Chapter 2 MOS Transistor Theory Deep Submicron Effects
Chapter 2 MOS Transistor Theory (Deep Submicron Effects)
Simplified Transistor Model From TSMC 035 N-transistor model User defined VDS=3 V VDS=1 V ID= 574 m. A ID= 373 m. A VGS = 3 V VGS = 2 V VDS=1 V Copyright © 2005 Pearson Addison-Wesley. All rights reserved. ID= 182 m. A VDS=3 V ID= 201 m. A 2 -2
Lab 2: Transistor Design W= 6 l = 1, 2 mm Copyright © 2005 Pearson Addison-Wesley. All rights reserved. L=6 l = 1, 2 mm 2 -3
Lab 2: Simulated Curves VDS=1 V ID= 95 m. A VDS=3 V VDS=1 V ID= 100 m. A ID= 178 m. A VDS=3 V VGS = 2 V ID= 231 m. A VGS = 3 V Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -4
Comparing Model Results Vgs (V) ID (m. A) (Vds=1 V) ID (m. A) (Vds=3 V) simulated simplified Error (%) 2 V 95 182 92 100 201 101 3 V 178 373 109 231 574 111 Being the simulated results quite accurate, the simplified model produces very over-estimated values !! Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -5
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. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -6
Velocity Saturation (contn´d) Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -7
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-VDSAT 2 /2] Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -8
Applying vsat model vsat = 1, 58 X 105 m/s VDSAT = L. vsat /mn = 1, 2 x 10 -6. 1, 58 X 105 /421, 39 X 10 -4 = 4, 49 V Observe that for L=1, 2 mm, since VDSAT is very high, pinch-off (VGS-VTH) will occur first !! But, for L=0, 4 mm, VDSAT = 1, 5 V Therefore, for VGS= 3 V, VGS-VTH=2, 45 V, and pinch-off will not occur since saturation occurs first, for VDS = =VDSAT = 1, 5 V Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -9
Applying vsat model (contn´d) Simulation was performed again for W=L=0, 4 mm In vsat model, vsat = 1, 58 X 105 m/s; VDSAT = 1, 5 V Vgs (V) ID (m. A) (Vds=1 V) ID (m. A) (Vds=3 V) simulated simplified vsat 2 V 75 (95) 182 ? ? 81 (100) 201 ? ? 3 V 146 (178) 373 ? ? 159 (231) 574 ? ? Observations: W=L=1, 2 mm 1) Simplified model values are the same as before. Why? 2) For 0, 4 mm, LEVEL 53 model shows its effectiveness Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -10
Computing ID by vsat model VDSAT= 1, 5 V A) VGS-VTH < VDSAT (pinch-off) IDSAT = kn. (VGS-VTH) 2. /2 B) VGS-VTH > VDSAT (velocity saturation) IDSAT = kn. [(VGSVTH). VDSAT-VDSAT 2 /2] ( the current is linear to VGS) VGS=2 V VGS-VTH= 1, 45 V Case A or B? VGS=3 V VGS-VTH= 2, 45 V Case A or B?
Applying vsat model-2 Simulation was performed again for W=L=0, 4 mm In vsat model, vsat = 1, 58 X 105 m/s; VDSAT = 1, 5 V Vgs (V) ID (m. A) (Vds=1 V) ID (m. A) (Vds=3 V) simulated simplified w/ vsat 2 V 75 182 81 201 3 V 146 373 159 574 488 Observation: vsat model still over-estimates values of ID Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -12
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 Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -13
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 Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -14
a-law model example Observations: 1. Shockley is the simplified model 2. Values of Pc, Pv and a are not provided in this example Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2 -15
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