There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The interest in nanoscale materials stems from the fact that new properties are acquired at this length scale and, equally important, that these properties * To whom correspondence should be addressed. Phone, 404-8940292; fax, 404-894-0294; e-mail, mostafa.el-sayed@ chemistry.gatech.edu. † Case Western Reserve UniversitysMillis 2258. ‡ Phone, 216-368-5918; fax, 216-368-3006; e-mail, burda@case.edu. § Georgia Institute of Technology. 1025 Chem. Rev. 2005, 105, 1025−1102

Chemistry and properties of nanocrystals of different shapes.

Quantum dot (QD) solar cells have the potential to increase the maximum attainable thermodynamic conversion efficiency of solar photon conversion up to about 66% by utilizing hot photogenerated carriers to produce higher photovoltages or higher photocurrents. The former effect is based on miniband transport and collection of hot carriers in QD array photoelectrodes before they relax to the band edges through phonon emission. The latter effect is based on utilizing hot carriers in QD solar cells to generate and collect additional electron–hole pairs through enhanced impact ionization processes. Three QD solar cell configurations are described: (1) photoelectrodes comprising QD arrays, (2) QD-sensitized nanocrystalline TiO 2 , and (3) QDs dispersed in a blend of electron- and hole-conducting polymers. These high-efficiency configurations require slow hot carrier cooling times, and we discuss initial results on slowed hot electron cooling in InP QDs.

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Quantum dot solar cells

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

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Spins in few-electron quantum dots

Adding optical functionality to a silicon microelectronic chip is one of the most challenging problems of materials research. Silicon is an indirect-bandgap semiconductor and so is an inefficient emitter of light. For this reason, integration of optically functional elements with silicon microelectronic circuitry has largely been achieved through the use of direct-bandgap compound semiconductors. For optoelectronic applications, the key device is the light source--a laser. Compound semiconductor lasers exploit low-dimensional electronic systems, such as quantum wells and quantum dots, as the active optical amplifying medium. Here we demonstrate that light amplification is possible using silicon itself, in the form of quantum dots dispersed in a silicon dioxide matrix. Net optical gain is seen in both waveguide and transmission configurations, with the material gain being of the same order as that of direct-bandgap quantum dots. We explain the observations using a model based on population inversion of radiative states associated with the Si/SiO2 interface. These findings open a route to the fabrication of a silicon laser.

Optical gain in silicon nanocrystals

Using a micron-sized photoluminescence (PL) probe enables us to study single islandlike interface defects of a thin GaAs/AlGaAs quantum well. The bound exciton ground state locally emits a distinct sharp line. With increasing excitation of this quantum dot level additional transition lines emerge at lower energy. They are attributed to localized biexciton states. The biexciton correlation energy is about 4 meV. A distinct two-photon resonant absorption peak of the biexciton ground state is observed in PL excitation spectroscopy. Its linewidth is only about 30 \ensuremath{\mu}eV. The spectra and their polarization properties are discussed on the basis of a discrete level scheme and the Pauli exclusion principle.

Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure.

The photoluminescence of excitons confined in an electric field tunable coupled AlAs/GaAs quantum well has been investigated at $T\ensuremath{\ge}350$ mK and magnetic fields $H\ensuremath{\le}14$ T. In the indirect regime where electrons and holes are separated both in real and in $k$ space, the magnetic field was found to result in (i) a strong change of both the photoluminescence intensity and decay time which is attributed to anomalies in the exciton transport and (ii) an appearance of a huge broad band noise in the photoluminescence intensity which is evidence for exciton condensation.

/pdf/condensation-of-indirect-excitons-in-coupled-alas-gaas-11g2u22cap.pdf

Condensation of indirect excitons in coupled AlAs/GaAs quantum wells.

The dynamics of photogenerated carriers in semiconductor structures with reduced dimensionality has been the subject of intensive investigations in recent years [1,2]. State-of-the-art band-gap engineering technologies enable us to tailor low-dimensional semiconductor systems with desirable optoelectronic properties and study the fundamental aspects of carrier dynamics. This has increased tremendously our fundamental understanding of the dynamic properties of artificial semiconductor structures and has also resulted in a wide range of novel devices such as quantum well lasers, modulators, and detectors, as well as all-optical switches. Nevertheless, the bulk band structure of semiconductors seems to dominate optoelectronic properties since the strength of interband transitions is largely governed by the atomiclike Bloch parts of the wave function [3]. Thus it appears at first glance unavoidable that strong interband optical transitions are linked to direct band-gap semiconductors with short radiative lifetimes such as GaAs, whereas long radiative lifetimes of photogenerated carriers imply utilization of semiconductors with indirect band gaps such as Si and correspondingly reduced interband absorption. Initial attempts to employ band-gap engineering in order to combine strong interband absorption with long radiative lifetimes have focused on so-called doping superlattices [4]. There, alternate n and p doping along the growth direction is utilized to combine a direct gap in momentum space with an indirect gap in real space which causes a spatial separation of photogenerated electron-hole se-hd pairs and hence considerably prolonged lifetimes. Here, we introduce a new way of band-gap engineering in which we expose a semiconductor quantum well of a direct gap material to a moving potential superlattice modulated in the plane of the well. We show that the confinement of photogenerated e-h pairs to two dimensions, together with the moving lateral superlattice, allows reversible charge separation [5]. We demonstrate that the combination of both the advantages of strong interband absorption and extremely long lifetimes of the optical excitations is achieved without affecting the superior optical quality of the quantum well material. The spatial separation of the electron-hole pairs is achieved via the piezoelectric potential of acoustic waves propagating along the surface of a semiconductor quantum well system. On a piezoelectric substrate, the elliptically polarized surface acoustic waves (SAWs) are accompanied by both lateral and vertical piezoelectric fields which propagate at the speed of sound. Those fields can be strong enough to field ionize optically generated excitons and to confine the resulting electrons and holes in the moving lateral potential wells separated by one-half wavelength of the SAW. The spatial separation dramatically reduces the recombination probability and increases the radiative lifetime by several orders of magnitude as compared to the unperturbed case. We further demonstrate that the dynamically trapped electron-hole pairs can be transported over macroscopic distances at the speed of sound and that deliberate screening of the lateral piezoelectric fields of the SAW leads to an induced radiative recombination after long storage times at a location remote from the one of e-h generation. This conversion of photons into a long lived e-h polarization which is efficiently reconverted into photons can serve as an optical delay line operating at sound velocities. The undoped quantum well samples used in our experiments are grown by molecular beam epitaxy on a (100)GaAs substrate. The quantum well consists of 10 nm pseudomorphic In0.15Ga0.85As grown on a 1 mm thick GaAs buffer and is covered by a 20 nm thick GaAs cap layer. The active area of the sample is etched into a 2.5 mm long and 0.3 mm wide mesa (see inset of Fig. 1) with two interdigital transducers (IDTs) at its ends. The IDTs are designed to operate at a center frequency fSAW › 840 MHz. They are partially impedance matched to the 50 V radio frequency (rf) circuitry using an on-chip matching network, thus reducing the insertion

https://arxiv.org/pdf/cond-mat/9704029.pdf

Acoustically Driven Storage of Light in a Quantum Well

Isolated single quantum dots of different size have been fabricated by laser-induced local interdiffusion of a GaAs/AlGaAs quantum-well structure. Microscopic photoluminescence (PL) reveals a splitting and a blueshift, which depend systematically on dot size. The distinct PL peaks separated in energy by up to 10 meV are attributed to recombination between zero-dimensional (0D) electron and hole states. Complete quantization and inherent exclusion of inhomogeneous broadening in a single dot structure cause PL linewidths below 0.5 meV. The strength of the higher-energy transitions indicates the slowed energy relaxation theoretically predicted for 0D systems.

Photoluminescence from a single GaAs/AlGaAs quantum dot

We report about optical experiments on electric field tunable AlAs/GaAs coupled quantum well structures in the regime of the electric field induced \ensuremath{\Gamma}-X transition. Using the energetically tunable X-point state in the AlAs layer as an internal energy spectrometer and charge reservoir we are able to map out the electronic states in the neighboring GaAs quantum well in great detail. In spatially resolved and bias voltage dependent photoluminescence experiments we find sets of extremely narrow emission lines below the fundamental band gap energy of the GaAs quantum well. The new emission lines are shown to originate from natural quantum dots which are formed by well width fluctuations of the GaAs quantum well.

G. Böhm

Papers

Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure.

Condensation of indirect excitons in coupled AlAs/GaAs quantum wells.

Acoustically Driven Storage of Light in a Quantum Well

Photoluminescence from a single GaAs/AlGaAs quantum dot

Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures.