Electron Injection Model for Linear and Parabolic 2D Materials: Noise as a Parabolic or Linear Band Detector

The proper modeling of the 2D materials requires a discussion on the boundary conditions between the device active region (open system) and the environment, to determine how and when electrons are injected. In devices with gapless materials, like graphene, the injection of electrons with positive and negative kinetic energies are needed for an accurate description of the band-to-band Klein tunneling. We develop a full quantum injection model for 2D materials based on quantum trajectories. Numerical results with the BITLLES simulator will be presented showing the successful application of the electron injection model for a full quantum treatment of DC, AC, transient and noise behaviors of 2D devices. We will also discuss how the noise (fluctuations) of the electrical current in ballistic devices, with parabolic or linear band dispersion have some peculiarities which can be used to discern between linear and parabolic band materials.