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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 1 st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine ²Moscow Institute of Physics and Technology

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

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

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

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

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

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

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

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

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

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

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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. Solution of 3D Schrödinger equation 1 st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Qubits based on space states 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 1 st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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

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

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

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

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

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

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

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

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Distribution of charge in a qubit Probability density For region Ω: Charge in a dot Ω: 1 st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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

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

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

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

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

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

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

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

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

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

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

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Summary The efficient program for 3D all quantum simulation of field effect nanotransistors is elaborated. The results of simulation demonstrate the impact of realistic channel inhomogeneities on transistor characteristics. SOI structure for quantum computation is proposed. 1 st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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Эпилог С Light at the end of the tunnel

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Acknowledgements Russian Foundation for Basic Reasearch, grant # а NIX Computer Company grant # F793/8-05 grant # st Ukrainian-French Seminar and 6 th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine

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