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 Schrödinger 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.

对具有更高性能和低功耗的小型化晶体管的需求不断增长，已将器件缩小到纳米级。此类小型设备的设计和建模需要可靠的计算技术进行仿真。由于电子在这种短通道中的流动是由于源极和漏极之间的电化学势差导致的弹道传输。使用经典方法研究新型微纳米电子器件是不准确的，其结果不可靠。当前公式的复杂性随着器件尺寸的减小而增加。由于器件中载流子的漂移和扩散，考虑了 FET 器件中电流的一般概念。但在现代观念中，电子流被解释为两种不同过程的组合，称为弹性传递和热生成。弹性传递是力驱动的，而热生成是熵驱动的。考虑到上述过程，电子的输运有两种理论研究，半经典输运理论和量子输运理论。半经典传输理论通过牛顿力学的力驱动和热力学的熵驱动相结合来解释电子的流动，称为玻尔兹曼传输方程 (BTE)。在介观物理学中，使用量子输运理论方法，其中电子的力驱动输运由量子力学很好地解释。量子传输理论是一种先进的理论，它正确地描述了电子设备中的电流并且是可靠的。在量子输运理论中，力驱动的流动使用薛定谔波动方程和熵驱动的热力学来表示，这两个过程的形式积分是通过非平衡格林函数（NEGF）方法获得的。NEGF 利用多体微扰理论 (MBPT) 的过程来解释分散熵生成实践，这依赖于第二量化语言。在平衡和非平衡条件下，NEGF 已经演变为检查多粒子量化系统。NEGF形式主义在量子光学领域的应用，BTE的量子校正，高场对应的体系统中的输运，不同材料和器件中的量子电子和空穴传输、III-V 族谐振隧道二极管、电子波导、量子级联激光器、Si 纳米柱、碳纳米管、石墨烯纳米带、金属线、有机分子、自旋电子器件、热和热电设备。NEGF 方法提供了一个细致的框架，以在通道中发生的 MBPT 的帮助下处理弹性（非耗散）或非弹性（耗散）的整个相互作用。本文将全面了解精确的载流子传输模型，该模型可用于经典理论失败的先进纳米级器件。它能够为在量子和弹道传输机制中积极工作的读者和研究人员群体提供强大的背景。