Hot-carrier constraints on transient transport in very small semiconductor devices

Current technology has progressed rapidly and is pushing toward fabrication of submicron dimensioned devices. As this occurs, we expect that the temporal and spatial scales in these devices will become sufficiently small that the semiclassical approach to transport theory, as expressed by the Boltzmann equation, becomes of questionable validity. In developing a corrected transport equation from quantum kinetic theory, several constraints arise on the normal concepts of transport parameters. The intra-collisional field effect, concomitant nonzero collision duration, and retarded collisional interactions have pronounced effects upon the carrier transport, especially in the transient dynamic response region in small devices. The description of diffusion is also complicated by the relatively long duration of the velocity auto-correlation function. Calculations have been carried out for the velocity autocorrelation function for Si. It is found that the autocorrelation
\phi'(t)
initially relaxes exponentially, due to momentum relaxation, goes negative and displays a local minimum, then relaxes to zero at a slower rate due to energy relaxation. This complicated behavior leads to enhanced diffusion and noise on the short-time scale.