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Atom based nanoelectronics - Politecnico di Milano-DEIB

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11/27/2014
Istituto di Fotonica e Nanotecnologie
Atom Based Nanoelectronics
Enrico Prati, PhD
The Moore’s law
14 nm
Silicon devices!
ITRS - International Technology Roadmap for Semiconductors
A body sponsored by:
•European Semiconductor Industry Association (ESIA)
•Japan Electronics and Information Technology Industries Association (JEITA)
•Korean Semiconductor Industry Association (KSIA)
•Taiwan Semiconductor Industry Association (TSIA)
Atomic scale
•United States Semiconductor Industry Association (SIA)
devices
IFN
Enrico Prati – CNR |
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11/27/2014
The Moore’s law: status and limits
More
Moore
INTRINSIC FABRICATION LIMIT FOR LITHOGRAPHY 3 nm
M. J. Kelly, “Intrinsic top-down unmanufacturability”, Nanotechnology, 22, 245303 (2011)
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Atomic scale
devices
Enrico Prati – CNR |
Towards atomic scale: doping
1st (bad) concept: losing the approximation of ideal homogeneity
2nd (good) concept: controlling the electronic device through
a single atom (dopant)
IFN
Atomic scale
devices
Enrico Prati – CNR |
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11/27/2014
More than Moore and Beyond CMOS
'More than Moore‘ (MtM) refers to a set of technologies that enable non digital
micro / nanoelectronic functions, based on, or derived from, silicon technology
but do not necessarily scaling with Moore's Law.
(Ex: conversion of non-digital as well as non-electronic
information, such as mechanical, thermal, acoustic, chemical, optical and
biomedical functions, to digital data and vice versa.)
‘Beyond CMOS’ refers to electronics using new state variables.
(Ex: spin, molecular state, photons, phonons, nanostructures, mechanical
state, resistance, quantum state (orbital state, including phase) and magnetic flux.)
More
Moore
Moore
IFN
More
Than Moore
Beyond
CMOS
Atomic scale
devices
Enrico Prati – CNR |
More than Moore and Beyond CMOS
Source
ITRS 2010
International Technology Roadmap for Semiconductors
IFN
Atomic scale
devices
Enrico Prati – CNR |
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11/27/2014
Single ion implantation Method
Waseda University
SINGLE ATOM /FEW ATOMS DOPED
TRANSISTOR
Atomic scale
devices
Enrico Prati – CNR |
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Scanning Tunneling Microscope Method
SINGLE ATOM DOPED
TRANSISTOR
Michelle Simmons
Atomic scale
devices
IFN
Enrico Prati – CNR |
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11/27/2014
What is atomic scale nanoelectronics?
Electronic
equipment
?
Device
Millikelvin
Cryostat
Experiments
Microwave
Irradiation
Conductance
Coulomb
blockade
Magnet
Kirchoff
method
Concepts
of
Physics
Quantum
tunneling
Spin dynamics
Quantized
Energy
Fermi
Energy/DOS
Enrico Prati – CNR |
IFN
Bridge: the current
Quantum
tunneling
Quantized
Energy
Coulomb
blockade
Millikelvin
Cryostat
Kirchoff
method
Device
Concepts
of
Physics
Fermi
Energy/DOS
Conductance
Experiments
Electronic
equipment
Magnet
Spin dynamics
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Microwave
Irradiation
Enrico Prati – CNR |
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11/27/2014
Layout
Framework
Theory
Experiments
Atomic scale
devices
Device
Single charge
manipulation
Qubits
Fermi
Energy/DOS
Single spin
manipulation
Quantum
Information
Quantized
Energy
Solid state
qubits
Quantum
tunneling
Band
formation
Coulomb
blockade
Conductance
Kirchoff
method
Enrico Prati – CNR |
IFN
Nanoelectronics
Framework
Atomic scale
devices
Qubits
Quantum
Computing
IFN
Tentative definition: Nanoelectronics is the use of
nanotechnology (less than 100 nm) on electronic components, so
that inter-atomic interactions and quantum mechanical properties
play the major role.
WARNING
1) As a result, current transistors do not fall under this category,
even though these devices are manufactured with
22 nm or 14 nm technology.
2) All the properties of semiconductors depend on quantum
mechanics. Here we refer to the dominant role of individual
objects (one or few electrons, one dopant…) so that the
peculiar properties of QM like superposition of states, spin and
entanglement have direct consequences.
Enrico Prati – CNR |
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Qubits for Quantum Algorithms
Definition: a qubit is a complex linear combination of 2 bits
Framework
CNOT LOGIC PORT
(Operator acting on a Hilbert space)
Atomic scale
devices
Qubits
Quantum
Information
Enrico Prati – CNR |
IFN
Motivations: solid state quantum information
Framework
Atomic scale
devices
Qubits
Quantum
Information
Old theoretical approach (1998)
IFN
Enrico Prati – CNR |
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11/27/2014
Motivations: solid state quantum information
D Wave (Canada): 128 superconductive qubits chip
For adiabatic quantum computation
Framework
Qubits
Atomic scale
devices
Quantum
Information
First experimental success (2011)
Enrico Prati – CNR |
IFN
Quantum information in biology
Framework
Qubits
Atomic scale
devices
Quantum
Information
PNAS 108, 20908, 2011
IFN
Enrico Prati – CNR |
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11/27/2014
Basic device: a single atom transistor
Theory
Ending
point:
Device
Fermi
Energy
P is a single phosphorus
atom below the gate
Quantized
Energy
Quantum
tunneling
Coulomb
blockade
Conductance
Kirchoff
method
IFN
Enrico Prati – CNR |
Density of States (DoS)
ni h
2L
Heuristic Quantization
Periodic Boundary
Condition
pi  k i 
Theory
Electron wavefunction
Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
tunneling
Coulomb
blockade
Conductance
Kirchoff
method
IFN



1d
2d
3d
dn( E ) d 1 
dE
L
E
dn( E ) d 2  dE
dn( E ) d 3  E dE
g(p)dp
L
d
d
d
2  h 
 h 
dn   dni    d d p  d   p d 1 dp
( 2 )  2 L 
i
 2L 
d
2
L
E=p2/2m
Volume of a
hyperphere
of dimension
d
Change variables
g ( E )  (2s  1)

d
d
d 2
d
 2L 
2
2
(
2
m
)
E


d
d
2 ( 2 )  h 
2
DoS =«how many states g(p) or g(E) you have in
a p (momentum) or E (energy) interval respectively»
Enrico Prati – CNR |
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11/27/2014
Density of states and Fermi Energy
Theory

Condition to see discrete energy levels related effects:

Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
tunneling


KT << DE
kT << 
energy level spacing
linewidth
Chemical potential: (of a thermodynamic
system) is the amount by which
the energy of the system would
change if an additional particle
were introduced, with the entropy
and volume held fixed.
Fermi Energy: chemical potential at T=0
Temperature:
4.2 K usual
300 K for 2nm QD
EF
Contacts
Impurity
atoms
Coulomb
blockade
Conductance
Kirchoff
method
IFN
Enrico Prati – CNR |
Confinement
Theory
Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
tunneling
Semiconductor nanostructures and quantum dots are fabricated by
1) Vertical confinement (d=3->2) via
• Semiconductor/insulator interface (Si/SiO2)
• Semiconductor/Semiconductor heterostructures
(GaAs/AlGaAs or Si/SiGe )
2) Lateral confinement (d=2->1,0)
• Split gate technique
• Lithographically defined structures
• Atomic inclusions
• Point defects
Nature, 2007
Coulomb
blockade
Conductance
Kirchoff
Colloquia
method
IFN
Enrico Prati – CNR |
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11/27/2014
Tunneling through a single barrier
Theory
Schroedinger
Device
Test function
Fermi
Energy/DOS
Quantized
Energy
New equation
Solution: Airy f.
(v1 coeff. X1 turning point)
Square potential
Quantum
Tunneling
Coulomb
blockade
Conductance
Kirchoff
ANM 2008
method
IFN
Enrico Prati – CNR |
Tunneling in a quantum dot
Theory
A quantum dot is a small box that can be filled with electrons.
Device
Fermi
Energy/DOS
Quantized
Energy
The box is coupled via tunnel barriers to a source and drain reservoirs
Quantum
Tunneling
(which tunes the electrostatic dot/reservoir potential)
(particles exchanges) capacitively coupled to a gate
Coulomb
blockade
Conductance
Kirchoff
method
IFN
Enrico Prati – CNR |
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11/27/2014
Quantum dots: sequential tunneling through 2 barriers
Theory
Device
Vg
Energy
Fermi
Energy/DOS
Quantized
Energy
eVds
EFL
Quantum
Tunneling
mL
EFR
+k
Coulomb
blockade
mR
0-D
Conductance
Kirchoff
ANM 2008
method
IFN
Enrico Prati – CNR |
Si nanoFETs tunneling
d=2
Theory
(250 mK)
d=1
W 280 nm x L 180 nm
Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
Tunneling Hopping between localized states
(non Lorentzian)
Coulomb
blockade
Disorder!
Conductance
Kirchoff
ANM 2008
method
IFN
Single
Donor
Quantum dot
Rogge PRL 06
Single localized states
(Lorentzian)
Clean coherent transport!
Enrico Prati – CNR |
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11/27/2014
Charging energy
Theory
Coulomb repulsion!
Device
DU (charging energy)
Increase Vg
Fermi
Energy/DOS
Quantized
Energy
Quantum
Tunneling
eVds
EFL
mL
Coulomb
Blockade
EFR
+k
Conductance
mR
0-D
Kirchoff
ANM 2008
method
IFN
Enrico Prati – CNR |
Charge stability diagram of a quantum dot
I=0
Double gate
Stability diagram
Vd=const
Change Vg1 top gate
and Vg2 back/side gate
Typical units of conductance
Quantum of conductance: 2e2/h and equals 77.48 microsiemens, (12.9kΩ)
IFN
Enrico Prati – CNR |
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11/27/2014
Quantum dots with a single ion implanted
Theory
Device
Fermi
Energy/DOS
Sellier et al PRL 2006
Golovach et al PRB 2010 Mazzeo et al APL 2012
Quantized
Energy
Quantum
Tunneling
Coulomb
Blockade
Conductance
Kirchoff
Theory
method
IFN
Enrico Prati – CNR |
The quantum of conductance
Theory
Classical
definition
Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
Tunneling
Coulomb
blockade
Conductance
Kirchoff
ANM 2008
method
IFN
Current of +k states given by linear density of electrons:
I+ = (e/L) S v f+(E)=
= (e/L) S (dE/dk) f+(E) / ħ
Quantum
formalism
f+ Fermi distribution for +k states
Which becomes in the continuum, with 2 spin states:
= (2e/h) ∫ dE f+(E) q (E-e cutoff)
= (2e2/h) M Dm / e= (M is the number of modes)
G= [(2e2/h) M ] -1 = 12.9 kW / M
(2e2/h) is the quantum of conductance
Enrico Prati – CNR |
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11/27/2014
Circuital view of the quantum dot and current
Theory
Device
Fermi
Energy/DOS
Quantized
Energy
Quantum
Tunneling
Coulomb
blockade
Conductance
Kirchoff
ANM 2008
method
IFN
Enrico Prati – CNR |
Spectroscopy: single As atom in FinFET
Recent experiments
Ec
Single charge
manipulation
Single spin
manipulation
Solid state
qubits
Band
formation
IFN
0
| 1
| 2
Sample: a commercial nanoFET
channel 70x50
contacts doped with As
1 good one every 10 samples
Enrico Prati – CNR |
15
11/27/2014
Moving an electron from a quantum dot to a donor
Recent experiments
Ec
Single charge
manipulation
E. Prati et al Applied
Physics Letters 2011
J exchange coupling
of the Nth electron of
the QD with the 3 electrons
already bound to the DQD
Single charge
manipulation
Enrico Prati – CNR |
IFN
Single charge state sensing
Recent experiments
Ec
Single charge
manipulation
Single spin
manipulation
Undoped sample:
no lines
Doped:
lines
Solid state
qubits
Band
formation
Normalized signal
1.0
0.5
0.0
0.0
Mazzeo et al., Applied
Physics Letters 2012
IFN
0.5
1.0
1.5
2.0
2.5
3.0
Time (ms)
Measurement possible thanks
to cryogenic amplifier (see G. Ferrari)
Enrico Prati – CNR |
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11/27/2014
Spin state sensing
Spin level separation
Recent experiments by Zeeman
Effect B= 1 T
Ec
Single charge
manipulation
Single spin
manipulation
Solid state
qubits
Band
formation
Single spin readout
A.Morello et al., Nature 2010
IFN
Enrico Prati – CNR |
Singlet-triplet qubit
Recent experiments
Ec
Single charge
manipulation
Single spin
manipulation
Energy splitting 140 ueV
T = 150 mK
Pulses: from 10 ns
Field 30 mT
Solid state
qubits
Band
formation
Maune et al.
Nature 2012
@HRL California
IFN
Enrico Prati – CNR |
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11/27/2014
Hubbard (impurity) bands formation with 4 atoms
Recent experiments
Ec
Single charge
manipulation
Single spin
manipulation
Solid state
qubits
Band
formation
E. Prati, M. Hori, F. Guagliardo, G. Ferrari, T. Shinada, Nature Nanotech. (2012)
IFN
Enrico Prati – CNR |
Thank you

Enrico Prati [email protected]
IFN
Enrico Prati – CNR |
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