Photomodulated Optical Reflectance: A Fundamental Study Aimed at Non-Destructive Carrier Profiling in Silicon

216 Pages·2012·5.77 MB·English

by  Janusz Bogdanowicz (auth.)

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Janusz Bogdanowicz
Photomodulated Optical
Reflectance
A Fundamental Study Aimed
at Non-Destructive Carrier Profiling
in Silicon
Doctoral Thesis accepted by
the University of Leuven, Belgium
123
Author Supervisor
Dr. JanuszBogdanowicz Prof.Dr. Ir.Wilfried Vandervorst
IMEC IMEC
Leuven Leuven
Belgium Belgium
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-642-30107-0 ISBN 978-3-642-30108-7 (eBook)
DOI 10.1007/978-3-642-30108-7
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012940720
(cid:2)Springer-VerlagBerlinHeidelberg2012
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Supervisor’s Foreword
Thecontinuousdownscalingofnanoelectroniccomponentsandtransistorsfollowing
Moore’slawleadstoevercheaper,morepowerfulcomputers,andmoremultifunc-
tionaldevices.To maintain this progressinscaling,materialscientists,andprocess
engineers explore new materials, novel processing steps and more complex device
structures.Thesetechnologicaldevelopmentsareextremelychallengingandcanonly
be achieved if based on profound physical insight and understanding. As such
metrology has become a key enabler toward successful product development and
inevitablysubjecttosimilarscalinglawsinordertoremainrelevant.Henceresearchin
metrologytargetingtheextensionofmeasurementstowardsmallerdimensions,higher
resolution,bettersensitivityandspecificity,andquantificationaccuracyisanimpor-
tantcornerstoneoftechnologicalprogressinsemiconductortechnology.
As dopants anddopant distributions constitutethe active heart of thetransistor
operation,engineeringofthesourceanddrainjunctionregionsofMOStransistors
has become an important research item listed in the International Technology
Roadmap for Semiconductors and the subject of a lot of advanced research
activities. Their strong impact on the device performance led to a continuous
scaling toward very shallow depths and an engineering of very detailed dopant
distributions (doping concentration, depth, abruptness, halo,..). Concurrently the
development of new doping and annealing processes as well as their production
control has becomeextremelydependent onthe availabilityofprecise (electrical)
characterization with adequate specifications. In particular the interest in in-line
monitoring and non-destructive characterization has spurred the search for junc-
tionmetrologybasedonopticalprobes;however,withtheimportantconstraintsto
provide also sub-nanometer accuracy, precision, and quantification.
Thisworkcontributestothisevolutionanddemonstratesthecapabilitiesofthe
Photomodulated Optical Reflectance (PMOR) which measures the variations in
reflectanceinducedbyamodulatedpumplaser.Basedonafastlaserpump-probe
technique, PMOR was originally designed as a non-contact concept for implant
dose metrology. However, a breakthrough has been realized in this work by
extending the concept from a simple process control tool for as-implant profiles
towardthequantitativeanalysisofacompleteactivecarrierprofilethroughavery
v
vi Supervisor’sForeword
detailed modeling ofthe fundamentalphysicsofthe PMOR technique.This work
provides a complete description of the carrier and heat generation/transport/
recombination phenomena as well as of their translation into reflectance signals
withanexcellentagreementtoexperimentaldata.Novelexperimentalapproaches
are introduced to extend PMOR from qualitative dose monitoring toward quan-
titativejunctiondepthmeasurementanddetailedcarrierprofilereconstruction.The
latter development represents a significant breakthrough in USJ metrology and
generated substantial industrial interest, up to the development of a new product
implementing the final recommendations of this book.
Leuven, January 2012 Prof. Dr. Ir. Wilfried Vandervorst
Acknowledgments
Firstandforemost,IwouldliketothankProf.WilfriedVandervorstforgivingme
the opportunity to carry out my Ph.D. studies under his supervision. I really
appreciatedhisguidanceandsupportthroughouttheseyears.Despitehisverybusy
agenda,healwaystookthetimeneededforshortexplanationsorlongdiscussions.
I also wish to sincerely acknowledge Trudo Clarysse, who really made the
difference all along these years. He was an excellent supervisor who always
pushed me to the best of myself. In so many instances, his invaluable assistance
andinvolvement were the keytotheresultsshown inthisthesis. Iamtodayfully
aware that I owe him much more than I could ever write in these
acknowledgments.
ThefollowingthanksgotoFabianDortu,whosehelpandwilltosharehisdeep
fundamentalandtechnicalunderstandinggavemearealboostintheearlyphaseof
this work. Even 3 years after he left imec, I still have the impression that the
numerous technical discussions we used to have paved the way to the final con-
clusions of this work. I should obviously not forget to mention that he is the
originaldeveloper of FSEM. Now that this work is reaching an end,I realize that
this tool is a real goldmine and I deeply acknowledge him for the energy he put
into its development.
IamalsoindebtedtoErikRosseel,whoIverymuchenjoyedworkingwith.The
numerous hours spent discussing technical issues next to the TP tool and all the
experimental results collected on his immense experimental database were clear
determining factors of this work.
I am very grateful to all the KLA-Thermawave team and more particularly to
Derrick Shaughnessy and Alex Salnik. My special thanks to Derrick for the very
nice company during my two stays in California.
This work would not have been possible without the help of Duy Nguyen,
Laurent Souriau, and all the epi group of imec, who provided me with very nice
layers.ThanksalsotoAlainMoussa,DanielleVanhaeren,JorisDelmotte,Bastien
Douhard,LucGeenen,PierreEyben,JozefienGoossens,andBennyVanDaelefor
kindlytakingcareofthecharacterizationoftheselayersandtotheFPSunitforthe
measurement time on the ThermaProbe tool.
vii
viii Acknowledgments
I certainly will not forget to thank all my (ex-)mca colleagues and friends and
most particularly Francesca, Simone, Wouter, Jay, Alain, Fabian, Cindy, Bart,
Bastien,Joris,Alexis,andDaniellefortheenjoyabletimespenttogether.Myimec
experience would not have been the same without you.
I would also like to acknowledge the Institute for the Promotion of Innovation
throughScienceandTechnologyinFlanders(IWT-Vlaanderen)fortheirfinancial
support.
Lastbutnotleast,Iwouldliketothankallthepeople,familyandfriends,whoI
love and who supported me along these years.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State of the Art of USJ Characterization . . . . . . . . . . . . . . . . . 3
1.2.1 Contacting and/or Destructive Techniques . . . . . . . . . . . 3
1.2.2 Non-Contacting and Non-Destructive Techniques. . . . . . 10
1.3 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Theory of Perturbation of the Reflectance. . . . . . . . . . . . . . . . . . . 21
2.1 Uniform Perturbation of the Complex Refractive Index . . . . . . . 25
2.2 Box-Like Perturbation of the Complex Refractive Index . . . . . . 26
2.3 Double Box-Like Perturbation of the Complex
Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Arbitrary Perturbation of the Complex Refractive Index. . . . . . . 31
2.5 Second-Order Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5.1 Impact of the Presence of a Native Oxide . . . . . . . . . . . 33
2.5.2 Impact of a Lateral Variation in Refractive
Index Perturbation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Theory of Perturbation of the Refractive Index. . . . . . . . . . . . . . . 39
3.1 Refractive Index of Electrically Conductive Materials . . . . . . . . 41
3.2 Electrooptical Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Drude Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Carrier-Induced Bandgap Narrowing (BGN) Effect. . . . . 43
3.2.3 Burstein Shift or Band-Filling (BF) Effect. . . . . . . . . . . 47
3.2.4 Pockels, Kerr and Franz-Keldysh Effects. . . . . . . . . . . . 48
ix
x Contents
3.3 Thermooptical Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Theory of Carrier and Heat Transport in Homogeneously
Doped Silicon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1 Thermodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.1 Generalized Ambipolar Diffusion Equation . . . . . . . . . . 58
4.1.2 Heat Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1.3 Steady-Periodic Model Equations . . . . . . . . . . . . . . . . . 63
4.1.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.1 One-Dimensional Linear Solution. . . . . . . . . . . . . . . . . 79
4.2.2 Three-Dimensional Linear Solution. . . . . . . . . . . . . . . . 83
4.2.3 Three-Dimensional Nonlinear Solution . . . . . . . . . . . . . 92
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5 Extension of the Transport Theory to Ultra-Shallow
Doped Silicon Layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.1 Simplified Transport Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Validity of the Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2.1 Flat Quasi-Fermi Level Approximation . . . . . . . . . . . . . 107
5.2.2 Impact of Doped Layers on Substrate Injection . . . . . . . 109
5.3 Steady-Periodic Model Equations . . . . . . . . . . . . . . . . . . . . . . 110
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 Assessment of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1 Homogeneous Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.1.1 Comparison of the Model with Experimental Data . . . . . 119
6.2 Box-Like Doping Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.1 Comparison of the Model with Experimental Data . . . . . 126
6.3 Discussion of the Modeling Error . . . . . . . . . . . . . . . . . . . . . . 133
6.3.1 Modeling Error on R . . . . . . . . . . . . . . . . . . . . . . . . 133
dc
6.3.2 Modeling Error on DRac . . . . . . . . . . . . . . . . . . . . . . . 134
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7 Application of the Model to Carrier Profiling. . . . . . . . . . . . . . . . 141
7.1 Model-Free Determination of Junction Depths . . . . . . . . . . . . . 141
7.1.1 Absolute Determination of Junction Depths . . . . . . . . . . 142
7.1.2 Relative Determination of Junction Depths . . . . . . . . . . 149