# Lecture 4: CMOS Transistor Theory

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1 Introduction to CMOS VLSI Design Lecture 4: CMOS Transistor Theory David Harris, Harvey Mudd College Kartik Mohanram and Steven Levitan University of Pittsburgh

2 Outline q Introduction q MOS Capacitor q nmos I-V Characteristics q pmos I-V Characteristics q Gate and Diffusion Capacitance q Pass Transistors q RC Delay Models 3: CMOS Transistor Theory CMOS VLSI Design Slide 2

3 Introduction q So far, we have treated transistors as ideal switches q An ON transistor passes a finite amount of current Depends on terminal voltages Derive current-voltage (I-V) relationships q Transistor gate, source, drain all have capacitance I = C (ΔV/Δt) -> Δt = (C/I) ΔV Capacitance and current determine speed q Also explore what a degraded level really means 3: CMOS Transistor Theory CMOS VLSI Design Slide 3

4 MOS Transistors - Types and Symbols D D G G S NMOS Enhancement NMOS D S Depletion D G G B PMOS S Enhancement S NMOS with Bulk Contact Digital Integrated Circuits 2nd Devices

5 The MOS Transistor Polysilicon Aluminum Digital Integrated Circuits 2nd Devices

6 Controlling current flow in an nfet. Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

7 Controlling current flow in a pfet. Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

8 What is a Transistor? A Switch! A MOS Transistor V GS V T R o n V GS S D Digital Integrated Circuits 2nd Devices

9 I-V Curves Current (I) vs. Voltage (V) I = f(v) 6 x I D (A) Resistor I = V/R Diode I = Is*exp(k*V-Vt) V DS MOS I = f(vgs, Vds)

10 Terminal Voltages q Mode of operation depends on V g, V d, V s V gs = V g V s V gd = V g V d V gs - + V g + V gd - q q q V ds = V d V s = V gs - V V gd s Source and drain are symmetric diffusion terminals By convention, source is terminal at lower voltage Hence V ds 0 nmos body is grounded. First assume source is 0 too. Three regions of operation Cutoff Linear Saturation - V + ds V d 3: CMOS Transistor Theory CMOS VLSI Design Slide 10

11 MOS Capacitor q Gate and body form MOS capacitor q Operating modes Accumulation Depletion Inversion In general, MOS gate capacitance is not constant (a) (b) V g < polysilicon gate silicon dioxide insulator p-type body 0 < V g < V t depletion region V g > V t + - inversion region depletion region (c) 3: CMOS Transistor Theory CMOS VLSI Design Slide 11

13 nmos Cutoff q No channel q I ds = 0 d V gs = g + - V gd g s n+ n+ d s p-type body b 3: CMOS Transistor Theory CMOS VLSI Design Slide 13

14 nmos Linear q Channel forms q Current flows from d to s e - from s to d q I ds increases with V ds q Similar to linear resistor g s d V gs > V t V gs > V t V gd = V gs n+ n+ V ds = 0 p-type body b + - s s g g + - V gs > V gd > V t n+ n+ 0 < V ds < V gs -V t p-type body b d d I ds 3: CMOS Transistor Theory CMOS VLSI Design Slide 14

15 Linear Region V gs >V t & V gd >V t S V GS G V DS D I D I ds n + V(x) + n + V gd L p-substrate x V gs R Positive Charge on Gate: Channel exists, Current Flows since V ds > 0 I ds = k (W/L)((V gs -V t )V ds -V ds2 /2) B I ds I=V/R R= 1/(k (W/L)(V gs -V t )) V ds Digital Integrated Circuits 2nd Devices

16 nmos Saturation q Channel pinches off q I ds independent of V ds q We say current saturates q Similar to current source g d V gs > V t + - s g + - V gd < V t d I ds s n+ n+ p-type body b V ds > V gs -V t 3: CMOS Transistor Theory CMOS VLSI Design Slide 16

17 Saturation: V gs >V t & V gd <V t V GS I ds S G V DS > V GS - V T D V gd I ds n+ - V GS - V T + n+ V gs Positive Charge on Gate: Channel exists, Current Flows since V ds > 0 But: channel is pinched off I ds = (k /2)(W/L)(V gs -V t ) 2 Digital Integrated Circuits 2nd Devices

18 I-V Characteristics q In Linear region, I ds depends on How much charge is in the channel? How fast is the charge moving? 3: CMOS Transistor Theory CMOS VLSI Design Slide 18

20 Channel Charge q MOS structure looks like parallel plate capacitor while operating in inversion Gate oxide channel q Q channel = gate t ox L n+ n+ p-type body polysilicon gate W SiO2 gate oxide (good insulator, ε ox = 3.9) V g + + source V gs C g V gd drain - - channel n+ - + n+ V s V ds p-type body V d 3: CMOS Transistor Theory CMOS VLSI Design Slide 20

21 Channel Charge q MOS structure looks like parallel plate capacitor while operating in inversion Gate oxide channel q Q channel = CV q C = gate t ox L n+ n+ p-type body polysilicon gate W SiO2 gate oxide (good insulator, ε ox = 3.9) V g + + source V gs C g V gd drain - - channel n+ - + n+ V s V ds p-type body V d 3: CMOS Transistor Theory CMOS VLSI Design Slide 21

22 Channel Charge q MOS structure looks like parallel plate capacitor while operating in inversion Gate oxide channel q Q channel = CV q C = C g = ε ox WL/t ox = C ox WL q V = C ox = ε ox / t ox C ox = 8.6*fF/um 2 gate t ox L n+ n+ p-type body polysilicon gate W SiO2 gate oxide (good insulator, ε ox = 3.9) V g + + source V gs C g V gd drain - - channel n+ - + n+ V s V ds p-type body V d 3: CMOS Transistor Theory CMOS VLSI Design Slide 22

23 Channel Charge q MOS structure looks like parallel plate capacitor while operating in inversion Gate oxide channel q Q channel = CV q C = C g = ε ox WL/t ox = C ox WL q V = V gc V t = (V gs V ds /2) V t C ox = ε ox / t ox gate t ox L n+ n+ p-type body polysilicon gate W SiO2 gate oxide (good insulator, ε ox = 3.9) V g + + source V gs C g V gd drain - - channel n+ - + n+ V s V ds p-type body V d 3: CMOS Transistor Theory CMOS VLSI Design Slide 23

24 Carrier velocity q Charge is carried by e- q Carrier velocity v proportional to lateral E-field between source and drain q v = 3: CMOS Transistor Theory CMOS VLSI Design Slide 24

25 Carrier velocity q Charge is carried by e- q Carrier velocity v proportional to lateral E-field between source and drain q v = µe µ called mobility q E = 3: CMOS Transistor Theory CMOS VLSI Design Slide 25

26 Carrier velocity q Charge is carried by e- q Carrier velocity v proportional to lateral E-field between source and drain q v = µe µ called mobility q E = V ds /L q Time for carrier to cross channel: t = 3: CMOS Transistor Theory CMOS VLSI Design Slide 26

27 Carrier velocity q Charge is carried by e- q Carrier velocity v proportional to lateral E-field between source and drain q v = µe µ called mobility q E = V ds /L q Time for carrier to cross channel: t = L / v 3: CMOS Transistor Theory CMOS VLSI Design Slide 27

28 nmos Linear I-V q Now we know How much charge Q channel is in the channel I ds = How much time t each carrier takes to cross 3: CMOS Transistor Theory CMOS VLSI Design Slide 28

29 nmos Linear I-V q Now we know How much charge Q channel is in the channel I ds How much time t each carrier takes to cross = = Q channel t 3: CMOS Transistor Theory CMOS VLSI Design Slide 29

30 nmos Linear I-V q Now we know How much charge Q channel is in the channel I ds How much time t each carrier takes to cross Qchannel = t W V = µ C V V V L V = β V ds gs V t V 2 ds ds ox gs t 2 ds W β = µcox L 3: CMOS Transistor Theory CMOS VLSI Design Slide 30

31 Computed Curves Linear Resistor Vgs = 5v Vgs = 4.5v Vgs = 4.0v Digital Integrated Circuits 2nd Devices

32 nmos Saturation I-V q If V gd < V t, channel pinches off near drain When V ds > V dsat = V gs V t q Now drain voltage no longer increases current I ds = 3: CMOS Transistor Theory CMOS VLSI Design Slide 32

33 nmos Saturation I-V q If V gd < V t, channel pinches off near drain When V ds > V dsat = V gs V t q Now drain voltage no longer increases current V I = β V V dsat V 2 ds gs t dsat 3: CMOS Transistor Theory CMOS VLSI Design Slide 33

34 nmos Saturation I-V q If V gd < V t, channel pinches off near drain When V ds > V dsat = V gs V t q Now drain voltage no longer increases current V I = β V V dsat V 2 β = ( V ) 2 gs Vt 2 ds gs t dsat 3: CMOS Transistor Theory CMOS VLSI Design Slide 34

35 Computed Curves Linear Resistor Vgs = 5v Vgs = 4.5v Vgs = 4.0v 3: CMOS Transistor Theory CMOS VLSI Design Slide 35

36 nmos I-V Summary q Shockley 1 st order transistor models 0 Vgs < V V I = β V V ds V V V 2 < β ( V V ) 2 V > V 2 ds gs t ds ds dsat gs t ds dsat t cutoff linear saturation 3: CMOS Transistor Theory CMOS VLSI Design Slide 36

37 Example q We will be using a µm process for your project From TSMC Semiconductor t ox = 40 Å µ = 180 cm 2 /V*s V t = 0.4 V q Plot I ds vs. V ds V gs = 0, 0.3,, 1.8 Use W/L = 4/2 λ 14 W W W β = µ Cox = ( ) 120 µ A/ V 8 L = L L 2 3: CMOS Transistor Theory CMOS VLSI Design Slide 37

38 pmos I-V q All dopings and voltages are inverted for pmos q Mobility µ p is determined by holes Typically 2-3x lower than that of electrons µ n q Thus pmos must be wider to provide same current Often, assume µ n / µ p = 2 3: CMOS Transistor Theory CMOS VLSI Design Slide 38

39 Current-Voltage Relations Long-Channel Device Cut-off (V GS V T < 0) no current (not really) Digital Integrated Circuits 2nd Devices

40 I D versus V DS short channel device I D (A) 6 x VGS= 2.5 V Resistive Saturation VGS= 2.0 V V DS = V GS - V T VGS= 1.5 V I D (A) x 10 VGS= 2.5 V VGS= 2.0 V VGS= 1.5 V 1 VGS= 1.0 V 0.5 VGS= 1.0 V V DS (V) Long Channel V DS (V) Short Channel Digital Integrated Circuits 2nd Devices

41 Rabaey s unified model for manual analysis G S D B Digital Integrated Circuits 2nd Devices

42 Transistor Model for Manual Analysis Digital Integrated Circuits 2nd Devices

43 Simple Model versus SPICE 2.5 x 10-4 V DS =V DSAT Velocity Saturated I D (A) 1 Linear 0.5 V DSAT =V GT V DS =V GT Saturated V DS (V) Digital Integrated Circuits 2nd Devices

44 Even Simpler: The Transistor as a Switch V GS V T R o n S I D D V GS = V DD R mid R 0 V DD /2 V DD V DS Digital Integrated Circuits 2nd Devices

45 The Transistor as a Switch This week s Lab find R eq for our TSMC 180nm process Digital Integrated Circuits 2nd Devices

46 Saturation Effects Discharge of 1pf capacitor, with Vgs of 3,4,5 volts. Also, 12k resistor. d g Which is the resistor? s Digital Integrated Circuits 2nd Devices

47 More on Capacitance q Any two conductors separated by an insulator have capacitance q Gate to channel capacitor is very important Creates channel charge necessary for operation q Source and drain have capacitance to body Across reverse-biased diodes Called diffusion capacitance because it is associated with source/drain diffusion 3: CMOS Transistor Theory CMOS VLSI Design Slide 47

48 Gate Capacitance q Approximate channel as connected to source q C gs = ε ox WL/t ox = C ox WL = C permicron W q C permicron is typically about 2 ff/µm polysilicon gate W t ox L n+ n+ p-type body SiO2 gate oxide (good insulator, ε ox = 3.9ε 0 ) 3: CMOS Transistor Theory CMOS VLSI Design Slide 48

49 The Gate Capacitance Polysilicon gate Source n + x d x d W Drain n + L d Top view Gate-bulk overlap t ox Gate oxide n + L n + Cross section Digital Integrated Circuits 2nd Devices

50 Dynamic Behavior of MOS Transistor G C GS C GD S D C SB C GB C DB B Digital Integrated Circuits 2nd Devices

51 Physical visualization of FET capacitances Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

53 Gate Capacitance Behavior G G G S C GC C GC C GC D S D S D Cut-off Resistive Saturation Most important regions in digital design: saturation and cut-off Digital Integrated Circuits 2nd Devices

54 Measuring the Gate Cap I V GS Gate Capacitance (F) V GS (V) Digital Integrated Circuits 2nd Devices

55 Diffusion Capacitance q C sb, C db q Undesirable, called parasitic capacitance q Capacitance depends on area and perimeter Use small diffusion nodes Comparable to C g for contacted diff ½ C g for uncontacted Varies with process 3: CMOS Transistor Theory CMOS VLSI Design Slide 55

56 Diffusion Capacitance Channel-stop implant N A 1 Side wall W Source N D Bottom x j Side wall L S Substrate N A Channel Digital Integrated Circuits 2nd Devices

57 Calculation of the FET junction capacitance Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

58 Capacitances in 0.25 µm CMOS process Values for a Typical Device: Digital Integrated Circuits 2nd Devices

59 Parasitic Resistances G Polysilicon gate L D Drain contact V GS,eff S D W R S R D Drain Digital Integrated Circuits 2nd Devices

60 Final construction of the nfet RC model C G Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

61 Latchup V DD V DD p + n + n + p + p + n + R nwell p-source n-well R nwell R psubs p-substrate n-source R psubs (a) Origin of latchup (b) Equivalent circuit Digital Integrated Circuits 2nd Devices

62 Summary of MOSFET Operating Regions q Strong Inversion V GS > V T Linear (Resistive) V DS < V DSAT Saturated (Constant Current) V DS V DSAT q Weak Inversion (Sub-Threshold) V GS V T Exponential in V GS with linear V DS dependence Digital Integrated Circuits 2nd Devices

63 SPICE MODELS Level 1: Long Channel Equations - Very Simple Level 2: Physical Model - Includes Velocity Saturation and Threshold Variations Level 3: Semi-Emperical - Based on curve fitting to measured devices Level 4 (BSIM): Emperical - Simple and Popular Digital Integrated Circuits 2nd Devices

64 Main MOS SPICE Parameters Digital Integrated Circuits 2nd Devices

65 SPICE Parameters for Parasitics Digital Integrated Circuits 2nd Devices

66 SPICE Transistors Parameters Digital Integrated Circuits 2nd Devices

67 Circuit Simulation Model of CMOS Inverter Digital Integrated Circuits 2nd Devices

68 Pass Transistors q We have assumed source is grounded q What if source > 0? e.g. pass transistor passing V DD V DD V DD Digital 3: Integrated CMOS Circuits Transistor Theory Slide 68 2nd Devices

69 Pass Transistors q We have assumed source is grounded q What if source > 0? e.g. pass transistor passing V DD V DD V DD q V g = V DD If V s > V DD -V t, V gs < V t Hence transistor would turn itself off q nmos pass transistors pull no higher than V DD -V tn Called a degraded 1 Approach degraded value slowly (low I ds ) q pmos pass transistors pull no lower than V tp Digital 3: Integrated CMOS Circuits Transistor Theory Slide 69 2nd Devices

70 Pass Transistor Ckts V DD V DD V DD V DD V DD V DD V DD V DD V SS Digital 3: Integrated CMOS Circuits Transistor Theory Slide 70 2nd Devices

71 Pass Transistor Ckts V DD V DD V DD V DD V DD V DD Vs = V DD -V tn VDD -Vtn VDD-Vtn V DD -V tn V s = V tp V DD V DD -V tn V DD V DD -2V tn V SS Digital 3: Integrated CMOS Circuits Transistor Theory Slide 71 2nd Devices

72 Effective Resistance q Shockley models have limited value Not accurate enough for modern transistors Too complicated for much hand analysis q Simplification: treat transistor as resistor Replace I ds (V ds, V gs ) with effective resistance R I ds = V ds /R R averaged across switching of digital gate q Too inaccurate to predict current at any given time But good enough to predict RC delay Digital 3: Integrated CMOS Circuits Transistor Theory Slide 72 2nd Devices

73 RC Delay Model q Use equivalent circuits for MOS transistors Ideal switch + capacitance and ON resistance Unit nmos has resistance R, capacitance C Unit pmos has resistance 2R, capacitance C q Capacitance proportional to width q Resistance inversely proportional to width g d k s g R/k kc d s kc kc g d k s g s kc 2R/k kc kc d Digital 3: Integrated CMOS Circuits Transistor Theory Slide 73 2nd Devices

74 RC Values q Capacitance C = C g = C s = C d = 2 ff/µm of gate width Values similar across many processes q Resistance R 6 KΩ*µm in 0.6um process Improves with shorter channel lengths q Unit transistors May refer to minimum contacted device (4/2 λ) Or maybe 1 µm wide device Doesn t matter as long as you are consistent Digital 3: Integrated CMOS Circuits Transistor Theory Slide 74 2nd Devices

75 Inverter Delay Estimate q Estimate the delay of a fanout-of-1 inverter A 2 1 Y 2 1 Digital 3: Integrated CMOS Circuits Transistor Theory Slide 75 2nd Devices

76 Inverter Delay Estimate q Estimate the delay of a fanout-of-1 2C inverter R A 2 1 Y 2 1 R 2C C Y 2C C C Digital 3: Integrated CMOS Circuits Transistor Theory Slide 76 2nd Devices

77 Inverter Delay Estimate q Estimate the delay of a fanout-of-1 2C inverter R A 2 1 Y 2 1 R 2C C Y 2C C R 2C C 2C C C Digital 3: Integrated CMOS Circuits Transistor Theory Slide 77 2nd Devices

78 Inverter Delay Estimate q Estimate the delay of a fanout-of-1 2C inverter R A 2 1 Y 2 1 R 2C C Y 2C C R 2C C 2C C C d = 6RC Digital 3: Integrated CMOS Circuits Transistor Theory Slide 78 2nd Devices

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