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, blick@engr.wisc.edu.

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)