Overall, this work introduces experimental and theoretical work that offers the reader an alternative perspective of looking at 28 nm MOSFET electrical performance and modeling. Chapter 1 introduces an alternative way to produce a negative differential resistance (NDR) effect that is achieved by the non-conventional biasing of a regular 28-nm n-type Metal-Oxide-Semiconductor Field-Effect Transistor (n-MOSFET). It has a controllable peak-to-valley current ratio (PVCR) that goes from about 3.0 up to a room-temperature value of 5.5, which is above the record of 5.3 previously reported on silicon heterostructures [1]. Two bipolar mechanisms working in parallel are demonstrated to occur inside the n-MOSFET, one at the surface and other in the bulk. Thermally activated electrons are injected into the gate contact through the drain-gate overlap, a situation that leads the transistor to the flat-band condition, blocking the surface conduction channel and triggering the NDR effect. I proposed a simple analytical model that correlates very well with experimental data. Chapter 2 provides a general perspective of the theoretical approaches that can lead to the determination of the charge current through a nano-scaled system from a full quantum mechanical perspective. It exposes the amount of information that, in principle, can be obtained from any physical system and the complications that arise in the determination of the current. The more realistic but still very difficult statistical quantum mechanical approach is briefly presented afterwards. Finally, the Landauer formalism is established as a series of assumptions that render a close-form expression for the current in terms of the probability of transmission. An analogy between the time-independent Maxwell and Schrödinger equations is developed in Chapter 3. It is applicable to two-dimensional systems with wave-guide (lead) boundary conditions. On the lead boundaries, the third-order boundary conditions for the electric field reduce to the normal derivative of its z-component, adopting the same form of the equivalent boundary conditions for the Schrödinger equation. The total energy and position-dependent potential energy are included in the set of quantities that have an equivalent electromagnetic parameter.