Microscopic structure of interfaces in condensed matter

A.A. GorbatsevichChair of Quantum Physics and

Nanoelectronics

Nanotechnology: flourishing diversity

A.A. GorbatsevichChair of Quantum Physics and

Nanoelectronics

Nanotechnologies in MIET:

• Growth technologies: molecular-beam epitaxy, arc plasma coating, electro-chemical nanostructure formation, porous alumina anodic oxide, Ge nanocluster in Si matrix formation using ion implantation.

• Scanning probe technologies: local oxidation based nanolithography, material placing, nanolithography cantilever creation.

Nanomaterials and nanosctructures for electronics

• semiconductor heterostructures based on A3B5 compounds, including resonant-tunneling heterostructures for ultra-high speed electronics;

• solid nanocoatings for various applications, including coatings for nanolithography, conducting and magnetic coatings for scanning probe microscopy cantilevers;

• carbon nanotubes for studies of quantum transport, development and creation of electronic devices based on quantum conductors;

• Ge quantum dots in Si matrix which were first obtained using ion implantation technique;

• nanoporous alumina oxide for optoelectronic applications as well as for terabit semiconductor memory cell creation;

• quasi-one-dimensional conductor based nanovaristors displaying quantum properties at room temperature, obtained by local anodicand current induced oxidation of various metals (Ti, Ta, Nb, Al)

Nanomaterials and nanosctructures for electronics

• semiconductor heterostructures based on A3B5 compounds, including resonant-tunneling heterostructures for ultra-high speed electronics;

HeterojunctionE,U

x

Envelope Function (or Effective Mass) Method

E,U

x

)rψ()rψ(U(r)2 *

22 rrh Em

=⎥⎦

⎤⎢⎣

⎡+

∇−

1. Quantum Wells and Superlattices

x

2. Quantum Wires 3. Quantum Dots

U y

• Heterostructures for high-speed IC applications

• Nanoelectronic elements for ultra-high-speed ICs

• Heterostructures for fundamental researches (microscopic structure of heterojunctions)

• Heterostructures for high-speed IC applications

• Nanoelectronic elements for ultra-high-speed ICs

• Heterostructures for fundamental researches (“dark matter” in crystals)

Applications

Molecular-beam epitaxy machine

General view of A3B5 compounds technology clean-room facilities

Comparison of FET based on doped epitaxialGaAs structure and heterostructure FET

Basic principal of sampler performance

Input signal expansion mode

EXAMPLES OF RF ICs AND MODULES

Analogs by Picosecond Pulse Labs 2004-2005 г.

Elements for nanoelectronics

GaAs nano FETs

V-AuSiO2

Омические контакты истока и стока

Structure

Optical microscopy image

SPM gate image

I-V characteristics

Resonant-tunneling diodes (RTD)

Electric circuits and current-voltage characteristics of basic MESFET inverters

Uin

Uout

R

TАCН

Vdd

IТ

IН

Uin

Uout

TАCН

Vdd

TН IН

IТUin

Uout

ТРД

TАCН

Vdd

IТ

IН

Resistive load transistor load RTD as a loadSwitching time ∆τ = Сн∆U(I)/ ∆Ι, for the RTD at the moment of switching Сн

decreases due to the RTD negative capacitance.IAIT

Uout

"0"

"1"

∆Uout

Ug"1"

Ug"0"

IT

∆Ι

IН

3V

IAIT

Ug"1"

Ug"0"

∆Uout

IН

∆Ι

Uout

3V

IAIT

Uo

∆Ι

0.5V

Transfer characteristics of inverters

Resistive load

Transistor

RTD load

Uout

Uin

RTD:1. High speed – up to tens of gigahertzs with lithographic dimensions 0.6-0.8 µm2. High gain3. High interference margin4. Power supply less than 1.5 V5. Low power consumption

Number of elements necessary to construct logic functions based on different element base types

Circuit TTL CMOS ECL RTD/MESFET

Two-stable-state XOR 33 16 11 4

Two-stable-statemajority gate

36 18 29 5

Memory element(with 9 states)

24 24 24 5

2NO-OR+trigger 14 12 33 4

2NO – AND + trigger 14 12 33 4

Planarization problem

I-V curve of planar RTD+transistor chip

Transistor scaling limits – up to 22nm. And what is below?

May be –CMOL- electronics orwaveguide nanoelectronics!?

CMOL - electronics

Quantum interference devices

Quantum interference transistorAharonov-Bohm interferometer

Vg

``

Vg

Quantum Т-shaped transistor

Vg

Directional splitter

E

Three-terminal devices with Y-splitters

VLVR

VC

T-shaped waveguide-like transistor(F. Sols, M. Macucci, U. Ravaioli, K. Hess, Appl. Phys. Lett. 54 (4), 350, 1989)

Schematic view of three-terminal structure Transmission coefficient as function

of the effective length of the stub for energyE (eV): A – 0.02; B – 0.118; C – 0.199

Complicated structure of conductance

0,10 0,12 0,14 0,16 0,180,0

0,5

1,0

1,5

2,0

2

G/G

0EF, eV

1

Conductance of the AB ring as a functionof the Fermi level of electrons The arrowsindicate the energies at which a newconducting channel in the lead is opened. Ra = 350 nm, Rb= is 630 nm. W = 200 nm. G0 = 2e2 /h

Phys. Rev. B 69, 235304 (2004)

Analogy between electronic transport insemiconductor heterostructures and

quantum wires with variable cross-section

z

E

y

x

x1 x2

Quantum Wells and Quantum Barriers onHeterostructurePotential (GaAs/AlxGa1-xAs) –Energy Space

Electronic Waveguide –Real SpaceGated 2D electron gas

Four basic resonances

• Resonant tunneling resonance• Over-barrier (Ramsauer-Townsend-like)

resonance• Fano resonance• Aharonov-Bohm resonance

Aharonov-Bohm interference

0 1 2 3 4 5 60,0

0,2

0,4

0,6

0,8

1,0

T

∆φ/π

1122 LkLk −=∆φ

Over-barrier resonances (Ramsauer-Townsend-like resonances)

T

E

1

0

T = 1 for

where

πκ ndn =)2(

( )22

)2( 2nn Em λκ −=

h

`

y

Eε2

λ21

λ11

λ12

λ22

λ13

λ23

E

Fano resonance

E

1T

0

`

y

Eε2

λ21

λ11

λ12

λ22

λ13

λ23

E

Solution of a scattering problem for a two-dimensional Schrodinger equation by expansion on

waveguide modes

0),()),((2),(),(22

2

2

2

=−+∂

∂+

∂∂ zyzyUEm

zzy

yzy ψψψ

h

)()]}(exp[{)](exp[{),( zZyyiByyiAzy jn

nj

jn

jnj

jn

jnj ∑ −−+−= κκψ

- eigenvalues of the one-dimensional Schrodinger equations with a potential Uj(z), Zn(z) а - corresponding wave functions.

( ) , 22

jn

jn Em λκ −=

h

jnλ

∑

∑

⎭⎬⎫

⎩⎨⎧

−++−=

⎭⎬⎫

⎩⎨⎧

−−++=

+++

+++

m

jmj

jmmnj

n

jmj

mjj

mmnjn

jmj

n

m

jmj

jmmnj

n

jmj

mjj

mmnjn

jmj

n

BdiAdiB

BdiAdiA

}exp{)1(}exp{)1(21

}exp{)1(}exp{)1(21

111

111

κµκκκµ

κκ

κµκκκµ

κκ

From a continuity condition at y = yj for ψ and we obtainrelations y∂

∂ψ

dzzZzZ jn

jmmn )()( 1+∫=µ

j

j

j

BA

DBA

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛+1

In the matrix form

Denoting and sequentially applying, we obtaintArBAA N ≡≡≡ ; ; 11

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛rA

Dt0

The transfer matrix of thestructure 1221 DDDDD NN ⋅⋅⋅⋅= −−

Geometry of Aharonov-Bohm interferometer

E

L

k1

k2

h1

h2

l

H1

H2

U1

U2

hin houtH

Step-like transition region

Optimal Channel Length

0,09 0,10 0,11 0,12 0,130,0

0,5

1,0

1,5

2,0

2,5

3,0

EA-B

2

13

kL/ π

E, eV

π211 =Lkπ=22Lkat

Over-barrier resonance in each channel and total minimum due to A-B interference

h1 = h2 = 50 A, L = 309 A

EA-B = 0.115 eV

∆U=0.02 eV

Phase change in channels 1 and 2 and interchannel phase difference (3)

Choice of incoming wave-guide widths

0,09 0,10 0,11 0,12 0,130,0

0,2

0,4

0,6

0,8

1,0

EA-B

3

T

E, эВ

1

2

1-st mode transmission at ∆U=0 (1)1-st (2) and 2-nd (3) modes transmission at∆U=0.02 eV

Absence of Fano resonancehin = hout =120 А 22

inL EE >

But BAL EE −<2

0 200 400 6000,000,020,040,060,080,100,120,14

E i , eV

y, A

1

2

EA-B

Transverse(z) quantization energy position along the direction of the wave-guide (y)

Conductance

0,09 0,10 0,11 0,12 0,130,0

0,5

1,0

1,5

2,0

G/G

0

E, эВ

1

2

EA-B

Conductance dependence on Fermi energy for hin= 120 A

1 - ∆U=0 , 2 - ∆U=0.02 eV

Transmittance for hin=110 A

0,09 0,10 0,11 0,12 0,130,0

0,2

0,4

0,6

0,8

1,0

3

T

E, eV

1

2

EA-B

Transmission in 1st mode for ∆U=0 (1) and in 1st (2) and 2nd (3) modes for∆U=0.02 eV

0 200 400 6000,000,020,040,060,080,100,120,14

EFano

EA-B

E i ,

eV

y, A

1

2

Quantization energy profile along the direction of the wave-guide (y)

Variation of conductance with changing of ∆U for hin=110 A

0,09 0,10 0,11 0,12 0,130,0

0,5

1,0

1,5

2,0

3

42

G/G

0

EF, eV

1EA-B

G(∆U) curve at EF = 0.115 eV

0,00 0,02 0,040,0

0,2

0,4

0,6

0,8

1,0

G/G

0

∆U, eV

1 ∆U (meV): 1 – 0; 2 – 10; 3 – 20; 4 -50

The role of a window in a waveguide barrier

Antisymmetric mode

Symmetric mode

Fundamental problems of physics in low dimensions

The fractional quantum Hall effect …is important …primarily for one:…particles carrying an exact fraction of the electron charge e and …gauge forces between these particles, two central postulates of the standard model of elementary particles, can arise spontaneously as emergentphenomena….idea whether the properties of the universe …are fundamental or emergent…Ibelieve…must give string theorists pause…

R.B.Laughlin “Nobel Lecture: Fractional quantization” Rev. Mod. Phys. v. 71, p. 863 (1999)

Dark matter

At present it is established that from 88% to 95% of matter in the Universe are of unknown origin(neutrino mass, new particles etc.?)

Can objects exist in crystal which are invisible?

Reflectionless quantum mechanical potentials

xchUxU α20)( −−=

)(kiet ϕ=

Uteikxeikx

E0

x

,2

)(22

mkkE h

=m

E2æ22

0h

−=

karctg æ2=ϕ

222 )12()/8(1 +=+ nmU αh

,0≡r

There exist hidden microscopic objects in crystals – extended objects which are “invisible” in respect to low-energy electron energy (r≡0 и t≡1 in continuum limit)

A.A.Gorbatsevich “Hidden Defect Pairs: Objects invisible in low energy electronscattering” e-print cond-mat/0511054 (2005)

Envelope Function (or Effective Mass) Method

E,U

x

)rψ()rψ(U(r)2 *

22 rrh Em

=⎥⎦

⎤⎢⎣

⎡+

∇−

Location of heterointerface can be determined exactly!

Scattering data

eikx

re-ikx

teikx

reikx

e-ikxte-ikx

Generalized Boundary Conditions

x0

1Ψ

2Ψ

−−+⎟⎟⎠

⎞⎜⎜⎝

⎛Ψ∇

Ψ⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛Ψ∇

Ψ∧=⎟⎟

⎠

⎞⎜⎜⎝

⎛Ψ∇

Ψ

02221

1211

00 xxx TTTT

T

Extraction procedure( ) ( )

( )⎪⎩

⎪⎨⎧

>

<+= −−

−−−

.0

.0,

,22

1111

xxtexxree

xik

xikxik

δ

δδψ

( )

122121112221

1221211122212 101

TkikiTTkTkTkikiTTkTker xik

−++−−−

= − δ

( ) ( )[ ]

122121112221

1

1

2 2202101

TkikiTTkTkk

mmet xkxki

−++= −−− δδ

( ) ,...421 102

1122

111

22 1 ⎥⎦

⎤⎢⎣

⎡+−∆−−≈ δxTikT

kker Naik

( ) ,...221 11122022

111

22 2 ⎥⎦

⎤⎢⎣

⎡+−−∆−−−≈′ − TTxikT

kker Naik δ

( ) ( )([ ] ⎥⎦⎤

⎢⎣⎡ ++∆−−∆+−+≈ −− ...1

21

20102

11121122

111

222

2

11 12 δδ xxTTTikTkkT

mmet Nakki

Model

rr rr−→/

[ (∑=

++++ +−=

2111

,2,1121

ˆnnj

nnnjnjj CtCCCHjj

ε

]..) *12 1

chCCCt jj MMjn +++ +−− ε

Scattering data in the model

( ) ( )[ ]( )[ ] ( ) ( )kkiL

kkkkkeffkk

effkkkkiikMeff

a

eUUviukkLvukkLUivu

er −+

−−

+∆−∆∆

∆+∆∆−=

2sinsin

21

2122 1 ς

( )( )[ ] ( ) ( )kkiL

kkkkkeffkk

kkkkkiLeffeffeUUviukkLvu

Uviuet

−+

−

+∆−∆∆−=

2sin

2

21

2

Dependence of effective interdefectdistance on wave-vector

Dependence of reflection coefficient on wave-vector

Hidden Defect Pair

rt

In continuum limit – homogeneous structure

t=1

Other examples of “dark matter” objects in systems without inversion center:

• HDP in the models with continuum potentials (generalized Kronig-Penney model, pseudopotentials)

• Quantum well with defects located at the heterointerfaces

There’s is Plenty of Room at the Bottom.

R.Feinman, 1959

Nanotechnology – a lot of applications and economics, science and new knowledge, and some room for…game!