Picosecond time-resolved transport studies in a two-dimensional electron system [Elektronische Ressource] / vorgelegt von Denis Maryenko

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• Physik

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2010
• Nombre de lectures: 26
• Poids de l'ouvrage: 8 Mo

Extrait

Picosecond time-resolved transport studies
in a two-dimensional electron system
Von der Fakultät Mathematik und Physik der Universität Stuttgart
zur Erlangung der Würde eines Doktors der Naturwissenschaften
(Dr. rer. nat.) genehmigte Abhandlung
vorgelegt von
DENIS MARYENKO
aus Kiew, Ukraine
Hauptberichter: Prof. Dr. K. v. KLITZING
Mitberichter: Prof. Dr. H. GIESSEN
Tag der Einreichung: 25. Februar 2010
Tag der mündlichen Prüfung: 26. März 2010
MAX-PLANCK-INSTITUT FÜR FESTKÖRPERFORSCHUNG
STUTTGART, 2010Contents
Symbole und Abkürzungen 4
1 Introduction 6
2 Experimental Method and Technique 1
2.1 Metal–Semiconductor–Metal–Switch . . . . . . . . . . . . . . . . . . . . . . 1
2.2 Coplanar waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Sampling technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.5 Experiments on pulse propagation along CPW . . . . . . . . . . . . . . . . . . 6
2.5.1 CPW with a bent parasitic waveguide . . . . . . . . . . . . . . . . . . 8
2.6 Sample Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.7 Coplanar waveguide with four switches . . . . . . . . . . . . . . . . . . . . . 13
3 DC-Experiment 19
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Quantum Point Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Caustic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Transverse magnetic focusing device . . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Corner Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.7 Numerical transport simulation in disorder-free landscape . . . . . . . . . . . . 28
3.8 Numerical transport simulation in disordered landscape . . . . . . . . . . . . . 29
3.9 Comparison of experimental results with simulation . . . . . . . . . . . . . . . 31
3.10 Ballistic cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Time Resolved Experiments 39
4.1 Time-dependent measurement on a corner device . . . . . . . . . . . . . . . . 39
4.1.1 Gate defined corner device . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.2 Etched corner device . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Time-dependent transport on a stripe of the 2DES . . . . . . . . . . . . . . . . 44
4.2.1 Plasmon modes in 2DES . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Fourier spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.3 140μm long stripe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Pulse propagation velocity in a stripe . . . . . . . . . . . . . . . . . . . . . . . 62CONTENTS 3
4.4 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Correlation of electrical pulses on a 2DES 67
5.1 Idea behind the electrical pulse correlation technique . . . . . . . . . . . . . . 67
5.2 Correlation in magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Excitation spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Summary and Outlook 75
A Calculations for CPW 87
B Fiber Alignment and Gluing 89
C Sample Fabrication 91
C.0.1 Mesa definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
C.0.2 Ohmic contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
C.0.3 Alignment marks for ebeam lithography . . . . . . . . . . . . . . . . . 93
C.0.4 Pads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
C.0.5 Coplanar waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
C.0.6 Three-chip assemble . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Acknowledgements 103Symbol table
2DES two-dimensional electron system
B strength of the magnetic field
CF composite fermion
CPW coplanar waveguide
LT-GaAs low temperature grown GaAs
MSM switch metal-semiconductor-metal switch
TMF transverse magnetic focusing
QPC quantum point contact
c velocity of light in vacuum
E Fermi energyF
ω electron cyclotron resonance frequencyc
ω plasmon frequency in zero magnetic fieldp
ω magnetoplasmon frequency in the magnetic fieldmpChapter 1
Introduction
The discovery of the Integer and Fractional Quantum Hall Effects [1, 2] inspires the research
in semiconductor electron systems confined to two dimensions already for 30 years. While
a picture of non-interacting electrons is sufficient to explain the Integer Quantum Hall Effect
(IQHE) [3,4], electron-electron interaction effects are essential for the Fractional Quantum Hall
Effect (FQHE) [5]. For an intuitive understanding of the FQHE, J. Jain introduced the concept
of Composite Fermions [6]. These are quasi-particles, each of which is assembled from one
electron and two magnetic flux quanta pointing opposite to the perpendicularly applied mag-
netic field. Within this framework, the FQHE can be understood as the IQHE of Composite
Fermions (CF) in an effective magnetic field, which is zero at the Landau level filling factor
1/2. Furthermore, Halperin et al. predicted the existence of the Fermi surface for CFs [7].
This led to the experiments which are analog to the experiments for the electron systems at low
magnetic field; the commensurability oscillations in periodic structures and transverse magnetic
focusing for CFs were demonstrated [8, 9]. Composite Fermions precess, like electrons, along
circular cyclotron orbits with a diameter given by the effective magnetic field. The frequency
of the cyclotron motion is determined by the effective mass, which is no longer related to the
conduction band properties of the host material, but is governed entirely by Coulomb interac-
tions. Kukushkin et al. devised an experiment to measure the cyclotron resonance for CFs, from
which the effective mass could be extracted [10].
An alternative approach to measure the mass of CFs is to perform time resolved trans-
port experiments for CFs in ballistic regime. The measurement of the transit time in a well
defined structure, e.g. transverse magnetic focusing device, provides information about the
quasi-particle dispersion, Fermi velocity and mass. For samples based on the well established
GaAs/AlGaAs heterostructure such measurements require subkelvin temperature and high mag-
netic field. Furthermore, the transient time of CFs in transverse magnetic focusing device is
expected to be on the order of 10 ps. Therefore, the experimental arrangement for time resolved
transport experiment has to fulfill several requirements:
• picosecond time resolution in order to access the characteristic transit time scales
• compatibility with the cryogenic environment
• applicability of high magnetic field.7
These requirements exclude all-electronic means and the use of the coaxial cables. They are,
however, conformed when using an all-on-one-chip photoconductive sampling technique. Here,
we make use of photoconductive switches that are operated by femtosecond laser pulses guided
via optical fibers. The switches are positioned in the vicinity of the device under study and act
as a source of electrical pulses as well as a detector of the ultrafast signal that probed the device
under study. Propagation of the pulses proceeds across a coplanar waveguide.
This thesis is an intermediate step toward ballistic time resolved transport experiments for
CFs and ties in with the work of our predecessor Martin Griebel [11], who worked out the
photoconductive sampling technique in our group. The scope of the thesis reaches from the in-
troduction and the demonstration of the photoconductive sampling technique, over DC transport
experiments in several ballistic devices, which are suitable for time resolved studies, to the ap-
plication of the time resolved photoconductive sampling technique to investigate the excitation
of the two-dimensional electron system.
The thesis is organized into four main chapters:
• Chapter 2 Photoconductive sampling technique is the basis for the time resolved trans-
port experiments. We introduce the photoconductive switches which are used to generate
short electrical pulse and to detect the ultrafast signal. We demonstrate that the electrical
pulses can be launched into the coplanar waveguide and be detected several millimeters
away from the source.
• Chapter 3 We perform DC transport experiment on ballistic devices, which can be em-
ployed for ballistic time resolved experiments. These devices are corner device and dif-
ferent cavity geometries. A large part of the chapter is devoted to the experiments in the
corner device, as it has surprisingly allowed to observe the branched electron flow in a
conventional DC transport experiment.
• Chapter 4 Time resolved transport experiments are performed in a corner geometry and
on a stripe of a two-dimensional electron system. We observed the excitation of various
modes of magnetoplasmon and measured the pulse propagation velocity in the stripe. The
experiments are performed for stripes of different length and for two values of electron
density in the stripe.