Velocity Saturation

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From the physics of semiconductors, it is proved that the velocity of charge carriers is linearly proportional to the electric field and the proportionality constant is called as mobility of carrier. When the electric field is increased beyond a certain velocity called as the thermal velocity or saturated velocity the velocity of the charge carrier does not change with electric field. The electric field at which the velocity of carrier saturates is called as the critical electric field. The loss of energy is because of the collisions of carriers called as scattering effect. The velocity saturates because electrons have more possibility to scatter at high electric fields. The loss of energy is because of the collisions of carriers called as scattering effect.

In MOSFETs when electrical field along the channel reaches a critical value, the velocity of carriers tends to saturate, and the mobility degrades. The saturation velocity for electrons and holes is approximately same and constant with an approximate value of 10e7 cm/s (for silicon). The critical field at which saturation occurs depends upon the doping levels and the vertical electric field applied.

The equation below is the classic expression for velocity saturated drain current. It may be noted that the drain current increases linearly with over-drive voltage. In reality, the current does not completely saturate, but increases slowly with drain voltage. Generally, velocity saturation is observed only in a long channel device.

The reference device was operated at various gate voltages and the drain current in the saturation region was calculated. A plot of the said current and the overdrive voltage was plotted. It was found that the drain current increased linearly with the overdrive voltage. It may be said that the device in question is velocity saturated.




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