” Solid State Communications, Vol. 65, No. 12, 1988, pp. 1111-1117. doi:10.1016/0038-1098(88)90904-0
[25]	N. T. Bagraev, N. G. Galkin, W. Gehlhoff, L. E. Klyachkin and A. M. Malyarenko, “Phase and Amplitude Response of the ‘0.7 Feature’ Caused by Holes in Silicon One-Dimensional Wires and Rings,” J. Phys.:Condens. Matter, Vol. 20, 2008, pp. 164202-1-12. doi:10.1088/0953-8984/20/16/164202
[26]	E. ?imánek, “Superconductivity at Disordered Interfaces,” Solid State Communications, Vol. 32, No 9, 1979, pp. 731-734.
[27]	C. S. Ting, D. N. Talwar, K. L. Ngai, “Possible Mechanism of Superconductivity in Metal-Semiconductor Eutectic Alloys,” Physical Review Letters, Vol. 45, No 14, 1980, pp. 1213-1216. doi:10.1103/PhysRevLett.45.1213
[28]	A. Alexandrov, J. Ranninger, “Bipolaronic supercond- uctivity,” Phys. Rev. B 24, No. 3, 1981, pp. 1164-1169. doi:10.1103/PhysRevB.24.1164
[29]	B. K. Chakraverty, “Bipolarons and Superconductivity,” Journal de Physique, Vol. 42, No. 9, 1981, pp. 1351- 1356.
[30]	A. S. Alexandrov and N. F. Mott, “Bipolarons,” Rep. Prog. Phys., Vol. 57, No. 12, 1994, pp. 1197-1288. doi:10.1088/0034-4885/57/12/001
[31]	A. F. Andreev, “The Thermal Conductivity of the Intermediate State in Superconductors,” Soviet Physics-JETP, Vol. 19, No. 6, 1964, pp. 1228-1232.
[32]	T. M. Klapwijk, “Proximity Effect from an Andreev Perspective,” Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 17, No. 5, 2004, pp. 593- 611.
[33]	J. A. van Dam, Y. V. Nazarov, E. P.A. M. Bakkers, S. De Franceschi and P. Kouwenhoven, “Supercurrent Reversal in Quantum Dots,” Nature, Vol. 442, No. 7103, 2006, pp. 667-670. doi:10.1038/nature05018
[34]	P. Jarillo-Herrero, J. A. van Dam and L. P. Kouwenhoven, “Quantum Supercurrent Transistors in Carbon Nanotubes,” Nature, Vol. 439, 2006, pp. 953-956. doi:10.1038/nature04550
[35]	X. Jie, A. Vidan, M. Tinkham, R. M. Westervelt and Ch. Lieber, “Ge/Si Nanowire Mesoscopic Josephson Junctions,” Nature Nanotechnology, Vol. 1, No. 3, December 2006, pp. 208-213.
[36]	O. Trovarelli, M. Weiden, R. Müller-Reisener, M. Gómez-Berisso, P. Gegenwart, M. Deppe, C. Geibel, J. G. Sereni and F. Steglich, “Evolution of Magnetism and Superconductivity In CeCu2(Si1-xGex)2, ” Physical Review B, Vol. 56, No. 2, 1997, pp. 678-685. doi:10.1103/PhysRevB.56.678
[37]	A. K. Geim, K. S. Novoselov, “The rise of Graphene,” Nature Materials, Vol. 6, No. 3, 2007, pp. 183-191. doi:10.1038/nmat1849
[38]	N. R. Werthamer, E. Helfand, P. C. Hohenberg, “Temperature and Purity Dependence of the Superconducting Critical Field, Hc2. III. Electron Spin and Spin-Orbit Effects,” Physical Review, Vol. 147, No. 1, 1966, pp. 295-302. doi:10.1103/PhysRev.147.295
[39]	D. Y. Vodolazov, D. S. Golubovi?, F. M. Peeters and V. V. Moshchalkov, “Enhancement and Decrease of Critical Current Due to Suppression of Superconductivity by a Magnetic Field,” Physical Review B, Vol. 76, No. 13, 2007, pp. 134505-1-7. doi:10.1103/PhysRevB.76.134505
[40]	C. C. de Souza Silva, J. van de Vondel, M. Morelle and V. V. Moshchalkov, “Controlled Multiple Reversals of a Ratchet Effect,” Nature, Vol. 440, No. 7084, 2006, pp. 651-654. doi:10.1038/nature04595
[41]	N. T. Bagraev, N. G. Galkin, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko and I.A. Shelykh, “Spin Interference in Silicon One-Dimensional Rings,” Physica E, Vol. 40, 2008, pp. 1338-1340. doi:10.1016/j.physe.2007.08.079
[42]	N. T. Bagraev, L. E. Klyachkin, A. M. Malyarenko and W. Gehlhoff, “High Temperature Single-Hole Silicon Transistors,” Superlattices and Microstructures, Vol. 23, No. 6, 1998, pp. 1333-1338. doi:10.1006/spmi.1996.0360
[43]	H. Suderow, E. Bascones, A. Izquierdo, F. Guinea and S. Vieira, “Proximity Effect and Strong-Coupling Superconductivity in Nanostructures Built with an STM,” Physical Review B, Vol. 65, No. 10, 2002, pp. 100519R- 1-4.
[44]	?. Fischer, M. Kugler, I. Maggio-Aprile, Ch. Berthod and Ch. Renner, “Scanning Tunneling Spectroscopy of High-Temperature Superconductors,” Reviews of Modern Physics, Vol. 79, No. 1, 2007, pp. 353-419. doi:10.1103/RevModPhys.79.353
[45]	R. Laiho, M. M. Afanasjev, M. P. Vlasenko and L. S. Vlasenko, “Electron Exchange Interaction in S = 1 Defects Observed by Level Crossing Spin Dependent Microwave Photoconductivity in Irradiated Silicon,” Physical Review Letters, Vol. 80, No. 7, 1998, pp. 1489-1492. doi:10.1103/PhysRevLett.80.1489
[46]	N. T. Bagraev, A. D. Bouravleuv, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko and V. V. Romanov, “Electron- Dipole Resonance of Impurity Centres Embedded in Silicon Microcavities,” Physica B, Vol. 340-342, 2003, pp. 1078- 1081. doi:10.1016/j.physb.2003.09.184
[47]	N. T. Bagraev, A. D. Bouravleuv, W. Gehlhoff, L. E. Klyachkin, A. M. Malyarenko and V. V. Romanov, “Erbium- Related Centres Embedded in Silicon Microcavities,” Physica B, Vol. 340-342, 2003, pp. 1074-1077. doi:10.1016/j.physb.2003.09.239
[48]	V. L. Ginzburg, “On Surface Superconductivity,” Physical Letters, Vol. 13, No. 2, 1964, pp. 101-104.
[49]	A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform State of Superconductors,” Soviet Physics-JETP, Vol. 20, No. 3, 1965, pp. 762-770.
[50]	P. Fulde and R. A. Ferrell, “Superconductivity in a Strong Spin-Exchange Field,” Physical Review, Vol. 135, No. 3A, 1964, pp. A550-A563. doi:10.1103/PhysRev.135.A550
[51]	W. A. Little, “Higher Temperatures: Theoretical Models,” Physica, Vol. 55, 1971, pp. 50-54. doi:10.1016/0031-8914(71)90240-0
[52]	S. M. Cronenwett, H. J. Lynch, D. Goldhaber-Gordon, L. P. Kouwenhoven, C. M. Marcus, K. Hirose, N. S. Wingreen and V. Umansky, “Low-Temperature Fate of the 0.7 Structure in a Point Contact: A Kondo-Like Correlated State in an Open System,” Physical Review Letters, Vol. 88, No. 22, 2002, pp. 226805-1-4. doi:10.1103/PhysRevLett.88.226805
[53]	J. P. Eisenstein, T. J. Gramila, L. N. Pfeiffer and K. W. West, “Probing a Two-Dimensional Fermi Surface by Tunneling,” Physical Review B, Vol. 44, No. 12, 1991, pp. 6511-6514. doi:10.1103/PhysRevB.44.6511
[54]	N. T. Bagraev, W. Gehlhoff, L. E. Klyachkin, A. A. Kudryavtsev, A. M. Malyarenko, G. A. Oganesyan, D. S. Poloskin and V. V. Romanov, “Spin-Dependent Transport of Holes in Silicon Quantum Wells Confined by Superconductor Barriers,” Physica C, Vol. 468, No. 7-10, 2008, pp. 840-843.doi:10.1016/j.physc.2007.11.060