MOS Transistor Theory

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1 CHAPTER 3 MOS Transistor Theory

2 Outline 2 1. Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

3 MOS Transistor symbols Introduction 3 nmos symbols pmos symbols

4 MOS Structure 4 Accumulation Mode Depletion Mode Inversion Mode

5 Cutoff nmos Operation Regions 5 V gs < V t : no channel Linear V gs > V t, V gd > V t : linear resistor Saturation V gs > V t, V gd < V t : channel pinchoff

6 Outline 6 1. Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

7 MOS Channel Charge Q C V V C V V V channel g gc t g gs ds t C WL t C WL g ox ox ox Qchannel L E, E Vds / L, Ids, tchannel t channel

8 Q C WL V V V 1 channel gs 2 ds t ds ox E, E V / L, 2 L L L E V I Q t channel channel, t ds ds channel Ideal I-V Equations 8 L Ideal I-V equation I ds Q t channel channel Qchannel L/ W Vds C V V V L 2 Vds Vgs Vt Vds 2 ox gs t ds Ids V V V 2 V 2 0 V 2 gs Vt gs t ds ds V gs V t V V V V ds dsat gs t V V V V ds dsat gs t cutoff linear saturation

9 Ideal I-V Characteristics 9 nmos I-V pmos I-V

10 Outline Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

11 Nonideal I-V Effects 11 Velocity saturation: at high V ds, the carrier velocity is not proportional to lateral field. I ds decrease. Mobility degradation: at high V gs, the carrier scatter more and mobility decrease. I ds decrease. Channel length modulation effect: at high V ds, depletion of S/D, effective L. I ds increase. Subthreshold conduction: V gs < V t, I ds is exponentially dropoff instead of abruptly becoming zero. Drain/Source leakage: reverse diode junction leakage. Non-zero gate current I g : carriers tunneling effect. Body effect: threshold voltage V t is influence by V bs (body-tosource voltage).

12 Velocity Saturation 12 Carrier velocity : non-linearly proportional to lateral electrical field before velocity saturation E 1E E lat lat sat : carrier velocity : mobility E V L : lateral electrical field E lat sat ds sat I ds will saturate due to velocity saturation, it depends on channel length L and applied V ds. Qchannel Qchannel I C W V V t L/ ds ox gs t sat channel sat

13 Ids I dsat 0 V V I dsat ds dsat α-power Law Model 13 α-power Law Model: piece-linear model to illustrate MOSs I-V characteristic with velocity saturation. V V V gs ds ds Idsat Pc Vgs V t 2 V t V V dsat dsat cutoff linear saturation, V /2 dsat P Vgs V t Empirical parameters: Pc, P, Because of μ p < μ n, pmos experience less velocity saturation than nmos, therefore α p > α n Mobility degradation is modeled by a μ eff < μ, and the it can be included in the parameter α

14 Channel Length Modulation 14 Effective channel length: is reduced due the wider depletion region at high V ds L L L eff d The I-V equation at saturation region with channel length modulation effect. λ is the empirical parameter 2 Vgs Vt Ids 1 Vds, / L 2 With shorter L, λ, result in output resistance, then MOSFET s intrinsic gain

15 Body Effect 15 The threshold voltage V t is increased by positive V sb. V sb < 0, V t, OFF leakage Design tradeoff N A Vt Vt 0 [ 2 s Vsb 2 s ], s 2T ln n V t0 : the threshold voltage for V sb = 0 φ f : fabrication-process parameter i t ox ox 2qN A si 2qN C ox A si γ : Body-effect parameter (fabrication-process parameter) N A : Doping concentration of p-type substrate ε s : permittivity of silicon=11.7 ε 0

16 Subthreshold Conduction 16 Leakage current at subthreshold region V gs < V t : weak inversion Ids I e e V V V nt T ds0 1 gs t ds I ds0 e T Leakage current = 0, when V ds = 0. It increase exponentially with V gs. Drain-Induced Barrier Lowering (DIBL) : the V t will be reduced by a positive V ds. It will worse the leakage at subthreshold. It acts like channel length modulation effect at active mode. VtV t Vds

17 Junction Leakage 17 S/D junction leakage from a reverse-biased diode VD T ID IS e 1 Junction leakage used to be the storage time limitation. In modern transistor with shorter length, subthreshold leakage far exceed junction leakage.

18 Tunneling 18 Gate leakage: from carriers' tunneling through gate oxide. It is exponentially reverse proportional to gate oxide. Hi-K (dielectric constant) gate insulator is used to reduce it.

19 Temperature Dependence 19 T μ : T T T r Tr k T V t : V T V T k T T t t r t r T I OFF I ON T I dsat T The circuit performance is improved: subthreshold leakage, saturation velocity, mobility, junction capacitance. But breakdown voltage.

20 Geometry Dependence 20 Effective channel length and width L L X 2L eff drawn L D X L, X : Poly over-etch W W W X 2W eff drawn W D L, W :Source-drian lateral diffusion Use identical and same orientation MOSFET to get a good matching. ex. Current mirror D D

21 Outline Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

22 C-V Characteristics 22 Gate capacitance: with advance technology, t ox, L, C permicron keeps constant. C C WL C W g ox permicron ox Cpermicron CoxL L tox Parasitic capacitance: C db and C sb are from reverse p-n junction and proportional to S/D area.

23 MOS Gate Capacitance Model 23 Gate capacitance: it varies with channel behavior at different operation region C C WL 0 ox S/D overlap capacitance: C gs(overlap) & C gd(overlap) are from S/D lateral diffusion, don t confused with C gs & C gd C C W gs( overlap ) gd ( overlap ) gsol C C W gdol

24 C gc vs. V gs & V ds 24 C gc vs. V gs C gc vs. V ds

25 Gate Capacitance vs. V ds 25 Long channel device: C gd will becomes near 0 at saturation Short channel device: more C gd(overlap) and C gs(overlap) factor

26 Data-Dependent Gate Capacitance 26

27 Outline Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

28 CMOS Inverter DC Characteristic I 28

29 CMOS Inverter DC Characteristic II 29 I ds vs. V ds (nmos & pmos) For pmos, I d, V gs, V ds, V th <0 pmos I-V as load-line of nmos input device.

30 CMOS Inverter DC Characteristic III 30 V in V out DC transfer curve Rail-to-rail operation V in I DD DC transfer curve Dynamic power dissipation

31 DC Response 31 DC Response: V out vs. V in for a gate Ex: Inverter When V in = 0 -> V out = V DD When V in = V DD -> V out = 0 In between, V out depends on transistor size and current By KCL, must settle such that I dsn = I dsp We could solve equations V in But graphical solution gives more insight V DD I dsp I dsn V out

32 Transistor Operation 32 Current depends on region of transistor behavior For what V in and V out are nmos and pmos in Cutoff? Linear? Saturation?

33 nmos Operation 33 Cutoff Linear Saturated V gsn < V gsn > V gsn > V dsn < V dsn > V DD V in I dsp I dsn V out

34 nmos Operation 34 Cutoff Linear Saturated V gsn < V tn V gsn > V tn V gsn > V tn V dsn < V gsn V tn V dsn > V gsn V tn V DD V in I dsp I dsn V out

35 nmos Operation 35 Cutoff Linear Saturated V gsn < V tn V gsn > V tn V gsn > V tn V dsn < V gsn V tn V dsn > V gsn V tn V DD V gsn = V in V dsn = V out V in I dsp I dsn V out

36 nmos Operation 33 Cutoff Linear Saturated V gsn < V tn V in < V tn V gsn > V tn V in > V tn V dsn < V gsn V tn V out < V in - V tn V gsn > V tn V in > V tn V dsn > V gsn V tn V out > V in - V tn V DD V gsn = V in V dsn = V out V in I dsp I dsn V out

37 pmos Operation 37 Cutoff Linear Saturated V gsp > V gsp < V gsp < V dsp > V dsp < V DD V in I dsp I dsn V out

38 pmos Operation 38 Cutoff Linear Saturated V gsp > V tp V gsp < V tp V gsp < V tp V dsp > V gsp V tp V dsp < V gsp V tp V DD V in I dsp I dsn V out

39 pmos Operation 39 Cutoff Linear Saturated V gsp > V tp V gsp < V tp V gsp < V tp V dsp > V gsp V tp V dsp < V gsp V tp V DD V gsp = V in - V DD V dsp = V out - V DD V tp < 0 V in I dsp I dsn V out

40 pmos Operation 40 Cutoff Linear Saturated V gsp > V tp V in > V DD + V tp V gsp < V tp V in < V DD + V tp V dsp > V gsp V tp V out > V in - V tp V gsp < V tp V in < V DD + V tp V dsp < V gsp V tp V out < V in - V tp V DD V gsp = V in - V DD V dsp = V out - V DD V tp < 0 V in I dsp I dsn V out

41 I-V Characteristics 41 Make pmos is wider than nmos such that n = p V gsn5 I dsn V gsn4 V gsn3 -V dsp V gsp1 V gsp2 -V DD 0 V DD V gsn2 V gsn1 V gsp3 V dsn V gsp4 -I dsp V gsp5

42 Current vs. V out, V in 42 V in0 V in5 I dsn, I dsp V in1 V in4 V in2 V in3 V in3 V in4 V in2 V in1 V out V DD

43 Load Line Analysis 43 For a given V in : Plot I dsn, I dsp vs. V out V out must be where currents are equal in V in0 V in5 I dsn, I dsp V in1 V in4 V in2 V in3 V DD I dsp V in3 V in4 V in2 V in1 V in I dsn V out V out V DD

44 Load Line Analysis 44 V in = 0 V in0 I dsn, I dsp V in0 V out V DD

45 Load Line Analysis 45 V in = 0.2V DD I dsn, I dsp V in1 V in1 V out V DD

46 Load Line Analysis 46 V in = 0.4V DD I dsn, I dsp V in2 V in2 V out V DD

47 Load Line Analysis 47 V in = 0.6V DD I dsn, I dsp V in3 V in3 V out V DD

48 Load Line Analysis 48 V in = 0.8V DD I dsn, I dsp V in4 V in4 V out V DD

49 Load Line Analysis 49 V in = V DD V in0 V in5 I dsn, I dsp V in1 V in2 V in3 V in4 V out V DD

50 Load Line Summary 50 V in0 V in5 I dsn, I dsp V in1 V in4 V in2 V in3 V in3 V in4 V in2 V in1 V out V DD

51 DC Transfer Curve 51 Transcribe points onto V in vs. V out plot V DD A B V in0 V in5 V in1 V in4 V out C V in2 V in3 V in3 V in4 V in2 V in1 0 D E V tn V DD /2 V DD +V tp V out V DD V in V DD

52 Operating Regions 52 Revisit transistor operating regions Region nmos pmos A B C D E V out V DD A B 0 C D E V tn V DD /2 V DD +V tp V in V DD

53 Operating Regions 53 Revisit transistor operating regions Region nmos pmos A Cutoff Linear B Saturation Linear C Saturation Saturation D Linear Saturation E Linear Cutoff V out V DD A B 0 C D E V tn V DD /2 V DD +V tp V in V DD

54 CMOS Inverter Operation 54

55 Beta Ratio Effect 55 β parameters and ratio C p p ox p C W L W L n n ox n ratio p n β ratio = 1: largest noise margin μ n > μ p, choose (W/L) p > (W/L) n to make β ratio = 1 β ratio > 1: HI-skewed inverter, switching threshold > 0.5V DD β ratio < 1: LO-skewed inverter, switching threshold < 0.5V DD

56 Noise Margin I 56 Noise margin definition The allowable noise voltage on the input that the output wont be corrupted. V V V V IH IL OH OL NM V V L IL OL NM V V H OH IH minimum HIGH input voltage maximum LOW input voltage minimum HIGH output voltage maximum LOW output voltage

57 Indeterminate region (forbidden zone) Noise Margin II 57 V V V : output unknown logic level IL in IH

58 β ratio > 1 β Ratio and Noise Margin 58 Switching threshold > 0.5V DD V IH NM H V IL NM L β ratio < 1 Switching threshold < 0.5V DD V IH NM H V IL NM L Noise is scaled with V DD VDD, smaller NM is acceptable.

59 Ratioed Inverter Transfer Function I 59 nmos inverters with resistive of constant current load Transfer function depends on the ratio of pull-down to the pull-up transistor (static load).

60 Ratioed Inverter Transfer Function II 60 Pseudo-nMOS inverters with turn-on pmos as load Turn-ON pmos is made by a depletion mode nmos in pure nmos process. Dissipating static power when V o = LOW Poor NM but smaller area & input capacitance loading

61 Pass Transistor DC Characteristic 61 Threshold drop nmos : can NOT pass 1 pmos : can NOT pass 0 Need to consider BODY EFFECT. ON resistance depends on V in Need to BOOST gate voltage with small V DD

62 Inverter + transmission gate Tristate Inverter 62 For the same size n and p devices, it is approximately half the speed of complementary CMOS inverter. The structure in (d) is suffered from A s toggle in tristate. Need to consider BODY EFFECT.

63 Outline Introduction 2. Ideal I-V Characteristics 3. Nonideal I-V Effects 4. C-V Characteristics 5. DC Transfer Characteristics 6. Switch-level RC Delay Models

64 Effective Resistance R 64 R: effective resistance of unit nmos (minimum W & L) An pmos has resistance 2R(or 3R) because of smaller mobility In linear region, it is inverse proportional to W/L and V gs 1 I ds 1 1 L 1 R Vds C W Vgs V t ox Vgs Vt C: gate capacitance of unit transistor (nmos & pmos) It is proportional to gate area W*L C: junction capacitance of S/D of unit transistor It is proportional to gate width W nmos of k times unit width has resistance R/k, gate capacitance kc and S/D capacitance kc.

65 RC Circuit Model 65 pmos of k times unit width has resistance 2R/k, gate capacitance kc and S/D capacitance kc nmos parasitic capacitors are referred to GND (p-body) and pmos parasitic capacitors are referred to VDD (n-well)

66 Inverter Propagation Delay 66 Fanout-of-1 Inverter Choose pmos width size to be x2~x3 of that of nmos t R 6C 6RC pd

67 R of Transmission Gate 67 Effective resistance of transmission gate is the parallel combination of nmos and pmos It depends on the signal to be pass pmos pass 0 weakly with larger resistance 4R nmos pass 1 weakly with larger resistance 2R Usually choose same size of nmos/pmos in transmission gate Increase MOS size R C : need to check the tradeoff

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