Early quantum theories of electrical conduction were semiclassical. Electrons were accelerated according to Bloch’s theorem; this was balanced by back scattering due to phonons and lattice defects. Cross sections for scattering, and band structures, were calculated quantum-mechanically, but the balancing process allowed only for occupation probabilities, not permitting a totally coherent process. Also, in most instances, scatterers at separate locations were presumed to act incoherently. Totally quantum-mechanical theories stem from the 1950s, and have diverse sources. Particularly intense concern with the need for more quantum mechanical approaches was manifested in Japan, and Kubo’s formulation became the most widely accepted version. Quantum theory, as described by the Schrodinger equation, is a theory of conservative systems, and does not allow for dissipation. The Schrodinger equation readily allows us to calculate polarizability for atoms, molecules, or other isolated systems that do not permit electrons to enter or leave. Kubo’s linear-response theory is essentially an extended theory of polarizability. Some supplementary handwaving is needed to calculate a dissipative effect such as conductance, for a sample with boundaries where electrons enter and leave (Anderson, 1997). After all, no theory that ignores the interfaces of a sample to the rest of its circuit can possibly calculate the resistance of such a sample of limited extent. Modern microelectronics has provided the techniques for fabricating very small samples. These permit us to study conductance in cases where the carriers have a totally quantum mechanically coherent history within the sample, making it essential to take the interfaces into account. Mesoscopic physics, concerned with samples that are intermediate in size between the atomic scale and the macroscopic one, can now demonstrate in manufactured structures much of the quantum mechanics we associate with atoms and molecules.

Conductance viewed as transmission

Quantum-dot-tagged reduced graphene oxide (QD-rGO) nanocomposites (left) internalized into targeted tumor cells display bright fluorescence from the QDs (right); by absorbing NIR radiation incident on the rGO and converting it into heat, they also cause simultaneous cell death and fluorescence reduction (bottom). The nanocomposite is thus capable of tumor imaging, photothermal therapy and in situ monitoring of treatment in progress.

https://ir.nctu.edu.tw:443/bitstream/11536/15766/1/000302014400012.pdf

Quantum-Dot-Tagged Reduced Graphene Oxide Nanocomposites for Bright Fluorescence Bioimaging and Photothermal Therapy Monitored In Situ

A single dopant atom can dominate the subthreshold behaviour of a field-effect transistor, and this effect is enhanced if the atom is located near a dielectric.

Single-donor ionization energies in a nanoscale CMOS channel

▪ Abstract Highly strained semiconductors grow epitaxially on mismatched substrates in the Stranski-Krastanow growth mode, wherein islands are formed after a few monolayers of layer-by-layer growth. Elastic relaxation on the facet edges, renormalization of the surface energy of the facets, and interaction between neighboring islands via the substrate are the driving forces for self-organized growth. The dimensions of the defect-free islands are of the order λB, the de Broglie wavelength, and provide three-dimensional quantum confinement of carriers. Self-organized In(Ga)As/GaAs quantum dots, or quantum boxes, are grown by molecular beam expitaxy (MBE) or metal-organic vapor phase epitaxy (MOVPE) on GaAs, InP, and other substrates and are being incorporated in microelectronic and opto-electronic devices. The use of strain to produce self-organized quantum dots has now become a well-accepted approach and is widely used in III–V semiconductors and other material systems. Much progress has been made in the ar...

Quantum dot opto-electronic devices

We report the room-temperature operating characteristics of InGaAs/GaAs self-organised quantum dot lasers grown by molecular beam epitaxy. The emission wavelength is 1.028 µm and Jth = 650 A/cm2 for a 90 µm × 1 mm broad-area laser. Steady-state and time-resolved photoluminescence measurements confirm that lasing occurs through the e1-hh2 higher-order transition, and the spontaneous recombination time for this transition is ≃ 200 ps.

Room-temperature operation of In0.4Ga0.6As/GaAs self-organised quantum dot lasers

We investigated the temperature effect on exciton localization in self‐organized InAs quantum dots Quenching energy for excitons in reference quantum well and quantum dots was found to be 2 and 7 meV, respectively Thermoactivation energy of electron‐hole emission through a GaAs barrier in the quantum dots was measured as 46 meV We observed an unusual decrease of photoluminescence peak full width at half maximum with temperature, suggesting suppression of nonpredominant size quantum dot emissions due to carrier tunneling between nearby dots

Exciton localization and temperature stability in self‐organized InAs quantum dots

We have observed a Fermi-edge singularity in the tunneling current between a two-dimensional electron gas (2DEG) and a zero-dimensional localized state. A sharp peak in the tunnel current is observed when the energy of the localized state matches the Fermi energy of the 2DEG. The peak grows and becomes sharper as the temperature is decreased to our lowest temperature of 70 mK. We attribute the singularity to the Coulomb interaction between the tunneling electron on the localized site and the Fermi sea.

Fermi-edge singularity in resonant tunneling.

We discuss the origin of zero-dimensional states, which give rise to resonant structure at the current onset in tunneling devices. The states can be identified as being due to random pairs of shallow donors.

Resonant tunneling through donor molecules.

We demonstrate that it is possible to observe transport through individual tunneling channels due to zero‐dimensional states in large area resonant tunneling devices (RTD). These localized states are found to be related to the presence of donor impurities in the vicinity of the quantum well but their binding energies are larger than that due to a single isolated hydrogenic donor. The states give rise to additional peaks in current voltage below the threshold for the main resonant peak. These peaks are visible in RTD with essentially any lateral dimension provided the current is measured with sufficient sensitivity.

Zero‐dimensional states in macroscopic resonant tunneling devices

We have investigated resonant tunnelling in GaAs/(AlGa)As heterostructures which have been fabricated into square mesas 6 x 6 mum. A delta-layer of donors (n approximately 2 x 10(9) cm-2) has been incorporated at the centre of the quantum well which is 9 nm wide. The I(V) characteristics show a feature at approximately 70 mV, which is below the threshold for the main resonance and is due to resonant tunnelling through single donor states in the well. This feature is also present in large area mesas. At lower biases and at low temperatures we see a new set of resonances which, although they occur in all small area mesas, differ in detail between devices with regard to their strength and bias position. The form of the low-bias structure is strongly dependent on temperature, T, below 4 K where several very sharp steps appear, becoming sharper as T is decreased. We have also investigated the dependence of the new structure on magnetic field, B, parallel to the current direction. We attribute the new features to tunnelling through potential fluctuations on the mesoscopic scale due to donor clustering.

N. La Scala

Papers

Exciton localization and temperature stability in self‐organized InAs quantum dots

Fermi-edge singularity in resonant tunneling.

Resonant tunneling through donor molecules.

Zero‐dimensional states in macroscopic resonant tunneling devices

Mesoscopic effects in resonant tunnelling diodes