Book Chapter 1: Devices and Modelling · Book Chapter 1: Devices and Modelling 13. Small Signal Models A linearized model that applies to a certain point of operation. All small signal

INF3410 — Fall 2014

Book Chapter 1: Devices and Modelling

Content

PN Junction Properties

Field Effect Transistor Large Signal Models

Field Effect Transistor Small Signal Models

Field Effect Transistor ‘Second Order’ Properties

Short Remark on Passive Devices

Summary

Book Chapter 1: Devices and Modelling 2

Content






Summary


Built in Potential/Junction Capacitance

Cj =Cj0

r

1 + VRΦ0

(1.17)

Cj0 =

√

√

√qKSϵ0

2Φ0

NAND

NA +ND(1.18)

Φ0 = UT ln

�

NAND

n2i

�

(1.6)


Content






Summary


nFET cross section and symbols


EKV Model

IDS = IF − IRfor an NFET:

IF(R) = IS ln2�

1 + eVG−VT0−nVS(D)

2nUT

�

where IS = 2nβU2Tβ = μCOX

W

L

Active region/in saturation: IF >> IRTriode region/linear region: IF ≈ IR


EKV Simplified in Weak Inversion

Weak inversion/subthreshold:

(IF << IS) = (VG − nVS < VT0)

⇒

IF = 2nβU2Te

VG−VT0−nVSnUT

Book model (in saturation):

ID = (n− 1)βU2Te

�

(VG−Vtn)nUT

�

(1.121)


EKV Simplified in Strong Inversion

Strong inversion/above threshold:

(IF >> IS) = (VG − nVS > VT0)

⇒

IF(R) =β

2n

�

VG − VT0 − nVS(D)

�2

Book model (in saturation/active region):

ID =β

2(VG − VS − Vtn)2 (1.63)


Basic Equation vs. EKV

0 0.5 1 1.5 2 2.5 3 3.510

−14

10−12

10−10

10−8

10−6

10−4

10−2

I D

VGS

basic strong inversionbasic weak inversionEKV


Channel Modulation/Early Effect Illustration

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3x 10

−5

I D

VDS

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3x 10

−5

I D

VDSBook Chapter 1: Devices and Modelling 11

Channel Modulation/Early Effect Formula

Strong Inversion

ID =β

2(Veff )

2 [1 + λ(VD − VS − Veff )] (1.67)

λ =kds

2Lp

VDS − Veff + Φ0


Content



Field Effect Transistor Small Signal ModelsLow Frequency Small Signal ModelHigh Frequency Small Signal ModelFigures of Merit



SummaryBook Chapter 1: Devices and Modelling 13

Small Signal Models

A linearized model that applies to a certain point ofoperation. All small signal variables (e.g. id) are thusonly the offset to the variables at this point of operation(e.g. ID). Sometimes the total of the two is refered to asiD (though not in the Carusone book!).

iD = ID + id

Those so inclined may think of it as a first order Taylorexpansion:

iD(~X + ~x) ≈ ID(~X) + ∇ID(~X)~xT = ID(~X) + id(~x)


Linear Approximation/Small Signal Model

0 0.5 1 1.5 2 2.5 3 3.5−2

0

2

4

6

8x 10

−4

I D

VGS

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3x 10

−5

I D

VDSBook Chapter 1: Devices and Modelling 15

Low Frequency Small Signal Model nFET


Small Signal Model Parameters

gm =

√

√

√

2μnCox

W

LID (1.77)(strong inversion)

rds ≈1

λID(1.86)


High Frequency Small Signal Model nFET





Cgs ≈2

3WLCox (1.89)

Csb ≈ (AS +ACH)Cjs (1.92)

Cgd ≈ CoxWLov (1.96)


Intrinsic (Voltage) Gain

Maximal voltage gain, no external load, common sourceamplifier with ideal current source as ‘load’

Ai =

�

�

�

�

∂Vout

∂Vin

�

�

�

�

= gmrds ≈2

λVeff(1.114/115)

⇒ Higher for long transistors (large L) and small Veff


Unity-Gain Frequency (Intrinsic Speed)

Unity current gain ( ∂Iout∂Iin= 1), no external load, common

source amplifier with ideal voltage source as ‘load’

ft ≈gm

2π(Cgs +Cgd)≈

3μnVeff

4πL2(1.116/117)

⇒ Higher speed for shorter transistors (small L) andlarge Veff


Content




Field Effect Transistor ‘Second Order’ PropertiesMobility-DegradationShort-Channel EffectsLeakage Currents



Mobility-Degradation/Velocity Saturation

ID =1

2βV2

eff

1

[1 + (θVeff )m]1m

, gm =1

2β

1

θfor Veff >

1

2θBook Chapter 1: Devices and Modelling 24

Short-Channel Effects


Leakage Currents

É subthreshold leakageÉ junction leakage (strongly temperature dependent)É gate leakage (depends on tox < 2nm: new

technologies!)


Leakage Currents


Content





Short Remark on Passive DevicesMOS capacitors


MOS capacitors, a word of caution


Content






Summary


Summary

All equations are summarized in the book section 1.3,starting from page 39.Realistic parameters for a few technology nodes can befound on in table 1.5 on page 54.


Book Chapter 1: Devices and Modelling · Book Chapter 1: Devices and Modelling 13. Small Signal Models A linearized model that applies to a certain point of operation. All small signal

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