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An expression for the computation of the current in phase-coherent devices driven under arbitrarily timedependent conditions is presented. The approach is developed for independent electrons in the time domain within a first-quantization formalism. The time-dependent current is computed by generalizing the Ramo-Shockley theorem to quantum systems. It is shown that the time-dependent conductance is not proportional to the quantum transmission coefficient, but to a parameter named the quantum current coefficient. As a test, it is proved that the present approach leads to the well-known Landauer model when static potentials are considered. As a simple numerical example, coherent quantum pumping is studied and applications for nanoscale solid-state field-effect transistors are predicted.

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In nanoscale devices, electron transport tends to become ballistic. Then, the current and the noise are mainly determined by the injection process. An electron injection model suitable for the semi-classical Monte Carlo (or timedependent quantum) simulation of nanoscale devices with (or without electron) confinement is presented. While the injection model is conceptually quite similar to the boundary conditions used in the Landauer formalism, its mathematical description is quite different because it is developed for time-dependent scenarios. As an application, numerical data show that the signal-to-noise ratio and the bit-error probability are degraded in nanoscale transistors because of electron confinement.

This work presents a general model for the electron injection from contacts into a device active region. The model is developed for cases where the electrons are confined in one or several directions. The implementation of the approach within the semiconductor Monte Carlo technique is discussed. The present contact model can be applied for non-degenerate or degenerate statistics. As an example, we apply our method to a quantum well nano-MOSFET.