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SemOI transistors: from classical to quantum computing

SemOI transistors: from classical to quantum computing. A. Orlikovsky ¹ , S. Filippov ¹² , V. Vyurkov ¹² , and I. Semenikhin ¹. ¹ Institute of Physics and Technology Russian Academy of Sciences Moscow, Russia. ФТИАН. ² Moscow Institute of Physics and Technology.

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SemOI transistors: from classical to quantum computing

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  1. SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology Russian Academy of Sciences Moscow, Russia ФТИАН ²Moscow Institute of Physics and Technology 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  2. Outline • Introduction: a brief review of the history of transistors • Simulation of fully depleted (FD) extremely thin (ET) SOI FET • Towards SemOI-based quantum computers 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  3. The end of Moore’s ‘law’? 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  4. Micrometer channel length Nanometer channel length Where does nanoelectronics start from? Semiconductors Metals 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  5. Evolution of models Charged waves: Schrödinger equation Charged particles: Boltzmann kinetic equation Charged fluid: Hydrodynamic equations 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  6. ET FD SOI FET 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  7. IBM Gains Confidence in 22 nm ETSOI(IEDMConf., Dec. 2009) 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  8. Quantum effects in nanotransistors Fermi-Dirac statistics. Transversal quantization in channel: Quantum longitudinal motion: a) interference on random impurities; b) quantum reflection; c) source-drain tunneling. 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  9. Silicon conduction band structure • Effective mass and transversal quantization energy 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  10. Quantum description Charged waves: Schrödinger equation • Transversal quantization • Wave-guide modes in the channel • Landauer-Buttiker formalism 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  11. High self-consistent barrier at S/D contacts • Few of incident particles surmounting the barrier is followed by equilibrium distribution for particles coming in the channel 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  12. Solution of 3D Schrödinger equation V(x,y,z) is a potential. The direct solution of the stationary 3D Schrödinger equation via a finite difference scheme comes across a well known instability caused by evanescent modes. In fact, the exponential growth of upper modes makes a computation impossible. 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  13. D.K.Ferry et al. (2005) (USA, Arizona State University):results of simulation 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  14. D.K.Ferry et al. (2005) (USA, Arizona State University):results of simulation 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  15. Solution of Schrödinger equation:transverse mode representation + some mathematical means where ψi(y,z) is the i-th transverse mode wave function, N is a number of involved modes. The space evolution of coefficients ai(x) is governed by matrix elements 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  16. Calculated transmission coefficient vs. electron energy E (4 random impurities in a channel) [100] and [010] valleys (small mass along the channel) [001] valleys (big mass along the channel) Transistor parameters are 10nm channel length and width, 5nm body thickness, 10^20 cm^-3 source/drain contact doping, 5nm spacers. 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  17. Gate voltage characteristics Sub-threshold swing is 71 mV per decade of current. 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  18. Corrugated channel: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  19. Corrugated channel: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  20. Impurities in channel: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  21. Impurities in channel: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  22. Dispersion of characteristics • 5-15% in calculated I-V curves • < 10% is an everlasting condition for large integrated circuits • More severe demands to technology may arise. 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  23. Semi-analytical models of FETs with low-dimensional channels • A. Khomyakov (IPT RAS) Poster P8 at 19-00! (Conference Abstracts, page 109) 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  24. Quantum Computers ФТИАН 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  25. Quantum bits 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  26. Charge qubits in double quantum dots (DQDs) 26 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  27. Solid state implementation Gorman et al, PRL, 2005 27 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  28. Two phosphorus atoms in silicon Solid state implementation Hollenberg et al, PRB, 2004 28 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  29. Solid state implementation Gate-engineered quantum dots Hayashi et al, PRL, 2003 29 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  30. Advantages: quite simple read-out (measurement of final state) explicit initialization scaling and integrity with modern microelectronic technology Disadvantages: strong decoherence caused by uncontrollable Coulomb interaction between even far-distant qubit decoherence caused by interaction with gates and phonons Qubits based on space states 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  31. Unavoidable obstacle • strong decoherence caused by uncontrollable Coulomb interaction between even far-distant qubit • independent of temperature • quantum calculations seem impossible 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  32. Coulomb interaction • Long range Coulomb interaction eˉ eˉ d eˉ D For , , one obtains 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  33. Qubit and its operation Consists of two double quantum dots ElectrodeЕoperates upon the strength of exchange interaction between electrons. ElectrodeТoperates upon tunnel coupling between dots. + 1eˉ — 1eˉ T + — E Vyurkov et al, PLA, 2010 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  34. Basic states in a DQD Electron wave-function in a DQD Symmetric Antisymmetric Potential in a DQD 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  35. Basic states of two DQDs basis* Potential in two DQDs Wave-function of two electrons in two DQDs 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  36. Basic states of a qubit Spin-polarized electrons: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  37. Qubit states 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  38. Qubit states 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  39. Distribution of charge in a qubit • Probability density • For regionΩ: • Charge in a dotΩ: 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  40. Distribution of charge in a qubit 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  41. Arbitrary qubit states • Arbitrary qubit state • Hamiltonian in matrix representation • Evolution operator 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  42. Initialization • Cooling in magnetic field,positive potential on gateТ • Transformation • Pumping of electrons along the chain 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  43. Initialization • Pumping electrons from a spin-polarized source, for instance, ferromagnetic Single-electron turnstile 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  44. Decoherence y • Particular symmetry makes the qubit insensitive to voltage fluctuations x • Small energy gap between basic states in a DQDsecures against the decoherence on phonons : deformation acoustic phonons piezoelectric acoustic phonons –VT 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  45. Decoherence • ‘Frozen’ qubit:only two-phonon processes are possible, • Decoherence rate is independent of energy gap 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  46. Read-out • To read-out one must distinguish from • An additional electrode by the DQD makes it possible tunneling of an electron into first or second dot depending on the initial state of DQD: or 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  47. Realistic structure 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  48. SemOI quantum register 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  49. Potential defined quantum dots Confinement energy Coulomb repulsion energy => one electron in a dot 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

  50. How a read-out is possible? Transistor current depends on position of an electron in the channel Compare with Tanamoto et al, PRA, 2000 1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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