Velocity Saturation Effects

Ohm’s “Law” This says the Drift Velocity V d is linear in the electric field E: μ  Mobility If this were true for all E, the charge carriers could be made to go fast without limit, just by increasing E! That would be nonsense! So, in every material, at high enough E, the V d vs E curve must saturate to a constant value!

Ohm’s “Law” Obviously, this says that the V d vs E curve looks qualitatively like: E

Measurement shows that, in all materials, at high enough E, the V d vs E curve looks qualitatively like: E Electrons Holes

E Field Dependence of Drift the Velocity The carrier velocity saturation at high E fields clearly places a FUNDAMENTAL upper limit on the speed of semiconductor devices. Velocity Saturation In n-type Si, the saturation velocity V s ~ 10 7 cm/s at a field E s ~ 10 4 V/cm In GaAs there is a velocity reduction (peak) before saturation. We’ll discuss this later

A Simple Empirical Model for Velocity Saturation sat vdvd E E E +  1  E << E sat, V d = μE E << E sat, V d  constant Or V d  μ(E)E Where μ(E)  “Field Dependent Mobility”

A Slightly Better Model for Velocity Saturation E << E sat, V d = μE E << E sat, V d  constant

Still Another Model for Velocity Saturation: The Two Region Model

Velocity Saturation in Si Measurements show that, at E  10 4 V/cm, the carrier velocity for electrons saturates to v sat  10 7 cm/s & for holes, it saturates to v sat  8  10 6 cm/s.

Velocity Saturation in Si To model the data, use Measurements show that, at E  10 4 V/cm, the carrier velocity for electrons saturates to v sat  10 7 cm/s & for holes, it saturates to v sat  8  10 6 cm/s.

Velocity Saturation in Si To model the data, use Measurements show that, at E  10 4 V/cm, the carrier velocity for electrons saturates to v sat  10 7 cm/s & for holes, it saturates to v sat  8  10 6 cm/s. Results

Temperature Dependence of Velocity Saturation in Si Measurements: Both v sat & E are temperature dependent! Electrons

Temperature Dependence of Velocity Saturation in Si Holes

Voltage-Current Behavior in Velocity Saturation Conditions For short channel devices As expected, in the linear, Ohm’s Law Region: I = V/R In the non-linear Velocity Saturation Region, the I vs V curve bends over & saturates: I = V sat /R = I sat

Qualitative I-V Curves in Velocity Saturation Conditions Long Channel Devices Short Channel Devices I V I = V/R V ssat V lsat

I-V Curves in Velocity Saturation Conditions