SemOI transistors: from classical to quantum computing

SemOI transistors:from classical toquantum computing

A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹

¹Institute of Physics and Technology

Russian Academy of Sciences

Moscow, Russia

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

²Moscow Institute of Physics and Technology

Outline

Introduction: a brief review of the history oftransistors

Simulation of fully depleted (FD) extremelythin (ET) SOI FET

Towards SemOI-based quantumcomputers

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

The end of Moore’s ‘law’?

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

Micrometer channel length

Nanometerchannel length

Semiconductors

Metals

Where does nanoelectronics startfrom?

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

Evolution of models

Charged fluid:

Hydrodynamic equations

Charged particles:

Boltzmann kinetic equation

Charged waves:

Schrödinger equation

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

ET FD SOI FET

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

IBM Gains Confidence in 22 nm ETSOI(IEDM Conf., Dec. 2009)

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

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

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

Silicon conduction band structure

Effective mass andtransversal quantizationenergy

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

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

High self-consistent barrier at S/Dcontacts

Few of incident particles surmounting the barrier isfollowed by equilibrium distribution for particles coming inthe channel

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



V(x,y,z) is a potential.

The direct solution of the stationary 3D Schrödingerequation via a finite difference scheme comes across awell known instability caused by evanescent modes.

In fact, the exponential growth of upper modes

makes a computation impossible.

Solution of 3D Schrödingerequation

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

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

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

Solution of Schrödinger equation:transverse mode representation + some mathematicalmeans



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

Calculated transmission coefficientvs. 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)

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

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

Corrugated channel:

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

Corrugated channel:

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

Impurities in channel:

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

Impurities in channel:

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

Dispersion of characteristics

5-15% in calculated I-V curves

< 10% is an everlasting condition for largeintegrated circuits

More severe demands to technology mayarise.

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

Semi-analytical models of FETswith 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

Quantum Computers

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

Quantum bits

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

Charge qubits in double quantum dots(DQDs)

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

Solid state implementation

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

Gorman et al, PRL, 2005

Two phosphorus atoms in silicon

Solid state implementation

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

Hollenberg et al, PRB, 2004

Solid state implementation

Gate-engineered quantum dots

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

Hayashi et al, PRL, 2003

Qubits based on space states

Advantages:

quite simple read-out(measurement offinal state)

explicit initialization

scaling and integritywith modernmicroelectronictechnology

Disadvantages:

strong decoherencecaused byuncontrollableCoulomb interactionbetween even far-distant qubit

decoherence causedby interaction withgates and phonons

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

Unavoidable obstacle

strong decoherence caused byuncontrollable Coulomb interactionbetween 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

Coulomb interaction

Long range Coulomb interaction

eˉ

For , , one obtains

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

Qubit and its operation

Consists of two doublequantum dots

Electrode Е operatesupon the strength ofexchange interactionbetween electrons.

Electrode Т operatesupon tunnel couplingbetween dots.

1eˉ

—

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

Vyurkov et al, PLA, 2010

Basic states in a DQD

Potential in a DQD

Symmetric

Antisymmetric

Electron wave-function in a DQD

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

Basic states of two DQDs

Potential in two DQDs

Wave-function of twoelectrons in two DQDs

basis*

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

Basic states of a qubit

Spin-polarized electrons:

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

Qubit states

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

Qubit states

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

Distribution of charge in a qubit

Probability density

For region Ω:

Charge in a dot Ω:

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

Distribution of charge in a qubit

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

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

Initialization

Cooling in magneticfield, positive potentialon gate Т

Transformation

Pumping of electronsalong the chain

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

Initialization

Pumpingelectrons from

a spin-polarizedsource,

for instance,ferromagnetic

Single-electron turnstile

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

Decoherence

Particular symmetry makes thequbit insensitive to voltagefluctuations

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

Decoherence

‘Frozen’ qubit: only two-phonon processes arepossible,

 Decoherence rate is independent of energy gap

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

Read-out

To read-out one must distinguish

from

An additional electrode by the DQDmakes it possible tunneling of anelectron into first or second dotdepending on the initial state of DQD:or

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

Realistic structure

$C:\DOCUME~1\F942~1\LOCALS~1\Temp\msohtml1\01\clip_image001.gif$

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

SemOI quantum register

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

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

How a read-out is possible?

Transistor current

depends on position of

an electron in the

channel

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

Compare with Tanamoto et al, PRA, 2000

Summary

The efficient program for 3D all quantumsimulation of field effect nanotransistors iselaborated.

The results of simulation demonstrate theimpact of realistic channelinhomogeneities on transistorcharacteristics.

SOI structure for quantum computation isproposed.

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

Эпилог

С

Light at the end of the tunnel

Acknowledgements

Russian Foundation for BasicReasearch, grant # 08-07-00486-а

NIX Computer Company(science@nix.ru), grant # F793/8-05

grant # 14.740.11.0497

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

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