11/27/2014 Istituto di Fotonica e Nanotecnologie Atom Based Nanoelectronics Enrico Prati, PhD The Moore’s law 14 nm Silicon devices! ITRS - International Technology Roadmap for Semiconductors A body sponsored by: •European Semiconductor Industry Association (ESIA) •Japan Electronics and Information Technology Industries Association (JEITA) •Korean Semiconductor Industry Association (KSIA) •Taiwan Semiconductor Industry Association (TSIA) Atomic scale •United States Semiconductor Industry Association (SIA) devices IFN Enrico Prati – CNR | 1 11/27/2014 The Moore’s law: status and limits More Moore INTRINSIC FABRICATION LIMIT FOR LITHOGRAPHY 3 nm M. J. Kelly, “Intrinsic top-down unmanufacturability”, Nanotechnology, 22, 245303 (2011) IFN Atomic scale devices Enrico Prati – CNR | Towards atomic scale: doping 1st (bad) concept: losing the approximation of ideal homogeneity 2nd (good) concept: controlling the electronic device through a single atom (dopant) IFN Atomic scale devices Enrico Prati – CNR | 2 11/27/2014 More than Moore and Beyond CMOS 'More than Moore‘ (MtM) refers to a set of technologies that enable non digital micro / nanoelectronic functions, based on, or derived from, silicon technology but do not necessarily scaling with Moore's Law. (Ex: conversion of non-digital as well as non-electronic information, such as mechanical, thermal, acoustic, chemical, optical and biomedical functions, to digital data and vice versa.) ‘Beyond CMOS’ refers to electronics using new state variables. (Ex: spin, molecular state, photons, phonons, nanostructures, mechanical state, resistance, quantum state (orbital state, including phase) and magnetic flux.) More Moore Moore IFN More Than Moore Beyond CMOS Atomic scale devices Enrico Prati – CNR | More than Moore and Beyond CMOS Source ITRS 2010 International Technology Roadmap for Semiconductors IFN Atomic scale devices Enrico Prati – CNR | 3 11/27/2014 Single ion implantation Method Waseda University SINGLE ATOM /FEW ATOMS DOPED TRANSISTOR Atomic scale devices Enrico Prati – CNR | IFN Scanning Tunneling Microscope Method SINGLE ATOM DOPED TRANSISTOR Michelle Simmons Atomic scale devices IFN Enrico Prati – CNR | 4 11/27/2014 What is atomic scale nanoelectronics? Electronic equipment ? Device Millikelvin Cryostat Experiments Microwave Irradiation Conductance Coulomb blockade Magnet Kirchoff method Concepts of Physics Quantum tunneling Spin dynamics Quantized Energy Fermi Energy/DOS Enrico Prati – CNR | IFN Bridge: the current Quantum tunneling Quantized Energy Coulomb blockade Millikelvin Cryostat Kirchoff method Device Concepts of Physics Fermi Energy/DOS Conductance Experiments Electronic equipment Magnet Spin dynamics IFN Microwave Irradiation Enrico Prati – CNR | 5 11/27/2014 Layout Framework Theory Experiments Atomic scale devices Device Single charge manipulation Qubits Fermi Energy/DOS Single spin manipulation Quantum Information Quantized Energy Solid state qubits Quantum tunneling Band formation Coulomb blockade Conductance Kirchoff method Enrico Prati – CNR | IFN Nanoelectronics Framework Atomic scale devices Qubits Quantum Computing IFN Tentative definition: Nanoelectronics is the use of nanotechnology (less than 100 nm) on electronic components, so that inter-atomic interactions and quantum mechanical properties play the major role. WARNING 1) As a result, current transistors do not fall under this category, even though these devices are manufactured with 22 nm or 14 nm technology. 2) All the properties of semiconductors depend on quantum mechanics. Here we refer to the dominant role of individual objects (one or few electrons, one dopant…) so that the peculiar properties of QM like superposition of states, spin and entanglement have direct consequences. Enrico Prati – CNR | 6 11/27/2014 Qubits for Quantum Algorithms Definition: a qubit is a complex linear combination of 2 bits Framework CNOT LOGIC PORT (Operator acting on a Hilbert space) Atomic scale devices Qubits Quantum Information Enrico Prati – CNR | IFN Motivations: solid state quantum information Framework Atomic scale devices Qubits Quantum Information Old theoretical approach (1998) IFN Enrico Prati – CNR | 7 11/27/2014 Motivations: solid state quantum information D Wave (Canada): 128 superconductive qubits chip For adiabatic quantum computation Framework Qubits Atomic scale devices Quantum Information First experimental success (2011) Enrico Prati – CNR | IFN Quantum information in biology Framework Qubits Atomic scale devices Quantum Information PNAS 108, 20908, 2011 IFN Enrico Prati – CNR | 8 11/27/2014 Basic device: a single atom transistor Theory Ending point: Device Fermi Energy P is a single phosphorus atom below the gate Quantized Energy Quantum tunneling Coulomb blockade Conductance Kirchoff method IFN Enrico Prati – CNR | Density of States (DoS) ni h 2L Heuristic Quantization Periodic Boundary Condition pi k i Theory Electron wavefunction Device Fermi Energy/DOS Quantized Energy Quantum tunneling Coulomb blockade Conductance Kirchoff method IFN 1d 2d 3d dn( E ) d 1 dE L E dn( E ) d 2 dE dn( E ) d 3 E dE g(p)dp L d d d 2 h h dn dni d d p d p d 1 dp ( 2 ) 2 L i 2L d 2 L E=p2/2m Volume of a hyperphere of dimension d Change variables g ( E ) (2s 1) d d d 2 d 2L 2 2 ( 2 m ) E d d 2 ( 2 ) h 2 DoS =«how many states g(p) or g(E) you have in a p (momentum) or E (energy) interval respectively» Enrico Prati – CNR | 9 11/27/2014 Density of states and Fermi Energy Theory Condition to see discrete energy levels related effects: Device Fermi Energy/DOS Quantized Energy Quantum tunneling KT << DE kT << energy level spacing linewidth Chemical potential: (of a thermodynamic system) is the amount by which the energy of the system would change if an additional particle were introduced, with the entropy and volume held fixed. Fermi Energy: chemical potential at T=0 Temperature: 4.2 K usual 300 K for 2nm QD EF Contacts Impurity atoms Coulomb blockade Conductance Kirchoff method IFN Enrico Prati – CNR | Confinement Theory Device Fermi Energy/DOS Quantized Energy Quantum tunneling Semiconductor nanostructures and quantum dots are fabricated by 1) Vertical confinement (d=3->2) via • Semiconductor/insulator interface (Si/SiO2) • Semiconductor/Semiconductor heterostructures (GaAs/AlGaAs or Si/SiGe ) 2) Lateral confinement (d=2->1,0) • Split gate technique • Lithographically defined structures • Atomic inclusions • Point defects Nature, 2007 Coulomb blockade Conductance Kirchoff Colloquia method IFN Enrico Prati – CNR | 10 11/27/2014 Tunneling through a single barrier Theory Schroedinger Device Test function Fermi Energy/DOS Quantized Energy New equation Solution: Airy f. (v1 coeff. X1 turning point) Square potential Quantum Tunneling Coulomb blockade Conductance Kirchoff ANM 2008 method IFN Enrico Prati – CNR | Tunneling in a quantum dot Theory A quantum dot is a small box that can be filled with electrons. Device Fermi Energy/DOS Quantized Energy The box is coupled via tunnel barriers to a source and drain reservoirs Quantum Tunneling (which tunes the electrostatic dot/reservoir potential) (particles exchanges) capacitively coupled to a gate Coulomb blockade Conductance Kirchoff method IFN Enrico Prati – CNR | 11 11/27/2014 Quantum dots: sequential tunneling through 2 barriers Theory Device Vg Energy Fermi Energy/DOS Quantized Energy eVds EFL Quantum Tunneling mL EFR +k Coulomb blockade mR 0-D Conductance Kirchoff ANM 2008 method IFN Enrico Prati – CNR | Si nanoFETs tunneling d=2 Theory (250 mK) d=1 W 280 nm x L 180 nm Device Fermi Energy/DOS Quantized Energy Quantum Tunneling Hopping between localized states (non Lorentzian) Coulomb blockade Disorder! Conductance Kirchoff ANM 2008 method IFN Single Donor Quantum dot Rogge PRL 06 Single localized states (Lorentzian) Clean coherent transport! Enrico Prati – CNR | 12 11/27/2014 Charging energy Theory Coulomb repulsion! Device DU (charging energy) Increase Vg Fermi Energy/DOS Quantized Energy Quantum Tunneling eVds EFL mL Coulomb Blockade EFR +k Conductance mR 0-D Kirchoff ANM 2008 method IFN Enrico Prati – CNR | Charge stability diagram of a quantum dot I=0 Double gate Stability diagram Vd=const Change Vg1 top gate and Vg2 back/side gate Typical units of conductance Quantum of conductance: 2e2/h and equals 77.48 microsiemens, (12.9kΩ) IFN Enrico Prati – CNR | 13 11/27/2014 Quantum dots with a single ion implanted Theory Device Fermi Energy/DOS Sellier et al PRL 2006 Golovach et al PRB 2010 Mazzeo et al APL 2012 Quantized Energy Quantum Tunneling Coulomb Blockade Conductance Kirchoff Theory method IFN Enrico Prati – CNR | The quantum of conductance Theory Classical definition Device Fermi Energy/DOS Quantized Energy Quantum Tunneling Coulomb blockade Conductance Kirchoff ANM 2008 method IFN Current of +k states given by linear density of electrons: I+ = (e/L) S v f+(E)= = (e/L) S (dE/dk) f+(E) / ħ Quantum formalism f+ Fermi distribution for +k states Which becomes in the continuum, with 2 spin states: = (2e/h) ∫ dE f+(E) q (E-e cutoff) = (2e2/h) M Dm / e= (M is the number of modes) G= [(2e2/h) M ] -1 = 12.9 kW / M (2e2/h) is the quantum of conductance Enrico Prati – CNR | 14 11/27/2014 Circuital view of the quantum dot and current Theory Device Fermi Energy/DOS Quantized Energy Quantum Tunneling Coulomb blockade Conductance Kirchoff ANM 2008 method IFN Enrico Prati – CNR | Spectroscopy: single As atom in FinFET Recent experiments Ec Single charge manipulation Single spin manipulation Solid state qubits Band formation IFN 0 | 1 | 2 Sample: a commercial nanoFET channel 70x50 contacts doped with As 1 good one every 10 samples Enrico Prati – CNR | 15 11/27/2014 Moving an electron from a quantum dot to a donor Recent experiments Ec Single charge manipulation E. Prati et al Applied Physics Letters 2011 J exchange coupling of the Nth electron of the QD with the 3 electrons already bound to the DQD Single charge manipulation Enrico Prati – CNR | IFN Single charge state sensing Recent experiments Ec Single charge manipulation Single spin manipulation Undoped sample: no lines Doped: lines Solid state qubits Band formation Normalized signal 1.0 0.5 0.0 0.0 Mazzeo et al., Applied Physics Letters 2012 IFN 0.5 1.0 1.5 2.0 2.5 3.0 Time (ms) Measurement possible thanks to cryogenic amplifier (see G. Ferrari) Enrico Prati – CNR | 16 11/27/2014 Spin state sensing Spin level separation Recent experiments by Zeeman Effect B= 1 T Ec Single charge manipulation Single spin manipulation Solid state qubits Band formation Single spin readout A.Morello et al., Nature 2010 IFN Enrico Prati – CNR | Singlet-triplet qubit Recent experiments Ec Single charge manipulation Single spin manipulation Energy splitting 140 ueV T = 150 mK Pulses: from 10 ns Field 30 mT Solid state qubits Band formation Maune et al. Nature 2012 @HRL California IFN Enrico Prati – CNR | 17 11/27/2014 Hubbard (impurity) bands formation with 4 atoms Recent experiments Ec Single charge manipulation Single spin manipulation Solid state qubits Band formation E. Prati, M. Hori, F. Guagliardo, G. Ferrari, T. Shinada, Nature Nanotech. (2012) IFN Enrico Prati – CNR | Thank you Enrico Prati [email protected] IFN Enrico Prati – CNR | 18

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