MOSFET: Mobility Models
Introduction:
Following section contains the Mobility Models of the MOSFET in details.
Mobility Models:
The mobility of carriers in the channel of a MOSFET is lower than in bulk semiconductors because there are additional scattering mechanisms. Since carriers in the channel are very close to the semiconductor-oxide interface, they are scattered by surface roughness and by coulombic interaction with fixed charges in the gate oxide. When the carriers travel in the inversion layer from the source to the drain, they encounter microscopic roughness on an atomistic scale at the oxide-silicon interface and undergo scattering because, any deviation from a perfectly periodic crystal potential results in scattering. This mobility degradation increases with the gate bias because a higher gate bias draws the carriers closer to the oxide-silicon interface, where they are more influenced by the interfacial roughness.
Mobility degradation curve:
It is very interesting to note that if we plot the effective carrier mobility in the MOSFET as a function of the average transverse electric field in the middle of the inversion layer, we get what is known as a "universal" mobility degradation curve for any MOSFET, which is independent of the technology or device structural parameters such as oxide thickness and channel doping shown in fig.
We see that the average transverse field in the middle of the inversion region is given by
While this model works quite well for electrons, for reasons that are not clearly understood at present, it has to be modified slightly for holes in the sense
that the average transverse field must now be defined as
This degradation of mobility with gate bias is often compactly described by writing the drain current expression as
where θ is called the mobility degradation parameter. Because of the additional (VG — VT) term in the denominator, the drain current increases sub-linearly with gate bias for high gate voltages.