Table Of ContentW
Computational Microelectronics
Edited by
Siegfried Selberherr
Technical University Vienna
Vienna, Austria
For further volumes:
www.springer.com/series/1263
Viktor Sverdlov
Strain-Induced Effects
in Advanced MOSFETs
SpringerWienNewYork
Viktor Sverdlov
Technical University Vienna
Institute for Microelectronics
Gusshausstrasse 27-29
1040Vienna
Austria
[email protected]
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ISBN978-3-7091-0381-4 e-ISBN978-3-7091-0382-1
DOI10.1007/978-3-7091-0382-1
SpringerWienNewYork
To Alexandra,Karin, Ludmila,&Nikolai
•
Preface
Strain is the main tool to boost current and enhance performance of advanced
silicon-basedmetal-oxide-semiconductorfield-effecttransistors(MOSFETs).Mod-
elingandunderstandingofstraineffectsonbandstructureandmobilityhasbecome
the important task of modern simulation tools used to design ultra-scaled MOS-
FETs.Thisbookfocusesonmodernmodelingapproachesandmethodsdescribing
strain in silicon. Contrary to the valence band, strain-induced conduction band
modifications have received substantially less attention. Peculiarities of subband
structuresin thin semiconductorfilms under stress are investigatedin detail using
numerical pseudopotential calculations as well as a k(cid:2)p theory, which includes
the two lowest conduction bands. Implementation of strain in transport modeling
for modern microelectronicsdesign tools is overviewed. Application ranges from
devicemodelingtoappliedmathematicsandsoftwaredevelopment.
Thebookisbasedonmyresearchandpartlyonmycourseoflecturesgivenfor
theMaster’sandPhDstudentsinelectricalengineering,microelectronics,physics,
and applied mathematicsat the Institute for Microelectronics,Technische Univer-
sita¨tWien.ThisbookwouldnothavebeenwrittenwithoutthesupportoftheInsti-
tuteforMicroelectronicsanditsDirectorUniv.Prof.Dipl.-Ing.Dr.techn.E.Langer.
I would like to thank Univ.Prof.Dipl.-Ing. Dr.techn. T. Grasser, Univ.Prof. Dipl.-
Ing. Dr.techn. H. Kosina, and Univ.Prof.Dipl.-Ing.Dr.techn. Dr.h.c. S. Selberherr
fortheiroverwhelmingencouragement,support,andhelpinwritingthebook.
Iwouldliketoacknowledgethecontributionstothebookmadebymycolleagues
and co-authors: O. Baumgartner, J. Cervenka, S. Dhar, T. Grasser, A. Gehring,
G. Karlowatz, M. Karner, H. Kosina, K. Likharev, M. Nedjalkov, M. Pourfath,
F. Schanovsky, S. Selberherr, Z. Stanojevic, M. Vasicek, E. Ungersboeck, and
T. Windbacher. I also would like to thank H. Ceric, R. Entner, O. Ertl, W. Goes,
P. Hehenberger, R. Heinzl, S. Holzer, A. Makarov, G. Milovanovich, N. Neo-
phytou, R. Orio, V. Palankovski, K. Rupp, P. Schwaha, I. Starkov, F. Stimpfl,
O.Triebl,S.Tyaginov,S.Vitanov,P.Wagner,S.Wagner,J.Weinbub,andW.Wess-
ner for many fruitful and stimulating discussions and C. Haslinger, E. Haslinger,
M.Katterbauer,and R. Winklerfor technicalsupportin preparingthe manuscript.
Specialthanksgoto O.Baumgartner,M.Nedjalkov,andK. Sitzwohl,whokindly
agreedtotaketheheavydutyofproof-readingandimprovingthemanuscript.
vii
viii Preface
Thenewscientificresultsdescribedinthelastsectionsofthebookwouldhave
been impossible to obtain without financial support from the Austrian Science
Fund FWF through the projects P-17285-N02 and P-19997-N14, from the Euro-
peanResearchCouncilthroughthegrant247056MOSILSPIN,fromtheEuropean
Commission, project SINANO IST-50684, and from the European Science Foun-
dation EUROCORES Program FoNE funded by the Austrian Science Fund FWF
(projectI79-N16),CNR,EPSRCandtheECSixthFrameworkProgram.
Vienna ViktorSverdlov
July2010
Contents
1 Introduction................................................................... 1
2 Scaling,PowerConsumption,andMobilityEnhancementTechniques 5
2.1 PowerScaling .......................................................... 5
2.2 StrainEngineering...................................................... 6
2.3 GlobalStrainTechniquesandSubstrateEngineering ................ 8
2.4 LocalStressTechniques ............................................... 10
2.5 AdvancedStressTechniques........................................... 12
2.6 HybridOrientationTechnologyandAlternativeChannelMaterials. 14
References...................................................................... 16
3 StrainandStress.............................................................. 23
3.1 StrainDefinition........................................................ 23
3.2 Stress.................................................................... 25
3.3 Relation Between Strain and Stress Tensor
inSiliconandGermanium............................................. 27
3.4 StrainandStressTensors:Examples.................................. 28
3.4.1 UniformAll-AroundCompression.......................... 28
3.4.2 BiaxialStrainResultingFromEpitaxialGrowth............ 29
3.4.3 UniaxialStress................................................ 32
References...................................................................... 34
4 BasicPropertiesoftheSiliconLattice...................................... 35
4.1 CrystalStructureofSiliconandGermanium ......................... 35
4.2 ReciprocalLatticeandFirstBrillouinZone .......................... 39
4.3 ParticleinaPeriodicPotential......................................... 41
References...................................................................... 44
5 BandStructureofRelaxedSilicon.......................................... 45
5.1 ConductionandValenceBands........................................ 45
5.2 First-PrincipleBandStructureCalculations .......................... 46
5.3 PseudopotentialBandStructureCalculations......................... 49
5.4 Semi-EmpiricalTightBindingMethod ............................... 56
ix
x Contents
5.5 ComparisonBetweenDifferentNumericalMethods................. 58
References...................................................................... 61
6 PerturbativeMethodsforBandStructureCalculationsinSilicon...... 63
6.1 Thek(cid:2)pMethodforaNon-DegenerateBand......................... 63
6.2 EffectiveMassTheoryforNon-DegenerateBands................... 64
6.2.1 ElectronEffectiveMassinRelaxedSilicon................. 66
6.2.2 ApproximationsfortheConductionBand
DispersionatHigherEnergies............................... 67
6.3 ValenceBand........................................................... 70
6.3.1 Spin–OrbitCouplingintheValenceBand .................. 72
6.3.2 DispersionoftheValenceBandinSilicon .................. 75
6.3.3 LuttingerParameters ......................................... 76
References...................................................................... 80
7 StrainEffectsontheSiliconCrystalStructure............................ 83
7.1 Strain-InducedSymmetryReductionofSiliconCrystalLattice..... 83
7.1.1 Oh Symmetry................................................. 83
7.1.2 D4h Symmetry................................................ 84
7.1.3 D3d Symmetry ............................................... 85
7.1.4 D2h Symmetry................................................ 85
7.1.5 C2hSymmetry................................................ 86
7.2 InternalStrainParameter............................................... 86
7.3 StrainandSymmetryoftheBrillouinZone........................... 88
References...................................................................... 90
8 StrainEffectsontheSiliconBandStructure.............................. 91
8.1 LinearDeformationPotentialTheory................................. 91
8.1.1 ConductionBand ............................................. 91
8.1.2 ValenceBand ................................................. 93
8.1.3 Stress-InducedBandSplittingoftheValenceBands ....... 94
8.2 InclusionofStrainintoPerturbativeBandStructureCalculations... 97
8.3 EmpiricalPseudopotentialMethodwithStrain.......................102
References......................................................................103
9 StrainEffectsontheConductionBandofSilicon ........................105
9.1 LimitationoftheEffectiveMassApproximation
fortheConductionBandofSilicon ...................................105
9.2 TheTwo-Bandk(cid:2)pModel .............................................107
9.2.1 ValleyShiftDuetoShearStrain.............................108
9.2.2 Stress-DependentTransversalEffectiveMasses............111
9.2.3 DependenceonStrainoftheLongitudinal
EffectiveMass................................................112
9.2.4 StressandNon-Parabolicity..................................115
