Velocity Saturation Effects

Velocity Saturation EffectsOhm’s “Law”

• This says the Drift Velocity Vd 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 Vd vs E curve must saturate to a constant value!

dV E

Ohm’s “Law”• Obviously, this says that the Vd vs E curve

looks qualitatively like:

dV E

dV

E

• Measurement shows that, in all materials, at high enough E, the Vd vs E curve looks qualitatively like:

dV

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 SaturationIn n-type Si, the saturation velocity

Vs ~ 107cm/s at a field

Es ~ 104 V/cmIn GaAs there is a velocity reduction

(peak) before saturation. We’ll discuss this later

A Simple Empirical Model for Velocity Saturation

E << Esat, Vd = μEE << Esat, Vd constant

Or Vd μ(E)EWhere μ(E) “Field Dependent Mobility”

A Slightly Better Model for Velocity Saturation

E << Esat, Vd = μEE << Esat, Vd constant

E

vEv

bv

bE

sat

sat

0

0

0

0

1

1

Still Another Model for Velocity Saturation:The Two Region Model

Velocity Saturation in Si• Measurements show that, at E 104 V/cm, the carrier

velocity for electrons saturates to vsat 107 cm/s & forholes, it saturates to vsat 8 106 cm/s.

Velocity Saturation in Si

To model the data, use

• Measurements show that, at E 104 V/cm, the carrier velocity for electrons saturates to vsat 107 cm/s & forholes, it saturates to vsat 8 106 cm/s.

Velocity Saturation in Si

To model the data, use

• Measurements show that, at E 104 V/cm, the carrier velocity for electrons saturates to vsat 107 cm/s & forholes, it saturates to vsat 8 106 cm/s.

Results

Temperature Dependence of Velocity Saturation in Si• Measurements: Both vsat & E are temperature

dependent!

Electrons

Temperature Dependence of Velocity Saturation in Si

Holes

Voltage-Current Behavior inVelocity 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 = Vsat/R = Isat

Qualitative I-V Curves in Velocity Saturation Conditions

0

10Long Channel

Devices

Short Channel Devices

I

V

I = V/R

VssatVlsat

I-V Curves in Velocity Saturation Conditions