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EE 330 Lecture 16 Devices in Semiconductor Processes

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EE 330 Lecture 16 Devices in Semiconductor Processes EE 330 Lecture 16 Devices in Semiconductor Processes • Capacitors • MOSFETs Review from Last Lecture Diode Models Diode Characteristics Diode Characteristics 0.01 0.008 0.01 0.008 0.006 0.006 0.004 Id (amps) 0.004 Id (amps) 0.002 Id (amps) 0.002 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vd (volts) Vd (volts) ID VD Which model should be used? The simplest model that will give acceptable results in the analysis of a circuit Use of Piecewise Models for Nonlinear Devices when Analyzing Electronic Circuits Process: 1. Guess state of the device 2. Analyze circuit 3. Verify State 4. Repeat steps 1 to 3 if verification fails 5. Verify model (if necessary) Observations: o Analysis generally simplified dramatically (particularly if piecewise model is linear) o Approach applicable to wide variety of nonlinear devices o Closed-form solutions give insight into performance of circuit Review from Last Lecture Last from Review o Usually much faster than solving the nonlinear circuit directly o Wrong guesses in the state of the device do not compromise solution (verification will fail) o Helps to guess right the first time o Detailed model is often not necessary with most nonlinear devices o Particularly useful if piecewise model is PWL (but not necessary) o For practical circuits, the simplified approach usually applies Key Concept For Analyzing Circuits with Nonlinear Devices Review from Last Lecture Types of Diodes pn junction diodes Id I Id Id d Id Id Vd Vd Vd Vd Vd Vd Pin or Light Emitting Signal or Zener Varactor or Rectifier Photo LED Varicap Laser Diode Metal-semiconductor junction diodes Id Id Id Vd Vd Vd Schottky Barrier Basic Devices and Device Models • Resistor • Diode • Capacitor • MOSFET • BJT Capacitors • Types – Parallel Plate – Fringe – Junction Parallel Plate Capacitors A2 C A1 cond1 cond2 d insulator A = area of intersection of A1 & A2 One (top) plate intentionally sized smaller to determine C A C d Parallel Plate Capacitors Cap If C d unit area ε A C d C CdA where ε C d d Fringe Capacitors C d ε A C d A is the area where the two plates are parallel Only a single layer is needed to make fringe capacitors Fringe Capacitors C Capacitance Junction Capacitor C V p D d d n depletion A region C d is dielectric constant Note: d is voltage dependent -capacitance is voltage dependent C A φ -usually parasitic caps C jo for V B n FB 2 -varicaps or varactor diodes exploit VD 1 voltage dep. of C φB φB 0.6V n ; 0.5 Capacitance Junction Capacitor C 1.6 CAj0 1.4 1.2 1 0.8 VD 0.6 0.4 0.2 VD 0 -4 -3 -2 -1 0 1 C A φ C jo for V B n FB 2 VD 1 φB Voltage dependence is substantial φB 0.6V n ; 0.5 Basic Devices and Device Models • Resistor • Diode • Capacitor • MOSFET • BJT Drain Summary of Existing Models (for n-channel) Gate Source 1. Switch-Level model D D G = 0 G = 1 S S 2. Improved switch-level model G D RSW Switch closed for |VGS|= large CGS Switch open for |V |= small VG S GS S Improved Switch-Level Model Drain Drain Gate Gate Bulk Source Source G D RSW CGS VG Switch closed for VGS=“1” S Switch-level model including gate capacitance and channel resistance • Connect the gate capacitance to the source to create lumped model • Still neglect bulk connection Limitations of Existing MOSFET Models B G D V A Y DD RSW CGS R VGS S A B For minimum-sized devices in a 0.5u process with VDD=5V CGS 1.5fF 2KΩ n channel Rsw 6KΩ p channel What is RSW if MOSFET is not What is power dissipation if A is What is Y when A=B=VDD minimum sized? stuck at an intermediate voltage? Better Model of MOSFET is Needed! n-Channel MOSFET Poly Gate oxide n-active p-sub n-Channel MOSFET Gate Drain Source L W LEFF Bulk n-Channel MOSFET Poly Gate oxide n-active p-sub depletion region (electrically induced) n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB Apply small VGS (VDS and VBS assumed to be small) ID=0 Depletion region electrically induced in channel I =0 Termed “cutoff” region of operation G IB=0 n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB Increase VGS (VDS and VBS assumed to be small) ID=0 Depletion region in channel becomes larger IG=0 IB=0 n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB ID=0 Model in Cutoff Region IG=0 IB=0 n-Channel MOSFET Operation and Model VDS Critical value of VGS ID V that creates GS VBS IG inversion layer IB termed threshold voltage, VT) (VDS and VBS small) Increase VGS more Inversion layer forms in channel IDRCH=VDS Inversion layer will support current flow from D to S IG=0 Channel behaves as thin-film resistor IB=0 Triode Region of Operation ID I G V DS RCH VDS VGS IB VBS = 0 For VDS small L 1 RCH W VGS VT COX Behaves as a resistor between drain and source W I D μCOX VGS VT VDS L Model in Deep Triode Region I G I B 0 Triode Region of Operation ID IG RCH VGS IB VBS = 0 For VDS small L 1 RCH W VGS VT COX Resistor is controlled by the voltage VGS Termed a “Voltage Controlled Resistor” (VCR) n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB (VDS and VBS small) Increase VGS more Inversion layer in channel thickens IDRCH=VDS I =0 RCH will decrease G Termed “ohmic” or “triode” region of operation IB=0 n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB (VBS small) Increase VDS Inversion layer thins near drain ID=? I =0 ID no longer linearly dependent upon VDS G Still termed “ohmic” or “triode” region of operation IB=0 Triode Region of Operation ID IG VDS VGS IB VBS = 0 For VDS larger W V L 1 I μC V V DS V R D OX GS T DS CH L 2 W VGS VT COX I G I B 0 Model in Triode Region n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB (VBS small) Increase VDS even more Inversion layer disappears near drain ID=? Termed “saturation”region of operation IG=0 IB=0 Saturation first occurs when VDS=VGS-VT Saturation Region of Operation ID IG VDS W VDS VGS I D μCOX VGS VT VDS IB L 2 or equivalently For VDS at onset of VBS = 0 saturation W VGS VT ID μCOX VGS VT VGS VT L 2 or equivalently μC W I OX V V 2 D 2L GS T I G I B 0 n-Channel MOSFET Operation and Model VDS VGS ID VBS IG IB (VBS small) Increase VDS even more (beyond VGS-VT) Nothing much changes !! ID=? I =0 Termed “saturation”region of operation G IB=0 Saturation Region of Operation ID IG VDS VGS IB VBS = 0 For VDS in Saturation μCOX W 2 ID VGS VT 2L Model in Saturation Region IG I B 0 Model Summary n-channel MOSFET ID 0 V V IG GS T Cutoff VDS W VDS IDμC OX V GS V T V DS V GS VT V DS V GS V T Triode L2VGS IB W 2 μC V V VV B VS = 0 V V V Saturation OX2L GS T GS T DS GS T IGB =I =0 L 1 Model Parameters: {µ, VT, COX} Design Parameters : {W, L} RCH ThisW is Va GSpiecewise VT modelCOX (not piecewise linear though) (Deep triode special case of triode where VDS is small ) Note: This is the third model we have introduced for the MOSFET Model Summary n-channel MOSFET ID 0 VGS VT W V IG DS ID μCOX VGS VT VDS VGS VT VDS VGS VT L 2 VDS VBS W 2 VGS IB μCOX VGS VT VGS VT VDS VGS VT 2L VBS = 0 IGB =I = 0 Observations about this model (developed for VBS=0): ID = f 1 V GS ,V DS IG = f 2 V GS ,V DS IB = f 3 V GS ,V DS This is a nonlinear model characterized by the functions f1, f2, and f3 where we have assumed that the port voltages VGS and VDS are the independent variables and the drain currents are the dependent variables General Nonlinear Models I1 I2 3-terminal I1 = f 1 V 1 ,V 2 Nonlinear v1 Device v2 I2 = f 2 V 1 ,V 2 I1 and I2 are 3-dimensional relationships which are often difficult to visualize Two-dimensional representation of 3-dimensional relationships Graphical Representation of MOS Model W V2 ID I=μC DS D OX L2 3 Triode VGS4 2.5 2 VGS3 1.5 Saturation 1 Deep Triode VGS2 RegionRegion 0.5 VGS1 0 0 1 2 3 4 5 VDS VDS 0 V V GS T Cutoff W V I μC V VDS V V V V V V D OX GS T DS GS T DS GS T L2 W 2 μCOX V GS V T V GS V T V DS V GS V T 2L Parabola separated triode and saturation I =I =0 GB regions and corresponds to VDS=VGS-VT PMOS and NMOS Models D S G G S D W ID I = μC V2 D OXL DS 3 Triode VGS4 2.5 2 VGS3 1.5 Saturation 1 Deep Triode VGS2 RegionRegion 0.5 VGS1 0 0 1 2 3 4 5 VDS VDS Cutoff • Functional form identical, sign changes and parameter values different • Will give details about p-channel model later Example: Determine the output voltage for the following circuit using the square-law model of the MOSFET.
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