The dependence of the electron mobility on the longitudinal electric field in MOSFETs

Abstract

The dependence of the electron mobility on the longitudinal electric field in MOSFETs has been studied in detail. To do so, a Monte Carlo simulation of the electron dynamics in the channel, coupled with a solution of the two-dimensional Poisson equation including inversion-layer quantization and drift-diffusion equations, has been developed. A simplified description of the silicon band structure in the effective-mass approximation including non-parabolicity has been considered. Different-channel-length MOSFETs and different biases have been taken into account. It has been shown that in order to accurately describe electron-mobility behaviour in short-channel MOSFETs it is necessary to take into account the electron-velocity overshoot. An analytical expression, easy to include in device simulators, is provided to account for the dependence of the electron mobility on the high values of the longitudinal electric field and of its gradient found in state-of-the-art MOSFETs.

A closed-loop evaluation and validation of a method for determining the dependence of the electron mobility on the longitudinal-electric field in MOSFETs

“…The simulator, which is described in [22] and [23], operates as follows: The total channel length is divided in subchannels with lengths , respectively. Instead of fixing the values, the channel potential values at the ends of the th subchannel and are defined as the separation between the quasifermi levels at these points, and being the potentials at the total channel ends.…”

“…Therefore, the electron mobility acquires a different value in each subchannel according to the longitudinal and transverse electric field values in it. The calculation of the electron distribution and surface potential was performed by self-consistently solving Poisson and Schroedinger equations [23], [24]. Once these data are known for each subchannel end, we calculated the drain current in each subchannel by adding drift and diffusion contributions [17].…”

“…In this respect, we have not dealt with the problems connected to the loss of inversion layer confinement in the pinch-off region at the channel drain end. This method is applicable to MOSFET's with effective channel lengths larger than 0.2 m, as we have checked out, by means of our Monte Carlo MOSFET simulator [23], that for devices shorter than 0.2 m, there might be important velocity overshoot effects, at least at the drain end of the channel. Therefore, there would not be saturation of the electron velocity in the high longitudinal electric field region of the MOSFET channel.…”

Deep submicrometer SOI MOSFET drain current model including series resistance, self-heating and velocity overshoot effects

“…The result is the following (4) where the channel length modulation has been calculated following [3]. In order to get a smooth transition between to we have used the following function: (5) where is a constant. We found to be a good choice.…”

“…transport regime of carriers crossing the channel under high longitudinal-electric field gradients, typical of deep submicron MOSFET's [5]- [7]. We have made use of a previously developed model [3] to obtain a new one in which series resistance, SH and VO effects are considered.…”