Istituto di Fotonica e Nanotecnologie

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Istituto i Fotonica e Nanotecnologie Atomic Scale Nanoelectronics Enrico Prati, PhD Research Scientist at Istituto i Fotonica e Nanotecnologie Milano, Italy Visiting Scholar Wasea University Tokyo,

1 Istituto i Fotonica e Nanotecnologie Atomic Scale Nanoelectronics Enrico Prati, PhD Research Scientist at Istituto i Fotonica e Nanotecnologie Milano, Italy Visiting Scholar Wasea University Tokyo, Japan The Moore s law 14 nm Silicon! ITRS - International Technology Roamap for Semiconuctors A boy sponsore by: European Semiconuctor Inustry Association (ESIA) Japan Electronics an Information Technology Inustries Association (JEITA) Korean Semiconuctor Inustry Association (KSIA) Taiwan Semiconuctor Inustry Association (TSIA) Unite States Semiconuctor Inustry Association (SIA) 1

unmanufacturability, Nanotechnology, 22,

1st (ba) concept: losing the approximation

2 The Moore s law: status an limits More Moore INTRINSIC FABRICATION LIMIT FOR LITHOGRAPHY 3 nm M. J. Kelly, Intrinsic top-own unmanufacturability, Nanotechnology, 22, (2011) Towars atomic scale: oping 1st (ba) concept: losing the approximation of ieal homogeneity 2n (goo) concept: controlling the electronic evice through a single atom (opant) 2

More than Moore an Beyon CMOS 'More than Moore (MtM) refers to a set of technologies that enable non igital micro / nanoelectronic functions, base on, or erive from, silicon technology but o

(Ex: conversion of non-igital as well as non-electronic information, such as mechanical, thermal, acoustic, chemical, optical an biomeical functions, to igital ata an vice versa.

3 More than Moore an Beyon CMOS 'More than Moore (MtM) refers to a set of technologies that enable non igital micro / nanoelectronic functions, base on, or erive from, silicon technology but o not necessarily scaling with Moore's Law. (Ex: conversion of non-igital as well as non-electronic information, such as mechanical, thermal, acoustic, chemical, optical an biomeical functions, to igital ata an vice versa.) Beyon CMOS refers to electronics using new state variables. (Ex: spin, molecular state, photons, phonons, nanostructures, mechanical state, resistance, quantum state (orbital state, incluing phase) an magnetic flux.) More Moore Moore More Than Moore Beyon CMOS More than Moore an Beyon CMOS Source ITRS 2010 International Technology Roamap for Semiconuctors 3

4 Single ion implantation Metho SINGLE ATOM /FEW ATOMS DOPED TRANSISTOR Prof. Ohomari-sensei Scanning Tunneling Microscope Metho SINGLE ATOM DOPED TRANSISTOR Prof. Michelle Simmons 4

5 What is atomic scale nanoelectronics?? Electronic equipment Millikelvin Cryostat Experiments Spin ynamics Concepts of Physics metho tunneling Cryomagnet Microwave Irraiation /DOS Brige: the current tunneling metho Millikelvin Cryostat Concepts of Physics /DOS Electronic equipment Experiments Cryomagnet Spin ynamics Microwave Irraiation 5

6 Layout Framework Experiments Single charge Qubits /DOS Single spin Information Soli state qubits tunneling Ban formation metho Nanoelectronics Framework Qubits Computing Tentative efinition: Nanoelectronics is the use of nanotechnology (less than 100 nm) on electronic components, so that inter-atomic interactions an quantum mechanical properties play the major role. WARNING 1) As a result, current transistors o not fall uner this category, even though these are manufacture with 22 nm or 14 nm technology. 2) All the properties of semiconuctors epen on quantum mechanics. Here we refer to the ominant role of iniviual objects (one or few electrons, one opant ) so that the peculiar properties of QM like superposition of states, spin an entanglement have irect consequences. 6

7 Qubits for Algorithms Definition: a qubit is a complex linear combination of 2 bits Framework CNOT LOGIC PORT (Operator acting on a Hilbert space) Qubits Information Motivations: soli state quantum information Framework Qubits Information Ol theoretical approach (1998) 7

8 Motivations: soli state quantum information D Wave (Canaa): 8x256 superconuctive qubits chip For aiabatic quantum computation Framework Qubits Information First experimental success (2011) Now also in CMOS CEA, by Silvano De Franceschi an Marc Sanquer Framework Qubits Information Pre-print on arxiv appeare in 2016 : 8

Bounary Conition n( E) E 2 2 h 2 h 1 n( E) EE n n p p p 3 i i 2L ( ) 2L E=p 2 /2m L L L Change variables 2 (2m) 2 DoS =«how

9 Single atom FETs Ening point: P is a single phosphorus atom below the gate tunneling metho Density of States (DoS) /DOS tunneling Electron wavefunction n( E) E E 1 2 g( E) (2s 1) 2 ( 2 2L ) h nih pi ki 2L Heuristic Quantization Perioic Bounary Conition n( E) E 2 2 h 2 h 1 n( E) EE n n p p p 3 i i 2L ( ) 2L E=p 2 /2m L L L Change variables 2 (2m) 2 DoS =«how many states g(p) or g(e) you have in a p (momentum) or E (energy) interval respectively» g(p)p E Volume of a hyperphere of imension 2 2 metho 9

10 Density of states an /DOS tunneling Conition to see iscrete energy levels relate effects: KT << DE energy level spacing kt << linewith Temperature: 4.2 K usual 300 K for 2nm QD EF Chemical potential: (of a thermoynamic system) is the amount by which the energy of the system woul change if an aitional particle were introuce, with the entropy an volume hel fixe. : chemical potential at T=0 Impurity atoms Contacts metho Confinement /DOS tunneling Semiconuctor nanostructures an quantum ots are fabricate by 1) Vertical confinement (=3->2) via Semiconuctor/insulator interface (Si/SiO2) Semiconuctor/Semiconuctor heterostructures (GaAs/AlGaAs or Si/SiGe ) 2) Lateral confinement (=2->1,0) Top gate technique for epletion Lithographically efine structures Atomic inclusions Point efects Nature, 2007 metho Colloquia 10

Tunneling through a single barrier /DOS Tunneling

Tunneling in a quantum ot A quantum ot is a small box

/DOS Tunneling The box is couple via tunnel barriers to

11 Tunneling through a single barrier /DOS Tunneling Schroeinger Test function New equation Solution: Airy f. (v1 coeff. X1 turning point) Square potential metho ANM 2008 Tunneling in a quantum ot A quantum ot is a small box that can be fille with electrons. /DOS Tunneling The box is couple via tunnel barriers to a source an rain reservoirs (particles exchanges) capacitively couple to a gate (which tunes the electrostatic ot/reservoir potential) metho 11

ots: sequential tunneling through 2 barriers Vg /DOS Tunneling EFL ml +k 0-D EFR mr evs metho ANM 2008 Si nanofets tunneling W 280 nm x L 180 nm = 2 (250 mk) = 1 /DOS

12 ots: sequential tunneling through 2 barriers Vg /DOS Tunneling EFL ml +k 0-D EFR mr evs metho ANM 2008 Si nanofets tunneling W 280 nm x L 180 nm = 2 (250 mk) = 1 /DOS Tunneling metho ANM 2008 Hopping between localize states (non Lorentzian) Disorer! Single Donor ot Single localize states Rogge PRL 06 (Lorentzian) Clean coherent transport! 12

13 Charging energy /DOS Increase Vg repulsion! DU (charging energy) Tunneling Blockae EFL ml +k EFR mr evs 0-D metho ANM 2008 Charge stability iagram of a quantum ot I = 0 Double gate Stability iagram V =const Change V g1 top gate an V g2 back/sie gate Typical units of conuctance of conuctance: 2e 2 /h an equals microsiemens, (12.9kΩ) 13

(e/l) S (E/k) f+(e) / ħ formalism f+ istribution for +k states Which becomes in the continuum, with 2 spin states: = (2e/h) E f+(e) q (E-e

14 ots with a single ion implante /DOS Sellier et al PRL 2006 Golovach et al PRB 2010 Mazzeo et al APL 2012 Tunneling Blockae metho The quantum of conuctance Classical efinition /DOS Tunneling Current of +k states given by linear ensity of electrons: I+ = (e/l) S v f+(e)= = (e/l) S (E/k) f+(e) / ħ formalism f+ istribution for +k states Which becomes in the continuum, with 2 spin states: = (2e/h) E f+(e) q (E-e cutoff) = (2e 2 /h) M Dm / e= (M is the number of moes) G= [(2e 2 /h) M ] -1 = 12.9 kw / M metho ANM 2008 (2e 2 /h) is the quantum of conuctance 14

15 Circuital view of the quantum ot an current /DOS Tunneling metho ANM 2008 Spectroscopy: single As atom in FinFET Recent experiments Single charge Ec Single spin Soli state qubits Ban formation Sample: a commercial nanofet channel 70x50 contacts ope with As 1 goo one every 10 samples 15

, Applie Physics Letters 2012 0.0 0.5 1.

16 Moving an electron from a quantum ot to a onor Recent experiments Single charge Ec E. Prati et al Applie Physics Letters 2011 J exchange coupling of the Nth electron of the QD with the 3 electrons alreay boun to the DQD Single charge Single charge state sensing Recent experiments Single charge Ec Single spin Soli state qubits Unope sample: no lines Dope: lines Ban formation 1.0 Normalize signal Mazzeo et al., Applie Physics Letters Time (ms) Measurement possible thanks to cryogenic amplifier (see G. Ferrari) 16

Spin state sensing Recent experiments Single

formation Spin level separation by Zeeman Effect

, Nature 2010 Singlet-triplet qubit Recent

state qubits splitting 140 uev T = 150 mk Pulses:

17 Spin state sensing Recent experiments Single charge Ec Single spin Soli state qubits Ban formation Spin level separation by Zeeman Effect B= 1 T Single spin reaout A.Morello et al., Nature 2010 Singlet-triplet qubit Recent experiments Single charge Ec Single spin Soli state qubits splitting 140 uev T = 150 mk Pulses: from 10 ns Fiel 30 mt Ban formation Maune et al. Nature California 17

18 Hubbar (impurity) bans formation with 4 atoms Recent experiments Single charge Ec Single spin Soli state qubits Ban formation E. Prati, M. Hori, F. Guagliaro, G. Ferrari, T. Shinaa, Nature Nanotech. (2012) Thank you Enrico Prati enrico.prati@cnr.it 18

Developing Quantum Logic Gates: Spin-Resonance-Transistors

Developing Quantum Logic Gates: Spin-Resonance-Transistors H. W. Jiang (UCLA) SRT: a Field Effect Transistor in which the channel resistance monitors electron spin resonance, and the resonance frequency