Low-Dimensional Semiconductor Structures

Abstract

In the last chapter, we have introduced the theories for calculating the band structures of bulk semiconductors and discussed the corresponding strain effects. However, carriers in most modern electron devices such as FETs are electrically or spatially confined. Confinement interrupts the periodic potential where an electron in a bulk semiconductor has. Quantum mechanically, electric confinement and spatial confinement have no essential difference. They alter the potential term V (r) in the single electron Schroinger equation (3.1) such that in the confinement direction(s), the potential loses the periodic characteristic the bulk crystals possess. This has significant effects on carrier transport properties, since electron systems are distinguished by this very potential term V (r), as discussed in Chap. 3. Typical confined electron systems include quantum wells, quantum wires, and quantum dots, which are 2D, 1D, and 0D structures, respectively. A MOSFET is a symbolic 2D electron system, which invention is probably the most important event in the history of modern semiconductor industry, and has been the locomotive for the technology development for half a century. The operation of a MOSFET is based on the control of the electronic behavior through tunable external electric field to create a 2D electron gas (2DEG) layer close to the semiconductor/oxide interface. Structural 2D systems such as quantum wells extend the means of 2DEG generation and present extensive research interest and electrical and optical applications as well, especially when the crystal growth techniques such as molecular beam epitaxy are very mature nowadays. Quantum wells can be created by growing a layer of semiconductor sandwiched by two semiconductor layers whose band gaps are larger than the former, or formed in a heterojunction such as GaAs/Ga1−x Al x As. The former sandwich structures are extensively found in quantum well lasers. The GaAs/Ga1−x Al x As heterojunction is the kernel part for a high electron mobility field effect transistor (HEMFET) since the similar lattice constant and coefficient of expansion of Ga1−x Al x As permits the growth of high mobility thin Ga1−x Al x As film on a GaAs substrate. With aggressive scaling of modern planar MOSFET devices, short channel effects become increasingly grave. Other device architectures such as fully depleted silicon-on-insulator (SOI), double-gate MOSFET, and FinFET devices are currently under intense investigation. Conceptual devices using carbon nanotubes and Si-nanowires also present promising application prospects. A Si-nanowire with transverse cross section length scale in nanometer scale is typically 1D structure. The motion of electrons is restricted along the nanowire and quantized in the transverse directions. In these nontraditional semiconductor structures, both electric and spatial confinement are present and often interact with each other.