The growing demand for miniaturized transistors with increased performance and low power consumption has scaled down the device to the nanoscale regime. The design and modeling of such small devices need a reliable computing technique for simulation. Since the flow of electrons in such short channels is due to differences in electrochemical potential between source and drain which of ballistic transport. The study of novel micro and nano-scaled electronic device using the classical approach is inaccurate whose results are not reliable. The complexity of the current formulation increase as the size of the device is reduced. The general concept for the current in the FET device is considered due to the drift and diffusion of carriers in the device. But in modern concepts, the flow of electrons is explained as a combination of two different processes which are termed elastic transfer and heat generation. The elastic transfer is force driven and the heat generation is entropy-driven. Considering the above-mentioned process the transport of electron is studied by two theories, Semi-classical transport theory, and quantum transport theory. The semi-classical transport theory explains the flow of electrons by a combination of Newtonian mechanics for force-driven and thermodynamics for entropy-driven, called Boltzmann transport equation (BTE). In mesoscopic physics, the quantum transport theory approach is used in which the force-driven transport of electrons is well explained by quantum mechanics. The quantum transport theory is the advanced one that properly describes the current flow in the electronic device and is reliable. In the quantum transport theory, force-driven flow is expressed using the Schrodinger wave equation and thermodynamics for entropy-driven, and the formal integration of these two processes is obtained by the Non-Equilibrium Green's Function (NEGF) method. The NEGF utilized the process of many-body perturbation theory (MBPT) to explain the dispersed entropy-generating practices, which are dependent upon the second quantization language. In both the equilibrium and non-equilibrium conditions, NEGF has been evolved to examine the many-particle quantization systems. The application of NEGF formalism in the field of quantum optics, quantum correction of BTE, transport in bulk systems corresponding to the high field, quantum electron and holes transport in different materials and devices, resonant tunnel diodes of III-V groups, electron waveguides, quantum cascade lasers, Si nano-pillars, carbon nanotubes, graphene nanoribbons, metal wires, organic molecules, spintronic devices, thermal and thermoelectric devices. A meticulous framework is provided by the NEGF method to deal with whole interaction either elastic (non-dissipative) or inelastic (dissipative) with the help of MBPT which occurs in the channel. This paper will provide a comprehensive understanding of the accurate carrier transport model which can be employed with advanced nanoscale devices where the classical theory fails is. And it is capable to set a strong background for the readers and researchers groups who are actively working in the quantum and ballistic transport regime. It would also be beneficial to graduate/undergraduate students, and industry people who are pursuing the same domain.
