Raphael Tsu

Optical Properties and Raman Scattering in Man-Made Quantum Systems

This chapter describes the optical properties and Raman scattering in man-made quantum systems. Alternate layers of materials with different masses, force constants, and effective ionic charges result in a superlattice that has interesting optical properties that are due to the interactions of photons and optical phonons. Photon conductivity serves as a powerful technique for characterizing the optical and transport properties of a superlattice and quantum well (QW). The folding of the dispersion in the regular Brillouin zone (BZ) into minizones (MZs) for a superlattice describes most of the important features of the man-made superlattice. These features include the formation of minibands, localization with large gaps between minibands, Bragg reflection giving rise to Bloch oscillation, and the foundation of the appearance of negative differential resistance (NDR). The reciprocal space for phonons is exactly the same as for the electrons because the real space and reciprocal space are determined by the structure. Results indicate that it is possible to probe the acoustic and optical phonon branches for large momenta by sandwiching a given material between potential barriers. In fact, as far as Raman scattering is concerned, a perfect periodic structure is not necessary, as long as all well widths are kept reasonably constant. This is due to the relative broadness of the spectra. The chapter presents two cases that serve as a model for understanding Raman scattering where wave functions are localized.

Quantum Step and Activation Energy

This chapter studies quantization with a quantum step. It develops ways to calculate the density of states (DOS) of quantum steps allowing scientists to sum the optical transitions and correlate them with the photo reflectance measurements. New understanding relating to band-edge alignment may be studied with quantum steps. In particular, it should be possible to utilize the quasi-discrete nature of the DOS of a quantum step in a variety of photo-assisted processes. With regard to the quantum step, electro-reflectance offers distinct simplicity. It is known that the quantum step offers another way of characterizing the heterojunction systems. Unlike quantum wells where many quantum devices have been explored and developed into routine applications such as oscillators, lasers, and amplifiers, it is conceivable that the quantum step may also be developed into useful devices. A quantum step can also provide various parameters that characterize a quantum system. The DOS is calculated using the residence time, which in turn is used in the calculation of electroreflectance.

Capacitance, Dielectric Constant, and Doping Quantum Dots

This chapter discusses quantum capacitance, size-dependent dielectric function, and doping of a quantum dot. They are all different in the quantum regime. The main difference in quantum capacitance from its classical definition is the fact that there is no such thing as storage of charge alone and the charge of the electron is discrete. As per the formulation, one electron in the ground state of a sphere is only the ground state of a hydrogen-like state, and two electrons are the ground state of a helium-like state. The chapter presents that taking into account the discreteness of electronic charge the classical capacitance is quite different when there are only a few electrons. Only when the number of electrons is large does the discreteness of the electronic charge cease to exhibit new features. When the size is below a couple of nanometers, quantum mechanically the kinetic energy of the stored electrons becomes dominant over the electrostatic stored energy. Paulis exclusion principle plays an additional role in quantum capacitance. The size-dependent dielectric function is not defined according to the usual definition, because of the loss of the global nature. The reduction of the dielectric constant at sizes approaching a couple of nanometers drastically reduces the dopant binding energy from 13.6 eV for the hydrogen atom to ∼ 1 eV. In other words, all quantum dots a couple of nanometers in size are intrinsic even the dopant happens to be inside a quantum dot.

Si Quantum Dots

This chapter discusses Si Quantum Dots (QD). The non-conducting QD is charged and raises the potential at the conducting QD so that no extra voltage is needed to move the charges into the conducting dot. This type of process is precisely what generates random telegraph-like signals. The reason such processes take place far more often in QD tunneling than quantum well tunneling is that a large number of electrons participate in the latter process from the transverse degree of freedom overwhelming the trapping effects. After discovering the effects of light, it is realized that the process seems to be caused by a variety of trappings, although the data do not rule out trapping from non-conducting dots, instead of some unknown defects.

Dielectric Function and Doping of a Superlattice

This chapter describes how to calculate the dielectric constant of a superlattice. The dielectric constant represents the screening of the applied electric field in a medium owing to the presence of charges and dipoles. The transverse dielectric constant of the Ga 0.5 Al 0.5 As/GaAs superlattice has been measured by Tsu, showing that the refractive index lies between the Ga 0.5 Al 0.5 As alloy and GaAs. The dielectric constant is important for impurity levels, excitons, and carrier screening in general. For polar semiconductors like GaAs, the ionic contribution to the static dielectric constant represents a significant factor compared with the part contributed by its covalent nature. When the energy states in a quantum confined system are pushed up, the reduction in the dielectric constant increases the binding energy of the dopants. Because the impurity sites intermingle with the barriers, which confine the electrons, the binding energy is position dependent. The matrix element has an energy denominator; the higher is the band gap of the solids, the lower is the dielectric function. Therefore, if the energy state is raised owing to quantum confinement, the dielectric function is reduced accordingly. In doping semiconductors, often the most important features in the operation of electronic devices, the binding energy of dopants is inversely proportional to the square of the dielectric constant, a major effect to be accounted for in 3D quantum confinement.

Quantum Impedance of Electrons

The pre-factor for the conductance per spin G 0 = e 2 /h for a closed system and is double this value, 2G 0 for an open system. Similar to electromagnetic waves, the wave impedance or wave conductance for various cases are different in detail, although all of them share the same origin, the wave nature of the electron. Generally contacts are not reflectionless, but the effects of reflection, as in the case of resonant tunneling, are accounted for by the transmission term in addition to the “pre-factor” G 0 . At low temperatures, different modes from different transverse degree of freedoms are truly independent. As soon as mixing of the longitudinal and transverse modes is present, longitudinal and transverse momenta are mixed, and these equal steps of conductance are smeared. But why, in the case of Si QD that Nicollian and I worked on, are there conductance jumps clearly in units of G 0 even at room temperatures? I think the answer lies in the fact that, for a size of a few nanometers, the quantized energies are so far apart that they are almost unaffected by phonons, a primary contributor to mixing of modes. And last, I discuss the need to consider coupled system of photons and electrons, and general coupled waves.

Resonant Tunneling via Man-Made Quantum Well States

The basic unit of resonant tunneling, consisting of a quantum well having two barriers on each side placed between two contacts, shows NDC when a voltage is applied to align the energy of the quantum states with the energy of the incident electron. As discussed it was conceived because Gunn, the discoverer of the Gunn effect, thought that the observed NDC in a superlattice was actually the manifestation of domain oscillation in a superlattice created by various alloys. Having only a single unit, a double barrier on each side of a quantum well, would have eliminated the possibility of domain formation, which could lead to domain formation under an applied field. The theoretical treatment was not at all obvious at the time when tunneling was only treated by approximation using the WKB or other perturbation techniques. Furthermore, solution of tunneling using the time-dependent Schrodinger equation was carried out for the first time, to describe the time evolution of a pulse of electrons incident onto a double barrier structure. The formulation include damping is introduced using the Green function to account for linewidth. A simple example is given to illustrate how to include self-consistent potential via solution of the Poisson equation. The instability was shown to be generated by the creation of a second quantum well from the applied voltage across the undoped portion of the contact, therefore, is not intrinsic to resonant tunneling.

Semiconductor Atomic Superlattice (SAS)

Superlattices and quantum wells were introduced as man-made quantum structures to engineer the quantum states for electrical and optical applications. The concept of the semiconductor atomic superlattice (SAS) materializes in stages. Initially it was thought that if oxide was made thin enough, it might form a strained-layer super-lattice. This chapter discusses the SAS stages by using polycrystalline silicon on polycrystalline silicon dioxide. The epitaxial growth is very aggressive; however, what counts is how low the defect density is. It takes a while to learn how to grow epitaxial silicon on saturated adsorbed oxygen. The chapter also provides theoretical study of hand-built models, calculating the strain and energy states and comparing with density functional calculation (DFC). DFC calculations basically agree with simple calculations, that the strain is surprisingly low. The chapter gives a good example of how an idea was developed and metamorphosed into an all epitaxially formed structure. The process is fundamentally different from atomic layered epitaxy (ALE), because in SAS, for Si–O superlattice, silicon dictates what sites oxygen can occupy consistent with the surface reconstruction, whereas in ALE, no one constituent dictates, resulting in a random alloy.

Why Super and Why Nano

Super refers to something bigger than atoms and molecules and nano refers to individual components having size in nanometer regime. How do we differentiate solids from gaint molecules? The original superlattice led its way through quantum dots to nano-components in general. What is most conspicuously current and fundamentally different from all we are used to except the universe itself is the role of symmetry. Nature builds us atoms and molecules from elementary particles, still mysterious where symmetry plays a pivotal role. Now with quantum dots and nanosolids, something new is added because nanosolids have inside and outside with specific shapes dictates certain symmetry, requiring specification in terms of location and directions, with complexity more than anything we know of. We are so used to statistics for the specification of complex events. We know how to apply Fermi-Dirac statistics for half integral spins and Bose-Einstein statistics for integral spins. But we do not know why. In closing, I want to point out that general relativity may be basically sound, but special relativity is not because it deals with a velocity only definable via statistical averages. In essence, dealing with nanosize regime, I do not think statistics mean very much because there might be only several events to be averaged. We need to think of ensemble average, even though there might be only a few events to be averaged, so that the confidence level is quite low. In everyday language, the scheme is lacking robustness and has low certainty. Such is the world of nanosolids.

Some Novel Devices

Field emission with QW and nm-thick multi-structured cathode is basically a DBQW as means to allow electron resonantly tunneling out into the vacuum. Scheme based on this has lowered the applied electric field for field emission by an order of magnitude. Recent activities in superlattice include: THz phonon laser with Stark ladder superlattice and quantum cascade laser as THz oscillators as well as IR lasers. A short section describes the feverish activities with graphene-related research. It is argued that because graphene is basically a 2D-electronic system, a graphene/X superlattice may represent the direction for future research.