Fundamentals of Modern VLSI Devices

A ballistic MOSFET is a hypothetical device in which the mobile carriers suffer no collisions in the channel. This may happen, in principle, when the channel length is shorter than the mean free path, the average distance carriers travel between collisions. In an ordinary MOSFET, carriers moving from the source to the drain under the influence of the applied field (Vds ) collide with the silicon lattice, impurity (dopant) atoms, and surfaces. These collisions limit the velocity they can acquire from the field (Appendix 3), resulting in a reduced drain current. Under low field conditions, the effect of these collisions is lumped into a mobility factor proportional to the mean free time between successive collisions (Appendix 3). For long-channel MOSFETs, the drain current is proportional to the mobility (Section 3.1.2). For short-channel MOSFETs under high drain bias conditions, high-field scattering becomes important. This is usually modeled by velocity saturation (Section 3.2.2). In the absence of any scattering, carriers entering the channel from the source are accelerated by the applied field ballistically toward the drain. They can attain very high speeds especially in the high-field region near the drain. However, such high speeds (velocity overshoot) do not necessarily translate into large currents. Since current must be continuous from source to drain, it is bounded by the rate at which carriers are injected from the source. In a ballistic MOSFET then, the bottleneck is near the source where carriers move into the channel at relatively low velocities (before field acceleration). Current continuity is satisfied by a decreased carrier density near the drain such that the product of carrier density and velocity at the drain is the same as that at the source (see Fig. 3.31). This appendix describes the drain current model for a ballistic MOSFET published by Natori in 1994 (Natori, 1994).