Device Models (PN Diode, MOSFET )

Device Models (PN Diode, MOSFET ) Instructor: Steven P. Levitan steve@ece.pitt.edu TA: Gayatri Mehta, José Martínez Book: Digital Integrated Circuits: A Design Perspective; Jan Rabaey Lab Notes: Handed out http://infopad.eecs.berkeley.edu/~icdesign/ ECE 1192, 2006, Steven Levitan, University of Pittsburgh

Goal of this chapter Present intuitive understanding of device operation Introduction of basic device equations Introduction of models for manual analysis Introduction of models for SPICE simulation Analysis of secondary and deep-submicron effects Future trends

The DIODE B Al A SiO 2 p n Cross-section of pn-junction in an IC process A p n B One-dimensional representation Al A B diode symbol Mostly occurring as parasitic element in Digital ICs

Diodes in a CMOS circuit Copyright 2005 Pearson Addison-Wesley. All rights reserved.

Depletion Region Formation hole diffusion electron diffusion p n (a) Current flow. hole drift electron drift Charge Density - ρ + x Distance (b) Charge density. Electrical Field ξ x (c) Electric field. Potential V ψ 0 -W 1 W 2 x (d) Electrostatic potential.

Formation and characteristics of a pn junction Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

Forward Bias p n (W 2 ) p n0 L p n p0 p-region -W 1 0 W 2 n-region x diffusion Typically avoided in Digital ICs

Reverse Bias p n0 n p0 p-region -W 1 0 W 2 n-region x diffusion The Dominant Operation Mode

Diode Current a Simple Model

Models for Manual Analysis V D + I D = I S (e V D/φT 1) V D + + I D V Don (a) Ideal diode model (b) First-order diode model

PN Junction Diode DC Model (Details) Thermal Voltage Ф T = kt/q 0.0259 V ( 300 K) k Boltzmann constant (1.38066x10-23 J/K) T Absolute temperature ( K) q Electron charge (1.60218x10-19 C) I s In practice, this term has to be obtained by characterization since it is highly dependent on doping concentration, dimension, operative temperature etc. ECE 1192 2006, Steven Levitan, University of Pittsburgh

PN Junction: Dynamic Effects Primary effects Junction Capacitance Diffusion Capacitance Secondary Effects Avalanche Breakdown ECE 1192 2006, Steven Levitan, University of Pittsburgh

Junction Capacitance

Diffusion Capacitance

Integrated Diode Model R S + V D - I D C D

SPICE Parameters

The MOS Transistor Polysilicon Aluminum

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.

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

What is a Transistor? A Switch! An MOS Transistor V GS V T V GS S Ron D

MOS Transistors - Types and Symbols D D G G S NMOS Enhancement D S NMOS Depletion D G G B PMOS Enhancement S S NMOS with Bulk Contact

MOS Transistors Regions Transitions Copyright 2005 Pearson Addison-Wesley. All rights reserved.

MOS Transistors Operating regions Copyright 2005 Pearson Addison-Wesley. All rights reserved.

Threshold Voltage: Concept S - V GS + G D n+ n+ n-channel p-substrate Depletion Region B

Threshold Voltage - Derivation

The Body Effect 0.9 0.85 0.8 2-input NAND gate V DD 0.75 V T (V) 0.7 0.65 0.6 0.55 0.5 0.45 0.4-2.5-2 -1.5-1 -0.5 0 V (V) BS B A N2 N1 Drain of N1 is Source of N2 VSB of N2 >= 0

Current-Voltage Relations A good ol transistor -4 x 10 6 VGS= 2.5 V 5 4 Resistive Saturation VGS= 2.0 V I D (A) 3 V DS = V GS -V T Quadratic Relationship 2 VGS= 1.5 V 1 VGS= 1.0 V 0 0 0.5 1 1.5 2 2.5 V DS (V)

Transistor in Linear S V GS G V DS D I D n + V(x) + n + L x p-substrate B MOS transistor and its bias conditions

Transistor in Saturation V GS G V DS > V GS - V T S D n+ - V GS - V T + n+ Pinch-off

Current-Voltage Relations Long-Channel Device Cut-off (V GS V T < 0) no current (not really)

Current-Voltage Relations The Deep-Submicron Era 2.5 x 10-4 2 Early Saturation VGS= 2.5 V 1.5 VGS= 2.0 V I D (A) 1 VGS= 1.5 V Linear Relationship 0.5 VGS= 1.0 V 0 0 0.5 1 1.5 2 2.5 V DS (V)

Velocity Saturation υ n (m/s) υ sat = 10 5 Constant velocity Constant mobility (slope = µ) ξ c = 1.5 ξ (V/µm)

Perspective I D Long-channel device V GS = V DD Short-channel device V DSAT V GS -V T V DS

I D versus V GS 6 x 10-4 2.5 x 10-4 5 4 quadratic 2 1.5 linear I D (A) 3 I D (A) 2 1 1 0 0 0.5 1 1.5 2 2.5 V GS (V) Long Channel 0.5 quadratic 0 0 0.5 1 1.5 2 2.5 V GS (V) Short Channel

I D versus V DS I D (A) 6 x 10-4 5 4 3 2 VGS= 2.5 V Resistive Saturation VGS= 2.0 V V DS = V GS -V T VGS= 1.5 V I D (A) 2 1.5 1-4 2.5 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 0 0 0.5 1 1.5 2 2.5 V DS (V) Long Channel 0 0 0.5 1 1.5 2 2.5 V DS (V) Short Channel

A unified model for manual analysis G S D B

Simple Model versus SPICE 2.5 x 10-4 V DS =V DSAT 2 1.5 Velocity Saturated I D (A) 1 Linear 0.5 V DSAT =V GT V DS =V GT Saturated 0 0 0.5 1 1.5 2 2.5 V DS (V)

A PMOS Transistor 0 x 10-4 VGS = -1.0V -0.2 VGS = -1.5V -0.4 I D (A) -0.6 VGS = -2.0V Assume all variables negative! -0.8 VGS = -2.5V -1-2.5-2 -1.5-1 -0.5 0 V DS (V)

Transistor Model for Manual Analysis

The Transistor as a Switch V GS V T S Ron I D D V GS = V DD R mid R 0 V DD /2 V DD V DS

The Transistor as a Switch 7 x 105 6 5 R eq (Ohm) 4 3 2 1 0 0.5 1 1.5 2 2.5 V DD (V)

The Transistor as a Switch

MOS Capacitances Dynamic Behavior

Dynamic Behavior of MOS Transistor G C GS C GD S D C SB C GB C DB B

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.

MOS Capacitances Behavior! Copyright 2005 Pearson Addison-Wesley. All rights reserved.

The Gate Capacitance in an n-channel n MOSFET Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

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

Gate Capacitance Copyright 2005 Pearson Addison-Wesley. All rights reserved.

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

Gate Capacitance Behavior WLC ox C GC WLC ox C GC 2WLC ox WLC ox 2 C GC B C GCS = C GCD WLC ox 2 C GCS C GCD 3 V GS 0 V DS /(V GS -V T ) 1 Capacitance as a function of VGS (with VDS = 0) Capacitance as a function of the degree of saturation

Measuring the Gate Cap 10 3 10 216 I V GS Gate Capacitance (F) 9 8 7 6 5 4 3 2 2221.52 1 2 0.5 0 0.5 1 1.5 2 V GS (V)

Diffusion Capacitance Channel-stop implant N A 1 Side wall W Source N D Bottom x j L S Side wall Substrate N A Channel

Junction capacitances in a MOSFET Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

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.

Junction capacitance variation with reverse voltage Digital Integrated Circuits 2nd Introduction to Circuits, Fourth Edition by Peter Uyemura, Devices Copyright 2004 John Wiley & Sons. All rights reserved.

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.

Capacitances in 0.25 μm m CMOS process Values for a Typical Device:

The Sub-Micron MOS Transistor Threshold Variations Sub-threshold Conduction Parasitic Resistances

Threshold Variations V T V T Long-channel threshold Low V DS threshold Threshold as a function of the length (for low V DS ) L V DS Drain-induced barrier lowering (for low L)

Sub-Threshold I D vs VGS qvgs nkt I D I0e 1 e qv = kt DS Log Scale V DS from 0 to 0.5V

Sub-Threshold I D vs VDS I D qvgs qv = nkt kt I e 0 1 e DS ( 1+ λ V ) DS V GS from 0 to 0.3V Linear scale

Summary of MOSFET Operating Regions Strong Inversion V GS >V T Linear (Resistive) V DS <V DSAT Saturated (Constant Current) V DS V DSAT Weak Inversion (Sub-Threshold) V GS V T Exponential in V GS with linear V DS dependence

Parasitic Resistances G Polysilicon gate L D Drain contact V GS,eff S D W R S R D Drain

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

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

Main MOS SPICE Parameters

SPICE Parameters for Parasitics

SPICE Transistors Parameters