Semiconductor Nanostructures

Basic processes responsible for the formation of quantum dot (QD) nanostructures occur on a large range of length and time scales. Understanding this complex phenomenon requires theoretical tools that span both the atomic-scale details of the first-principles methods and the more coarse-scale continuum approach. By discussing the time scale hierarchy of different elementary kinetic processes we emphasize several levels of constraint equilibrium of the system and elucidate pathways to reach corresponding stable or metastable states. Main focus is given to the InAs/GaAs material system which is the most advanced one for applying QDs in optoelectronics. First principles calculations of the potential energy surfaces by the density functional theory (DFT) gain the knowledge about potential minima corresponding to the preferred adsorption sites and barriers that govern the rates of diffusion, desorption, and island nucleation in both unstrained and strained systems. Based on these ab initio parameters, kinetic Monte Carlo (kMC) simulations have allowed a detailed theoretical description of GaAs/GaAs and InAs/InAs homoepitaxial growth and elucidated the nucleation and evolution of InAs islands on GaAs. A hybrid approach combining DFT calculations of the surface energies and continuum elasticity theory for the strain relaxation energy has given the equilibrium shape of InAs/GaAs QDs as a function of volume and explained the observed shape transitions. For the ensembles of strained QDs, the Fokker-Planck evolution equation has explained the formation of different types of metastable states in sparse and dense arrays, and the kMC simulations have proposed a tool to distinguish kinetically controlled and thermodynamically controlled QD growth. By continuum elasticity theory in elastically anisotropic semiconductor systems, transitions between vertically correlated and vertically anticorrelated growth of QD stacks has been explained, and yet another approach has been proposed to control the formation of complex nanoworlds.

Self-organized growth of InAs, InGaAs, and GaSb quantum dots in GaAs matrix is investigated to establish a basis for a targeted engineering. All studied dots form in the Stranski–Krastanow mode on a two-dimensional wetting layer in a regime which is predominantly controlled by kinetics. Equilibrium-near conditions are found on a local scale. The material transfer during dot formation shows distinct differences for the three studied kind of dots. For InGaAs and GaSb dots a pronounced transfer from an intermixed wetting layer to the dots is found. Such dots have an inhomogenous composition, and dot ensembles with a bimodal size distribution may be obtained in both cases. For InAs dots material transfer is observed solely between the purely binary dots, while the wetting layer remains unaffected and is not intermixed. Dots with a multimodal size distribution are demonstrated, referring to well-defined self-similar dot shapes and size variations in steps of integral InAs monolayers.

This chapter describes the advances achieved in the last decades for in-situ monitoring of gas phase epitaxial growth (MOVPE) with resolution down to the atomic scale. By spatial resolution electron diffraction would be the tool of choice. However, by mean free path arguments it cannot be applied in the gasphase environment of MOVPE. Optical in-situ techniques on the other hand, easy to setup, have been developed to such a level in the last decades that monolayer resolution is now possible. Even a simple single wavelength reflectance measurement can determine growth rates, composition and temperature. In-situ analysis on the submonolayer scale is routinely possible using Reflectance Anisotropy Spectroscopy (RAS). RAS is best suited to follow online the epitaxial growth evolution of surfaces, revealing surface structure and stochiometry as a function of time (ms). Doping profiling has been achieved as well by combining reflectance and RAS. The chapter closes with an outlook to the ultimate surface tool, the most recent application of a scanning tunneling microscope in MOVPE.

The fabrication of single-crystal semiconductor nanostructures which—due to their atomic-like discrete energy levels—are suitable for laser applications, has been a topic of intense research since the early 1990s (Mo et al., Phys. Rev. Lett. 65, 1020, 1990; Eaglesham and Cerullo, Phys. Rev. Lett. 64, 1943, 1990; Lott et al., Electron. Lett. 36, 1384, 2000). A drawback of the common preparation procedure of such quantum dots, namely film growth by the Stranski–Krastanow (SK) mode, is the nonuniform size distribution that broadens the optical spectra compared to quantum-well devices. We follow an alternative approach based on the growth on patterned substrates, which promises dense, uniformly sized, spatially ordered, and wetting-layer-free quantum dot arrays. This article reviews our recent studies on the nanopatterning of Si(001).

X-ray diffraction and transmission electron microscopy (TEM) provide complementary structural data on semiconductor quantum dots. While TEM characterizes single structures with atomic resolution X-ray diffraction yields information on statistical averages of large ensembles. For the work reported here, established methods were refined and some new methods were developed. Materials systems investigated were (In,Ga)As/GaAs, Ga(Sb,As)/GaAs and (Si,Ge)/Si. The composition of wetting layer and quantum dots could be quantitatively determined, showing a good agreement between quite a number of different X-ray and TEM methods. For all systems the depletion of the wetting layer and the enrichment of the strain providing species in the upper part of the quantum dot could be quantitatively analysed. For the model system (Si,Ge)/Si it was found that a ring of deep wetting layer depletion forms around the (Si,Ge)-islands. It was shown that this strain driven depletion prevents further lateral nucleation and thus eventually limits the size of the islands. A specific three-dimensional ordering of multilayered (In,Ga)As quantum dots grown on GaAs high-index surfaces was demonstrated and could be explained in the framework of elasticity theory and surface kinetics.

In this chapter, the atomic structure of both uncapped and buried quantum dots is described as derived from scanning tunneling microscopy in both top-view and cross-sectional geometry. Important conclusions are drawn also on the growth processes during quantum dot formation as well as during overgrowth. It is demonstrated that uncapped InAs quantum dots on GaAs(001) have a pyramidal shape with dominating {137} side facets and—in the case of larger dots—also {101} and {111} side facets. Buried InAs and InGaAs quantum dots, in contrast, are characterized by a truncated pyramidal shape with a (001) top facet and rather steep side facets. In addition, segregation processes during capping lead to strong intermixing and—under special overgrowth conditions—even to concave top facets or to the formation of nanovoids. Buried GaSb quantum dots are found to be much smaller, but also show a truncated pyramidal shape and strong intermixing effects. The experimental results will be discussed in the framework of the strain-induced segregation processes occurring during the different stages of quantum dot formation and overgrowth.

We employ the configuration interaction (CI) method in order to discuss many-particle properties of quantum dots as functions of the dots’ size, shape and composition. Single-particle states, necessary for the CI-basis expansion, are calculated by eight-band k⋅p theory. Special emphasis is put on the role of strain and piezoelectricity, where the latter is treated up to second order. Finally, we address the inverse problem of fitting spectroscopic data to our detailed theoretical model leading to the determination of size, shape and composition as adjustable parameters.

The acoustic phonon spectrum is significantly modified for embedded quantum dots by inhomogeneous change of material properties and intrinsic strain. The change of the local elastic properties due to strain is calculated employing density functional theory and used as input for phonon calculations within continuum elasticity model. It is demonstrated that overall the exciton–phonon coupling strength is reduced, characteristic oscillations appear in the excitonic polarization, and the spectral broadband is modified compared to a bulk phonon assumption. The zero phonon line broadening is discussed in terms of real and virtual phonon-assisted transitions between different exciton levels in a quantum dot. A microscopic theory of the excitonic multilevel system coupled to acoustic phonons is developed, and the full time-dependent polarization and absorption are calculated using the cumulant expansion. Examples are given for dephasing of optical excitations in single and vertically coupled quantum dots.

Due to their quasi-zero-dimensional structure, quantum dots show optical properties which are different from those of nanostructures with spatial confinement in less than three dimensions. In this chapter, the theory of both the linear optical properties and nonlinear dynamics of semiconductor quan- tum dots is discussed. The main focus is on the experimentally accessible quantities such as absorption/luminescence and pump-probe spectra. The results are calculated for single and coupled quantum dots (Förster coupling) as well as quantum dot ensembles. The focus is on obtaining a microscopic understanding of the interactions of optically excited quantum dot electrons with the surrounding crystal vibrations (electron–phonon coupling). The discussed interactions are important for applications in, e.g., quantum information processing and laser devices.

This chapter demonstrates the feasibility of a QD-based memory to replace today’s Flash and dynamic random access memory (DRAM). A novel memory concept based on QDs is presented, enabling very fast write times below picoseconds, only limited by the charge carrier relaxation time. A thermal activation energy of 710 meV for hole emission from InAs/GaAs QDs across an Al_0.9Ga_0.1As barrier is determined by using time-resolved capacitance spectroscopy. A hole storage time of 1.6 seconds at room temperature is measured, three orders of magnitude longer than the typical DRAM refresh time. In addition, the dependence of the hole storage time in different III–V QDs on their localization energy is determined and a retention time of more than 10 years in (In)(Ga)Sb/AlAs QDs is predicted. Therefore, a future QD-based memory will show improved performance in comparison to both DRAM and Flash having fast write/read times and good endurance.

The epitaxial growth of self-assembled CdSe/ZnSe quantum dot structures is described. Optical studies on a single-dot level uncover the fundamental electronic excitations of these quasi-zero dimensional structures and their dynamical interactions. The spin finestructure of electron–hole pairs in neutral and charged quantum dots is elaborated. Coherent control of the exciton–biexciton system is experimentally achieved by two-photon excitation. The spin dynamics of holes, electrons, and excitons is investigated. The hyperfine interaction of the electron spin with the nuclear moments of the surrounding lattice atoms is elucidated and a new type of dynamical nuclear polarization is demonstrated. The spin interactions in diluted magnetic quantum dot structures are addressed.

The presented work provides insight into MBE-growth and growth- optimization of HgSe and HgSe:Fe on different buffer/substrate systems as well as its utilization to fabricate zero-gap II–VI semiconductor quantum structures: quantum wells, quantum wires, and quantum dots. The special feature of these nanostructures is the intrinsic population of the quantum states by electrons (as many as 50–500 electrons in a single dot for example), which allows them to be directly investigated by magneto-transport measurements and infrared magneto-resonance spectroscopy in high magnetic fields up to 300 Tesla. The investigation showed strong correlation effects manifested in a 50% increase of the cyclotron mass with respect to that in a bulk structure.

Results on excitonic properties of few and many particles-complexes confined in self-organized In(Ga)As/GaAs and InGaN/GaN quantum dots (QDs) are highlighted. The renormalization of transition energies in InGaAs QDs is found to be proportional to the number of excitons per dot and in the wetting layer. Resonant Raman scattering on such dots reveals localized TO- and LO-like phonon modes being blue shifted with respect to unstrained InAs bulk modes, and a localized interface mode. The localized modes are largely independent on the structural properties of QDs within different samples. Embedding InAs QDs in an InGaAs well shifts the QDs’ emission to lower energies. The reduction of strain is identified as the main reason for this redshift. Binary InAs/GaAs dot ensembles show a distinct formation of subensembles due to self-similar shapes and height variations in steps of integral InAs monolayers. A decreasing number of excited states with decreasing QD size is observed. Spectra of individual dots in such ensembles reveal a biexciton binding energy changing from binding to antibinding as the size of the dots decreases. The trend is well explained by a varying number of bound hole states. Furthermore, a monotonous decrease of the exciton fine-structure splitting with QD size from large values of 0.5 meV to small and even negative values is found, highlighting the effect of piezoelectricity. For nitride structures a clear proof of the quantum-dot nature is provided by resonantly excited time-resolved photoluminescence. Single InGaN QD emission-lines show a pronounced linear polarization, which is attributed to the valence band structure of the wurtzite type nitrides.

This chapter summarizes our recent work—performed within the project B6 of the Sonderforschungsbereich 296—on combining ultrafast spectroscopy and near-field microscopy to probe the nonlinear optical response of a single quantum dot and of a pair of dipole-coupled quantum dots on a femtosecond time scale. We demonstrate coherent control of both amplitude and phase of the coherent quantum dot polarization by studying Rabi oscillations and the optical Stark effect in an individual interface quantum dot. By probing Rabi oscillations in a pair of laterally coupled interface quantum dots, we identify couplings between excitonic dipole moments and reveal the microscopic origin of these couplings. Our results show that although semiconductor quantum dots resemble in many respects atomic systems, Coulomb many-body interactions can contribute significantly to their optical nonlinearities on ultrashort time scales. This is important for realizing potentially scalable nonlocal quantum gates in chains of dipole-coupled dots, but also means that decoherence phenomena induced by many-body interactions need to be carefully controlled.

Single photons from single quantum dots have already found their way into many important realizations in quantum information processing. In this chapter, we review several demonstrations using a deterministic single-photon source based on InP/GalnP quantum dots. Single-photon generation is described and verified by auto-correlation measurements. Additionally, photon pairs and triplets from multi-exciton cascades are observed. Using a Michelson interferometer, an efficient separation of photon pairs can be achieved allowing multiplexing on the single-photon level. We also show the generation of non-classical states of light from electrically pumped quantum dots. The applicability of our sources in quantum information experiments is demonstrated in quantum key distribution and in a realization of a two-qubit Deutsch-Jozsa algorithm which uses different degrees of freedom of a single photon. By encoding the quantum information in appropriate bases, we implement passive error correction in the presence of phase fluctuations.