Nano-Electro-Mechanical Systems (NEMS) in the Quantum Limit

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 1. 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

molecular beam epitaxy GaAs/AlGaAs heterostructure containing both a two-dimensional electron gas and a sacrificial layer 2DEG 2DEG sacrificial layer GaAs GaAs AlGaAs δ-doped AlGaAs GaAs GaAs δ-doped AlGaAs AlGaAs GaAs GaAs AlAs AlAs GaAs GaAs 5 nm GaAs Cap 35 nm Al 0.3 Ga 0.7 As (δ-doped) 25 nm GaAs 55 nm Al 0.3 Ga 0.7 As (δ-doped) 10 nm GaAs 400 nm Al 0.8 Ga 0.2 As 200 nm GaAs buffer active layer d = 90, 110, 130 nm n S = 9.1 H 10 11 cm -2 µ = 234,000 cm 2 /Vs sacrificial layer substrate W. Wegscheider, M. Bichler, D. Schuh (University of Regensburg and Walter-Schottky-Institut, Technische Universität München)

electron beam lithography nanostructuring of the sample in two steps Au electrodes Ni etch mask metal evaporation gates, marks etc. Au etch mask Ni alignment precision ~ 10-20 nm

reactive ion etching transferring the structure into the 2DEG SiCl 4 highly anisotropic reactive ion etching (ICP RIE) with SiCl 4 : steep side walls side depletion w d ~ 50-80 nm carrier density n S ~ 5-6 H 10 11 cm -2 mobility ~ 20 000-40 000 cm 2 /Vs

wet chemical etching suspending the nanostructure HF dissolving the sacrificial layer in 0.1 % hydrofluoric acid; critical point drying resistance carrier density mobility R 0 > const n S > const > const BUT damage of the Al containing parts of the heterostructure E. M. Höhberger et al., Physica E 12, 487 (2002).

readily processed suspended quantum dots examples for sample geometries 500 nm 500 nm defined by geometrical constrictions with nanomechanical resonator defined by gate electrodes

suspended or not suspended? characteristic low-field magnetoresistance of suspended billiards magnetoresistance at T = 4.2 K: not suspended suspended Shubnikov-de Haas oscillations & negative magnetoresistance K. K. Choi et al., PRB 33, 8216 (1986), A. D. Mirlin et al., PRL 87, 126805 (2001)

suspended or not suspended? characteristic low-field magnetoresistance of suspended billiards not suspended dissolution of the Al 0.8 Ga 0.2 As sacrificial layer damages also the Al 0.3 Ga 0.7 As part of the active layer: short-range boundary roughness suspended smooth boundary roughness increase of shortrange boundary roughness J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002).

coherent scattering in ballistic billiards underetching increases short-range boundary roughness sample A sample B sample C sample D zero-field peak resistance fluctuations coherent backscattering coherent forward scattering J. P. Bird et al., PRB 52, 14336 (1995) C. M. Marcus et al., PRL 69, 506 (1992) J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002).

... and forming tunneling barriers by depletion of the constrictions from a side gate Gate Drain Source V g V ds

Coulomb blockade in a free-standing quantum dot V sd ~0 mv characterization of the quantum dot at B = 500 mt: charging energy capacitances size & charge E C = e 2 /2C Σ = 0.56 mev C Σ = e 2 /E C = 140 af C g = e/ V g = 14 af C Σ = 8ε 0 ε r R N-1 N N+1 N-1 N N+1 R = 160 nm N = 480 e -

ultrasensitive displacement detection integrating a free-standing quantum dot and a nanomechanical resonator SET as an extremely sensitive charge detector capacitive coupling between SET and resonator is a function of the displacement C g,q g rf 500 nm operating point C,Q d d -Ne C,Q s s B 500 nm charge sensitivity displacement sensitivity dqg dqg I dq g 4 = S(0) = = 3.3 10 e / Hz f di f di f dx f I dcg dqdx g = Vg f dx di f 3 2.9 10 nm / Hz = J. Kirschbaum, E. M. Höhberger, R. H. Blick, W. Wegscheider, M. Bichler, Appl. Phys. Lett. 81, 280 (2002). 1 V sd

nanomechanical displacement detection using Coulomb blockade-based and related schemes A.Hörner et al., capacitive detection using NEMS & on-chippreamp dx 2 = 1.5 10 nm / f Hz M.P.Blen cow e et al., APL 77,3845 (2000) dx 2 6 (10 e ) = 3 10 nm / f Hz K.Schw ab, APL 80,1276 (2002) dx 3 = 3 10 nm / f Hz R.Knobelet al., APL 81,2258 (2002) A.N.Cleland et al., APL 81,1699 (2002) dx 8 = 1 10 nm / f Hz (quantum lim ited )

free-standing quantum dots as electron-phonon cavities quantum dot: 0D electron island discrete electronic states single electon tunneling (SET) free-standing nanostructure: phonon cavity discrete phonon spectrum vanhove singularities electron-phonon cavity: single electron - single phonon interaction control of phonon-mediated dissipation for Quantum Electro-Mechanics (QEM)

Coulomb blockade in a freely suspended quantum dot V sd =0 mv additional blockade effect at B = 0 mt total suppression of single electron tunneling conductance peaks in linear transport energy gap in the Coulomb diamond ε = 100 µev asymmetric energy gap V sd V sd = 0 ev sd = ε ε = 100 µv V g

van Hove singularities in the cavity suppression of linear transport due to excitation of a localized cavity phonon? dilatational modes: flexural modes: energy gap ε = 100 µev S. Debald S. Debald 3 c ε L 0 = h ε0 = 73µ ev, f0 = = 18GHz ε 0 = 145µ ev, f0 = 35GHz z h c L = 4.77 H 10 5 cm/s

Franck-Condon principle & phonon blockade electronic 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 a simple model for phonon blockade excitation of a localized cavity phonon in the electron-phonon cavity blocks single electron tunneling E.M. Weig, R.H. Blick et al., Phys. Rev. Lett. 92, 046804 (2004)

temperature dependence zero-bias conductance peaks re-appear E.M. Weig, R.H. Blick et al., Phys. Rev. Lett. 92, 046804 (2004) V sd ~ 0 mv V sd ~ 0 mv T ~ 10 mk (T el y100 mk ) T ~ 350 mk 4k B T y energy gap thermal broadening of the Fermi distribution in the leads

Coulomb blockade in a C 60 molecule single electron tunneling with strong coupling to a vibrational mode H. Park et al., Nature 407, 57 (2000) blockade

freely suspended gate-tunable 2DEG in-situ control of electronic dimensionality five independently tunable gate electrodes (plus backgate) increased control of the lowdimensional electron system dimensionality of the sample can 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 regime all gates unbiased G = di/dv sd at T = 5 K: 2D 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 3 n s = 6.25. 10 11 cm -2 µ = 5,500 cm 2 /Vs

formation of a quantum point contact depletion of gate #1 G = di/dv sd at T = 5 K: conductance quantization steps pinch-off at V g1 = -2 V 1D G = di/dv sd at T = 1.5 K: formation of magnetoelectric subbands: broadening of conductance plateaus degree of depletion can be adjusted individually under the available gates

weakly coupled quantum dot depletion of gates #1 and #3 0D G = di/dv sd at T = 1.5 K: V g1 is varied while V g3 is kept at a fixed value zero bias V sd = 0 mv curve shows Coulomb blockade oscillations variation of V g1 and V sd produces Coulomb diamonds with E C = 2.74 mev C Σ = 30 af gate-tunable free-standing quantum 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 Courtesy V. Prinz R. Blick, New J. of Physics 7, 241 (2005) online

Geometric potentials

Geometric potentials Nakul Shaji et al., Appl. Phys. Lett., in press (2006)

ACKNOWLEDGEMENTS Eva Weig & Florian Beil Jochen Kirschbaum, Tomas Krämer, Daniel Schröer University of Munich, Germany Hyun-Seok Kim, Hyun-Cheol Shin, Ryan Toonen, Nakul Shaji, Hua Qin University of Wisconsin-Madison Max Lagally, Mark Eriksson, Irena Knezevic, and Jack Ma University of Wisconsin-Madison Achim Wixforth, Armin Kriele, Jörg Kotthaus University of Munich, Germany Werner Wegscheider, Dieter Schuh Max Bichler Tobias Brandes Universität Regensburg, Germany WSI, Technical University Muich, Germany Technical University of Berlin Funding current: National Science Foundation (MRSEC/IRG1) earlier: BMBF (German Ministry of Science and Technology)