Mesoscopic physics and nanoelectronics: nanoscience and nanotechnology

Overview of nanoelectronic devices

“…Two essential quantum mechanical effects are exhibited by electrons confined to nanometer-scale islands between closely spaced potential energy barriers [16], [124], [129], [176]. First, quantum mechanics restricts each electron's energy to one of a finite number of one-electron energy levels (quantum states with discrete, "quantized" energies).…”

“…Although resonant tunneling devices [16], [28], [123], [124] were not the first category of solid-state nanoelectronic device listed above, we explain their operation in detail first, because it illustrates energy quantization and tunneling in their simplest form.…”

“…That breakthrough and the results of simultaneous investigations by Reed [97] led Capasso and Kiehl [123] to develop an early RTT. Work on resonant tunneling devices is being carried on by a number of groups [16], [176], [211], with particular progress on the hybrid RTT's and circuitry by Seabaugh and his collaborators at Texas Instruments [20], [78]. Also notable is MIT Lincoln Laboratory's construction of a fabrication facility that is producing very large scale integration (VLSI) wafers containing large numbers of RTD's in high-speed circuits intended for digital signal processing applications [77], [93].…”

“…A resonant-tunneling device [16], [28], [123], [124] usually has a long and narrow island (i.e., a "quantum wire" or "pancake") with shortest dimension 5-10 nm [184]. The island is made from a semiconductor containing many mobile electrons.…”

Lagrangian for RLC circuits using analogy with the classical mechanics concepts

“…The quantum mechanics treatment of the RLC circuit with discrete charge and semiclassical consideration can be found in Utreras-Diaz [6] that obtained the approximation of energy eigenvalues in term of a dimensionless parameter h e C L 2 (e is the electron charge, and h is the Planck constant). In literature, we found most analysis of the RC, RL, LC, and RLC circuits, as a mesoscopic system or nanophysics, are commonly discussed and formulated by using the concept of quantum mechanics [7][8][9][10]. As we have already known that the energy operator in quantum mechanics is the Hamiltonian which is defined as the sum of energy kinetic and energy potential of the physical system.…”