velocity saturation effects. ohms law this says the drift velocity v d is linear in the electric...
DESCRIPTION
Ohm’s “Law” Obviously, this says that the V d vs E curve looks qualitatively like: ETRANSCRIPT
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