1、Nonideal Effects05 For long-channel MOSFET, We assume the mobility to be constant, which means that the drift velocity increases without limit as the electric field increases. In this ideal case, the carrier velocity increases until the ideal current is attained. However, we have seen that the carri
2、er velocity saturates with increasing electric field. Velocity saturation will become more prominent in shorter-channel devices since the corresponding horizontal electric field is generally larger.Velocity SaturationVelocity Saturation However, velocity saturation can change this saturation conditi
3、on. For example, when the horizontal electric field is approximately 104V/cm. If VDS5V in a device with a channel length of L 1 m, the average electric field is 5 104V/cm. Velocity saturation, then, is very likely to occur in short-channel devices. In the ideal IV relationship, current saturation oc
4、curs when the inversion charge density becomes zero at the drain terminal, or when(12.14) The saturation velocity will decrease somewhat with applied VGbecause of the vertical electric field and surface scattering. Velocity saturation will yield an ID(sat) value smaller than that predicted by the id
5、eal relation, and it will yield a smaller VDS(sat)value than predicted. The ID(sat) current is also approximately linear with VGS, instead of having the ideal square law dependence predicted previously.Ideally:Velocity Saturation The modified ID(sat) characteristics are approximately: There are seve
6、ral models of mobility versus electric field. One particular relation that is commonly used is(12.15)(12.16)Where satis the saturation velocity (approximately 107cm/s for electrons in bulk silicon) and Coxis the gate oxide capacitance per cm2.Velocity Saturation The smaller values of ID(sat) and the
7、 approximate linear dependence on VGSmay be noted for the field-dependent mobility curves.Comparison of IDversus VDcharacteristics for constant mobility (dashed curves) and for field-dependent mobility and velocity saturation effects (solid curves)Velocity SaturationImpact on the transconductance an
8、d the cutoff frequency ： The transconductance is found from ：which is now independent of VGS andVDSwhen velocity saturation occurs.The drain current is saturated by the velocity saturation effect, which leads to a constant transconductance.where the parasitic capacitances are assumed to be negligibl
9、e.(12.18)(12.17) When velocity saturation occurs, the cutoff frequency is given byVelocity Saturation Scattering events in a semiconductor limit the velocity of carriers to an average drift velocity. The average drift velocity is a function of the mean time between collisions or the mean distance be
10、tween scattering events. In the long-channel device, the channel length L is much longer than the mean distance between collisions l, so that an average carrier drift velocity exists. As the MOSFET channel length is reduced, the mean distance between collisions l may become comparable to L so that t
11、he previous analysis may not be valid.Ballistic Transportation Ballistic transport ： If the channel length is further reduced so that L l, then a large fraction of carriers could travel from the source to the drain without experiencing a scattering event. This motion of carriers is called ballistic
12、transport. Ballistic transport means that carriers travel faster than the average drift velocity or the saturation velocity, and this effect can lead to very fast devices Ballistic transport occurs in submicron (L1 m) devices. As the MOSFET technology continues to shrink the channel length toward the 0.1 m value, the ballistic transport phenomenon will become more important.Ballistic Transportation
