Lecture 21 OUTLINE The MOSFET (cont’d) • P-channel MOSFET • CMOS inverter analysis • Sub-threshold current • Small signal model Reading: Pierret 17.3; Hu 6.7, 7.2 P-Channel MOSFET • The PMOSFET turns on when VGS < VT – Holes flow from SOURCE to DRAIN DRAIN is biased at a lower potential than the SOURCE VG VS • VDS < 0 VD GATE P+ ID P+ N VB • IDS < 0 • |IDS| increases with • |VGS - VT| • |VDS| (linear region) • In a CMOS technology, the PMOS & NMOS threshold voltages are usually symmetric about 0, i.e. VTp = -VTn EE130/230A Fall 2013 Lecture 21, Slide 2 Long-Channel PMOSFET I-V • Linear region: I DS 0 VDS VGS VTp m W m Coxe p ,eff (VGS VTp VDS )VDS L 2 • Saturation region: I DS I Dsat VDS VGS VTp m W Coxe p ,eff (VGS VTp ) 2 2mL m = 1 + (3Toxe/WT) is the bulk-charge factor EE130/230A Fall 2013 Lecture 21, Slide 3 CMOS Inverter: Intuitive Perspective SWITCH MODELS VDD VDD CIRCUIT VDD G S Rp D VOUT = 0V VOUT = VDD VOUT VIN D G S Low static power consumption, since one MOSFET is always off in steady state EE130/230A Fall 2013 Rn VIN = VDD Lecture 21, Slide 4 VIN = 0V Voltage Transfer Characteristic N: sat P: sat VOUT N: off P: lin VDD C N: sat P: lin A B D E N: lin P: sat N: lin P: off 0 0 EE130/230A Fall 2013 VDD Lecture 21, Slide 5 VIN CMOS Inverter Load-Line Analysis VIN = VDD + VGSp IDn=-IDp increasing VIN VIN = 0 V – VOUT = VDD + VDSp VDSp=VOUT-VDD + VIN = VDD IDn=-IDp increasing VIN 0 VDD 0 VDSp = - VDD EE130/230A Fall 2013 VDSp = 0 Lecture 21, Slide 6 VOUT=VDSn Load-Line Analysis: Region A – IDn=-IDp VDSp=VOUT-VDD VIN VTn + IDn=-IDp 0 VDD 0 EE130/230A Fall 2013 Lecture 21, Slide 7 VOUT=VDSn Load-Line Analysis: Region B – IDn=-IDp VDSp=VOUT-VDD + IDn=-IDp VDD/2 > VIN > VTn 0 VDD 0 EE130/230A Fall 2013 Lecture 21, Slide 8 VOUT=VDSn Load-Line Analysis: Region D – IDn=-IDp VDSp=VOUT-VDD + IDn=-IDp VDD – |VTp| > VIN > VDD/2 0 VDD 0 EE130/230A Fall 2013 Lecture 21, Slide 9 VOUT=VDSn Load-Line Analysis: Region E – IDn=-IDp VDSp=VOUT-VDD VIN > VDD – |VTp| + IDn=-IDp 0 VDD 0 EE130/230A Fall 2013 Lecture 21, Slide 10 VOUT=VDSn MOSFET Effective Drive Current, IEFF M. H. Na et al., IEDM Technical Digest, pp. 121-124, 2002 CMOS inverter chain: V1 V2 V3 VDD CMOS VDD S inverter: D VIN D GND VOUT S NMOS DRAIN CURRENT VDD/2 IH + IL IEFF = 2 V2 t V3 pLH V1 tpHL TIME IH VIN = VDD IL 0.5VDD NMOS DRAIN VOLTAGE = VOUT EE130/230A Fall 2013 IDsat Lecture 21, Slide 11 VIN = ½VDD VDD Propagation Delay, td CMOS inverter chain: C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Fig. 6-20 VDD Voltage waveforms: VDD 1 CVDD t d t pHL t pLH 2 I EFF td is reduced by increasing IEFF and reducing load capacitance C EE130/230A Fall 2013 Lecture 21, Slide 12 Sub-Threshold Current • For |VG| < |VT|, MOSFET current flow is limited by carrier diffusion into the channel region. • The electric potential in the channel region varies linearly with VG, according to the capacitive voltage divider formula: Coxe 1 VC VG VG Coxe Cdep m • As the potential barrier to diffusion increases linearly with decreasing VG, the diffusion current decreases exponentially: I DS e EE130/230A Fall 2013 qVG / mkT Lecture 21, Slide 13 Sub-Threshold Swing, S 1 d (log 10 I DS ) S dVGS Cdep,min kT ln (10)(1 ) q Coxe log ID NMOSFET Energy Band Profile increasing E n(E) exp(-E/kT) Source increasing VGS Drain distance EE130/230A Fall 2013 Lecture 21, Slide 14 Inverse slope is subthreshold swing, S [mV/dec] 0 VT VGS VT Design Trade-off • Low VT is desirable for high ON current: IDsat (VDD - VT) 1<<2 • But high VT is needed for low OFF current: log ID Low VT VT cannot be aggressively reduced! High VT IOFF,low VT IOFF,high VT 0 EE130/230A Fall 2013 VGS Lecture 21, Slide 15 How to minimize S? Cdep,min kT S ln (10)(1 ) q Coxe EE130/230A Fall 2013 Lecture 21, Slide 16 MOSFET Small Signal Model (Saturation Region) • Conductance parameters: low-frequency: high-frequency: A small change in VG or VDS will result in a small change in ID id g d vd g m vg gd I D VD I D gm VG R. F. Pierret, Semiconductor Device Fundamentals, Fig. 17.12 EE130/230A Fall 2013 Lecture 21, Slide 17 I Dsat0 VG const VD const W eff Coxe mL (VGS VT ) Parasitic Components EE130/230A Fall 2013 Lecture 21, Slide 18 R.S. Muller & T.I. Kamins, Device Electronics for Integrated Circuits, Fig. 8.12 MOSFET Cutoff Frequency, fT The cut-off frequency fT is defined as the frequency when the current gain is reduced to 1. input current = j CG vG output current = g m vG vG here is ac signal CG is approximately equal to the gate capacitance, W L Cox g m vG 1 At the cutoff frequency (T = 2fT): 2 fT CG vG eff gm fT (VGS VT ) 2 2Coxe 2mL Higher MOSFET operating frequency is achieved by decreasing the channel length L EE130/230A Fall 2013 Lecture 21, Slide 19