1. MOS Transistor Theory (Deep Submicron Effects)
Chapter 2
MOS Transistor Theory
(Deep Submicron Effects)

2. Simplified Transistor Model
From TSMC035 N-transistor model
User defined
VGS = 3V
VDS=3V ID= 574 mA
VGS = 3V
VDS=1V ID= 373 mA
VGS = 2V
VDS=1V ID= 182 mA
VGS = 2V
VDS=3V ID= 201 mA
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3. Lab 2: Transistor Design
W= 6l = 1,2mm L=6l = 1,2mm
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4. Lab 2: Simulated Curves VGS = 2V VDS=1V ID= 95 mA VGS = 2V
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5. Comparing Model Results
Vgs (V)
ID (mA) (Vds=1V)
ID (mA) (Vds=3V)
simulated
simplified
Error
(%) 2V 95
182 92
100
201
101 3V
178
373
109
231
574
111
Being the simulated results quite accurate, the simplified model produces very over-estimated values !!
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6. Velocity Saturation
VDS produces an electric field from Drain to Source
In old large transistor technology (large L):
Fields are low (remember, for electric field E, potential difference DV and distance d: E=DV/d)
Carrier drift velocity is proportional to E.
In Deep Submicron Technologies (small L):
d is very small, and longitudinal electric field is high
Field gets to a critical value, Ecrit, reducing mobility.
Carrier drift velocity is not proportional to E anymore; velocity saturates.
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7. Velocity Saturation (contn´d)
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8. Traditional vsat model
Well before pinch-off (VDS = VGS-VTH), ID reaches to a saturation value due to velocity saturation (vsat is a SPICE technological parameter).
Simplifying assumptions are adopted:
Velocity saturates abruptly at Ecrit ; vsat= mn.Ecrit
VDSAT due to velocity saturation is constant (for any VGS); VDSAT = L.Ecrit = L. vsat /mn
If VGS-VTH < VDSAT, saturation occurs by pinch-off (we use the simplified ID saturation equation)
If VGS-VTH > VDSAT, saturation occurs by velocity saturation  IDSAT = kn. [(VGS-VTH). VDSAT-VDSAT2 /2]
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9. Applying vsat model vsat = 1,58 X 105 m/s
VDSAT = L. vsat /mn = 1,2x ,58 X 105 /421,39X10-4 = 4,49V
Observe that for L=1,2mm, since VDSAT is very high, pinch-off (VGS-VTH) will occur first !!
But, for L=0,4mm, VDSAT = 1,5 V
Therefore, for VGS= 3V, VGS-VTH=2,45V, and
pinch-off will not occur since saturation occurs first, for VDS = =VDSAT = 1,5 V
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10. Applying vsat model (contn´d)
Simulation was performed again for W=L=0,4mm
In vsat model, vsat = 1,58 X 105 m/s; VDSAT = 1,5 V
Vgs (V)
ID (mA) (Vds=1V)
ID (mA) (Vds=3V)
simulated
simplified
vsat 2V
75 (95)
182 ??
81 (100)
201 3V
146 (178)
373
159 (231)
574
W=L=1,2mm
Observations:
Simplified model values are the same as before. Why?
For 0,4 mm, LEVEL 53 model shows its effectiveness
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11. Computing ID by vsat model
VDSAT= 1,5V
A) VGS-VTH < VDSAT (pinch-off) IDSAT = kn. (VGS-VTH) 2./2
B) VGS-VTH > VDSAT (velocity saturation) IDSAT = kn. [(VGS-VTH). VDSAT-VDSAT2 /2] ( the current is linear to VGS)
VGS=2V  VGS-VTH= 1,45V  Case A or B?
VGS=3V  VGS-VTH= 2,45V  Case A or B?

12. Applying vsat model-2 Simulation was performed again for W=L=0,4mm
In vsat model, vsat = 1,58 X 105 m/s; VDSAT = 1,5 V
Vgs (V)
ID (mA) (Vds=1V)
ID (mA) (Vds=3V)
simulated
simplified
w/ vsat 2V 75
182 81
201 3V
146
373
159
574
488
Observation:
vsat model still over-estimates values of ID
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2-12

13. Mobility Degradation Up to now, VDSAT is the same for any VGS
Transversal electrical field due to VGS is also critical for Deep Submicron Technologies (vertical dimensions are also small)
Relatively high values of transversal electrical field leads to carrier scattering and mobility degradation
The values of mn and mp are smaller than the ideal ones
These effects are taken into account in the SPICE model LEVEL 53
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14. Empirical a-law model a-law is a simplified empirical model including:
Mobility degradation
Velocity saturation
It is not part of SPICE models
ID is given as: 0 (VGS<VTH : cutoff)
IDSAT.VDS/VDSAT (VDS<VDSAT : linear)
IDSAT (VDS>VDSAT : saturation)
IDSAT= Pc.(b/2) .(VGS-VTH)a ; VDSAT= Pv.(VGS-VTH) a/2
Pc, Pv and a are empirically extracted parameters
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15. a-law model example Observations: 1. Shockley is the simplified model
2. Values of Pc, Pv and a are not provided in this example
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