IL 2222 - MOSFET Professor Ahmed Hemani Dept. Of ES, School of ICT, KTH Kista Email: hemani@kth.se Website: www.it.kth.se/~hemani

Usually made of Poly Silicon MOS Capacitor, MOSFET MOS: Metal-Oxide-Semiconductor ~1.5nm thick Few oxide molecules Usually made of Poly Silicon Vg Vg gate metal gate SiO2 SiO2 N+ N+ Si body P-body MOS transistor MOS capacitor Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Energy Diagram at Vg= 0

Flat-band Condition and Flat-band Voltage

Fs is neglible in accumulation Surface Accumulation Fs is neglible in accumulation fs : surface potential, band bending Vox: voltage across the oxide Make Vg < Vfb

Surface Depletion ( vg > vfb )

Surface Depletion Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Threshold Condition and Threshold Voltage Threshold (of inversion): ns = Na , or (Ec–Ef)surface= (Ef – Ev)bulk , or  A = B, and C = D Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Threshold Voltage At threshold, Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Threshold Voltage + for P-body, – for N-body

Strong Inversion–Beyond Threshold Vg > Vt

Inversion Layer Charge, Qinv (C/cm2) Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Choice of Vt and Gate Doping Type Vt is generally set at a small positive value So that, at Vg = 0, the transistor does not have an inversion layer and current does not flow between the two N+ regions. Enhancement type device P-body is normally paired with N+-gate to achieve a small positive threshold voltage. N-body is normally paired with P+-gate to achieve a small negative threshold voltage. Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Review : Basic MOS Capacitor Theory Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Review : Basic MOS Capacitor Theory total substrate charge, Qs Review : Basic MOS Capacitor Theory Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOS CV Characteristics Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOS CV Characteristics The quasi-static CV is obtained by the application of a slow linear- ramp voltage (< 0.1V/s) to the gate, while measuring Ig with a very sensitive DC ammeter. C is calculated from Ig = C·dVg/dt. This allows sufficient time for Qinv to respond to the slow-changing Vg . Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Equivalent circuit in the depletion and the inversion regimes (b) (c) (d) General case for both depletion and inversion regions. In the depletion regions Vg  Vt Strong inversion Modern Semiconductor Devices for Integrated Circuits (C. Hu) 18

Modern Semiconductor Devices for Integrated Circuits (C. Hu) MOSFET The MOSFET (MOS Field-Effect Transistor) is the building block of Gb memory chips, GHz microprocessors, analog, and RF circuits. MOSFET the following characteristics: small size high speed low power high gain Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Introduction to the MOSFET Basic MOSFET structure and IV characteristics Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Introduction to the MOSFET Two ways of representing a MOSFET: Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Complementary MOSFETs Technology Modern Semiconductor Devices for Integrated Circuits (C. Hu)

CMOS (Complementary MOS) Inverter Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOSFET Vt and the Body Effect Two capacitors => two charge components Redefine Vt as Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOSFET Vt and the Body Effect Body effect: Vt is a function of Vsb. When the source-body junction is reverse-biased, Vt increases. Body effect coefficient: a = Cdep/Coxe = 3Toxe / Wdep Body effect slows down circuits? How can it be reduced? Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Retrograde Body Doping Profiles Wdmax for retrograde doping Wdmax for uniform doping Wdep does not vary with Vsb . Retrograde doping is popular because it reduces off-state leakage and allows higher surface mobility. Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Modern Semiconductor Devices for Integrated Circuits (C. Hu) Uniform Body Doping When the source/body junction is reverse-biased, there are two quasi-Fermi levels (Efn and Efp) which are separated by qVsb. An NMOSFET reaches threshold of inversion when Ec is close to Efn , not Efp . This requires the band-bending to be 2fB + Vsb , not 2fB. g is the body-effect parameter. Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Modern Semiconductor Devices for Integrated Circuits (C. Hu) Channel voltage Vcs (x) x = 0: Vcs = Vs x = L: Vcs = Vd Qinv in MOSFET Qinv = – Coxe(Vgs – Vcs – Vt0 – a (Vsb+Vcs) = – Coxe(Vgs – Vcs – (Vt0 + a Vsb) – a Vcs) = – Coxe(Vgs – mVcs – Vt) m º 1 +a = 1 + 3Toxe/Wdmax m is called the bulk-charge factor Typically m is 1.2 but can be simplified to 1 Modern Semiconductor Devices for Integrated Circuits (C. Hu)

How to Measure the Vt of a MOSFET ? B Method A. Vt is measured by extrapolating the Ids versus Vgs curve to Ids = 0. Method B. The Vg at which Ids =0.1mA W/L Modern Semiconductor Devices for Integrated Circuits (C. Hu)

m is typically 1.2 but can be simplified to 1 Basic MOSFET IV Model Ids= WQinvv= WQinvmnE = WCox(Vgs– mVcs – Vt)mndVcs/dx IdsL = WCoxmn(Vgs – Vt – mVds/2)Vds Process Transconductance Gain factor m is typically 1.2 but can be simplified to 1 Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Vdsat : Drain Saturation Voltage Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Saturation Current and Transconductance Drain current in saturation region Transconductance: gm= dIds/dVgs Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Modern Semiconductor Devices for Integrated Circuits (C. Hu) Saturation – Pinch Off Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Channel Length Modulation Increasing the Vds has the effect of the reducing the channel length as the depletion region on the drain side increases. Channel length reduction  lower resistance  Increase in Drain Current More pronounced for short channels One of the five short channel effects

Modern Semiconductor Devices for Integrated Circuits (C. Hu) Velocity Saturation x (V/µm) c = 1.5 u n ( m / s ) sat = 10 5 Constant mobility (slope = µ) Constant velocity sat n v E + = 1 m E << Esat : v = m E n E >> Esat : v = m Esat n Velocity saturation has large and deleterious effect on the Ion of MOSFETS Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOSFET IV Model with Velocity Saturation Vcs /L– the average electric field is replaced by inv ds v WQ I = sat cs ns t gs oxe ds E dx dV V mV WC I / 1 ) ( + - = m cs sat L V ds t gs ns oxe dV E I mV WC dx ] / ) ( [ - = ò m sat ds t gs ns oxe E V I m WC L / ) 2 ( - = Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOSFET IV Model with Velocity Saturation ds t gs ns oxe + - = 1 ) 2 ( L E V I channel - long sat ds / 1 + = Modern Semiconductor Devices for Integrated Circuits (C. Hu)

MOSFET IV Model with Velocity Saturation dV dI ds , Solving = L mE V m sat t gs dsat / ) ( 2 1 - + = A simpler and more accurate Vdsat is: L E V m sat t gs dsat 1 + - = 2 v º E dsat sat m ns Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Modern Semiconductor Devices for Integrated Circuits (C. Hu) EXAMPLE: Drain Saturation Voltage Question: At Vgs = 1.8 V, what is the Vdsat of an NFET with Toxe = 3 nm, Vt = 0.25 V, and Wdmax = 45 nm for (a) L =10 mm, (b) L = 1 um, (c) L = 0.1 mm, and (d) L = 0.05 mm? Solution: From Vgs , Vt , and Toxe , mns is 200 cm2V-1s-1. Esat= 2vsat/m ns = 8 104 V/cm m = 1 + 3Toxe/Wdmax = 1.2 1 - | ø ö ç è æ + = L E V m sat t gs dsat Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Modern Semiconductor Devices for Integrated Circuits (C. Hu) EXAMPLE: Drain Saturation Voltage 1 ç è æ + - = L E V m sat t gs dsat | ø ö (a) L = 10 mm, Vdsat= (1/1.3V + 1/80V)-1 = 1.3 V (b) L = 1 mm, Vdsat= (1/1.3V + 1/8V)-1 = 1.1 V (c) L = 0.1 mm, Vdsat= (1/1.3V + 1/.8V)-1 = 0.5 V (d) L = 0.05 mm, Vdsat= (1/1.3V + 1/.4V)-1 = 0.3 V Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Idsat with Velocity Saturation Substituting Vdsat for Vds in Ids equation gives: L mE V I channel - long C mL W sat t gs dsat s ox + = 1 ) ( 2 m Very short channel case: t gs sat V L E - << ) ( L mE V C Wv I sat t gs ox dsat - = ) ( V C Wv I t gs ox sat dsat - = Idsat is proportional to Vgs–Vt rather than (Vgs – Vt)2 , not as sensitive to L Modern Semiconductor Devices for Integrated Circuits (C. Hu)

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

Velocity Saturation I V The IDSAT in short Channel Device has linear dependence on VGS as opposed to square dependence thus significantly reducing the drain current delivered for a given voltage and thus slows down the device I D V DS DSAT GS - V T = V DD Long-channel device Short-channel device The Short Channel Device enters saturation before VDS > VGS - VT

Modern Semiconductor Devices for Integrated Circuits (C. Hu) Velocity Saturation What is the main difference between the Vg dependence of the long- and short-channel length IV curves? Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Sub-Threshold Conduction 0.5 1 1.5 2 2.5 10 -12 -10 -8 -6 -4 -2 V GS (V) I D (A) VT Linear Exponential Quadratic The Slope Factor S is DVGS for ID2/ID1 =10 Typical values for S: 60 .. 100 mV/decade

A Unified Model Velocity Saturated Linear Saturated G S D B VDS=VDSAT 0.5 1 1.5 2 2.5 x 10 -4 V DS (V) I D (A) Velocity Saturated Linear Saturated VDSAT=VGT VDS=VDSAT VDS=VGT A Unified Model S D G B

Transistor Model for Manual Analysis

The Transistor as a Switch

The Transistor as a Switch

Dynamic Behavior of MOS Transistor

The Gate Capacitance x L Polysilicon gate Top view Gate-bulk overlap d L Polysilicon gate Top view Gate-bulk overlap Source n + Drain W t ox n + Cross section L Gate oxide

Gate Capacitance Cut-off Resistive Saturation Most important regions in digital design: saturation and cut-off

Gate Capacitance Capacitance as a function of VGS (with VDS = 0) Capacitance as a function of the degree of saturation

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

Capacitances in 0.25 mm CMOS process

MOSFET – Some Secondary Effects V T V T Low V threshold Long-channel threshold DS VDS L Threshold as a function of Drain-induced barrier lowering the length (for low V ) (for low L ) DS

Parasitic Resistances Polysilicon gate Drain contact R G D S VGS,eff RS RD L D W Drain RS,D = R LS,D/W + RC

SPICE Models for the MOS Transistor Three Levels Level 1 Long Channel, Channel Length Modulation Level 2 Geometry based that includes detailed device physics Velocity saturation, mobility degradation, DIBL Analytical physics based model makes it complex and inaccurate Level 3 Semi-empirical model Measured data to calibrate and decide the main parameters Accurate and efficient. Widely used.

BSIM3-V3 Parameter Category Description Control Selection of level and models for mobility, capacitance and noise DC Parameters for threshold and current and calculations AC & Capacitance Parameters for capacitance computations dW and dL Derivation of effective channel length and width Process Process parameters such as oxide thickness and doping concentrations TOX, XJ, GAMMA1, NCH, NSUB Temperature Nominal temperature and temperature coefficients for various device parameters TNOM Bin Bounds device dimensions for which the model is valid LMIN, LMAX, WMIN, WMAX Flicker Noise Noise model parameters

SPICE Transistor Parameters Parameter Name Symbol SPICE Name Units Default Value Drawn Length L m - Effective Width W Source Area AREA AS m2 Drain Area AD Source Perimeter PERIM PS Drain Perimeter PD Squares of Source Diffusion NRS 1 Squares of Drain Diffusion NRD