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
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 3
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)
Book Chapter 1: Devices and Modelling 4
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 5
nFET cross section and symbols
Book Chapter 1: Devices and Modelling 6
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
Book Chapter 1: Devices and Modelling 7
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)
Book Chapter 1: Devices and Modelling 8
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)
Book Chapter 1: Devices and Modelling 9
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
Book Chapter 1: Devices and Modelling 10
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
Book Chapter 1: Devices and Modelling 12
Content
PN Junction Properties
Field Effect Transistor Large Signal Models
Field Effect Transistor Small Signal ModelsLow Frequency Small Signal ModelHigh Frequency Small Signal ModelFigures of Merit
Field Effect Transistor ‘Second Order’ Properties
Short Remark on Passive Devices
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)
Book Chapter 1: Devices and Modelling 14
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
Book Chapter 1: Devices and Modelling 16
Small Signal Model Parameters
gm =
√
√
√
2μnCox
W
LID (1.77)(strong inversion)
rds ≈1
λID(1.86)
Book Chapter 1: Devices and Modelling 17
High Frequency Small Signal Model nFET
Book Chapter 1: Devices and Modelling 18
High Frequency Small Signal Model nFET
Book Chapter 1: Devices and Modelling 19
High Frequency Small Signal Model nFET
Cgs ≈2
3WLCox (1.89)
Csb ≈ (AS +ACH)Cjs (1.92)
Cgd ≈ CoxWLov (1.96)
Book Chapter 1: Devices and Modelling 20
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
Book Chapter 1: Devices and Modelling 21
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
Book Chapter 1: Devices and Modelling 22
Content
PN Junction Properties
Field Effect Transistor Large Signal Models
Field Effect Transistor Small Signal Models
Field Effect Transistor ‘Second Order’ PropertiesMobility-DegradationShort-Channel EffectsLeakage Currents
Short Remark on Passive Devices
SummaryBook Chapter 1: Devices and Modelling 23
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
Book Chapter 1: Devices and Modelling 25
Leakage Currents
É subthreshold leakageÉ junction leakage (strongly temperature dependent)É gate leakage (depends on tox < 2nm: new
technologies!)
Book Chapter 1: Devices and Modelling 26
Leakage Currents
Book Chapter 1: Devices and Modelling 27
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 DevicesMOS capacitors
SummaryBook Chapter 1: Devices and Modelling 28
MOS capacitors, a word of caution
Book Chapter 1: Devices and Modelling 29
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 30
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 31