SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V....
-
Upload
coby-finkel -
Category
Documents
-
view
217 -
download
0
Transcript of SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V....
![Page 1: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/1.jpg)
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
![Page 2: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/2.jpg)
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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 3: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/3.jpg)
The end of Moore’s ‘law’?
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 4: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/4.jpg)
Micrometer channel length
Nanometer channel length
Semiconductors
Metals
Where does nanoelectronics start from?
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 5: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/5.jpg)
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
![Page 6: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/6.jpg)
ET FD SOI FET
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 7: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/7.jpg)
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
![Page 8: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/8.jpg)
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
![Page 9: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/9.jpg)
Silicon conduction band structure
Effective mass and transversal quantization energy
0 00.19 , 0.98t lm m m m
22
0 2
Sidm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 10: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/10.jpg)
Quantum descriptionCharged waves:Schrödinger equation
Transversal quantization Wave-guide modes in the channel Landauer-Buttiker formalism
)()()(2
)(0
EfEfEdETh
eVI dsi
isd
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 11: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/11.jpg)
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
0.0
2.0x10-1
Pote
ntia
l energ
y, [
eV
]
x, [nm]
Potential energy for different drain voltage Fermi level in source contact
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 12: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/12.jpg)
2
( , , ) ( , , ) ( , , ) ( , , )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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 13: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/13.jpg)
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
![Page 14: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/14.jpg)
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
![Page 15: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/15.jpg)
Solution of Schrödinger equation: transverse mode representation + some mathematical means
1
( , , ) ( ) ( , )N
i ii
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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 16: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/16.jpg)
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
0,2
0,4
0,6
0,8
1
1,2
0 0,1 0,2 0,3 0,4 0,5
Energy, eV
Tra
nsm
issi
on
0
0,2
0,4
0,6
0,8
1
1,2
0 0,1 0,2 0,3 0,4 0,5
Energy, eV
Tra
nsm
issi
on
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 17: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/17.jpg)
Gate voltage characteristics
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
1E-8
1E-7
1E-6
1E-5
Vd=0.9
Vd=0.05
Dra
in C
urr
ent,
[A
]
Gate Voltage, [V]
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
![Page 18: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/18.jpg)
Corrugated channel:
0.0 0.2 0.4 0.6 0.8 1.0
0.0
4.0x10-6
8.0x10-6
1.2x10-5
Dra
in C
urr
en
t, [A
]
Drain Voltage, [V]
flat channel corrugated channel ( 0.5 nm step)
channel thickness 3 nm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 19: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/19.jpg)
Corrugated channel:
0.0 0.2 0.4 0.6 0.8 1.0
0.0
4.0x10-6
8.0x10-6
1.2x10-5
Dra
in C
urr
en
t, [A
]
Drain Voltage, [V]
without narrow in channel Narrow Left 0.5 nm Narrow Right 0.5 nm
channel thickness 3 nm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 20: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/20.jpg)
Impurities in channel:
0.0 0.2 0.4 0.6 0.8 1.0
0.0
4.0x10-6
8.0x10-6
1.2x10-5
Dra
in C
urr
en
t, [A
]
Drain Voltage, [V]
without impurities in channel 1 positive impurity in channel 1 negative impurity in channel
channel thickness 3 nm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 21: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/21.jpg)
Impurities in channel:
0.0 0.2 0.4 0.6 0.8 1.0
0.0
4.0x10-6
8.0x10-6
1.2x10-5
Dra
in C
urre
nt, [
A]
Drain Voltage, [V]
without impurities in channel 1 impurity near drain 1 impurity near source
channel thickness 3 nm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 22: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/22.jpg)
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.
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 23: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/23.jpg)
Semi-analytical models of FETs with 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
![Page 24: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/24.jpg)
Quantum Computers
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 25: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/25.jpg)
Quantum bits
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 26: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/26.jpg)
26
Charge qubits in double quantum dots (DQDs)
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 27: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/27.jpg)
27
Solid state implementation
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
Gorman et al, PRL, 2005
![Page 28: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/28.jpg)
28
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
![Page 29: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/29.jpg)
29
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
![Page 30: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/30.jpg)
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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 31: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/31.jpg)
Unavoidable obstacle
strong decoherence caused by uncontrollable Coulomb interaction between 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
![Page 32: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/32.jpg)
Coulomb interaction Long range Coulomb interaction
d
D
eˉeˉ
eˉ
2 2 21
32 2
1 1~ ~
2phase
e e d
D DD d
For , , one obtains100D nm 10d nm 10 10~ 10 s
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 33: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/33.jpg)
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
T1eˉ
1eˉ+—
—+
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
Vyurkov et al, PLA, 2010
![Page 34: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/34.jpg)
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
![Page 35: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/35.jpg)
Basic states of two DQDs
Potential in two DQDs Wave-function of two electrons in two DQDs
basis*
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 36: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/36.jpg)
1 2 2 1
10
2
1 2 2 1
11
2
Basic states of a qubit
Spin-polarized electrons:
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 37: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/37.jpg)
1 2 2 1
10
2
Qubit states
1r
2r
1r
2r
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 38: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/38.jpg)
Qubit states
1r
2r
1r
2r
1 2 2 1
11
2
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 39: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/39.jpg)
Distribution of charge in a qubit Probability density
For region Ω:
Charge in a dot Ω:
1(1) (2) (2) (1)
2
1, 2 1 2 1 2( , ) 0P dr dr r r
3
1 2 1 21, 2
\
1( , )
4R
P dr dr r r
3
1 2 1 21, 2
\
1( , )
4R
P dr dr r r
1, 2 1, 2 1, 2
12
2q P e P e P e e
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 40: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/40.jpg)
Distribution of charge in a qubit
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 41: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/41.jpg)
Arbitrary qubit states Arbitrary qubit state
Hamiltonian in matrix representation
Evolution operator
2 2
0 1a b
a b
0 1 1 0ˆ1 0 0 1
H A P
0
ˆ ( )
ˆ ˆ( )
tiH d
U t Te
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 42: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/42.jpg)
Initialization
Cooling in magnetic field, positive potential on gate Т
Transformation
Pumping of electrons along the chain
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 43: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/43.jpg)
Initialization
Pumping electrons from
a spin-polarized source,
for instance, ferromagnetic
Single-electron turnstile
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 44: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/44.jpg)
Decoherence
Particular symmetry makes the qubit insensitive to voltage fluctuations
5~ ( ) 3~ ( )
x
y
Small energy gap between basic states in a DQD secures against the decoherence on phonons :
deformation acoustic phononspiezoelectric acoustic phonons
–VT
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 45: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/45.jpg)
Decoherence ‘Frozen’ qubit: only two-phonon processes are possible, Decoherence rate is independent of energy gap
2 2' '
'
2
'
2
'
( )
2| | | | ( ) 1 ( )
( )
q q q qq q
iq r iqr
z
z q
f q q
W f
F F n n
f e z z e
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 46: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/46.jpg)
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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 47: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/47.jpg)
Realistic structure
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 48: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/48.jpg)
SemOI quantum register
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 49: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/49.jpg)
Potential defined quantum dotsConfinement energy
20
1 1~
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
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 50: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/50.jpg)
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
0.0
4.0x10-6
8.0x10-6
1.2x10-5
Dra
in C
urre
nt, [
A]
Drain Voltage, [V]
without impurities in channel 1 impurity near drain 1 impurity near source
channel thickness 3 nm
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
Compare with Tanamoto et al, PRA, 2000
![Page 51: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/51.jpg)
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.
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 52: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/52.jpg)
Эпилог
С
Light at the end of the tunnel
![Page 53: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/53.jpg)
AcknowledgementsRussian Foundation for Basic Reasearch, grant # 08-07-00486-а
NIX Computer Company ([email protected]), grant # F793/8-05
grant # 14.740.11.0497
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine
![Page 54: SemOI transistors: from classical to quantum computing A. Orlikovsky¹, S. Filippov¹², V. Vyurkov¹², and I. Semenikhin¹ ¹Institute of Physics and Technology.](https://reader035.fdocuments.net/reader035/viewer/2022062620/551a7de05503466b3a8b461c/html5/thumbnails/54.jpg)
1st Ukrainian-French Seminar and 6th International SemOI Workshop, October 25-29, 2010, Kyiv, Ukraine