semoi transistors: from classical to quantum computing a. orlikovsky¹, s. filippov¹², v....

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

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 of transistors

Simulation of fully depleted (FD) extremely thin (ET) SOI FET

Towards SemOI-based quantum computers

The end of Moore’s ‘law’?

Micrometer channel length

Nanometer channel length

Semiconductors

Metals

Where does nanoelectronics start from?

Evolution of models

Charged fluid:Hydrodynamic equations

Charged particles:Boltzmann kinetic equation

Charged waves:Schrödinger equation

ET FD SOI FET

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

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

Silicon conduction band structure

Effective mass and transversal quantization energy

0 00.19 , 0.98t lm m m m

Quantum descriptionCharged waves:Schrödinger equation

Transversal quantization Wave-guide modes in the channel Landauer-Buttiker formalism

)()()(2

EfEfEdETh

eVI dsi

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

-10 -5 0 5 10-1.0x100

-8.0x10-1

-6.0x10-1

-4.0x10-1

-2.0x10-1

2.0x10-1

l energ

x, [nm]

Potential energy for different drain voltage Fermi level in source contact

( , , ) ( , , ) ( , , ) ( , , )2

x y z V x y z x y z x y zm

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

D.K.Ferry et al. (2005) (USA, Arizona State University):results of simulation

Solution of Schrödinger equation: transverse mode representation + some mathematical means

( , , ) ( ) ( , )N

x y z a x y z

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

( ) ( , ) | ( , , ) | ( , )ij i jM x y z V x y z y z

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)

0 0,1 0,2 0,3 0,4 0,5

Energy, eV

0 0,1 0,2 0,3 0,4 0,5

Energy, eV

Gate voltage characteristics

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Vd=0.9

Vd=0.05

Gate Voltage, [V]

Sub-threshold swing is 71 mV per decade of current.

Corrugated channel:

0.0 0.2 0.4 0.6 0.8 1.0

4.0x10-6

8.0x10-6

1.2x10-5

Drain Voltage, [V]

flat channel corrugated channel ( 0.5 nm step)

channel thickness 3 nm

Corrugated channel:

0.0 0.2 0.4 0.6 0.8 1.0

4.0x10-6

8.0x10-6

1.2x10-5

Drain Voltage, [V]

without narrow in channel Narrow Left 0.5 nm Narrow Right 0.5 nm

Impurities in channel:

0.0 0.2 0.4 0.6 0.8 1.0

4.0x10-6

8.0x10-6

1.2x10-5

Drain Voltage, [V]

without impurities in channel 1 positive impurity in channel 1 negative impurity in channel

Impurities in channel:

0.0 0.2 0.4 0.6 0.8 1.0

4.0x10-6

8.0x10-6

1.2x10-5

Drain Voltage, [V]

without impurities in channel 1 impurity near drain 1 impurity near source

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.

Semi-analytical models of FETs with low-dimensional channels A. Khomyakov (IPT RAS)

Poster P8 at 19-00!

(Conference Abstracts, page 109)

Quantum Computers

Quantum bits

Charge qubits in double quantum dots (DQDs)

Solid state implementation

Gorman et al, PRL, 2005

Two phosphorus atoms in silicon

Hollenberg et al, PRB, 2004

Gate-engineered quantum dots

Hayashi et al, PRL, 2003

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

Unavoidable obstacle

strong decoherence caused by uncontrollable Coulomb interaction between even far-distant qubit

independent of temperature quantum calculations seem impossible

Coulomb interaction Long range Coulomb interaction

eˉeˉ

2 2 21

1 1~ ~

2phase

D DD d

For , , one obtains100D nm 10d nm 10 10~ 10 s

Qubit and its operationConsists 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

1eˉ+—

Vyurkov et al, PLA, 2010

Basic states in a DQD

Potential in a DQD

Symmetric Antisymmetric

Electron wave-function in a DQD

Basic states of two DQDs

Potential in two DQDs Wave-function of two electrons in two DQDs

basis*

1 2 2 1

Basic states of a qubit

Spin-polarized electrons:

1 2 2 1

Qubit states

1 2 2 1

Distribution of charge in a qubit Probability density

For region Ω:

Charge in a dot Ω:

1(1) (2) (2) (1)

1, 2 1 2 1 2( , ) 0P dr dr r r

1 2 1 21, 2

1( , )

P dr dr r r

1 2 1 21, 2

1( , )

P dr dr r r

1, 2 1, 2 1, 2

2q P e P e P e e

Distribution of charge in a qubit

Arbitrary qubit states Arbitrary qubit state

Hamiltonian in matrix representation

Evolution operator

0 1a b

0 1 1 0ˆ1 0 0 1

ˆ ( )

ˆ ˆ( )

U t Te

Initialization

Cooling in magnetic field, positive potential on gate Т

Transformation

Pumping of electrons along the chain

Initialization

Pumping electrons from

a spin-polarized source,

for instance, ferromagnetic

Single-electron turnstile

Decoherence

Particular symmetry makes the qubit insensitive to voltage fluctuations

5~ ( ) 3~ ( )

Small energy gap between basic states in a DQD secures against the decoherence on phonons :

deformation acoustic phononspiezoelectric acoustic phonons

Decoherence ‘Frozen’ qubit: only two-phonon processes are possible, Decoherence rate is independent of energy gap

2 2' '

2| | | | ( ) 1 ( )

q q q qq q

iq r iqr

F F n n

f e z z e

Read-out

To read-out one must distinguish

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

Realistic structure

SemOI quantum register

Potential defined quantum dotsConfinement energy

l Si tm d m D

0 00.19 , 0.98t lm m m m ~ 2 , ~ 10Sid nm D nm

0 ~ 0.02eVCoulomb repulsion energy

~ 0.01C eV=> one electron in a dot

How a read-out is possible?

Transistor current

depends on position of

an electron in the

channel

0.0 0.2 0.4 0.6 0.8 1.0

4.0x10-6

8.0x10-6

1.2x10-5

Drain Voltage, [V]

without impurities in channel 1 impurity near drain 1 impurity near source

Compare with Tanamoto et al, PRA, 2000

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.

Эпилог

Light at the end of the tunnel

AcknowledgementsRussian Foundation for Basic Reasearch, grant # 08-07-00486-а

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

grant # 14.740.11.0497

semoi transistors: from classical to quantum computing a. orlikovsky¹, s. filippov¹², v....

ukrainianfrench seminar

ukraine slide

semoi transistors

technology slide

semoibased quantum computers

corrugated channel

nm channel length

d schrdinger equation

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