Velocity Saturation Effects Velocity Saturation Effects Ohms Law

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Velocity Saturation Effects

Velocity Saturation Effects

Velocity Saturation Effects Ohm’s “Law” • This says the Drift Velocity Vd is linear

Velocity Saturation Effects Ohm’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!

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

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

 • Measurement shows that, in all materials, at high enough E, the Vd

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

E Field Dependence of Drift the Velocity Saturation In n-type Si, the saturation velocity

E Field Dependence of Drift the Velocity Saturation In n-type Si, the saturation velocity Vs ~ 107 cm/s at a field Es ~ 104 V/cm In Ga. As there is a velocity reduction (peak) before saturation. We’ll discuss this later The carrier velocity saturation at high E fields clearly places a FUNDAMENTAL upper limit on the speed of semiconductor devices.

A Simple Empirical Model for Velocity Saturation Or Vd μ(E)E Where μ(E) “Field Dependent

A Simple Empirical Model for Velocity Saturation Or Vd μ(E)E Where μ(E) “Field Dependent Mobility” E << Esat, Vd = μE E << Esat, Vd constant

A Slightly Better Model for Velocity Saturation E << Esat, Vd = μE E

A Slightly Better Model for Velocity Saturation E << Esat, Vd = μE E << Esat, Vd constant

Still Another Model for Velocity Saturation: The Two Region Model

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

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

Velocity Saturation in Si • Measurements show that, at E 104 V/cm, the carrier velocity for electrons saturates to vsat 107 cm/s & for holes, it saturates to vsat 8 106 cm/s. To model the data, use

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

Velocity Saturation in Si • Measurements show that, at E 104 V/cm, the carrier velocity for electrons saturates to vsat 107 cm/s & for holes, it saturates to vsat 8 106 cm/s. To model the data, use Results

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

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

Temperature Dependence of Velocity Saturation in Si Holes

Temperature Dependence of Velocity Saturation in Si Holes

Voltage-Current Behavior in Velocity Saturation Conditions For short channel devices • As expected, in

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 = Vsat/R = Isat

Qualitative I-V Curves in Velocity Saturation Conditions Long Channel Devices I Short Channel Devices

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

I-V Curves in Velocity Saturation Conditions

I-V Curves in Velocity Saturation Conditions