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Velocity Saturation Effects

Velocity Saturation Effects. Velocity Saturation Effects. Ohm’s “ Law ” This says the Drift Velocity V d is linear in the electric field E: μ  Mobility

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Velocity Saturation Effects

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  1. Velocity Saturation Effects

  2. Velocity Saturation Effects Ohm’s “Law” • This says the Drift Velocity Vdis 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 enoughE, the Vd vs E curve must saturate to a constant value!

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

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

  5. Velocity Saturation In n-type Si, the saturation velocity Vs ~ 107cm/s at a field Es ~ 104 V/cm In GaAsthere is a velocity reduction (peak) before saturation. We’ll discuss this later 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.

  6. m E vd  E 1 + E sat A Simple Empirical Model for Velocity Saturation OrVd μ(E)E Where μ(E)  “Field Dependent Mobility” E << Esat, Vd = μE E << Esat, Vd  constant

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

  8. Still Another Model for Velocity Saturation: The Two Region Model

  9. 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

  10. 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 To model the data, use

  11. 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 To model the data, use Results

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

  13. Temperature Dependence of Velocity Saturation in Si Holes

  14. 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

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

  16. I-V Curves in Velocity Saturation Conditions

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