Table Of ContentTibor Grasser Editor
Noise in
Nanoscale
Semiconductor
Devices
Noise in Nanoscale Semiconductor Devices
Tibor Grasser
Editor
Noise in Nanoscale
Semiconductor Devices
Editor
TiborGrasser
InstituteforMicroelectronics
TechnischeUniversita¨tWien
Wien,Austria
ISBN978-3-030-37499-0 ISBN978-3-030-37500-3 (eBook)
https://doi.org/10.1007/978-3-030-37500-3
©SpringerNatureSwitzerlandAG2020
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG.
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Contents
Origins of 1/f Noise in Electronic Materials and Devices:
AHistoricalPerspective......................................................... 1
D.M.Fleetwood
NoiseandFluctuationsinFullyDepletedSilicon-on-Insulator
MOSFETs......................................................................... 33
ChristoforosTheodorouandGérardGhibaudo
NoiseinResistiveRandomAccessMemoryDevices......................... 87
F.M.Puglisi
SystematicCharacterizationofRandomTelegraphNoiseandIts
DependencewithMagneticFieldsinMOSFETDevices..................... 135
CarlosMarquez,OscarHuerta,AdrianI.Tec-Chim,FernandoGuarin,
EdmundoA.Gutierrez-D,andFranciscoGamiz
PrinciplesandApplicationsofI -RTNinNano-scaledMOSFET.......... 175
g
SteveS.ChungandE.R.Hsieh
RandomTelegraphNoiseinFlashMemories................................. 201
AlessandroS.Spinelli,ChristianMonzioCompagnoni,
andAndreaL.Lacaita
Advanced Electrical Characterization of Single Oxide Defects
UtilizingNoiseSignals........................................................... 229
BernhardStampfer,AlexanderGrill,andMichaelWaltl
Measurement and Simulation Methods for Assessing SRAM
ReliabilityAgainstRandomTelegraphNoise................................. 259
KiyoshiTakeuchi
RandomTelegraphNoiseUnderSwitchingOperation...................... 285
KazutoshiKobayashi,MahfuzulIslam,TakashiMatsumoto,
andRyoKishida
v
vi Contents
Low-FrequencyNoiseinIII–V,Ge,and2DTransistors .................... 335
MengweiSi,XuefeiLi,WangranWu,SamiAlghamdi,andPeideYe
DetectionandCharacterizationofSingleDefectsinMOSFETs............ 359
ToshiakiTsuchiya
RandomTelegraphNoiseNano-spectroscopyinHigh-κDielectrics
UsingScanningProbeMicroscopyTechniques............................... 417
Alok Ranjan, Nagarajan Raghavan, Kalya Shubhakar,
SeanJosephO’Shea,andKinLeongPey
RTN and Its Intrinsic Interaction with Statistical Variability
SourcesinAdvancedNano-ScaleDevices:ASimulationStudy ............ 441
F.Adamu-Lema,C.MonzioCompagnoni,O.Badami,V.Georgiev,
andA.Asenov
AdvancedCharacterizationandAnalysisofRandomTelegraph
NoiseinCMOSDevices ......................................................... 467
J.Martin-Martinez,R.Rodriguez,andM.Nafria
AnOverviewonStatisticalModelingofRandomTelegraphNoise
intheFrequencyDomain ....................................................... 495
ThiagoH.Both,MaurícioBanaszeskidaSilva,GilsonI.Wirth,
HansP.Tuinhout,AdrieZegers-vanDuijnhoven,JeroenA.Croon,
andAndriesJ.Scholten
Defect-BasedCompactModelingofRandomTelegraphNoise............. 517
PieterWeckx,BenKaczer,MarkoSimicic,BertrandParvais,
andDimitriLinten
OxideTrap-InducedRTSinMOSFETs....................................... 553
A.S. M.ShamsurRoufandZeynepÇelik-Butler
AtomisticModelingofOxideDefects.......................................... 609
DominicWaldhoer,Al-MoatasemBellahEl-Sayed,YannickWimmer,
MichaelWaltl,andTiborGrasser
TheLangevin–BoltzmannEquationforNoiseCalculation.................. 649
ChristophJungemann
BenchmarkTestsforMOSFETThermalNoiseModels..................... 687
AndriesJ.Scholten,G.D.J.Smit,R.M.T.Pijper,andL.F.Tiemeijer
Index............................................................................... 711
Origins of 1/f Noise in Electronic
Materials and Devices: A Historical
Perspective
D.M.Fleetwood
1 Introduction
Low-frequency(1/f)noiseisobservedinaremarkablenumberofdiversecosmolog-
ical[1–3],biological[4–7],economic[8–10],andelectronicmaterialsanddevices
[11–48].Ithasalsobeenfoundinmusicandspeech[49–51],dynamicsofsandpiles
andavalanches[52–54],automotiveandcomputer-networktrafficflow[55–57],and
statisticsofearthquakes,floods,andothernaturalphenomena[1,50,58,59].Dueto
itstechnological relevance, thenoise ofelectronic materials has received the most
attention.
Fromitsdiscoveryin1925byJohnson[11]untilthelate1960s,itwasgenerally
accepted that the low-frequency excess (1/f) noise of electronic materials and
devices was caused primarily by defects and impurities [12–17]. The 1/f noise of
semiconductor devices was considered to be a surface effect caused by surface
charge trapping [14]. This model was generalized and extended to MOSFETs
(metal–oxide–semiconductorfield-effecttransistors)shortlyaftertheirintroduction
into commercial use [15–17, 22, 25]. The discovery of 1/f noise in thin metal
films [19] and its similarly-scaled magnitude to noise in semiconductors [18] led
Hooge and Vandamme to propose instead that the noise was due to bulk mobility
fluctuationscausedbylattice(phonon)scattering[21].Theseandothermodelswere
testedextensivelyfrom∼1969to∼1994[1,23,24,27,29–31,36,37,39–42,48].
Afteralotofdebate,itisnowclearthat,formosttechnologicallyrelevantelectronic
devices, carrier number fluctuations due to charge trapping predominantly cause
the observed noise [29, 31, 38, 48]. For thin metal films, the noise is generally
duetomobilityfluctuationscausedbycarrier-defectscattering[24,28–30,48].The
D.M.Fleetwood((cid:2))
VanderbiltUniversity,Nashville,TN,USA
e-mail:dan.fl[email protected]
©SpringerNatureSwitzerlandAG2020 1
T.Grasser(ed.),NoiseinNanoscaleSemiconductorDevices,
https://doi.org/10.1007/978-3-030-37500-3_1
2 D.M.Fleetwood
defect-activation model of Dutta and Horn describes the noise of most metals and
semiconductordevicesremarkablywell[24,29,48].Overthelast∼25years,noise
measurementshavebeenincreasinglyusedincombinationwithotherexperimental,
computational,andtheoreticalmethodstoobtaininformationaboutthedefectsand
impuritiesthataretheunderlyingcauseoftheobservedfluctuations[29,31,35,37,
39,43–46,48].
In this chapter, the principles that underlie the number and (Hooge) mobility
fluctuationmodelsoflow-frequencynoiseinelectronicdevicesarereviewed.Evi-
dence is summarized that demonstrates the applicability of the number fluctuation
model [14, 17] and the importance of defects and impurities [48] to the noise
of typical electronic devices, e.g., MOSFETs (including those based on SiC and
two-dimensional materials) and HEMTs (high electron mobility transistors). The
Dutta–Horn model of 1/f noise [24] is briefly reviewed. This model provides a
detailed description of the effective energy distributions of defects that largely
determinethelow-frequencynoiseofmetalfilmsandmicroelectronicdevicesand
materials[48].Examplesareprovidedforanumberofdiversematerialsystemsthat
emphasizeitsgeneralapplicabilityandutility.
2 NumberFluctuations:ApplicationtoMOSFETs
A random process with a single characteristic time τ leads to a Lorentzian power
spectrum Eq. (1). At high frequency, the voltage-noise power spectral density S
V
scalesas∼1/f2,andatlowfrequency,thenoiseisnearlyindependentoffrequency
[1,11,13].Bernamontshowedin1937[12]that,ifthenoiseresultsfromprocesses
with a distribution of characteristic times D(τ), and if D(τ) ∼ 1/τ for times
τ < τ < τ , and the pre-factor A is independent of frequency, then the resulting
1 2
noise,
(cid:2)τ2(cid:3) (cid:4) (cid:5) (cid:6)
−1
S =A D(τ) 1+ω2τ2 d τ, (1)
V
τ1
isproportionalto∼1/f for1/τ <f <1/τ [1,11–14].Typically,theobservednoise
2 1
resultsfromathermallyactivatedrandomprocess,forwhich
τ =τ exp(E/kT), (2)
o
whereτ isaconstant,Eistheactivationenergy,kistheBoltzmannconstant,and
o
T isthetemperature.WhenD(E)isnearlyconstant,thenD(τ)isproportionalto∼
1/τ,theaboveconditionsaresatisfied,and1/f noiseisfound[24,29,48].
Noise due to pure tunneling processes is also observed, more often at low
temperature than at room temperature [60]. A first-order tunneling model was
developed by McWhorter in 1957 to describe noise in Ge due to the exchange
Originsof1/f NoiseinElectronicMaterialsandDevices:AHistoricalPerspective 3
of carriers between the semiconductor and surface oxide traps [14]. The simplest
form of the model, as applied to a large area Si MOSFET with oxide thicker
than∼3–5nm,attributesthenoisetotunnel-assistedchargeexchangebetweenthe
channel and defects in the near-interfacial SiO [14–17]. For defects distributed
2
approximatelyuniformlyinspacewithinthenear-interfacialoxideanduniformlyin
energywithinthebandgap,fluctuationsinthedensityoftrapsN leadtoapower-
t
spectraldensityS givenby[14,17,61]:
Nt
kTD (E )
S (f,T)= t f (3)
Nt LW ln(τ /τ )f
1 0
whereD(E )isthenumberoftrapsperunitenergyperunitareaattheFermilevel
t f
E (Fig. 1 [62]), and τ and τ are the minimum and maximum tunneling times,
f 0 1
respectively[14,17,39,61].
For constant drain current I and gate bias V , in the linear region of MOS
d g
operation,fluctuationsingatevoltageδV arerelatedtochangesintrappedcharge
g
densityδQ via:
t
δV =δQ/C =q δN/C (4)
g t ox t ox
Fig.1 Energybandsfora SiO Si
2
pMOSSi/SiO2transistorfor (a)
(a)lowerand(b)higher
appliedelectricfield.The
dotsrepresenttrappingsites
inSiO2.(AfterSuryaand
Hsiang[62],©1986, E
c
AmericanInstituteof
E
Physics,AIP) f
E
Z v
(b)
E
c
E
f
E
v
4 D.M.Fleetwood
whereC isthegateoxidecapacitanceperunitarea,andqisthemagnitudeofthe
ox
electroncharge.FluctuationsingatevoltageδV leadtofluctuationsindrainvoltage
g
δV [17,61]:
d
(cid:7) (cid:8)
δV = ∂V /∂V δV . (5)
d d g g
ForaMOSFETinthelinearmodeofoperation,intermsofδN,thisreducesto
t
[17,61]:
qV
δV = (cid:7) d (cid:8)δN (6)
d C V −V t
ox g t
whereV,V ,andV arethethreshold,gate,anddrainvoltages.Thus,drainvoltage
t g d
fluctuationsarerelatedtothefluctuationsinthetrappedchargedensityvia[17,61]:
q2V 2
S (f,T)= (cid:7) d (cid:8) S (f,T) (7)
Vd C 2 V −V 2 Nt
ox g t
where S is the excess drain-voltage noise power spectral density, which is the
Vd
quantitymeasuredinatypicalnoisestudy.
Combining Eqs. (3) and (7) yields a first-order expression that relates the
measured excess drain-voltage noise power spectral density S of a MOSFET to
Vd
thedensityofrelevanttrapsD(E )[17,25,39,48,61]:
t f
q2 V2 k TD (E ) 1
S = (cid:7) d (cid:8) B (cid:7)t f (cid:8) . (8)
Vd Co2x Vg−Vt 2LWln τ1/τ0 f
This model has been extended to include the effects of nonuniform spatial and
energy distributions [24, 29, 48] and/or correlated mobility fluctuations associated
withchangesinchargestatesofthedefectsresponsibleforthenoise[33,63].
Figure 1 shows that, when the gate bias is changed, the Si surface potential
changes only slightly, but band bending is more significant in the SiO insulator
2
[61,62].Thus,varyingtheappliedgatebiasenablesonetoprobedifferentregions
of semiconductor and/or insulator band gaps via 1/f noise measurements [25, 38,
48, 61, 62]. In the simplest form of the number fluctuation model, which assumes
tunneling is the rate-limiting step that leads to 1/f noise, the portion of the SiO
2
defectenergydistributionmosteasilyaccessibletomeasurementsisthatclosestto
theSiandwithinafewkToftheFermilevelinenergy[13,14,17,38,48,64].When
D(E )isapproximatelyconstant,S ∼(V −V)−2,asadirectconsequenceofthe
t f Vd g t
assumptionsembodiedinEqs.(3)–(7).However,neitherD(E )norD(τ)areoften
t f
constant in MOSFETs or other electronic devices [24, 29, 35, 48, 65]. Hence, the
gate voltage dependence of the noise can be more complex than anticipated under
the assumptions of the original McWhorter model [14, 38, 48, 66]. Nonconstant
valuesofD(E )and/orD(τ)alsoleadtodeviationsofthefrequencydependenceof
t f
thenoisefromapure1/f powerlaw[24,29,48].
