nano-electro-mechanical systems (nems) in the … · nano-electro-mechanical systems (nems) in the...
TRANSCRIPT
Nano-Electro-Mechanical Systems (NEMS)
in the Quantum Limit
Eva Weig, now postdoc at University of California at Santa Barbara.
Robert H. Blick, University of Wisconsin-Madison,Electrical & Computer Engineering, Madison, WI 53706, USA, [email protected].
hotting up: dissipation in nanoscale systems
Landauer, Nature 335, 779 (1988).
The quantum limit of NEMS:
OUTLINE
4. free-standing quantum dot as electron-phonon cavity: phonon quantum confinement & phonon blockade
3. free-standing quantum dot as detector: coupling to nanoelectromechanical systems (NEMS)
5. suspended gate-tunable nanostructures:in-situ electron system control
1. low-dimensional electron systems in free-standing nanostructures:sample processing
2. ballistic billiards:suspended and unsuspended samples
molecular beam epitaxyGaAs/AlGaAs heterostructure
containing both a two-dimensional electron gas and a sacrificial layer
5 nm GaAs Cap35 nm Al0.3Ga0.7As
(δ-doped)25 nm GaAs55 nm Al0.3Ga0.7As
(δ-doped)10 nm GaAs
400 nm Al0.8Ga0.2As200 nm GaAs buffer
W. Wegscheider, M. Bichler, D. Schuh(University of Regensburg and Walter-Schottky-Institut, Technische Universität München)
active layer
sacrificial layersubstrate
d = 90, 110, 130 nmnS = 9.1 H 1011 cm-2
µ = 234,000 cm2/Vs
sacrificiallayer
2DEG
GaAs
AlGaA
sAlA
sAlG
aAs
GaAs
GaAs
GaAs
sacrificiallayer
2DEG
GaAs
AlGaA
sAlA
sAlG
aAs
GaAs
GaAs
GaAs
δ-dop
ed
δ-dop
ed
electron beam lithographynanostructuring of the sample in two steps
metal evaporation
• gates, marks etc. Au• etch mask Ni
alignment precision~ 10 - 20 nm
Nietch mask
Au electrodes
reactive ion etchingtransferring the structure into the 2DEG
highly anisotropicreactive ion etching (ICP RIE) with SiCl4:
• steep side walls
• side depletionwd ~ 50 - 80 nm
• carrier densitynS ~ 5 - 6 H 1011 cm-2
• mobility~ 20 000 -
40 000 cm2/Vs
SiCl4
wet chemical etchingsuspending the nanostructure
dissolving the sacrificial layer in 0.1 % hydrofluoric acid; critical point drying
• resistance R0 > const • carrier density nS > const• mobility > const
BUTdamage of the Al containing parts of the heterostructure
E. M. Höhberger et al., Physica E 12, 487 (2002).
HF
500 nm
500 nm
readily processed suspended quantum dotsexamples for sample geometries
with nanomechanical resonator
defined by gate electrodes
defined by geometrical constrictions
OUTLINE1. low-dimensional electron systems in free-standing nanostructures:
sample processing
2. ballistic billiards:suspended and unsuspended samples
3. free-standing quantum dot as detector: coupling to nanoelectromechanical systems (NEMS)
4. free-standing quantum dot as electron-phonon cavity: phonon quantum confinement & phonon blockade
5. suspended gate-tunable nanostructures:in-situ electron system control
suspended or not suspended?characteristic low-field magnetoresistance of suspended billiards
not suspended suspended
K. K. Choi et al., PRB 33, 8216 (1986), A. D. Mirlin et al., PRL 87, 126805 (2001)
Shubnikov-de Haas oscillations& negative magnetoresistance
magnetoresistance at T = 4.2 K:
dissolution of the Al0.8Ga0.2As sacrificial layer damages also
the Al0.3Ga0.7As part of theactive layer:
short-range boundary roughness
suspended or not suspended?characteristic low-field magnetoresistance of suspended billiards
not suspended suspended
increase of short-range boundary roughness
J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002).
smooth boundary roughness
coherent scattering in ballistic billiardsunderetching increases short-range boundary roughness
C. M. Marcus et al., PRL 69, 506 (1992)J. P. Bird et al., PRB 52, 14336 (1995)
sample A sample B sample C sample D
coherent backscattering coherent forward scattering
zero-field peak resistance fluctuations
J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002).
OUTLINE1. low-dimensional electron systems in free-standing nanostructures:
sample processing
2. ballistic billiards:suspended and unsuspended samples
3. free-standing quantum dot as detector: coupling to nanoelectromechanical systems (NEMS)
4. free-standing quantum dot as electron-phonon cavity: phonon quantum confinement & phonon blockade
5. suspended gate-tunable nanostructures:in-situ electron system control
Vds
Vg
Gate
Drain Source
... and forming tunneling barriersby depletion of the constrictions from a side gate
Coulomb blockade in a free-standing quantum dot
N-1 N N+1
N-1 N N+1
EC = e2/2CΣ= 0.56 meV
CΣ = e2/EC= 140 aF
Cg = e/ Vg= 14 aF
CΣ = 8ε0εrR
R = 160 nmN = 480 e-
Vsd ~ 0 mV
characterization of the quantum dotat B = 500 mT:
• charging energy
• capacitances
• size & charge
ultrasensitive displacement detection integrating a free-standing quantum dot and a nanomechanical resonator
J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002).
charge sensitivity
displacement sensitivity∆
−= ⋅ 3dx 2.9 10 nm / Hzf
∆∆ ∆
−⎛ ⎞
= ⎜ ⎟⎝ ⎠
1g g
g
dC dQdx I Vdx dIf f
• SET as an extremely sensitive charge detector• capacitive coupling between SET and resonator is a function of the displacement
Vsd
C ,Qg g
C ,Qs sC ,Qd d
-Ne
rf
B
500 nm
500 nm
operating point
∆−= ⋅g 4dQ
3.3 10 e / Hzf
∆∆ ∆
= =g g gdQ dQ dQIS(0)dI dIf f
nanomechanical displacement detectionusing Coulomb blockade-based and related schemes
K. Schw ab, APL 80, 1276 (2002)
M . P. Blencow e et al., APL 77, 3845 (2000)
Hz/nm103)e10(f
dx 62 −− ⋅=∆
A. N . Cleland et al., APL 81, 1699 (2002)
R. Knobel et al., APL 81, 2258 (2002)
Hz/nm103f
dx 3−⋅=∆
)itedlimquantum(
Hz/nm101f
dx 8−⋅=∆
A. H örner et al., capacitive detection using N EM S & on-chip pream p
Hz/nm105.1f
dx 2−⋅=∆
OUTLINE1. low-dimensional electron systems in free-standing nanostructures:
sample processing
2. ballistic billiards:suspended and unsuspended samples
3. free-standing quantum dot as detector: coupling to nanoelectromechanical systems (NEMS)
4. free-standing quantum dot as electron-phonon cavity: phonon quantum confinement & phonon blockade
5. suspended gate-tunable nanostructures:in-situ electron system control
free-standing quantum dotsas electron-phonon cavities
electron-phonon cavity:
single electron - single phonon interactioncontrol of phonon-mediated dissipationfor Quantum Electro-Mechanics (QEM)
free-standing nanostructure:
• phonon cavity• discrete phononspectrum
• van Hove singularities
quantum dot:
• 0D electron island• discrete electronic
states• single electon
tunneling (SET)
Coulomb blockade in a freely suspended quantum dot
• total suppression of single electron tunneling conductance peaks in linear transport
Vsd = 0 mV
additional blockade effect at B = 0 mT
• energy gap in the Coulomb diamond ε = 100 µeV
ε = 100 µV
Vsd
eVsd = ε
Vsd = 0
Vg
• asymmetric energy gap
van Hove singularities in the cavitysuppression of linear transport due to excitation of a localized cavity phonon?
,eV73zc3 L
0 µε ==h 0
0 18f GHzhε
= = ,eV1450 µε = 0 35f GHz=
cL = 4.77 H 105 cm/s
flexural modes: dilatational modes:
energy gapε = 100 µeV
S. Debald S. Debald
a simple model for phonon blockade
excitation of alocalized cavityphonon in theelectron-phonon cavity blocks single electrontunneling
Franck-Condon principle & phonon blockadeelectronic transitions of an (artificial) atom
1. electronic transitions are much faster than a change of the atomic configuration
2. relaxation to a state of minimized energy occurs after the transition
3. excitation of a local bosonic mode, e.g. a cavity phonon
4. transition governed by overlap of the two wavefunctions
E.M. Weig, R.H. Blick et al., Phys. Rev. Lett. 92, 046804 (2004)
temperature dependence zero-bias conductance peaks re-appear
T ~ 10 mK (Tel y100 mK ) T ~ 350 mK
Vsd ~ 0 mV Vsd ~ 0 mV
4kBT y energy gap
thermal broadening of the Fermi distribution in the leads
E.M. Weig, R.H. Blick et al.,Phys. Rev. Lett. 92, 046804 (2004)
Coulomb blockade in a C60 moleculesingle electron tunneling with strong coupling to a vibrational mode
H. Park et al., Nature 407, 57 (2000)
blockade
OUTLINE1. low-dimensional electron systems in free-standing nanostructures:
sample processing
2. ballistic billiards:suspended and unsuspended samples
3. free-standing quantum dot as detector: coupling to nanoelectromechanical systems (NEMS)
5. suspended gate-tunable nanostructures:in-situ electron system control
4. free-standing quantum dot as electron-phonon cavity: phonon quantum confinement & phonon blockade
freely suspended gate-tunable 2DEGin-situ control of electronic dimensionality
• five independently tunable gateelectrodes (plus backgate)
• increased control of the low-dimensional electron system
• dimensionality of the samplecan be continuously reduced
• no gates:2DEG
• gate #1:quantum point contact
• gate #1, #3 and #2:quantum dot A
• gate #1, #3, #5 and #2, #4:serial double dot AB
E. M. Höhberger, T. Krämer, W. Wegscheider, R. H. Blick, Appl. Phys. Lett. 82, 4160 (2003).
operation in the quantum Hall regimeall gates unbiased
G = dI/dVsd at T = 5 K:
• Shubnikov-de Haas oscillations down to B = 0.6 T for gated and ungated but otherwise identical beams
• minima are reached at the same fields B• zero-field conductance remains unchanged
unbiased Schottky gates do not affect the 2DEG
spin splitting for ν = 7, 5 and 3ns = 6.25 . 1011 cm-2
µ = 5,500 cm2/Vs
2D
formation of a quantum point contactdepletion of gate #1
G = dI/dVsd at T = 1.5 K:• formation of magnetoelectric subbands:broadening of conductance plateaus
degree of depletion can be adjusted individually under the available gates
G = dI/dVsd at T = 5 K:• conductance quantization steps• pinch-off at Vg1 = -2 V
1D
weakly coupled quantum dotdepletion of gates #1 and #3
0D
G = dI/dVsd at T = 1.5 K:
• Vg1 is varied while Vg3 is kept at a fixed value
• zero bias Vsd = 0 mV curve showsCoulomb blockade oscillations
• variation of Vg1 and Vsd producesCoulomb diamonds with
EC = 2.74 meVCΣ = 30 aF
gate-tunable free-standingquantum dots
freely suspended gate-tunable quantum dot structures controlling the dimensionality of the electron system
2DEG quantum point contact quantum dot serial double dot
?
E. M. Höhberger, T. Krämer, W. Wegscheider, R. H. Blick, Applied Physics Letters 82, 4160 (2003).
outlook – membranes and topology
R. Blick, New J. of Physics 7, 241 (2005) online
Courtesy V. Prinz
Geometric potentials
Nakul Shaji et al., Appl. Phys. Lett., in press (2006)
Geometric potentials
ACKNOWLEDGEMENTS –Eva Weig & Florian BeilJochen Kirschbaum, Tomas Krämer, Daniel Schröer
University of Munich, Germany
Hyun-Seok Kim, Hyun-Cheol Shin, Ryan Toonen, Nakul Shaji, Hua QinUniversity of Wisconsin-Madison
Max Lagally, Mark Eriksson, Irena Knezevic, and Jack MaUniversity of Wisconsin-Madison
Achim Wixforth, Armin Kriele, Jörg KotthausUniversity of Munich, Germany
Werner Wegscheider, Dieter Schuh Universität Regensburg, Germany Max Bichler WSI, Technical University Muich, Germany
Tobias Brandes Technical University of Berlin
Funding – current: National Science Foundation (MRSEC/IRG1) earlier: BMBF (German Ministry of Science and Technology)