Organization of This Dissertation - 自組式第一型量子環與第二型量子點之磁場光學研究

Chapter 1: Introduction

1.4 Organization of This Dissertation

In this dissertation, we study the magneto-optical properties of several quantum structures with ring-like carrier wave functions, such as the InAs/GaAs QRs, the GaSb/GaAs QDs, and the GaAs/GaSb QDs. The experimental techniques used are described in chapter 2, including MBE growth, material characterization methods, and magneto-photoluminescence measurement techniques.

In chapter 3, the diamagnetic response of the ground-state neutral excitons and biexcitons confined in single self-assembled QRs is investigated. The diamagnetic coefficient of the biexcitons is considerably larger than that of the excitons. We found that the inherent structural asymmetry and imperfection of the QR play a crucial role in the distribution of X and XX wave function. Our results suggest that the phase coherence of neutral excitons, i.e.

the Aharonov-Bohm effect, in QRs is smeared out due to the structural asymmetry.

In chapter 4, we report the magneto-photoluminescence measurement results on type-II self-assembled GaSb/GaAs quantum dots with the magnetic field applied in Faraday and Voigt configurations. When the magnetic field was in the Voigt configuration, an unusual red shift in the emission peak accompanied with a rapid increase of the PL intensity was observed.

This anomalous red shift is attributed to the reduction of the vertical e-h separation and the resulting increase of the radiative e-h recombination rate in the magnetic fields applied in the Voigt configuration.

In chapter 5, we study the magneto-optical properties of GaAs QDs in GaSb matrix. As the size of the QDs is changed, an unusual correlation was found between the diamagnetic coefficient and the emission energy. We attributed this phenomenon to the weak localization of electrons within the small-sized QDs in the tensily-strained system.

In chapter 6, we model the magnetic response of the GaSb/GaAs QDs with AlGaAs vertical confinement layers. Aharonov-Bohm oscillation is clearly observed in the calculation.

Finally, conclusions and a plan for future work are given in chapter 7.

Chapter 2 Experimental Techniques

In this chapter, the used experimental techniques in this study are briefly described. The samples studied in this dissertation were all grown by the molecular beam epitaxy (MBE) system. The structural properties of the semiconductor nanoscale objects in the samples were characterized by the atomic force microscopy (AFM) or transmission electron microscopy (TEM). The optical properties, the magnetic response, and the electronic structures were investigated by the photoluminescence (PL), magneto-PL, and micro-PL (μ-PL) techniques.

2.1 Molecular Beam Epitaxy

The molecular beam epitaxy (MBE) is a physical deposition process in an ultra-high vacuum (UHV) environment. The reactive molecules are able to directly strike the substrate without any scattering because the mean free path of the molecules is longer than the distance between the sources and the substrate. The deposition amount is therefore well controlled, and the layer structures with precise thickness and abrupt interfaces can be achieved. The UHV Gen II (solid-source based) system. Each system comprises three chambers: entry/exit chamber, buffer chamber, and growth chamber as drawn in Fig 2.1. Two gate valves are used to isolate these three chambers. In order to maintain UHV, all the pumping machines are oil

free to reduce the contamination. A turbo-molecular pump cascaded by a scroll pump is used for rough pumping. Besides, a cryo-pump, an ion-pump, and a titanium-sublimation pump (TSP) are used in the growth chamber, an ion-pump and a TSP are used in the buffer chamber, and a cryo-pump is used in the entry/exit chamber for UHV pumping. In addition, a liquid-nitrogen-cooled cryo-panel is installed within the growth chamber to improve the vacuum level during growth and eliminate the thermal cross-talk between different cells.

FIG. 2.1. Drawing of the Veeco Gen II MBE system in our lab.

The Varian Gen-II system is named as Lm-MBE and is used for arsenide-based III-V materials with high epitaxy quality. Eight effusion cells are equipped on the Lm growth chamber. Two gallium (Ga) cells, one indium (In) cell and one aluminum (Al) cell are used for group III sources. One arsenic (As) valved cracker cell and one arsenic Kunsden cell are used for group V sources. Besides, one silicon (Si) cell and one beryllium (Be) cell are used for n-type doping and p-type doping, respectively. The Veeco Gen-II system is named as Rn-MBE and provides the growth of antimony related III-V materials. In addition to the sources in Lm-MBE, one antimony (Sb) valve cracker cell for another group V source and one tellurium (Te) cell for n-type doping in GaSb material are added in Rn-MBE.

2.1-2 In-situ analysis instruments

Two analysis instruments, the residue gas analyzer (RGA) and the reflection high-energy electron diffraction (RHEED) monitor, are also equipped in each growth chamber. The RGA is used to analyze the residue gas in the chamber for understanding the cleanness in the chamber. The RGA also serves as a sensitive leakage detector by helium (He) gas leakage detecting. The RHEED allows us to in-situ monitor the sample surface condition during the epitaxy. The high energy electron beam with a very small angle strikes the surface of the sample, and the reflective beam builds a reconstruction structure on the screen. The reconstruction structure represents the diffraction patterns and indicates the surface morphology. For example, the clear streaky RHEED pattern indicates a clean oxide free surface with excellent flatness as depicted in Fig 2.2 (a), and a spotty RHEED pattern represents a 3-dimensional structure is formed, such as the quantum dots (QDs) as shown in Fig. 2.2(b).

FIG. 2.2. RHEED patterns of (a) GaAs epi-layer and (b) GaSb QDs on GaAs substrate.

2.1-3 Growth condition

The structural properties and the crystal quality of the epitaxial material are determined by the growth temperature, the growth rate, and the V/III BEP ratio. The V/III BEP ratio is the beam equivalent flux pressure ratio of the group V beam flux to the group III one. Generally, the suitable growth temperature is around 580 °C for GaAs, 500 °C for InAs, and 500 °C for GaSb. The typical V/III ratio for Stranski-Krastanov mode quantum dot formation is 10~20 for III-arsenic and 1~5 for III-antimonide. To ensure the epitaxial quality and flatness of the epi-layers, the suitable growth parameters are necessary. Besides, for 3-D quantum structures, such as the InAs and GaSb self-assembled quantum dots (SAQDs), the size, the composition, the strain distribution, and the sheet density of the QDs are highly dependent on these parameters. In general, high growth temperature, low growth rate, and low V/III BEP ratio enhance the mobility of deposited atoms on the sample surface, which increases the QD size and reduces the QD density. The growth of the QDs with ultra-low dot density of < 1x10⁸ cm^-2 for single dot spectroscopy can be achieved on this growth condition.

2.2 Structure Characterization

The geometry of the nanoscale objects is able to be analyzed by the atomic force microscopy (AFM) and transmission electron microscopy (TEM) techniques. AFM is a fast and non-destructive method for surface structure characterization due to the minimal sample preparation. TEM is a powerful tool to observe the quantum structures embedded inside the sample with extremely high resolution. Note that the dimension of the embedded structures is somewhat different from that of the surface structures due to the strain from the capping layer.

2.2-1 Atomic force microscope

The AFM system mainly consists of a cantilever with a sharp tip on the end. The cantilever is vibrated by a piezoelectric ceramic with the frequency close to its resonant frequency. The van der Waals force between the AFM tip and the sample surface will dump the oscillation of the cantilever. Since this force is sensitive to the distance between the AFM tip and the sample surface, the surface topography can be detected by scanning the sample and recording the oscillation amplitude.

The AFM is performed for QDs (and QRs) by a Veeco D3100 commercial system in tapping mode in our study. The QDs with the same growth condition as the embedded QDs is grown on the sample surface for AFM measurement. The sheet density, geometry, size, and the uniformity of the surface QDs can be obtained by the AFM. However, the size of the surface QDs is expected to be different from the embedded QDs. For the common compressively strained QD system, InAs QDs in GaAs matrix, the embedded QDs are expected to be smaller than the surface QDs due to the compressive strain from the capping layer. Besides, the AFM resolution is limited to around 2-10 nm by the AFM tip, which also makes the AFM overestimate the size of the QDs.

2.2-2 Transmission electron microscope

Unlike the AFM, the TEM technique needs complicated sample preparation procedure which takes much time. However, TEM images directly represent the geometry of the embedded quantum structures with high magnification. The resolution is determined by the matter wavelength of the high energy electrons and is able to reach 1-2 Å . The image brightness is determined by the intensity of those electrons transmitted through the sample to the detector. Dislocation, strain field, and heavy elements in the crystalline specimen cause more electron scattering and lead to darker images in bright-field images. Therefore, the variation of the strain, element mass, and the thickness leads to the contrast of the TEM images.

In this study, the TEM images are taken by JEOL 2010F TEM system operated at 200 keV. The cross-sectional and plan-view specimens are prepared by mechanical polishing and further thinning in a Gatan 691 ion mill along the [010] and [001] zone axis, respectively. The thickness of the prepared samples should be a few tens to a few hundred nm to be transparent for the electrons. The cross-sectional images reveal the geometric shapes of the QDs, and the plan-view images are used to estimate the sheet density and the average diameter of the QDs.

2.3 Photoluminescence Spectroscopy

The photoluminescence (PL) spectroscopy is used to investigate the electronic band structure and the crystal quality of our samples. Since all these III-V semiconductor quantum structures grown in our study are direct bandgap materials, the radiative recombination of electron-hole pairs is efficient enough for PL measurement. The samples are excited by an optical source with the photon energy hν larger than the bandgap of the barrier materials.

Electron-hole pairs (e-h pairs) are generated in the barriers. After a series of carrier thermalization process (including diffusion, capture, and relaxation), the spontaneous emission from the designed quantum structure occurs due to the radiative e-h recombination

and is analyzed by a set of detection system (including a monochromator and an optical detector).

In this study, three homemade PL systems are used for different aims. The conventional PL is used for the preliminary characterization of a mass of samples. The micro-PL is able to measure single QD or QR in magnetic fields up to 6 Tesla. The high-magnetic-field PL supplies the magnetic field up to 14 Tesla for the magneto-optical study at high field. For each system, the temperature of the measured samples can be cooled down to below 20 K in order to enhance emission intensity and reduce the thermal noise.

2.3-1 Conventional photoluminescence setup

The conventional PL is a convenient tool to investigate the fundamental optical properties of the semiconductor quantum structures, such as the emission energy, the PL intensity, the full width in half maximum (FWHM), the excitation power dependence, and the temperature dependence.

For conventional PL measurement, a mass of samples can be simultaneously mounted in a helium close-cycled cryostat, where the sample temperature can be controlled from 13K to room temperature. As depicted in Fig 2.3, the excitation source for conventional PL is an argon laser with wavelength of 514.5 nm. The luminescence of the sample is collected by a couple of plano-convex lenses, dispersed by a 550 mm monochromator, and detected by a thermal-electric cooled InGaAs (detection wavelength form 750 nm to 1750 nm) or an wavelength extended InGaAsSb (from 1750 nm to 2600 nm) photodiode. Via modulating the laser beams by a mechanical chopper, the emission signal is also modulated, and the lock-in amplifier is used to enhance the signal with the same modulation frequency and greatly improve the signal-to-noise ratio.

FIG. 2.3. The conventional PL system setup.

2.3-2 Micro-photoluminescence setup

By a 100 times long-working-distance objective lens, the spot size of the excitation beam can be focused down to only ~1.5 µm in this micro-PL system. The small spot size can provide ultra-high excitation power density to observe the emissions of the high-lying excited states in the QDs (or QRs). Besides, it allows the most important application, single QD spectroscopy. Sharp emission peaks from the single 3-D confined quantum system (QD and QR) can be observed in the single QD spectroscopy due to the delta-function-like density of states. The PL line width of single dot is limited by the system resolution (~50 µeV). By

eliminating the nonhomogeneous broadening, the fine structure of a single QD can be clearly distinguished and be further studied with magnetic fields applied parallel to the sample growth direction.

For micro-PL measurement, few samples are simultaneously mounted in a helium flow cryostat, where the sample temperature maintains at 10K. As depicted in Fig 2.4, the excitation source is a He-Ne laser with wavelength of 633 nm, and the excitation beam is focused by an objective lens. The luminescence of the sample is collimated by the same objective, dispersed by a 750 mm monochromator, and detected by a silicon charged coupled device camera (CCD) with the detection wavelength from 400 nm to 1000 nm. This silicon CCD contains 1024 x 256 pixels and is able to generate a spectrum without rotating the grating. The lock-in technique is unavailable for the CCD detection system.

In order to excite one QD only, an aluminum metal shadow mask with arrays of 300 nm diameter apertures is placed on the sample surface to isolate other QDs. Moreover, a very low dot areal density (about 1x10⁷ – 1x10⁹ cm^-2) is also necessary to reduce the dot number inside the aperture. Since this dot density is less than 1/10 of the usual density (about 1x10¹⁰ cm^-2), the control of the growth condition (including the deposited amount of the dot material, the growth temperature, and the growth rate) is very critical for the kind of QD formation.

Fig. 2.4. The micro-PL system setup.

2.3-3 High-magnetic-field photoluminescence setup

In atomic physics, the magnetic field is usually applied to observe and analyze the splitting of the spectrum lines of atoms. The magnetic response reflects the orbital magnetic quantum number, the spin magnetic quantum number, and the spatial distribution of the excitonic wave function. Since the 0-D quantum dots and rings reveal the atom-like electronic structures, the magneto-PL can be used to study the excitonic fine structure states and the carrier wave function spatial extent of them.

For high-magnetic-field PL measurement, the sample is individually measured in an Oxford variable temperature insert (VTI) system with a base temperature about 1.4 K. A superconducting magnet provides a tunable and uniform magnetic field of up to 14 Tesla. The excitation source is a 532 nm Nd:yttrium aluminum garnet (YAG) laser or a wavelength-tunable Ti-sapphire laser ranging from 700 to 1000 nm. The latter is used for the photoluminescence excitation (PLE) measurement. A fiber bundle is used to couple the excitation source to excite the sample and collect the PL signal to the detection system.

Two designs of fiber bundles are shown as the inset in Fig 2.5. The simple one, design A, has a much larger laser spot size with diameter of around 4 mm and hence a much smaller excitation density. With a 45° Au-plated mirror, the magneto-PL can be performed in Voigt configuration (the magnetic field is applied perpendicular to the growth direction) as shown in the inset A-2. In order to improve the excitation power, another fiber bundle with a focusing lens, design B, reduces the laser spot size to 0.5 mm. The 30° tilted incident laser beam also minimizes the collection of laser beam to the detection system, which is important for the PLE measurement. However, due to the complicated and fixed design, the magneto-PL measurement in Voigt configuration is invalid for design B.

FIG. 2.5. The high-magnetic-field PL system setup.

Chapter 3 Impacts of Structural Asymmetry on the Magnetic Response of Single Self-Assembled In(Ga)As Quantum Rings

In this chapter, the diamagnetic shifts of neutral excitons and biexcitons confined in single self-assembled In(Ga)As/GaAs quantum rings are investigated. Unlike quantum dots, quantum rings reveal a considerably large biexciton diamagnetic shift, about two times larger than that of single excitons. Based on model calculations, we found that the inherent structural asymmetry and imperfection, combined with the inter-particle Coulomb interactions, is the fundamental cause of the more extended biexciton wave function in the quantum rings. The exciton wave function tends to be localized in one of the potential valleys induced by structural imperfections of the quantum ring due to the strong localization of hole and the electron-hole Coulomb attraction, resembling the behavior in single dots. Our results suggest that the phase coherence of neutral excitons in quantum rings will be smeared out by such wave function localizations.

3.1 Introduction

Charged particles confined to a nanoscopic quantum ring (QR) are expected to show unique magnetic responses, i.e., the well-known Aharonov-Bohm (AB) effect, due to the quantum interference of the carrier’s wave function in the ring-shaped geometry.

Experimental evidence of such a purely quantum mechanical effect has been observed in metallic and semiconductor mesoscopic rings [23-26] and recently in nanoscopic QRs [27-29].

On the other hand, the exciton properties in ring-like nanostructures also gained a lot of interest recently. Because an exciton is a charge-neutral composite, the AB effect is not expected to occur unless the electron and hole can propagate coherently in different

trajectories with a nonzero electric dipole moment [30]. Such a case appears naturally in type-II quantum dot (QD) systems [7, 8], where the electron and hole are spatially separated, resembling the behavior of single charges. However, for nanoscopic rings, such as InGaAs self-assembled QRs formed via partial capping of InAs QDs and subsequent annealing [13, 31], it is still an open question whether the excitonic AB effect can be observed when both the electron and hole are confined in the rings. In fact, this issue is further complicated by the inherent structural asymmetry and imperfections presented inevitably in self-assembled QRs.

Although it has been demonstrated both experimentally and theoretical that the phase coherence of electron wave function in self-assembled QRs could survive [29], the impacts of inherent structural asymmetry and imperfection on the magnetic response of neutral excitonic species, such as excitons (X) and biexcitons (XX) with the presence of Coulomb interactions, have yet to be investigated.

In this work, we report the diamagnetic response of X and XX in single self-assembled QRs. Unlike single QDs, the XX confined in single QRs shows a considerably larger diamagnetic coefficient than the X. Guided by numerical model calculations, we found that the inherent structural asymmetry and imperfection, combined with the inter-particle Coulomb interactions, play a crucial role in the distribution of X and XX wave function in self-assembled QRs. Our results suggest that the phase coherence of neutral excitons in QRs will be smeared out by the wave function localization due to the structural asymmetry and imperfections.

3.2 Growth Condition

The InAs QRs were fabricated by Varian Gen-II molecular beam epitaxy (MBE) on a

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