We examine device physics and study characteristics of single-molecule multi-terminal electronic devices. These devices exhibit quantum phenomena such as highly nonlinear tunneling, resonance and other. The device physics is based on the controlled propagation of electrons. The aforementioned microscopic devices must be examined quantum-mechanically. By applying quantum mechanics and advanced numeric schemes, we perform the device level analysis researching propagation, transitions and interactions of electrons. Our ultimate objective is to analyze the controlled electron transport, study tunneling, evaluate performance and assess device capabilities. Using three-dimensional Schrodinger and Poisson equations, we examine the electron transport by numerically solving the above mentioned equations using a self-consistent scheme. The controlled electron transport, super-fast transitions and highly nonlinear tunneling are observed. Solutions are applicable to various sensing and processing devices.