# Towards inline metrology of thin materials in semiconductor environment

Emmanuel Nolot

<figure><img src="image_1.png" /></figure>

## To cite this version:

Emmanuel Nolot. Towards inline metrology of thin materials in semiconductor environment. Physics [physics]. Université Grenoble Alpes, 2023. tel-04445255

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Submitted on 7 Feb 2024

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Mémoire

Présenté pour obtenir le diplôme d'

HABILITATION À DIRIGER DES RECHERCHES DE
L'UNIVERSITÉ GRENOBLE ALPES

Spécialité : Physique

Arrêté ministériel : 23 novembre 1988

Présentée par

Emmanuel Nolot
Docteur

préparée au sein du CEA-LETI
dans l'École Doctorale de Physique

Towards inline metrology of thin materials
in semiconductor environment

HDR soutenue publiquement le 14 décembre 2023,
devant le jury composé de :

**Luc BIDEUX**, Professeur des Universités, Université Clermont
Auvergne, Président du jury

**Franck DELMOTTE**, Professeur des Universités, Université Paris
Saclay, Rapporteur du jury

**Anouk GALTAYRIES**, Maîtresse de conférences HDR, Chimie
Paris Tech - Université PSL, Rapporteure du jury

**Remi LAZZARI**, Directeur de recherche, CRNS - Institut des
Nanosciences de Paris, Rapporteur du jury

**Arnaud ETCHEBERRY**, Directeur de recherche émérite, CNRS,
Institut Lavoisier de Versailles, Examinateur

**Etienne GHEERAERT**, Professeur des Universités, Institut Neel,
Université Grenoble Alpes, Examinateur

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Table of contents

<table><tr><td>1</td><td>Introduction</td><td>6</td></tr><tr><td>2</td><td>A brief introduction to metrology for semiconductors</td><td>8</td></tr><tr><td>3</td><td>Metrology with optical techniques</td><td>11</td></tr><tr><td>3.1</td><td>Introduction</td><td>13</td></tr><tr><td>3.2</td><td>Few words about the uncertainties in spectroscopic ellipsometry and reflectometry</td><td>13</td></tr><tr><td>3.3</td><td>Optical constants of strained silicon germanium</td><td>19</td></tr><tr><td>3.4</td><td>Optical constants of ultrathin silicon on oxide films</td><td>24</td></tr><tr><td>3.5</td><td>Towards in situ optical metrology?</td><td>27</td></tr><tr><td>4</td><td>X-ray Metrology of thickness and composition</td><td>29</td></tr><tr><td>4.1</td><td>Introduction</td><td>31</td></tr><tr><td>4.2</td><td>Compositional analysis with X-ray fluorescence</td><td>34</td></tr><tr><td>4.3</td><td>Quantifying thin sulfide materials with XPS and XRF</td><td>40</td></tr><tr><td>4.4</td><td>Quantifying light elements in thin inorganic materials with XRF</td><td>46</td></tr><tr><td>5</td><td>Elemental Depth-profiling</td><td>51</td></tr><tr><td>5.1</td><td>Introduction</td><td>54</td></tr><tr><td>5.2</td><td>Combined grazing-incidence X-ray fluorescence and X-ray reflectometry</td><td>55</td></tr><tr><td>5.3</td><td>X-ray photoemission</td><td>63</td></tr><tr><td>5.4</td><td>Plasma profiling time-of-flight mass spectrometry</td><td>73</td></tr><tr><td>6</td><td>Material characterization for Phase Change Memory</td><td>80</td></tr><tr><td>6.1</td><td>Introduction</td><td>82</td></tr><tr><td>6.2</td><td>Characterization after deposition</td><td>82</td></tr><tr><td>6.2.1</td><td>Key methodological aspects</td><td>82</td></tr><tr><td>6.2.2</td><td>Characterization of N-doped elemental materials</td><td>83</td></tr><tr><td>6.2.3</td><td>Characterization of undoped and N-doped Ge, Sb, Te alloys</td><td>86</td></tr><tr><td>6.3</td><td>Impact of the thermal budget</td><td>91</td></tr><tr><td>6.3.1</td><td>Analytical techniques</td><td>91</td></tr><tr><td>6.3.2</td><td>Characterization of GST and GST-N alloys</td><td>95</td></tr><tr><td>7</td><td>Perspectives</td><td>97</td></tr><tr><td>7.1</td><td>Towards accurate and NMI traceable optical constants</td><td>97</td></tr><tr><td>7.2</td><td>Comprehensive Raman spectroscopy analysis in cleanroom environment</td><td>98</td></tr><tr><td>7.3</td><td>Extend the range of chemical characterization</td><td>99</td></tr><tr><td>7.4</td><td>Combine XRR and (GI)-XRF in Leti cleanroom</td><td>100</td></tr><tr><td>7.5</td><td>Improve inline quantification of low-Z elements in thin inorganic films</td><td>102</td></tr><tr><td>7.6</td><td>Development of (quasi) in situ and in operando metrology</td><td>103</td></tr></table>
<table><tr><td>8</td><td>List of publications</td><td>104</td></tr><tr><td>9</td><td>Curriculum Vitae</td><td>112</td></tr></table>
Glossary

<table>
   <tr>
    <td>ALD</td>
    <td>Atomic layer deposition</td>
   </tr>
   <tr>
    <td>AMC</td>
    <td>Airborne molecular contamination</td>
   </tr>
   <tr>
    <td>AOI</td>
    <td>Angle of incidence</td>
   </tr>
   <tr>
    <td>BE</td>
    <td>Binding energy</td>
   </tr>
   <tr>
    <td>EBS</td>
    <td>Elastic Back Scattering</td>
   </tr>
   <tr>
    <td>EDXRF</td>
    <td>Energy dispersive X-ray fluorescence</td>
   </tr>
   <tr>
    <td>EMA</td>
    <td>Effective Medium Approximation</td>
   </tr>
   <tr>
    <td>FDSOI</td>
    <td>Fully Depleted Silicon On Insulator</td>
   </tr>
   <tr>
    <td>FP</td>
    <td>Fundamental parameters</td>
   </tr>
   <tr>
    <td>FFT</td>
    <td>Fast Fourier Transform</td>
   </tr>
   <tr>
    <td>FTIR</td>
    <td>Fourier-transform infrared spectroscopy</td>
   </tr>
   <tr>
    <td>FWHM</td>
    <td>Full width at half maximum</td>
   </tr>
   <tr>
    <td>GA</td>
    <td>Genetic algorithm</td>
   </tr>
   <tr>
    <td>GCIB</td>
    <td>Gas cluster ion beams</td>
   </tr>
   <tr>
    <td>GD</td>
    <td>Glow discharge</td>
   </tr>
   <tr>
    <td>GD-MS</td>
    <td>Glow discharge mass spectrometry</td>
   </tr>
   <tr>
    <td>GIXRF</td>
    <td>Grazing-incidence X-ray fluorescence</td>
   </tr>
   <tr>
    <td>GST</td>
    <td>GeSbTe alloy</td>
   </tr>
   <tr>
    <td>HAXPES</td>
    <td>Hard X-ray X-ray photoelectron spectroscopy</td>
   </tr>
   <tr>
    <td>HEMT</td>
    <td>High electron mobility transistors</td>
   </tr>
   <tr>
    <td>IBA</td>
    <td>Ion Beam Analysis<br>or<br>Inelastic background analysis (in XPS section only)</td>
   </tr>
   <tr>
    <td>IBR</td>
    <td>Ion beam ratio</td>
   </tr>
   <tr>
    <td>IMFP</td>
    <td>Inelastic mean free path</td>
   </tr>
   <tr>
    <td>LEIS</td>
    <td>Low energy ion scattering</td>
   </tr>
   <tr>
    <td>LP-CVD</td>
    <td>Low-pressure chemical vapor deposition</td>
   </tr>
   <tr>
    <td>LPD-ICPMS</td>
    <td>Liquid Phase Decomposition coupled to Inductively Coupled Plasma<br>Mass Spectrometry</td>
   </tr>
   <tr>
    <td>MO-CVD</td>
    <td>Metal-organic chemical vapor deposition</td>
   </tr>
   <tr>
    <td>NIST</td>
    <td>National Institute of Standards and Technology</td>
   </tr>
   <tr>
    <td>NMI</td>
    <td>National Metrology Institute</td>
   </tr>
   <tr>
    <td>NPL</td>
    <td>National Physical Laboratory</td>
   </tr>
   <tr>
    <td>NRA</td>
    <td>Nuclear Reaction Analysis</td>
   </tr>
   <tr>
    <td>p-ARXPS</td>
    <td>Parallel-angle X-ray photoelectron spectroscopy</td>
   </tr>
   <tr>
    <td>PCM</td>
    <td>Phase-change memory</td>
   </tr>
   <tr>
    <td>PE-ALD</td>
    <td>Plasma Enhanced Atomic Layer Deposition</td>
   </tr>
   <tr>
    <td>PE-CVD</td>
    <td>Plasma Enhanced Chemical Vapour Deposition</td>
   </tr>
   <tr>
    <td>PIXE</td>
    <td>Particle Induced X-ray Experiment</td>
   </tr>
   <tr>
    <td>PP-TOFMS</td>
    <td>Plasma profiling time-of-flight mass spectrometry tool</td>
   </tr>
   <tr>
    <td>PTB</td>
    <td>Physikalisch-Technische Bundesanstalt</td>
   </tr>
   <tr>
    <td>PVD</td>
    <td>Physical Vapor Deposition</td>
   </tr>
   <tr>
    <td>RBS</td>
    <td>Rutherford Back Scattering</td>
   </tr>
   <tr>
    <td>RTO</td>
    <td>Research and Technology Organization</td>
   </tr>
   <tr>
    <td>SDD</td>
    <td>Silicon drift detector</td>
   </tr>
   <tr>
    <td>SE</td>
    <td>Spectroscopic ellipsometry</td>
   </tr>
   <tr>
    <td>SOI</td>
    <td>Silicon On Insulator</td>
   </tr>
   <tr>
    <td>TEM</td>
    <td>Transmission electron microscopy</td>
   </tr>
   <tr>
    <td>TOF-SIMS</td>
    <td>Time-of-flight secondary ion mass spectrometry</td>
   </tr>
   <tr>
    <td>TXRF</td>
    <td>Total Reflection X-Ray Fluorescence</td>
   </tr>
   <tr>
    <td>WDXRF</td>
    <td>Wavelength-dispersive X-ray fluorescence</td>
   </tr>
  </table>
XPS X-ray photoelectron spectroscopy

XRD X-ray diffraction

XRF X-ray fluorescence

XRR X-ray reflectometry

XSW X-ray standing wave
# 1 Introduction

In this document, I try to illustrate some of the metrological challenges I faced during the last 15 years in the semiconductor world, more precisely in the inline metrology group at CEA-Leti.

This document does **not** include any review of the literature dedicated to the characterization techniques and/or to a specific material system. Conversely, this document is based on the work done during these 15 years, either my work, or the work performed under my supervision by great post doctoral fellow, PhD or master students, and non-permanent colleagues hired in the frame of metrology-oriented programs. Consequently, all the Figures and Tables you will find in the *Sections 3 to 6* come from the main publications I have been involved in, or from the manuscripts of some PhD or master students.

I did my best to tell a coherent story, which led to some (difficult) choice in the topics and research directions I included in or excluded from this document. For instance, I excluded the beautiful work done in the frame of a 2-year collaboration with KLA Tencor about laser scattering, in which François Grossi (master) and Brice Arrazat (18-months non-permanent position) produced interesting scientific results<fnref n="1" />. I also excluded the great work done by Victor Yon (PhD) about strain analysis of GaN films<fnref n="2" />, because I failed to put it in the frame of the whole story. However, an extension of Victor's work to Raman-based (and XRD complemented) strain analysis is indeed part of the perspectives I present in *Section 7*.

Apart from this short introduction, this document includes 6 main sections:

- *Section 2* will briefly introduce the need for *metrology* (and not only *characterization*) in semiconductor environment

- *Section 3* will illustrate the work done around the metrology of thickness and optical constants using inline optical techniques such as spectroscopic ellipsometry or M-line spectroscopy

- *Section 4* is dedicated to the metrology of thickness and composition using X-ray techniques, with a strong focus on the quantitative analysis of high-Z, medium-Z and low-Z materials by X-ray fluorescence

- *Section 5* illustrates the work done around the elemental-depth profiling in thin layered materials of thicknesses from nm to µm and with nm-like depth resolution, by means of X-ray photoemission, combination of X-ray fluorescence and reflectometry in grazing incidence, and plasma-profiling time-of-flight mass spectrometry

- *Section 6* is dedicated to the metrology and characterization work required to support the development of innovative phase change materials for non-volatile memory

- In *Section 7*, I included some perspectives, either as continuity of the work presented in the previous sections, and as new research directions.

<footnote n="1">¹ - Milesi, F., Nolot, E., Mehrez, Z., Mazen, F., & Favier, S. (2008). *Evaluation of laser scattering technique and spectroscopic ellipsometry for in-line ion implantation characterization*. Paper presented at the AIP Conference Proceedings, 1066 182-185. https://doi.org/10.1063/1.3033587</footnote>

<footnote>- Arrazat, B., Danel, A., Nolot, E., Favier, S., Carron, V., Nemouchi, F., Hartmann, J.M., Rolland, G., Vandelle, P., Kermarrec, O., Campidelli, Y., Descombes, S. ; *Characterization of CMOS sub-65 nm metallic contact by laser scattering: Thermal stability of Ni(Si₁-xGex) ;* (2007) *Microelectronic Engineering*, 84 (11), pp. 2558-2562. ; https://doi.org/10.1016/j.mee.2007.05.021</footnote>

<footnote>- Nolot, E., Arrazat, B., Favier, S., Borde, Y., Damlencourt, J.F., Vincent, B., Kermarrec, O., Carron, V., Nemouchi, F., Vandelle, P., Bogumilowicz, Y., Danel, A. ; *Laser scattering: A fast, sensitive, in-line technique for advanced process development and monitoring* ; (2007) AIP Conference Proceedings, 931, pp. 116-120. ; https://doi.org/10.1063/1.2799354</footnote>

<footnote n="2">² - Yon, V., Rochat, N., Charles, M., Nolot, E., Gergaud, P., *X-Ray Diffraction Microstrain Analysis for Extraction of Threading Dislocation Density of GaN Films Grown on Silicon, Sapphire, and SiC Substrates*, Physica Status Solidi (B) Basic Research, 2020, 257(4), 1900579, https://doi.org/10.1002/pssb.201900579</footnote>
Every section from **Section 3** to **Section 6** starts with a list of the main contributors, the major supporting programs, and some relevant publications we produced in the frame of this research. In these sections, references to literature are included (only) in footnotes.
## 2 A brief introduction to metrology for semiconductors

The micro and nano electronic world tackles new challenges in terms of miniaturization, power consumption, power density and processing speed. Novel inorganic semiconductor materials and new 3D-architectures are replacing traditional silicon devices. Fig. 2.1 shows the continuous introduction of new elements in the semiconductor devices, whereas Fig. 2.2 illustrates the resulting complexity for both More Moore ("scaling") and More-than-Moore (additional "function") options, which translates into intensive research around innovative substrates and advanced materials. For instance, a large diversity of substrates are being investigated to meet the requirements of advanced technology nodes (fully-depleted SOI, ...), RF (engineered SOI, lithium niobate and tantalate, ...), optoelectronics and photonics (Ge, InP, AsGa, GaN...), power electronics (SiC, GaN, ...). Meanwhile, ultrathin 2D transition metal dichalcogenides are moving from labs to fabs and now explored for future transistors, photodetectors, light emitting diodes, chemical sensors and many other potential applications. Most of advanced materials feature composition-driven properties, as highlighted in Fig. 2.3 in the case of phase change materials investigated for non-volatile memories, thermoelectric device and others.

<figure><img src="image_3.png" /><figcaption>**Fig 2.1:** Growth in elements used in semiconductor industry
[https://newsroom.lamresearch.com/Happy-150th-Birthday-to-the-Periodic-Table]</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.2:** Intel illustrated in 2015 the variety of materials and architectures investigated for More-Moore (X scale) and More-than-Moore (Y scale) applications [Intel investor meeting 2015].</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.3:** Lencer demonstrated that the phase-change materials could be found in an area of small ionicity and a limited degree of hybridization. Lencer's plot enables to identify suitable candidates for phase-change materials (used for phase-change memory, thermoelectrics, etc) on the basis only of the material stoichiometry<fnref n="3" />.</figcaption></figure>

At the same time, there is a critical need for the metrology of such new materials. Why do we require metrology here, when measurement might be found sufficient? Metrology is the science of measurement. It has its own vocabulary, detailed in the “International Vocabulary of Metrology”<fnref n="4" />, where the subtle but profound difference between measurement and metrology is explained. Measurement is “the process of experimentally obtaining one or more numerical values that can reasonably be attributed to a quantity or property (length, amount of substance, concentration ...)$^{5}$. Metrology is “the science of measurement and its application”. As highlighted on the website of the National Physical Laboratory (NPL)<fnref n="5" />, one the National Metrology Institute (NMI), then one of the major players in the metrology world, “metrology is not just about the routine making of measurements, it’s about the infrastructure that ensures that we have confidence in the accuracy of the measurement. It establishes a common understanding of units and measurement processes, crucial to human activity. Metrology covers the accuracy, precision and repeatability of a measurement. It involves traceability or comparison with a standard or between different measuring systems. Metrology includes all theoretical and practical aspects of measurement, whatever the measurement uncertainty or the field of application”. NMIs are major pillars of the metrology infrastructure. They develop and disseminate accurate SI-traceable standards and methods required by industry and end-users, for an incredibly wide range of applications (manufacturing, satellite navigation systems and international time correlation, accurate medical diagnosis, amount of petrol delivered by a pump ...)$^6$.

In the semiconductor environment, indeed, in-fab monitoring of a mastered process may only require measurement capabilities with tight specifications in terms of repeatability and stability. However, such approach is inadequate to support material development or to guarantee process transfer from one tool to another or from one site to another. For instance:

- The development of materials with composition-driven properties must be supported by the traceable and quantitative measurement of the chemical composition. This is a prerequisite to interact with partners (from research to industry) and to investigate the modeling of the material properties.

- A Research and Technology Organization (RTO) such as CEA-Leti may develop a new material process that would represent a major innovation, and may then want to transfer this process to an industrial partner. This transfer must include the main properties of this new material (e.g.

<footnote n="3">³ Lencer, D., Salinga, M., Grabowski, B. et al. *A map for phase-change materials*. Nature Mater 7, 972–977 (2008). https://doi.org/10.1038/nmat2330</footnote>

<footnote n="4">⁴ “International Vocabulary of Metrology - Basic and General Concepts and Associated Terms” (VIM 3rd edition)</footnote>

<footnote n="5">⁵ https://www.npl.co.uk/resources/q-a/the-difference-between-metrology-and-measurement</footnote>

<footnote n="6">⁶ https://www.bipm.org/en/worldwide-metrology/#metrology</footnote>
composition, optical properties, structure ...) along with the way to measure such properties.
Since the industrial partner may use different process tools to grow the material and different
metrology fab tools to measure its properties, the measurement scheme must be traceable, when
possible to NMIs and SI units, thereby translating into a metrology scheme.

Therefore, there is a critical need for the metrology of new materials in complex spatial arrangements
with buried interfaces and with nm depth resolution. The challenges here are for metrology at the
nanoscale and it is clear that no single technique can provide all the answers required by industry. EAG
Lab provides a comprehensive map of analytical techniques that are used to probe chemical, physical,
optical and electrical properties of substrates and thin materials (Fig. 2.4), most of which are extensively
used and combined at CEA-Leti, either in the lab and/or in the cleanrooms. For each individual technique
and related analytical tool, to move from measurement to metrology requires:

- To assess the uncertainty budget related to the tool, by virtue of NMI-approved protocols and using SI-traceable standards

- To assess the uncertainty budget related to the sample of interest, which might come with undesired lateral or in-depth non uniformity, major influence of surface and/or interface, contamination, aging-induced evolution, ...

In this document, I show the way we tried to develop metrology protocols dedicated to thin inorganic
materials, mostly based on optical (ellipsometry), X-ray (fluorescence, reflectometry, photoemission)
and ion beam (plasma-profiling time-of-flight mass spectrometry) techniques. I highlight the need to
engage with NMI, to evaluate carefully the tool-related and material/sample-related uncertainty budget,
and the difficulty to master surface and interface impact of the deduced quantitative information.

<figure><img src="image_6.png" /><figcaption>**Fig. 2.4:** Visual reference for comparing the detection limit and analytical spot size of analytical techniques that are used to probe chemical, physical, optical and electrical properties of substrates and thin materials<sup>7</sup></figcaption></figure>

<footnote n="7">7 https://www.eag.com/techniques/</footnote>
## 3 Metrology with optical techniques

### Abstract – supervision – collaboration – key papers

The general objective of this research direction was to reduce the uncertainty budget in the determination of the thickness and optical properties of thin materials with spectroscopic reflectometry and ellipsometry.

The specific objectives were:

- The evaluation of instrument-related and sample-related contributions to the uncertainty budget (Section 3.2)

- The suggestion of metrology paths, for instance based on the combination of ellipsometry and X-ray reflectometry, to reduce the uncertainty budget (Section 3.2)

- The application of rigorous protocols to deduce accurate optical constants in challenging materials, such as strained silicon germanium films (Section 3.3) or ultrathin silicon on oxides (Section 3.4), the latter being addressed in the frame of Loïc Schneider's master training and more globally within the bilateral program with ST Microelectronics.

In addition, we investigated ellipsometry as one of the key technique required to probe indium-free transparent conductive oxides (Hélène Rottela post doc, ThinErgy program). Section 3.5 includes few words about this work and about in situ optical monitoring in 300 mm PECVD reactor conducted in the frame of AMAT/CEA-Leti bilateral program.

**Post doc:** Hélène Rotella (2015-2016, European program EMRP – ThinErgy Traceable characterization of thin-film materials for energy applications).

**CDD:** Rémi Elizalde (2020-2021, 2 year collaborative program with Applied Materials around in situ optical monitoring in 300 mm PECVD reactor)

**Master training:** Loïc Schneider (ST/CEA shared training about ultrathin SOI)

Long-term **collaboration** with Nanometrics (now Onto Innovations) in the frame of Joint Development Program associated to new production-type ellipsometers acquired by CEA-Leti.

Collaboration with James Hilfiker (Woollam) around the optimization of ellipsometry-based metrology, for instance dedicated to anisotropic samples.

Collaboration with Applied Materials (Julien Fort, Khogan Paul) around in situ optical monitoring in 300 mm PECVD reactor

Collaboration with two NMI: BAM (Andreas Hertwig) and PTB/Berlin (Sebastian Heidenreich, Victor Soltwisch) about the assessment of optical metrology uncertainties in the frame of the European Metrology Program EMPIR ATMOC, "Advanced Traceable Metrology for Optical Constants", 2021-2024

Long term collaboration with STM Crolles (Francesco Abbate, Delphine Le Cunff) about the optical metrology of ultrathin inorganic layer with industry-driven requirements

[N-3.1] Nolot, E., Lefevre, A., Hilfiker, J.N. ; Ellipsometry characterization of bulk acoustic wave filters ; (2008) Physica Status Solidi (C) Current Topics in Solid State Physics, 5 (5), pp. 1168-1171, https://doi.org/10.1002/pssc.200777795

[N-3.2] Nolot, E., André, A. ; Systematic combination of X-ray reflectometry and spectroscopic ellipsometry: A powerful technique for reliable in-fab metrology ; (2011) Thin Solid Films, 519 (9), pp. 2782-2786. ; https://doi.org/10.1016/j.tsf.2010.12.075

[N-3.3] Nolot, E., André, A., Michallet, A.; Performances and limitations of Lab-to-Fab strategies for inline optical metrology ; (2012) Proceedings of SPIE - The International Society for Optical Engineering, 8466, N°846605 ; https://doi.org/10.1117/12.928368
[N-3.4] Nolot, E., André, A., Scibetta, C., Poulingue, M., Levin, L., Vignoud, L., Isselé, H. ;
*Optical metrology of thick photoresist process for advanced 3D applications* ; (2014) Thin Solid
Films, 571 (P3), pp. 609-614. https://doi.org/10.1016/j.tsf.2014.04.058

[N-3.5] Nolot, E., Hartmann, J.M., Hilfiker, J.; *Optical constants determination of pseudomorphic Si1-xGex layers on Si(001), with 0<x<0.54* ; (2014) ECS Transactions, 64 (6), pp. 455-465. ; https://doi.org/10.1149/06406.0455ecst

[N-3.6] Schneider, L., Abbate, F., Le Cunff, D., Nolot, E., Michallet, A.; *Optical properties determination of Fully Depleted Silicon on Insulator (FDSOI) substrates by ellipsometry*; (2015) 26th Annual SEMI Advanced Semiconductor Manufacturing Conference, ASMC 2015, 7164469, pp. 195-200. ; https://doi.org/10.1109/ASMC.2015.7164469

[N-3.7] Kriso, C., Triozon, F., Delerue, C., Schneider, L., Abbate, F., Nolot, E., Rideau, D., Niquet, Y.-M., Mugny, G., Tavernier, C. ; *Modeled optical properties of SiGe and Si layers compared to spectroscopic ellipsometry measurements* , Solid-State Electronics, 129, pp. 93-96, 2017, https://doi.org/10.1016/j.sse.2016.12.011

[N-3.8] Rotella H, Mazel Y, Brochen S, Valla A, Pautrat A, Licitra C, Rochat N, Sabbione C, Rodriguez G. and Nolot E, *Role of vacancy defects in Al doped ZnO thin films for optoelectronic devices*, Journal of Physics D: Applied Physics, Volume 50, Number 48, Nov 2017, https://doi.org/10.1088/1361-6463/aa920b

**Complementary publications** (process / applications oriented or second-level involvement)

[c-3.1] Signamarcheix, T., Biasse, B., Papon, A.-M., Nolot, E., Ghyselen, B., Clavelier, L. ;
*Engineering silicon-on-insulator (SOI) substrates for hybrid orientation technologies (HOT)* ;
(2009) Proceedings - IEEE International SOI Conference, art. no. 5318773 ;
https://doi.org/10.1109/SOI.2009.5318773

[c-3.2] Signamarcheix, T., Biasse, B., Papon, A.-M., Nolot, E., Mazen, F., Leveneur, J., Faynot, O., Clavelier, L., Ghyselen, B. ; *Crystallographic orientation engineering in silicon-on-insulator substrates* ; (2010) Applied Physics Letters, 96 (26), N° 262111 ; https://doi.org/10.1063/1.3459966

[c-3.3] Stragier, A.-S., Signamarcheix, T., Salvetat, T., Nolot, E., Dechamp, J., Mercier, D., Gergaud, P., Tauzin, A., Clavelier, L., Lemiti, M. ; *200 mm silicon on porous layer substrates made by the smart cut™ technology for double layer transfer applications* ; (2010) ECS Transactions, 33 (4), pp. 207-216. ; https://doi.org/10.1149/1.3483509

[c-3.4] Stragier, A.-S., Signamarcheix, T., Salvetat, T., Nolot, E., Dechamp, J., Mercier, D., Gergaud, P., Tauzin, A., Clavelier, L., Lemiti, M. ; *200 mm silicon on porous layer substrates made by the smart cut technology for double layer-transfer applications* ; (2011) Journal of the Electrochemical Society, 158 (5), . https://doi.org/10.1149/1.3568947

[c-3.5] Signamarcheix, T., Andrieu, F., Biasse, B., Cassé, M., Papon, A.-M., Nolot, E., Ghyselen, B., Faynot, O., Clavelier, L. ; *Fully depleted silicon on insulator MOSFETs on (1 1 0) surface for hybrid orientation technologies* ; (2011) Solid-State Electronics, 59 (1), pp. 8-12. ; https://doi.org/10.1016/j.sse.2011.01.013
## 3.1 Introduction

Metrology tools based on optical techniques such as spectroscopic reflectometry and spectroscopic ellipsometry are widespread in semiconductor labs and fabs as they can provide fast (few sec / point), non-destructive (in most cases) analysis of the thickness and optical constants of thin materials with reasonable lateral resolution (few µm).

I was introduced to ellipsometry in 2004, as a basic user of a production tool with limited capability and un-documented analysis software. I really entered in the ellipsometry world in 2006 when I motivated the acquisition of Woollam M2000 R&D tool, which featured spectral range from UV to NIR, variable angle of incidence and a powerful modeling software that allowed : i/ to describe the dielectric function with appropriate Kramers-Kronig consistent oscillator-based model, ii/ to account for sample-related non-idealities and iii/ to account for tool-related non-idealities.

First, I mostly focused on the modeling of optical constants required to support the development of engineered substrates such as silicon on oxide [c-3.1, c3.2, c3.5] or porous silicon [c-3.3, c-3.4]. I realized the influence of sample-related non-idealities such as surface roughness or index gradient on the evaluated thicknesses. I also understood that the comparison with other techniques should be considered carefully : for instance, X-ray diffraction sees porous silicon as a highly crystalline material, whereas the optical properties deduced from ellipsometry significantly differ for crystalline silicon due to the lack of long range order in the material. Then, I investigated ways to identify and reduce or account for sample-related and tool-related uncertainties in ellipsometry-based metrology of thin materials (Section 3.2). Finally, careful measurement strategies were used to characterize different challenging materials such as thin silicon germanium (Section 3.3) and ultrathin silicon on oxide (Section 3.4).

## 3.2 Few words about the uncertainties in spectroscopic ellipsometry and reflectometry

Spectroscopic ellipsometry (SE) uses the change in the polarization state induced by the reflection on a sample to model the thickness and optical constant of the sample (Fig. 3.1). This technique can be highly sensitive to any change in thickness and/or optical properties, for instance capable of resolving 0.1nm variation in sub-nm SiO₂ thermally grown on silicon substrate. However, this model-based technique does not feature elemental sensitivity and may lead to ambiguous and/or correlated solutions (Fig. 3.2).

<figure><img src="image_7.png" /><figcaption>Fig. 3.1: Measurement principle of ellipsometry<fnref n="8" /></figcaption></figure>

<footnote n="8">⁸ Modern instruments do not directly measure $\psi$ and $\Delta$, which are calculated from a non-linear transform of the measured signal</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 3.2** : The ellipsometry data of a thin Aluminum film deposited on silicon (left) may be equally modeled with 20 nm or 30 nm-thick layer with realistic optical constants in both cases (right), due to the strong correlation between thickness and optical properties in thin absorbing materials [Nolot et al, oral presentation @ SPIE 2012]</figcaption></figure>

In general, the modeling of Psi and Delta spectroscopic data using Fresnel equation and Snell’s law permits reasonably accurate characterization of homogeneous, isotropic films deposited on infinitely thick substrate and measured to ideal instrument. In the real world, lots of non-idealities may affect the accuracy of the quantities deduced by ellipsometry analysis :

- Sample-related non-idealities :

o Aging effect, such as oxidation or airborne molecular contamination (AMC). For instance, AMC on native silicon oxide is artificially detected as an additional oxide thickness and needs to be managed, either by annealing procedure (230°C during 4 min according to NIST) or HF-last chemical step (Fig. 3.3), in order to accurately measure the thickness of ultrathin gate oxides.

o Roughness, which is often treated as an Effective Medium Approximation (EMA) consisting of 50/50 mixture of film and void (n=1), as in our study of thin AlN material for bulk acoustic wave filters [N-3.1]. Even though the actual surface is likely a mixture of roughness and oxidation, the surface layer would too thin to uniquely characterize with ellipsometry.

o The film may feature index gradient and/or anisotropic optical constants, as for uniaxial AlN films in [N-3.1].

o The thickness and/or optical properties may not be homogeneous at the lateral scale of the spot size of the ellipsometer, which may induce some depolarisation of the light.

o The thin layered film may be deposited on a transparent substrate (e.g glass, sapphire, or silicon for $\lambda > 1 \mu m$). There will be coherent propagation of the light in the layers but incoherent propagation in the transparent substrate, here again resulting in partial depolarization of the light.
<figure><img src="image_9.png" /><figcaption>**Fig. 3.3** Kinetics of the SE-deduced regrowth of silicon oxide layer after HF-last cleaning procedure (left). The SE-deduced thickness of a silicon wafer freshly introduced in the cleanroom environment is constantly increasing over a 2-week period due to airborne molecular contamination (right), when no modification is detected after 6 months in the cleanroom (stable wafer) [N-3.3]</figcaption></figure>

- **Tool-related non-idealities :**

o Imperfect collimation of the primary beam or angular spread in the case of small-spot focused beam production tools, for which the spread of angles of incidence (AOI) must be considered instead of one-only AOI (Fig. 3.4)

o A grating or prism is used to spread wavelengths out and collect a small region on the detector. The resolution of the detector translates into a range of accepted wavelengths or light bandwidth (Fig. 3.5).

o Angular spread and finite light bandwidth also result in partial depolarization of the light.

o ...

<figure><img src="image_10.png" /><figcaption>**Fig. 3.4** : Influence of tool non-idealities on the ellipsometry data related to 700 nm-thick thermal SiO₂ grown on silicon substrate. The light bandwidth evaluated among inline ellipsometers at CEA-Leti ranges from 1.0 to 6.0 nm whereas the angular spread of focused beam instruments is close to 6°</figcaption></figure>

We did not perform a systematic evaluation of the systematic errors of the optical components of the different ellipsometers in the cleanroom. Nevertheless, we addressed the following items:

- We suggested a way to accurately determine the reduced instrumental function of an ellisometer, using a set of thermally grown silicon oxides to access the angular spread and light bandwidth and 25 nm-thick silicon oxide to assess the angle of incidence [N-3.3]. This methodology was transferred to Nanometrics, a major industrial partner, supplier of fab-oriented ellipsometers. To account for accurately-determined instrument-related non-idealities translated in improved precision of the measured optical constants (Fig. 3.5, Table 3.1).
<figure><img src="image_11.png" /><figcaption>**Fig. 3.5** : Analysis of 25 nm-thick SiO₂ thermal grown on silicon substrate. To account for tool-related non-idealities allows to decrease the difference between experimental data and modeling with parametrized dielectric function of SiO₂ [N-3.3]</figcaption></figure>

<table><caption>**Table 3.1** : The lack of correction of tool-related non-idealities leads to extended uncertainties in the deduced optical constants of thermal oxide with varying thickness [N-3.3]</caption><thead><tr><th rowspan="2">T SiO<sub>2</sub><br>(nm)</th><th colspan="3">Refractive index @ 633nm</th></tr><tr><th>Tool A<br>LB correction</th><th>Tool C<br>No correction</th><th>Tool C<br>AS correction</th></tr></thead><tbody><tr><td>55.6</td><td>1.464</td><td>1.470</td><td>1.461</td></tr><tr><td>97.3</td><td>1.460</td><td>1.470</td><td>1.461</td></tr><tr><td>409.4</td><td>1.458</td><td>1.456</td><td>1.459</td></tr><tr><td>967.2</td><td>1.459</td><td>1.469</td><td>1.458</td></tr></tbody></table>

- We suggested the combination of ellipsometry and X-ray reflectometry as a way to reduce the correlation concerns that sometimes alters the precision of ellipsometry [N-3.2]. X-ray reflectometry was chosen as a complementary technique as it is also present as a non-destructive thin-film oriented technique in every cleanroom. Moreover, XRR is capable of uncorrelated determination of the thickness of thin films in most cases. We highlighted the interest of such combination on various materials systems such as transparent conducting indium oxide with depth-dependent properties and hydrogenated amorphous carbon films [N-3.2]. In that case, ellipsometry-only analysis of layer grown at 400°C was not able to reveal anisotropy and led to ~15% error in the deduced thickness (Fig. 3.6 and 3.7). The analysis of SE data at XRR-deduced thickness permitted to evidence the uniaxial anisotropy of the material, which was significantly less than for hydrogenated amorphous carbon processed at 550°C. The XRR-SE combination is now almost systematically used in CEA-Leti cleanrooms, when new material / new process conditions are introduced.

<figure><img src="image_12.png" /><figcaption>**Fig. 3.6** : Ellipsometric angle Ψ at several angles of incidence for PECVD a-C:H film grown at 400°C matches almost perfectly (left) the best-model calculation using isotropic dielectric constant (right) but results in erroneous estimate of the film thickness [from N-3.2]</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 3.7:** Experimental X-ray reflectivity scan from a hydrogenated amorphous carbon layer grown at 400 °C on a silicon substrate (left) and the ordinary and extraordinary optical constants of PECVD a-C:H film grown at 400 °C deduced from combined XRR-SE analysis (right) [from N-3.2]</figcaption></figure>

Dedicated NMI-approved standards and standardized methods should support the assessment of ellipsometer-based metrology of thickness and optical constants. The evaluation of the accuracy of thickness measurement with in-line ellipsometers is usually based on VLSI (NIST-traceable) standards made of SiO₂ thin films thermally grown on silicon wafers, with the SiO₂ thickness typically in the 2–1000 nm range. These wafers come with a specific baking procedure (4 min at 230 °C) which aims at removing the airborne molecular contamination layer. Among the few other types of standards available for such purpose, we evaluated a nitride thickness standard (VLSI Model number NFTS 8-900, Serial Number 7841-001) to draw a comparison between the certified thickness reported on VLSI certificate (t<sub>ref</sub>=89.6±0.4 nm), and the thicknesses measured by spectroscopic ellipsometry (Woollam M2000 tool) and XRR. The electron density difference between silicon nitride and silicon was indeed more appropriate to perform XRR analysis than for SiO₂/Si systems [N-3.2]. The certification of the thickness value was based on numerous assumptions on the SE experimental data (angle of incidence 74.99°±0.01°; wavelength range 400–800 nm), the SE model (Cauchy model) and the layer itself (single transparent homogeneous layer). XRR-SE combined analysis revealed that these assumptions were not enough to describe the thin material stack, where both thin interfacial and surface layers should be considered, resulting in ~ 2 nm offset of the nitride thickness value (Fig. 3.8).

<table><caption>**Fig. 3.8:** XRR evidences that the silicon nitride standard provided by VLSI could not be described by one uniform layer. A two-layer model based on XRR allowed better description of the SE data, both in terms of fit quality (Mean Squared Error) and accuracy of the material arrangement [N-3.2]</caption><thead><tr><th>Technique</th><th>Model</th><th>T<sub>Si3N4</sub> (nm)</th><th>MSE</th></tr></thead><tbody><tr><td>XRR</td><td>GA / FFT</td><td>88.0 / 87.9</td><td></td></tr><tr><td>SE / 75°<br>400-800nm</td><td>Cauchy</td><td>89.4</td><td>15</td></tr><tr><td>VASE / 60-80°<br>400-800nm</td><td>Cauchy</td><td>89.5</td><td>15</td></tr><tr><td>VASE / 60-80°<br>190-1700nm</td><td>Cauchy</td><td>89.5</td><td>22</td></tr><tr><td>VASE / 60-80°<br>190-1700nm</td><td>2-layer, XRR-based</td><td>87.8</td><td>8</td></tr></tbody></table>

To the best of our knowledge, there is no ellipsometer-compatible NIST-traceable standards for optical constants, whereas ellipsometers are extensively used to model process-dependent optical constants of
a huge variety of materials. In [N-3.4] we used M-line prism-coupling as a reference technique to deduce
the refractive index of a thick transparent resist layer. Such strategy can be extended to other thick
transparent films but does not fill the need for standards and standardized methods for absorbing
materials for which the accuracy of refractive index and absorption coefficient should be assessed.
In M-line prism-coupling experiment (Fig. 3.9), the sample is brought into contact with the base of a
high-index prism, creating a small air gap between the film and the prism. A laser beam strikes the base
of the prism and is totally reflected at the prism base onto a photodetector. At certain discrete values of
the incident angle θ, referred as mode angles, photons can tunnel across the air gap into the film and
enter into a guided optical propagation mode, causing a sharp drop in the intensity of light reaching the
detector. We used Metricon 2010/M prism-coupling system operated at discrete wavelengths (633, 1313
and 1548 nm) and high-index symmetric prism (n = 2.02 at λ = 632.8 nm) to characterize the resist layer.
The position of the critical angle (Fig. 3.10) allows for index-only measurement and, when combined
with measurement of the angular positions of the propagation modes, permits to access thickness and
refractive index independently. A possible source of uncertainty in the determination of optical constant
of thick films with such method is that the first modes (lowest incident angles) cannot be resolved.
Missing modes at the start of the pattern introduce errors in the numbering of the propagation modes
and, consequently, in the determination of the thickness and the refractive index. Fortunately, as the film
gets thicker, the angle at which the first propagation mode occurs asymptotically approaches the critical
angle for total reflection. In the case of films thicker than 10 µm, the error in the measured refractive
index due to the approximation that the angle of the first propagation mode equals the critical angle is
less than 3 × 10⁻⁴. As a comparison, the calibration and the monitoring of our prism-coupling system
are based on NIST (National Institute of Standards and Technology) standard reference materials
(ICS15), resulting in a better than 10⁻³ accuracy for the refractive index.

<figure><img src="image_14.png" /><figcaption>**Fig. 3.9** : Schematics of prism-coupling system.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 3.10** : Prism-coupling data acquired at 633 nm for 44 µm-thick photoresist sample. Both thickness and refractive index can be deduced by virtue of clear definition of the critical angle and appropriate angular resolution [N-3.4]</figcaption></figure>

The most important part of the work reported in this 3.2 section was conducted during 2010 – 2014
period. However, the need for standards and standardized methods that could support the assessment of
the accuracy of ellipsometry for thickness and optical constants is still an important topic. After three
failures, we finally got a European Metrology Program dedicated to Optical constants (EMPIR ATMOC,
“*Advanced Traceable Metrology for Optical Constants*”, 2021-2024) that aims at covering at least part
of the needs.
3.3 Optical constants of strained silicon germanium

Thin silicon germanium layers epitaxially grown on silicon or silicon on oxide substrates are designed to optimize strain-induced carrier mobility at the junction level in advanced CMOS architectures. The optical constants of strained SiGe are used to access thickness and composition with fab-ellipsometer in production lines, which puts strong requirements in terms of reliability and accuracy in the determination of the optical constants. In this section, I give a flavor of the work done in 2012-2013 when we determined the composition-dependent optical constants of strained silicon germanium with germanium content up to 54% [N-3.5]. At that time, this was a significant extension of Zollner’s work <fnref n="9" /> related to germanium content up to 27.5%. The robustness of the deduced optical functions relies on an appropriate management of sample-related uncertainties (surface effects) together with a rigorous combination of X-ray based and optical-based analysis so as to build the required alloy model. This model was extensively tested, demonstrating a 0.5-1 at.% accuracy concerning the Ge content in fully-strained Si₁₋ₓGeₓ epitaxial layers. The composition-dependent optical constants determined in 2013 has been shared with end-users (ST Microelectronics, ...) and with Woollam and Nanometrics/Onto : they are now available on every lab or fab tool of these ellipsometry suppliers.

We have used an Epi Centura RP-CVD industrial cluster tool manufactured by Applied Materials to grow a “reference set” consisting of ten fully strained Si₁₋ₓGeₓ layers with different Ge content in the 5 to 55% range on 200 mm Si(001) wafers, along with an “evaluation set” that included strained and relaxed SiGe films. Prior to any deposition, a “HF-last” wet cleaning was performed, followed by an *in situ* hydrogen bake in order to remove surface contaminants on the wafer. Growth temperature was reduced from 750 °C to 550°C, as the Ge content increased from 5% to 55% in order to obtain smooth, pseudomorphic SiGe layers.

Conventional Ω-2θ scans around the (004) diffraction order (Fig. 3.11) were performed using a Panalytical X'Pert high-resolution diffractometer with a copper anode and a four-crystal Ge(220) monochromator as the beam conditioner. The thickness and Ge content of the Si₁₋ₓGeₓ layers were deduced from best-model calculations of the XRD data. The Ge content was extracted from the following relationship: aₛᵢGe(Å)=5.43105+0.1988x+0.028x², where the bulk, unstrained SiGe lattice parameter is generated according to the XRD-deduced perpendicular lattice parameter of the layer and to a linear extrapolation between the Poisson ratio of Si (0.278) and that of Ge (0.271). The very good agreement between experimental X-ray diffraction profiles and their associated dynamical scattering simulations (concerning the width and shape of the SiGe layer peak) and the presence of marked thickness interference fringes is characteristic of pseudomorphic stacks, i.e. without significant misfit dislocations or stacking faults and with abrupt interfaces between Si and SiGe.

Each sample of the *reference set* went through a “HF-last” cleaning step immediately followed by SE and XRR measurements. The SE data were collected at 6 angles of incidence (70° to 80°, 2° step) using Woollam M2000 instrument. Spectra were averaged over 200 compensator rotations (about 10 seconds) in order to reduce noise. XRR measurements (Fig. 3.11) were run on a Jordan Valley JV5200 fully-automated tool, based on focused beam geometry and equipped with a copper anode. The SiGe thickness by fast Fourier transform of the XRR profile (T<sub>FFT</sub>) and by best-model calculation of {SiO<sub>2</sub> / Si<sub>1-x</sub>Ge<sub>x</sub> / Si substrate} system with a genetic algorithm (T<sub>GA</sub>). XRR and XRD-deduced thicknesses of the various SiGe layers of the *reference set* were in very good agreement (Table. 3.2). XRR and XRD-deduced thicknesses of the various SiGe layers of the *reference set* were in very good agreement. XRR and SE experiments were completed within 2 hours after the “HF-last” cleaning step for every wafer, resulting in limited evolution of surface overlayer, as verified by dynamic SE measurements over the first 2 hours (Fig. 3.12).

<footnote n="9">⁹ S. Zollner, Jill Hildreth, Ran Liu, P. Zaumseil, M. Weidner, B. Tillack, *Optical constants and ellipsometric thickness determination of strained Si₁₋ₓGeₓ: C layers on Si (100) and related heterostructures*, J. Appl. Phys. Vol. 88 (2000) 4102, https://doi.org/10.1063/1.1308070</footnote>
In other words, we did our best to minimize SE-tool uncertainties (pre-determination of instrumental function, long acquisition time at 6 angles of incidence) and sample-related uncertainties (management of SiGe/Si interface, assessment of sharp interfaces between SiGe and Si substrate, management of SiGe surface layer).

<figure><img src="image_16.png" /><figcaption>**Figure 3.11** : X-Ray Reflectivity curves (left) and Omega-2Theta scans around the (004) associated with five different Ge contents SiGe layers from the reference sample set [N-3.5].</figcaption></figure>

<table><caption>**Table 3.2** : Process conditions, thickness and germanium content of the SiGe layers from the reference wafer set. The XRR-GA value was used as a reference when building the SE model [N-3.5].</caption><thead><tr><th rowspan="2">Temperature<br>(°C)</th><th rowspan="2">F(GeH<sub>4</sub>)/F(H<sub>2</sub>)</th><th rowspan="2">Growth<br>rate<br>(nm.min<sup>-1</sup>)</th><th colspan="3">Thickness (nm)</th><th rowspan="2">Ge content<br>(%)</th></tr><tr><th>XRR-FFT</th><th>XRR-GA</th><th>XRD</th></tr></thead><tbody><tr><td>750</td><td>4.17.10<sup>-5</sup></td><td>30.7</td><td>73.0</td><td>73.4</td><td>73.0</td><td>5.17</td></tr><tr><td>750</td><td>1.04.10<sup>-4</sup></td><td>60.6</td><td>63.0</td><td>62.8</td><td>63.0</td><td>9.82</td></tr><tr><td>700</td><td>8.33.10<sup>-5</sup></td><td>27.6</td><td>45.9</td><td>45.2</td><td>45.0</td><td>15.50</td></tr><tr><td>650</td><td>8.33.10<sup>-5</sup></td><td>10.4</td><td>35.9</td><td>35.8</td><td>35.0</td><td>20.40</td></tr><tr><td>650</td><td>1.67.10<sup>-4</sup></td><td>22.5</td><td>33.6</td><td>33.0</td><td>33.0</td><td>26.30</td></tr><tr><td>650</td><td>2.92.10<sup>-4</sup></td><td>39.4</td><td>28.3</td><td>27.2</td><td>27.0</td><td>31.90</td></tr><tr><td>600</td><td>2.50.10<sup>-4</sup></td><td>11.7</td><td>24.1</td><td>23.1</td><td>23.0</td><td>37.10</td></tr><tr><td>600</td><td>4.17.10<sup>-4</sup></td><td>22.9</td><td>20.0</td><td>19.2</td><td>19.0</td><td>42.25</td></tr><tr><td>550</td><td>4.17.10<sup>-4</sup></td><td>6.2</td><td>20.0</td><td>19.7</td><td>19.0</td><td>49.25</td></tr><tr><td>550</td><td>6.25.10<sup>-4</sup></td><td>11.4</td><td>21.2</td><td>20.3</td><td>20.0</td><td>53.85</td></tr></tbody></table>
<figure><img src="image_17.png" /><figcaption>**Figure 3.12** : Evolution of the ellipsometry angle ψ measured at three incidence angles (72°, 76° and 80°) for the 35 nm thick SiGe 20.4% reference sample either right after or 2 hours after a “HF-last” wet cleaning, demonstrating the stability of the SiGe layer during this 2-hour period [N-3.5].</figcaption></figure>

For each sample of the reference wafer set, the SE data were described with an {over-layer/ Si₁₋ₓGeₓ /substrate} system. Because of the well-controlled surface conditioning used, the over-layer was assumed to be SiO₂ with a fixed thickness equal to 0.7 nm. The substrate was described using the optical constants of silicon. The optical constants of each Si₁₋ₓGeₓ layer was evaluated by first calculating the optical functions on a wavelength-by-wavelength basis using fixed, XRR-deduced thickness. These results are then used to create a Kramers-Kronig consistent B-Spline description of the dielectric function. The B-spline approach was preferred to classical oscillator-based description since the latter required at least six different oscillators in order to describe all the spectral features, with poor physical meaning of each individual oscillator. Finally, the set of ten Si₁₋ₓGeₓ optical functions (Fig. 3.13) was used to build a composition-dependent “alloy” model based on critical-point shifting algorithm. This alloy model provides the optical constants of pseudomorphic Si₁₋ₓGeₓ material for arbitrary Ge composition in the 0 to 54% range.

<figure><img src="image_18.png" /><figcaption>**Figure 3.13** : Real part (left) and imaginary part (right) of the dielectric function of pseudomorphic Si₁₋ₓGeₓ layers grown on Si(001), with 0 < x < 0.54 [N-3.5]</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Figure 3.14** : Maximum intensity of the E2 peak extracted from our alloy model and from a SE-only modelling of the data from the reference sample set [N-3.5]</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 3.15** : Discrepancy between the thicknesses of the SiGe strained layers of the reference sample set as deduced from XRR-based analysis (optimized alloy model) and SE-only modelling [N-3.5]</figcaption></figure>

The evolution of the dielectric function of our Si₁ₓGeₓ alloy with increasing Ge content (Table 2) is well-aligned with previous work by Pickering and Carline<fnref n="10" /> and Zollner<fnref n="11" />: the E₁ peak (~3.4 eV for Si) broadens and moves to lower energies due to alloy scattering effects, strain effects and spin-orbit splitting. The position of the E₂ peak (4.25 eV, interpreted as interband transitions at the X point and along the Σ line<fnref n="12" />) remains constant with increasing Ge content, while significant broadening occurs. The magnitudes of both the E₁ and the E₂ peaks decrease with increasing Ge content. Finally, the E'₁ peak (~5.4 eV for Si) broadens significantly and finally vanishes with increasing Ge content.
We believe our surface management protocol limited the possible variability of the top layers in the reference set and thus improved the reliability of the deduced optical constants of Si₁ₓGeₓ. The E₂ peak maximum extracted from our alloy model follows a rather linear trend for 0.05<x<0.54, with I<sub>E2</sub>(x)=45.9-21.88.x (Fig. 3.14). This linear trend is not valid for x<0.05 since the E₂ peak magnitude is then driven by the optical constants of silicon that are included in the alloy model for x=0 Ge content, with E₂ peak magnitude of 47.6. To understand the influence of the surface layer on the intensity of the E₂ peak, one should keep in mind that a 0.1 nm increase in the SiO₂ top layer of a {SiO₂/Si substrate} results in a 0.6 decrease of the E₂ peak magnitude of the pseudo dielectric function.

The importance of combining SE and X-Ray data for this study is examined by repeating the modeling of each sample with only the SE data. For some of the reference samples, uncertainty in the film and surface-layer thickness is produced through correlation with the optical constants. When fitting the SE data with a summation of Kramers-Kronig consistent oscillators, the choice of oscillators can be very critical, specifically if non-zero absorption is allowed below the bandgap. The data extracted from our "alloy" model using combined tools show a linear trend of the E2 peak magnitude with increasing Ge content (Figure 3.14). SE-only results produce a deviation from this linear trend, due to differences in the resulting SiGe and over-layer thickness values. Fig. 3.15 shows the difference between SiGe thickness determined from SE-only and from XRR with increasing Ge content. Incorrect thickness leads to incorrect dielectric functions for the SE-only analysis. The method we have proposed and implemented helps avoid correlation between thickness and optical constants that has plagued the SE-only analysis and thus avoids these inaccuracies.

<footnote n="10">¹⁰ C. Pickering, R. T. Carline, J. Appl. Phys. 75, (1994) 4642-4647, https://doi.org/10.1063/1.355914</footnote>

<footnote n="11">¹¹ S. Zollner, Jill Hildreth, Ran Liu, P. Zaumseil, M. Weidner, B. Tillack, J. Appl. Phys. Vol. 88 (2000) 4102, https://doi.org/10.1063/1.1308070</footnote>

<footnote n="12">¹² R. Ahuja, C. Persson, A. Ferreira da Silva, J. Souza de Almeida, C. Moyses Araujo, B. Johansson, J. Appl. Phys., Vol. 93, No. 7 (2003), 3832-3836, https://doi.org/10.1063/1.1555702</footnote>
<figure><img src="image_21.png" /></figure>

**Figure 3.16** : Ellipsometric angles ψ and Δ measured at three angles of incidence for the 19 nm-thick SiGe 42.25% layer of the reference sample set. The figure demonstrates the excellent agreement between the experimental data (lines) and the best-model calculation (dots) [N-3.5].

<figure><img src="image_22.png" /></figure>

**Figure 3.17** : Difference between XRD-deduced and SE-deduced Germanium contents of the fully strained SiGe layers and the partially relaxed SiGe layers (with R>10%) of the evaluation sample set [N-3.5]

The Si₁-xGex alloy model was evaluated on *evaluation set*, consisting of 43 wafers with Si₁-xGex layers grown by RP-CVD on prime 200 mm slightly p-type bulk Si(001) wafers. The thickness of Si₁-xGex layer was significantly varied for each Ge content (12%, 22%, 32%, 42%, 52%), resulting in a large variety (fully pseudomorphic to partially relaxed) of Si₁-xGex layers. Each wafer went through the same surface conditioning and measurement protocol as used for the *reference sample set*. In addition to the Ge content, the macroscopic degree of strain relaxation R for each plastically relaxed SiGe layer was calculated from high resolution X-ray diffraction experiments. The SE data were modelled using an {SiO₂/ Si₁-xGex /Silicon substrate} system, with SiGe layer described with the reported alloy model, resulting in three floating parameters: the thickness of the SiO₂ and the SiGe layers, and the Ge content. As an example, Figure 3.16 shows the remarkable agreement between the experimental ellipsometry data and the best-model calculation based on the above described optimized alloy model, for 20 nm thick SiGe 42.3% sample from the *evaluation set*.

The Ge content deduced from XRD and SE are in very good agreement for fully pseudomorphic SiGe layers (Fig. 3.17): over a set of 33 fully-strained SiGe layers, the averaged difference between XRD-derived and SE-derived Ge content is equal to 0.26%, with a maximum discrepancy of 1.0%. The same conclusions can be drawn for the almost fully-strained SiGe layers (R ≤ 2%). On the contrary, the discrepancy is significant for relaxed SiGe layers with R > 2% (Fig. 3.17). Whereas SE fits the needs for fast, accurate full-wafer mapping of pseudomorphic layers, it demonstrates low sensitivity to the transition from pseudomorphic to plastically relaxed layers when compared to AFM or XRD techniques.

The resulted composition-dependent alloy model available on Woollam and Nanometrics/Onto ellipsometers is illustrated in Fig. 3.18.
<figure><img src="image_23.png" /><figcaption>**Figure 3.18:** Imaginary part of the dielectric function of the SiGe alloy model, which is now available on Woollam and Nanometrics/Onto ellipsometers</figcaption></figure>

## 3.4 Optical constants of ultrathin silicon on oxide films

The metrology of ultrathin silicon on oxide [N-3.6] conducted in the frame of Loïc Schneider's master is another case where the management of sample-related and tool-related uncertainty was key to improve the accuracy in the modelling of SE data.

In 28 nm FDSOI (Fully Depleted Silicon On Insulator) technologies, the SOI substrates consist of a thin (~ 10 nm) crystalline silicon superficial layer reported on a buried oxide layer. The optical constants of the thin SOI differ from the bulk silicon and this discrepancy is enhanced when SOI thickness decreases. In [N-3.6], we determined the thickness-dependent optical constant of SOI in the 3 to 12 nm range for implementation of production ellipsometers at ST Microelectronics, whereas complementary work supported the understanding of the thickness-dependency of SOI dielectric function [N-3.7]. At that time, this work was complementing Kamineni's study <fnref n="13" />, with significant focus on the management of sample-related and tool-related uncertainty.

After careful determination of the instrumental function of the ellipsometry toolset (angular spread, light bandwidth, angle of incidence), we had to account for a sample-related uncertainties. Most of the work was conducted on focused-beam production ellipsometers that featured 30 µm spot size. We had to consider the variation of SOI thickness within the 30-µm spot size highlighted by complementary beam profile reflectometry experiments (Fig. 3.19).

In this study, we focused on FDSOI substrates constituted of a buried oxide of 25 nm and 12 nm SOI. We used process/measurement loops consisting of successive thinning of the same wafers in order to limit sample-induced variability while maintaining controlled surface conditions. In this strategy, the thickness of the buried oxide, which enables multi-sample analysis. We used cycles of chemical oxidation and oxide removal steps in order to remove fixed quantity of superficial silicon, each cycle consisting of the removal of native oxide in HF solution followed by the oxidation of superficial silicon using ozone process. This process had previously been characterized on silicon substrate, resulting in SE-deduced 1.1 ± 0.05 nm top oxide layer and unmodified roughness of the surface roughness as characterized by AFM.

<footnote n="13">¹³ V. K. Kamineni and A. C. Diebold, Appl. Phys. Lett. 99, 151903 (2011); https://doi.org/10.1063/1.3650470</footnote>
<figure><img src="image_24.png" /><figcaption>**Fig. 3.19:** Beam profile reflectometry reveals ~ 0.5 nm variability of the SOI thickness of FDSOI substrates within the 30 µm spot size of fab ellipsometers. Such thickness non-uniformity must be considered when modeling the SE data [N-3.6].</figcaption></figure>

Fig. 3.20 illustrates the protocol of successive thinning of SOI. First, FDSOI substrate went through 12 oxidation cycles in order to get a thin remaining silicon thickness of ~ 7.2 nm. Then every 2 cycles, we performed ellipsometry and XRR measurements. In spite of low contrast between the density of silicon and silicon oxide, the XRR data of smooth high-grade SOI permitted to use XRR as a reference for SOI thickness. The SOI thinning was constant at each cycle, with silicon removal rate of 0.4 nm/cycle (Fig. 3.20).

<figure><img src="image_25.png" /><figcaption>**Fig. 3.20:** Illustration of successive thinning of FDOI substrate (left). XRR confirms a constant removal rate of 0.4 nm/cycle (right) [N-3.6].</figcaption></figure>

We accounted for tool-related non-idealities and thickness non-uniformity to model the SE data at each (fixed) XRR-deduced SOI thickness, assuming constant thickness over cycles for both buried oxide and top oxide layers. The imaginary part of the thickness-dependent dielectric function (Fig. 3.21) highlights the blue shift of E1 critical point and the decrease of the intensity of E2 critical point along SOI thinning, both relating to quantum confinement effect as confirmed by complementary simulation work performed at ST Microelectronics on the same sample case (Fig. 3.22), [N-3.7].
<figure><img src="image_26.png" /><figcaption>**Fig. 3.21** : Thickness-dependent imaginary part of the dielectric function of SOI (left) and the exponential decay of the intensity of E2 critical point with SOI thinning (right) [N-3.6]</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Fig. 3.22** : Same trends are observed in the thickness-dependent dielectric function of SOI derived by the experimental data and related semi-empirical tight-binding calculations [N-3.7]</figcaption></figure>
## 3.5 Towards *in situ* optical metrology ?

We continue to work on the optimization of *ex situ* optical metrology paths to support material process development. For instance, in the frame of Hélène Rotella's post doc, we combined ellipsometry with photoluminescence, X-ray diffraction, X-ray reflectometry and Hall effect to characterize the role of Zn and oxygen vacancies in the performances of industry-ready Al doped ZnO thin films for optoelectronic devices [N-3.8].

In the frame of ATMOC project, we continue to work with NMIs on the assessment of tool-related and sample-related uncertainties for optical metrology and in particular for ellipsometry-based analysis.

We also engaged in a bilateral program with Applied Materials that aimed at investigating *in situ* optical metrology dedicated to complex layers arrangements for optical filter application. During this 2 year program, we evaluated the added value of UV-visible reflectometry “ISM module” to perform accurate real-time *in operando* characterization of complex optical stacks grown at 400°C by Plasma Enhanced Chemical Vapour Deposition on 300 mm wafers. We have been able to probe the thickness of individual layers in up to 80-layers stacks by virtue of reflectance data collected every 100 ms all along the deposition process. TEM analysis confirmed the ± 1 nm accuracy in the determination of individual thicknesses that could not be resolved by *ex situ* post process ellipsometry analysis.

<figure><img src="image_28.png" /><figcaption>**Fig. 3.23** : *Ex situ* spectro-reflectance measurement of complex optical stacks grown on the two sides of the process tool. The shift between the two data sets is due to a systematic 6% difference in the silicon oxide thicknesses as revealed by *in operando* ISM analysis</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Fig. 3.24** : *Ex situ* spectro-reflectance measurement (“CARY”) of complex optical stack compared with *in operando* ISM measurement and simulation from ISM determined thickness. The method described here enables room temperature reflectance spectrum determination from *in operando* metrology only</figcaption></figure>

This technique is particularly adequate to reveal process deviation<fnref n="14" /> (Fig. 3.23). When combined with temperature ellipsometry (to determine optical constant at process temperature), it permits to deduce the

<footnote n="14">¹⁴ R. Elizalde, J-P. Nieto, C. Licitra, J. Fort, K. Paul, T. Egan, E. Budiarto, E. Nolot, *In Operando Metrology for Real Time Monitoring of Complex Optical Stacks*, poster at 2022 International Conference on Frontiers of Characterization and Metrology for Nanoelectronics (FCMN), Monterey</footnote>
room temperature reflectance spectrum of the final layer arrangement from *in operando* analysis at 400°C (Fig. 3.24).

This program, supported by Rémi Elizalde during a one-year non-permanent position, confirmed the added value of *in situ* and *in operando* optical analysis for accurate monitoring of thin materials, by suppressing aging-induced uncertainties and limiting correlation concerns in the modelling of complex stacks. We even demonstrated that the tool was capable of accurate thickness analysis on challenging multi-layered substrates that could be described by pseudo dielectric function prior to deposition and *in operando* analysis. However, the modeling part, and for instance the way to extract and then use the pseudo dielectric function of complex substrates was performed with Applied Material proprietary software, without clear accessible information about the implemented equations. Further work around *in situ* and *in operando* optical metrology with mastered modelling part is of my key perspective.
# 4 X-ray Metrology of thickness and composition

## Abstract – supervision – collaboration – key papers

The general objective of this research direction was to improve the accuracy of thickness and composition analysis of thin inorganic materials with X-ray reflectometry, X-ray fluorescence and X-ray photoemission spectroscopy.

The specific objectives were:

- To assess the interest of XRF and XRR for thickness measurement (Section 4.1)

- To assess the accuracy of X-ray fluorescence based on fundamental parameters and calibration against pure elements for composition analysis (Section 4.2)

- To develop metrological strategy to access the composition of thin epitaxial materials, using combination of XRF with XRR or X-ray diffraction (Section 4.2)

- To optimize metrological paths to analyze the composition of thin sulfur-based materials despite the lack of related XRF standards, and to use such strategy to support the development of ultrathin 2D material processes (Section 4.3). For this work, we collaborated with the German NMI PTB/Berlin to get compositional information with mastered uncertainty budget.

- To evaluate the specific challenges relating to XRF-based compositional analysis of thin materials doped with light elements, and to draw specific metrological paths dedicated to nitrogen-doped GeSbTe phase change materials for memory applications (Section 4.4). This work was required to support the transfer of N-doped GeSbTe material process to industry, in the frame of STM/CEA-Leti bilateral program. We faced unexpected difficulties to identify accurate reference techniques for the evaluation of nitrogen content, which was finally deduced from the careful analysis of Elastic Back Scattering experiments conducted at the University of Surrey in the frame of a dedicated collaboration.

**PhD**: Walter Pessoa (composition of N-doped phase change materials)

**Master training**: David Pagnon (accuracy of XRF with fundamental parameters)

**Collaboration** with PTB/Berlin (Philipp Hönicke) for the evaluation of the composition of ultrathin MoS₂ films using reference-free XRF analysis at PTB beamline @ Bessy 2 (2019-2020)

Collaboration with Ion Beam Center at Surrey University (Chris Jeynes) for the evaluation of the composition of N-doped GeSbTe materials using Elastic Back Scattering experiments (2019-2020)

Collaboration with IBM Fishkill (Patrick Dehaven) and STM (Delphine Le Cunff) to assess the accuracy of XRR for thickness and density measurement of thin materials (2013-2016)

Collaboration with STM (Caterina Carpanese, Delphine Le Cunff) to support the transfer of XRF-based metrology of N-doped GeSbTe from CEA-Leti to STM cleanrooms.

[N-4.1] J.F. Damlencourt; B. Vincent; P. Rivallin; P. Holliger; D. Rouchon; E. Nolot; C. Licitra; Y. Morand; L. Clavelier; T. Billon., "Fabrication of SiGe-On-Insulator by Improved Ge Condensation Technique," 2006 International SiGe Technology and Device Meeting, Princeton, NJ, USA, 2006, pp. 1-2, https://doi.org/10.1109/ISTDM.2006.246531

[N-4.2] Vincent, B., Damlencourt, J.-F., Rivallin, P., Nolot, E., Licitra, C., Morand, Y., Clavelier, L., *Fabrication of SiGe-on-insulator substrates by a condensation technique: An experimental and modelling study* ; (2007) Semiconductor Science and Technology, 22 (3), art. N° 011, pp. 237-244. ; https://doi.org/10.1088/0268-1242/22/3/011

[N-4.3] Nolot, E., Mazel, Y., Barnes, J.-P., Sabbione C, Navarro G., Tempez, A., Legendre, S., *Accelerating the development of phase-change random access memory with in-fab plasma profiling time-of-flight mass spectrometry*, Surface and Interface Analysis, 2020, 52(12), pp. 895–899, https://doi.org/10.1002/sia.6823 (Cover SIA Journal)
[N-4.4] Nolot, E., André, A. ; Systematic combination of X-ray reflectometry and spectroscopic ellipsometry: A powerful technique for reliable in-fab metrology ; (2011) Thin Solid Films, 519 (9), pp. 2782-2786. ; https://doi.org/10.1016/j.tsf.2010.12.075

[N-4.5] Pelloquin, S., Le Rhun, G., Defaÿ, E., Renaux, P., Nolot, E., Abergel, J., Sibuet, H. ; Improvement of capacitive behavior on gradient-free PZT thin films ; (2014) Integrated Ferroelectrics, 157 (1), pp. 132-138 ; https://doi.org/10.1080/10584587.2014.912887

[N-4.6] Cadot, S., Renault, O., Frégnaux, M., Rouchon, D., Nolot, E., Szeto, K., Thieuleux, C., Veyre, L., Okuno, H., Martin, F., Quadrelli, E.A. ; A novel 2-step ALD route to ultra-thin MoS2 films on SiO2 through a surface organometallic intermediate (2017) Nanoscale, 9 (2), pp. 538-546, http://doi.org/10.1039/c6nr06021h

[N-4.7] M. Barlas, A. Grossi, L. Grenouillet, E. Vianello, E. Nolot, N. Vaxelaire, P. Blaise, B. Traoré, J. Coignus, F. Perrin, R. Crochemore, F. Mazen, L. Lachal, S. Pauliac, C. Pellissier, S. Bernasconi, S. Chevalliez, J.F. Nodin, L. Perniola, E. Nowak, Improvement of HfO2 based RRAM array performances by local Si implantation, 2017 IEEE International Electron Devices Meeting (IEDM) p.14.6.1-14.6.4, https://doi.org/10.1109/IEDM.2017.8268392

[N-4.8] Cadot, S., Renault, O., Frégnaux, M., Rouchon, D., Nolot, E., Szeto, K., Thieuleux, C., Veyre, L., Okuno, H., Martin, F., Quadrelli, E.A. Low-temperature and scalable CVD route to WS2 monolayers on SiO2/Si substrates, Journal of Vacuum Science & Technology A 35, 061502 (2017); https://doi.org/10.1116/1.4996550

[N-4.9] Khazaka R., Nolot E., Aubin J. and Hartmann J.M, Investigation of the Growth of Si-Ge-Sn Pseudomorphic Layers on 200 mm Ge Virtual Substrates: Impact of Growth Pressure, HCl and Si2H6 Flows, ECS Transactions 86 (7) 207 (2018), https://doi.org/10.1149/08607.0207ecst

[N-4.10] Khazaka R., Nolot E., Aubin J. and Hartmann J.M, Growth and characterization of SiGeSn pseudomorphic layers on 200mm Ge virtual substrates, Semiconductor Science and Technology 33, 124011 (2018), https://doi.org/10.1088/1361-6641/aaea32

[N-4.11] Le Maoult, C., Vaufrey, D., Martin, F., Martinez E, Nolot E., Cadot, S., Gheeraert, E., Analysis of InGaN surfaces after chemical treatments and atomic layer deposition of Al2O3 for µLED applications, Proceedings of SPIE - The International Society for Optical Engineering, 2020, 11280, 112801C, https://doi.org/10.1117/12.2544787

[N-4.12] Nolot, E., Cadot, S., Martin, F., Hönicke P., Zech, C., Beckhoff, B., In-line characterization of ultrathin transition metal dichalcogenides using X-ray fluorescence and X-ray photoelectron spectroscopy, Spectrochimica Acta - Part B Atomic Spectroscopy, 2020, 166, 105788, https://doi.org/10.1016/j.sab.2020.105788

[N-4.13] Jeynes, C., Nolot, E., Costa, C., ...Navarro, G., Mantler, M., Quantifying nitrogen in GeSbTe:N alloys, Journal of Analytical Atomic Spectrometry, 2020, 35(4), pp. 701–712, https://doi.org/10.1039/C9JA00382G (Cover of JAAS)

[N-4.14] Frauenrath, M., Hartmann, J.M., Nolot, E., Boron and phosphorous doping of GeSn for photodetectors and light emitting diodes, ECS Transactions, 2020, 98(5), pp. 325–338, 325, https://doi.org/10.1149/09805.0325ecst

[N-4.15] Frauenrath M, Kiyek V., von den Driesch N., Veillerot1 M., Nolot E., Buca D. and Hartmann J-M, An In-Depth Study of the Boron and Phosphorous Doping of GeSn, 2021 ECS J. Solid State Sci. Technol. 10 085006, http://dx.doi.org/10.1149/2162-8777/ac1d27

[N-4.16] M. Frauenrath, L. Casie, O. Concepción, N. Coudurier, N. Gauthier, S. M. N’hari, E. Nolot, P. Rodriguez, D. Buca, N. Pauc, V. Reboud, J.-M. Hartmann, Advances in In-situ Boron and Phosphorous Doping of SiGeSn, 2022 ECS Trans. 109 3, https://doi.org/10.1149/10904.0003ecst

[N-4.17] B. Chatmaneeringcharoen, M. Fraccaroli, F. Martin, C. Guedj, E. Nolot, D. Rouchon, N. Vaxelaire, R. Templier, A. Grenier, A-M. Papon, H. Roussel, L. Rapenne, H. Renevier and S. Cadot, Synthesis of In-Plane Oriented Tin Sulfides by Organosulfur-Mediated Sulfurization of Ultrathin SnO2 Films, Chemistry of Materials, 2022, 34(13), pp. 5842–5851, https://doi.org/10.1021/acs.chemmater.2c00567
## 4.1 Introduction

X-ray analytical techniques are widespread in semiconductor fabs and labs where they permit non-destructive evaluation of thickness, composition, binding states, crystallinity, strain, ... Process experts and end-users often ask for specific X-ray characterization of thin materials. However, as for any analytical techniques, one must keep in mind that the metrology and the semiconductor worlds do not always speak the same language, and inline metrology scientists, engineers and technicians are here to translate process needs into metrology requirements and specifications. A basic example of possible misunderstanding is the metrology of the thickness of thin inorganic layers deposited on silicon wafers. We present hereafter two short cases to illustrate the need for common (metrological) language.

**Case 1:** thickness of thin silicon oxides and nitrides deposited on silicon wafers

We have measured the thickness of i/ thermally grown silicon oxides and ii/ silicon nitrides grown by low-pressure chemical vapor deposition (LPCVD). Both materials were deposited on silicon wafers Si(001) using high temperature process. We have used two measurement techniques available in fabs, spectroscopic ellipsometry (SE) and X-ray reflectometry (XRR). The comparison between the thicknesses measured by SE and XRR shows rather linear trends along with a significant offset, the value of this offset being different for oxides and nitrides<fnref n="15" /> (Fig. 4.1).

Indeed, XRR deduces the thickness from the electronic density profile normal to the sample surface, whereas SE uses thickness and optical properties as parameters to model the change in polarization as light reflects from the material stack.

XRR experiments conducted at synchrotron beamlines on *thermal silicon oxides*<fnref n="16" /> evidenced the existence of a dense (~2.4 g/cm³), thin (~ 1.0 nm, depending of the process) layer at the SiO₂/Si interface. As the electronic density of this interfacial layer is closer to silicon (2.33 g/cm³) than thermal oxide (~2.1 g/cm³), the main XRR features captures by inline XRR tools relate to oxide thickness, whereas the XRR dynamics is not enough to extract the thickness of the interface. Consequently, inline XRR tools measure the thickness of the deposited oxide diminished by the contribution of the interface. On the contrary, the optical properties of the interfacial layer is much closer to the thermal oxide than the silicon. The SE data can be reasonably modelled using the total oxide thickness, which includes the interface contribution. The offset observed in Fig. 4.1 is due to the interface, which is probed differently by XRR and SE techniques. Herzinger et al. went a step further in establishing the optical properties (spectral dependence of refractive index and extinction coefficient) of this interfacial layer, using multi-sample, multi-wavelength, multi-angle SE investigation<fnref n="17" />.

This case highlights the need for adequate definition of extensively used quantities such as thickness, in the semiconductor world where surface and interface contribution may become significant and even predominant. NMI-traceable standards and methods along with related uncertainty budget are crucial to meet industrial requirements for thickness metrology.

<footnote n="15">¹⁵ P. DeHaven, E. Nolot, A. Madan, A. Michallet, S. Favier, D. Le Cunff, R. Duru, *Evaluation of possible standards for X-ray reflectometry*, presentation @ EXRS'2012 in Vienna</footnote>

<footnote n="16">¹⁶ N. Awaji, Y. Sugita, T. Nakanishi, S. Ohkubo, K. Takasaki, and S. Komiya, *High-precision x-ray reflectivity study of ultrathin SiO₂ on Si*, Journal of Vacuum Science & Technology A 14, 971 (1996); https://doi.org/10.1116/1.580424</footnote>

<footnote n="17">¹⁷ C. M. Herzinger, B. Johns, W. A. McGahan, and J. A. Woollam, *Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation*, Journal of Applied Physics 83, 3323 (1998); https://doi.org/10.1063/1.367101</footnote>
<figure><img src="image_30.png" /><figcaption>**Figure 4.1.** Comparison between the thickness values determined with SE and XRR for thermally grown silicon oxides.</figcaption></figure>

**Case 2:** thickness of thin tungsten layers grown by physical vapor deposition on silicon wafers

The metrology scientists keep translating the process needs into metrology requirements, and must often explain why different measurement techniques may produce results that may look different. For instance, we have estimated the thickness of a thin tungsten layer grown on top of a TiN film by XRR and by X-ray fluorescence (XRF). The modeling of XRR data must include the contribution of a native tungsten oxide (Fig. 4.2). On the other hand, XRF measures the deposited mass of tungsten (whatever its oxidation state) from the intensity of W-Lα line, then calculates the thickness (t) of an equivalent homogeneous tungsten layer with density (d) fixed to 19.3 g/cm³. The apparent difference between the total thickness measured by XRR (3.8 nm) and the XRF value (2.5 nm) can be explained if we translate the XRR results into mass deposition referential, then correct by the assumed equivalent density (Eq. 1).

$$ \frac{(d * t)_{WO3} + (d * t)_{W}}{19.3} = 2.5 \text{ nm} \quad (1) $$

This second case study aims at demonstrating how crucial is the understanding of the needs of the end-users. If their target is the thickness of the tungsten layer prior to any aging-induced oxidation, XRF analysis is more appropriate, above all via the analysis of the deposited mass (in µg/cm²) without any assumption of the mass density. This option may lead to the establishment of NMI-traceable measurement of the tungsten mass deposition prior to the accurate inline metrology of tungsten films with mastered uncertainty budget. On the contrary, if the individual contributions of the oxide and the metal layers are important information, for instance to study the oxidation kinetics, XRR is a better option.
<figure><img src="image_31.png" /><figcaption>**Fig. 4.2:** (left) XRF spectra of a thin tungsten layer, acquired in high-resolution mode using inline wavelength-dispersive XRF setup, and (right) XRR spectra of the same sample acquired using inline tool operated with focusing optics and fixed linear detector. The best-model calculation is reported on the graph.</figcaption></figure>

The interaction with the end-users permits to clarify the needs:

1. Are repeatability, sensitivity and stability sufficient? Do we need accuracy?

2. What is the targeted accuracy? This point is often difficult, as it requires the proper evaluation of acceptable process variations that must be accurately captured by metrology. However, over-specified accuracy may lead to significant increase of the cost and time for the establishment of the metrology scheme.

3. Do we need standards with traceability to NMIs? Are such standards available? Do they come with uncertainty budget aligned with end-users/industry requirements?

4. Do we need to establish internal standards and to perform the metrology of these standards with reference techniques? What is the accuracy of such techniques? Are they strictly applicable to the case of thin inorganic materials?

5. How dependent is the accuracy of inline metrology on the modeling software (e.g. accuracy of the fundamental parameters in the database of XRF tools)?

6. Can inline metrology tools meet the required level of accuracy? What is the contribution of instrumental errors in the total uncertainty budget?

7. Is it necessary to build a consortium/program with RTO, industry and NMIs in order to fill the gap between needs and available standards and standardized protocols?
## 4.2 Compositional analysis with X-ray fluorescence

Photo-absorption is responsible for the emission of fluorescent X-rays<fnref n="18" />. A photon with an energy greater than the binding energy of an electron in an inner shell (e.g., the K-shell) is absorbed and its energy transferred to that electron. This is particularly of interest if the photon energy $E_{\text{Photon}}$ is higher than the ionization energy $E_{\text{ion}}$ of that electronic energy level; the energy $E_{\text{Photon}}$ is then entirely transferred to the electron, which is ejected from the atom ("photo-electron"); the electron's kinetic energy (that is measured in the frame of XPS analysis) equals the energy of the absorbed photon reduced by its binding energy, $E_{\text{Photon}}-E_{\text{ion}}$. The atom is left in an ionized state. With respect to XRF, the de-excitation process, which returns the atom to the ground state, can be radiative (emission of an X-ray photon, detected in XRF experiment) or non-radiative (emission of an electron via Auger or Coster Kronig effect).

In the following section, we mostly assess the accuracy of Rigaku AZX 400 wavelength-dispersive XRF (WDXRF) tool operated with polychromatic radiation from a Rhodium anode and operated under vacuum in order to access low-energy XRF lines, such as K-lines for light elements (from Be or B). One should note that, for such light elements, non-radiative Auger effect becomes predominant against XRF, whereas XRF cross sections are significantly larger for tender and hard X-rays.

Quantitative analysis of XRF mainly involves fundamental parameters modelling, which accounts for values of atomic constants<fnref n="19" /> along with the spectral distributions of radiation from X-ray tubes. The fundamental parameters software also include the instrumental contribution (e.g. solid angle of detection). The instrumental contribution could be exhaustively integrated in the frame of reference-free analysis using radiometrically calibrated instrumentation and mostly performed at PTB/Berlin (Section 4.3) or derived from the measurement of standards samples, which may be thin films or pure metal targets.

In this section, I will first comment on the benefit of versatile WDXRF tool in semiconductor environment. Then I will introduce our work to assess the accuracy of reference-based fundamental parameters analysis of thin materials using Rigaku AZX 400 WDXRF tool.

AZX 400 WDXRF instrument comes with ten different natural and synthetic (multi-layered) crystals and two detectors (proportional counter and scintillator) that allow to access XRF lines of elements from Z=4 (Be), with resolution in the 4 to 20 eV range. Rigaku had developed this tool to measure up-to 400 mm PVD targets, but they agreed to modify the handling so as to permit the measurement of wafers (with Foup and open cassette capability) and samples. The combination of high resolution (when compared to ED-XRF) and multi-crystal configuration is appropriate to access different XRF lines in order to optimize the sensitivity and/or to limit overlap concerns, which are prerequisite to quantitative analysis. Fig. 4.3 and 4.4 illustrate the use of WDXRF for inline qualitative analysis of perovskite PZT (PbZrTiO₃) films doped with niobium (Fig. 4.3) or lanthanum (Fig. 4.4). The added value of high-resolution XRF for the characterization of ultrathin MoS₂ 2D materials will be illustrated in Section 4.3.

<footnote n="18">¹⁸ See the beautiful section written by Michael Mantler in "Handbook of Practical X-Ray Fluorescence Analysis", Springer Berlin, Heidelberg 2006, https://doi.org/10.1007/978-3-540-36722-2</footnote>

<footnote n="19">¹⁹ Atomic energy levels, emission line energies, transition probabilities, probabilities of radiative de-excitation (fluorescent yields), Auger-probabilities, Coster-Kronig probabilities, interaction probabilities with photons (photo-absorption, coherent scattering, incoherent scattering) ...</footnote>
<figure><img src="image_32.png" /><figcaption>**Fig. 4.3** : The WDXRF analysis Nb-Lα and Nb-Lβ₁ lines with Ge (111) crystal unambiguously shows the presence of Nb-doped PZT on a product wafer. The X-ray tube conditions have been selected to enhance the intensity of Rh-L lines that are just above Pt M and Nb L edges, resulting in lower limit of detection appropriate to probe mm-area of the product wafer in spite of 20-mm spot size [E. Nolot et al, oral presentation at Colloque Rayons X et Matières, 2015].</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>**Fig. 4.4** : The lanthanum doping of thin PZT material is poorly resolved by EDXRF while WDXRF analysis of Ti-Kα and La-Lα lines with LiF (200) crystal allows accurate quantification of lanthanum doping [E. Nolot et al, oral presentation at Colloque Rayons X et Matières, 2015].</figcaption></figure>

In addition, the use of primary vacuum conditions permits to detect low-energy XRF lines, therefore to probe light elements such as boron, carbon, nitrogen, which are extensively included in semiconductor stacks. Fig. 4.5 illustrates the use of WDXRF equipped with synthetic multi-layer crystal to monitor the evolution of carbon content in thin titanium nitride films grown by metal-organic chemical vapor deposition (MOCVD) and treated with various plasma conditions. Specific difficulty related to the XRF quantification of light elements will be discussed in **Section 4.4**.
<figure><img src="image_34.png" /><figcaption>**Fig. 4.5** : Thin titanium nitride films have been deposited by MOCVD to serve as barrier against copper diffusion. Different plasma treatments have been evaluated, resulting in film densification, lower resistivity (removal of $TiC_x$ and $TiO_x$ phases). WDXRF was able to catch the evolution of carbon content in the film along with plasma treatments, with sensitivity comparable with nuclear reaction analysis (NRA) conducted on a particle accelerator [E. Nolot et al, oral presentation at EXRS conference, 2014]</figcaption></figure>

Rigaku reference-based fundamental parameters software uses measured XRF intensities to calculate the mass deposition (in µg/cm²) of each detected element, thereby the elemental composition of materials. From 2014 (acquisition of Rigaku AZX tool), we have extensively compared WDXRF to standard techniques and/or standardized protocols for composition analysis. In the case of **high-Z materials** measured in hard or tender X-ray range, we mostly used pure metal targets or crystal substrates with XRD-deduced composition (AsGa, InP, ...) to account for WDXRF instrumental function. In all cases, WDXRF composition fell in the uncertainty of Rutherford Back Scattering (RBS), i.e. in the 1 at% abs. range. In the case of thin GeSbTe phase change materials, WDXRF calibrated against pure germanium, antimony and tellurium targets led to RBS-like uncertainty for germanium content. RBS could not access accurate content of antimony and tellurium due to small mass differences between the two atoms. WDXRF was able to reveal some incorrect evaluation of Sb and Te contents by (subcontracted) Particle Induced X-ray Experiment (PIXE). We extended the evaluation to **medium-Z materials** (Si, Al, ...), still using pure metal targets to account for the instrumental function. The accuracy of WDXRF for ultrathin Al dose in $Al_2O_3$ ultrathin high-k materials was assessed against LPD-ICPMS and is discussed in **Section 5.3**. For silicon, we used WDXRF to evaluate the Si doping of GeSbTe material grown by magnetron sputtering. As WDXRF could not discriminate the silicon contribution from GeSbTe and Si substrate, we stuck small sapphire substrate on 300-mm silicon substrate prior to the deposition process. Then, we unambiguously measured silicon content in GeSbTe on sapphire. The comparison between RBS and WDXRF-deduced silicon content in GeSbTe films again fell in the RBS uncertainty (Fig. 4.6, [N-4.3]).

At the end, more than 90% of the compositional analysis initially oriented to subcontracted ion beam analysis on particle accelerators (RBS, PIXE) are now redirected to automated inline WDXRF measurement.
<figure><img src="image_35.png" /><figcaption>**Fig. 4.6** : Reference-based WDXRF analysis estimate of Si content in Si-doped GeSbTe is aligned with RBS (5.5 at%) with significantly better dynamics [N-4.3]</figcaption></figure>

It is sometimes impossible to use alternative substrate for deposition. For instance, we had to characterize the composition thin strained GeSnSi films<fnref n="20" /> [N-4.9, N-4.10]. In order to accommodate the significant lattice mismatch between Ge₁-xSnx and Si, 2.5 µm thick Ge StrainRelaxed Buffers (SRBs) were first grown in the epitaxy chamber, and thin GeSn films were then epitaxially grown on this virtual germanium substrate. High-resolution X-ray diffraction can access the composition of strained GeSn or GeSi films (Fig. 4.7). However, as the position of the GeSn:Si peak is determined by both Sn and Si contents, the composition of the ternary alloy cannot be deduced from XRD-only analysis. On the other hand, WDXRF only cannot access to GeSn (resp. GeSi) composition from the measurement of Ge and Sn (resp. Si) XRF lines as the Ge XRF intensity mostly comes from the Ge StrainRelaxed Buffers. Therefore, we used the following strategy based on the combination of XRD and WDXRF (Fig. 4.7):

* Sets of GeSn and GeSi binary layers were epitaxially grown on Ge SRBs. Thickness and Sn (resp. Si) content were determined by high-resolution XRD.

* The intensity of Sn-Lα (resp. Si-Kα) XRF line was recorded and plotted as a function of the Sn (resp. Si) deposited mass, which is the product of the thickness of GeSn (resp. GeSi) film times the Sn (resp. Si) weight content. This allowed to account for the limited impact of matrix effect (self-absorption, ...) on the XRF intensities in thin GeSn films

* Then, the mass deposition of Sn and Si in GeSnSi ternary materials was determined from WDXRF intensities (Fig. 4.8), and the composition was extracted by virtue of the additional information obtained from X-ray diffraction (peak position, thickness).

This approach has been extended to the evaluation of the composition of thin GeSn material doped with phosphorous or boron ([N-4.14, N-4.15, N-4.16]), also deposited on Ge SRBs (Fig. 4.9). Similar methodology was deployed to access the Ge content in thin SiGe films grown by condensation method on top of thin silicon of oxide substrate: XRF provided the mass deposition of Ge, which was completed by thickness information deduced from XRR, resulting in XRR-XRF determination of Ge content in thin SiGe films [N-4.1, N-4.2].

<footnote n="20">²⁰ GeSn alloys can be used to fabricate mid infra-red lasers, photo-diodes, Light Emitting Devices, Fin-type Field Effect Transistors, vertical gate-all-around FETs and so on</footnote>
<figure><img src="image_36.png" /><figcaption>**Fig. 4.7.** Ω-2θ XRD scans for (a) GeSn/Ge/Si heterostructures with different Sn concentrations and (b) GeSi/Ge/Si heterostructures with different Si concentrations. XRF calibration curves using binary compounds: (c) GeSn and (d) GeSi. Dashed lines are linear fitting curves [N-4.10].</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>**Fig. 4.8:** (a) Ω-2θ XRD scans of SiGeSn/Ge(2.5 µm)/Si heterostructures. (b) Red spheres are intensities for Sn-Lα in ternary SiGeSn alloys and (c) Red spheres are intensities for Si-Kα in ternary SiGeSn alloys [N-4.10].</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>**Fig. 4.9:** (top) Ω-2θ XRD scans for different GeSn:P layers (left) and GeSn:B layers (right). The intensity of Sn-Lα lines of intrinsic GeSn layers grown on Ge SRBs at various temperatures (bottom left) is then plotted as a function of the product of the GeSn (GeSn:B, GeSn:P) layer thickness times its Sn content (bottom right) [N-4.15].</figcaption></figure>
4.3 Quantifying thin sulfide materials with XPS and XRF

The investigation compositional metrology of sulfide materials was driven by the development of industry-compatible deposition processes of 2D transition metal dichalcogenide materials such as MoS₂ or WS₂ at CEA-Leti. More precisely, we assessed the accuracy of XRF for the determination of the mass deposition of molybdenum and sulfur to support the development of innovative two-step ALD MoS₂ deposition process, consisting in the layer-by-layer deposition of an amorphous surface Mo(IV) thiolate at 50 °C, followed by a subsequent annealing at higher temperature leading to ultra-thin MoS₂ nanocrystals (~20 nm-large) in the 1–2 monolayer range [N-4.6].

The challenges of the compositional metrology of ~ 1 nm thick (or less) MoS₂ films were :

- The optimization of analytical conditions to optimize signal to noise for ultrathin materials

- The management of overlapping XRF lines (Mo-Lα @ 2.293 keV, S-Kα @ 2.308 keV, Mo-Lβ₁ @ 2.395 keV)

- The lack of sulfur XRF standards

- The uncertainty in the fundamental parameters of sulfur.

We explained in [N-4.12] the XRF-based metrology path used to access the accurate measurement of MoS₂ reported in [N-4.6]. First, we optimized the analytical conditions and the calibration strategy at CEA-Leti. Then, we assessed the precision of the deduced MoS₂ composition against reference-free XRF conducted at PTB/Berlin using PTB beamline at Bessy II, in the frame of the collaboration with Philipp Hönicke. In parallel, we compared XRF-deduced composition with XPS, which was also extensively used to probe the binding states and the quality of the thin 2D materials. We include in the next section the highlights of this work.

The establishment of XRF methodology and the comparison with PTB/Berlin and XPS were conducted on a *preparation set*: we deposited ultrathin MoSₓ materials on 270 nm-thick silicon dioxide layer thermally grown on 200 mm silicon (001) wafers. The process conditions were varied so as to obtain samples with different S/Mo ratios. A set of three samples was grown by chemical vapor deposition at 145°C using Mo(CO)₆ and 1,2-ethanedithiol as precursors, then kept as deposited (*A* sample), annealed at 800°C under Argon (*B1* sample) or annealed at 800°C under sulfiding conditions (*B2* sample). A last sample (*C* sample) was deposited using the two-step ALD process described in [N-4.6]. We applied WDXRF to a *process set* consisting of three samples with MoS₂ deposited using the two-step ALD process described in [N-4.6] and 2, 3 and 8 ALD steps.

At CEA-Leti, in-line WDXRF experiments were carried out in the primary-vacuum chamber of Rigaku AZX400 tool. The samples were irradiated with the polychromatic radiation of a rhodium tube operated at 30 kV and 100 mA. We selected these conditions in order to enhance the intensity of rhodium L lines (Lα at 2.697 keV), which are just above S-K and Mo-L3 absorption edges (2.472 and 2.520 keV respectively), resulting in the optimal excitation of S-Kα and Mo-L X-ray fluorescence. We used a Ge (111) crystal mounted on a high-resolution goniometer to select the wavelengths related to S-Kα and Mo-L lines. Then, the X-ray fluorescence intensities were recorded with a gas flow type proportional counter. The energy resolution of the WDXRF instrumental setup with Ge (111) analyzer crystal permits to separate S-Kα, Mo-Lα and Mo-Lβ₁ contributions. We used a two-step procedure to quantify the elemental composition of MoSₓ materials using the X-ray fluorescence intensities collected with 20 mm spot size. First, we acquired qualitative data by moving the angular position of the analyzer crystal. The comparison of XRF spectra (Fig. 4.10) evidences the ability of the chosen WDXRF configuration to demonstrate unambiguous trends amid ultrathin MoSₓ films. In addition, the modeling of this qualitative spectra, using pseudo-Voigt oscillators and after background removal (Fig. 4.11), allowed to estimate XRF net intensities and to confirm the values of two quantities provided by Rigaku software: the intensity ratio between molybdenum Mo-Lα and Mo-Lβ₁, and the relative overlap of Mo-Lα (resp. S-Kα) on S-Kα (resp. Mo-Lα) spectra. These values are important as they support the quantitative analysis. Of course, such qualitative approach cannot be included in operator-compatible automated recipes, first because it requires 10 minutes acquisition time per sample for poor statistics, and above all
due to the fact that the extraction of the net intensities must be done manually, for each sample. Then, we performed a quantitative analysis, using the intensities collected at discrete angular positions related to the three XRF lines of interest and the background. The Mo-Lβ1 intensity was used for the quantification of molybdenum. The intensity of the Mo-Lα was deduced from the Lα / Lβ1 ratio, and the S-Kα net intensity was then calculated after correction of Mo-Lα overlap.

<figure><img src="image_39.png" /><figcaption>**Fig. 4.10** : Qualitative WDXRF scan of A, B1 and B2 samples using Ge (111) analyzer crystal and 10-min total acquisition time</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>**Fig. 4.11.** Qualitative WDXRF scan of B1 sample and related decomposition after background removal, using Pseudo-Voigt oscillators for both Mo-Lα and S-Kα fluorescence lines.</figcaption></figure>

We used fundamental parameters approach to quantify the deposited mass of molybdenum and sulfur, then the elemental composition of MoSₓ materials. Rigaku AZX 400 WDXRF tool does not feature fully calibrated instrumentation that would permit reference-free measurement. Nevertheless, quantification strategies based on fundamental parameters can be developed using spectrometer sensitivity values. In the case of Mo-L lines, we have determined the spectrometer sensitivity values by virtue of a 31 nm-thick molybdenum layer grown par Physical Vapor Deposition on Si (001) substrate and measured few minutes after deposition by X-Ray Reflectometry (XRR) on Bruker D8 Fabline tool operated at Cu-Kα energy. Due to very limited oxidation, a one-layer model was sufficient to describe the XRR data, calculate the thickness and the mass density of the molybdenum layer, and finally deduce the deposited mass of molybdenum (thickness*mass density) that was required to determine the spectrometer sensitivity values. For S-Kα line, as we could neither rely on a certified standard, nor grow sulfur-only layer, we decided to rely on the spectrometer sensitivity values available in the internal library of the Rigaku tool. We used a pyrite (FeS₂) crystal to assess the accuracy of sulfur measurement, resulting in ratio of atomic fraction aligned with expectation (S/Fe ~ 2.05).

PTB/Berlin carried out XRF experiment in grazing-incidence geometry (GIXRF) at the four-crystal monochromator (FCM) beamline at the synchrotron radiation facility BESSY II. The quantification was based on the reference-free approach that PTB had developed for a long time (over 15 years) and that lies on two main pillars : i/ the use of a radiometrically calibrated instrumentation of the PTB and ii/ a fundamental parameter-based reference-free quantification approach<fnref n="21" />. The preparation of the experiment included careful control of the geometrical parameters (beam and sample alignment, detector positioning), the monitoring of the incident photon flux using calibrated photodiodes, and the calibration of the detector response functions and detection efficiency of the silicon drift detector (SDD) for the measurement of the emitted fluorescence radiation.

The 15 eV difference between X-ray fluorescence energy of Mo-Lα and S-Kα is highly challenging for GIXRF analysis using a SDD detector due to its limited energy resolution. Therefore, we took advantage

<footnote n="21">²¹ B. Beckhoff, *Reference-free X-ray spectrometry based on metrology using synchrotron radiation*, J. Anal. At. Spectrom. 2008, 23, 845–853, https://doi.org/10.1039/B718355K</footnote>
of the tunable monochromatic excitation of the FCM beamline to run GIXRF measurements at two distinct energies: E₁ = 2510 eV for the selective excitation of S-Kα; then E₂ = 2575 eV, slightly above Mo-L3 edge, so as to excite both S-Kα and Mo-Lα lines.

PTB's in-house spectral deconvolution procedure was used to obtain the count rates of each line fluorescence lines, as illustrated in Figures 4.12 and 4.13, for B2 sample measured below and above Mo-L3 edge, respectively. This procedure fits a model spectrum to the measured spectrum, which consists of single fluorescence lines or multi fluorescence line sets (e.g. for the Mo-L3 lines, consisting of the Mo-L1, -Lα, -Lβ₆ and the -Lβ₂,₁₅ fluorescence lines), relevant pile up peaks (e.g. Si-Kα + O-Kα and background contributions, e.g. Bremsstrahlung produced by photo-electrons. In addition, the model spectrum is convoluted with the detector response function in order to take into account instrumental line broadening and artifacts in the spectrum like escape lines, shelf, and tailing. The knowledge of the relevant instrumental and fundamental parameters permits to calculate the mass deposition of Mo and S elements per unit area.

<figure><img src="image_41.png" /><figcaption>**Fig. 4.12:** Fluorescence spectrum (black line) of the B2 sample excited by a 2.510 keV X-ray beam (below Mo L3 edge) under a glancing angle of 2.0° at the FCM beamline. The deconvolution of the spectra was performed by fitting a model spectrum (green line) employing the detector response functions. The fluorescence lines, the Rayleigh peak and the Pile-up contributions are marked in different colors.</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Fig. 4.13:** Fluorescence spectrum (black line) of the B2 sample excited by a 2.575 keV X-ray beam (above Mo L3 edge) under a glancing angle of 2.0° at the FCM beamline. For the Mo-L3 shell fluorescence, we used a fixed lineset to stabilize the deconvolution consisting of the Mo-L1, -Lα, -Lβ₆ and the -Lβ₂,₁₅ fluorescence lines.</figcaption></figure>

PTB determined the different contributions of the uncertainty budget that are reported in Table 4.1: i/ the estimated uncertainties of the fundamental parameter data (X-ray fluorescence yield, Subshell photo-ionization cross section) used for the calculation of the fluorescence production cross section; ii/ the instrumentation-related contributions such as the incident photon flux I₀, the detector efficiency and the effective solid angle of detection; iii/ the counting statistics and the spectral deconvolution, which contributes significantly to the uncertainty budget of the molybdenum mass deposition due to the strong fluorescence line overlap. For sulfur, the atomic fundamental parameters were taken from X-raylib<fnref n="22" />, whereas for molybdenum, an experimentally determined fluorescence yield was used. All uncertainty contributions sum up to a total relative uncertainty of the reference-free quantification of 10% for S and 11% for Mo. Despite the larger uncertainty for the Mo-L3 deconvolution, the overall relative uncertainty budgets are almost the same. This is due to the fact, that larger estimated uncertainties for the tabulated fluorescence yield of sulfur are required.

<footnote n="22">²² T. Schoonjans, A. Brunetti, B. Golosio, M. Sanchez del Rio, V.A Solé, C. Ferrero, L. Vincze, *The xraylib library for X-ray-matter interactions*. *Recent developments*, Spectrochimica Acta Part B 66 (2011) 776–784, https://doi.org/10.1016/j.sab.2011.09.011</footnote>
<table><caption>**Table 4.1:** Total relative uncertainty budget of the mass deposition of molybdenum and sulfur depends on fundamental parameter contribution (X-ray fluorescence yield, subshell photo-ionization cross section), instrumentation contribution (intensity of the primary beam, detector efficiency, effective solid angle of detection), spectral deconvolution and counting statistics. The table relates to sample B2, but the uncertainty budget remains constant over the sample set.</caption><thead><tr><th>Uncertainty budget (relative)</th><th>Sulfur</th><th>Molybdenum</th></tr></thead><tbody><tr><td>Fundamental parameters contribution</td><td></td><td></td></tr><tr><td>- X-ray fluorescence yield</td><td>0.075</td><td>0.035</td></tr><tr><td>- Subshell photo-ionization cross section</td><td>0.05</td><td>0.05</td></tr><tr><td>Instrumentation contribution</td><td></td><td></td></tr><tr><td>- Detector efficiency</td><td>0.015</td><td>0.015</td></tr><tr><td>- Effective solid angle of detection</td><td>0.04</td><td>0.04</td></tr><tr><td>- Intensity of the primary beam</td><td>0.01</td><td>0.01</td></tr><tr><td>Spectral deconvolution</td><td>0.03</td><td>0.08</td></tr><tr><td>Counting statistics</td><td>0.01</td><td>0.02</td></tr><tr><td>Total</td><td>0.10</td><td>0.11</td></tr></tbody></table>

The mass deposition of sulfur and molybdenum deduced from reference-free GIXRF and inline WDXRF are reported in Table 4.2. The mass deposition of molybdenum appear almost constant within the sample set, which is aligned with the WDXRF qualitative data (Figure 6). The difference between the values determine by reference-free GIXRF and WDXRF looks like a small offset, leading to ~5% relative difference, which is below the estimated uncertainty budget for GIXRF experiment. In the case of sulfur, the differences between GIXRF and inline WDXRF quantification depend on the sample, remaining below the estimated uncertainty budget for the GIXRF experiments for both A and B2 sample, while reaching ~27% relative difference in the case of B1 sample. Although we do not have a definite explanation for this deviation, it might be due to ageing of the B1 sample during the 6 months characterization scheme, or to the different probing areas of WDXRF and GIXRF analysis that reveal S/Mo non-uniformity within the sample.

Complementary work could be run to refine this hypothesis: on the one hand by comparing WDXRF and GIXRF on fresh, stable and uniform crystallized MoS₂ (now available at CEA-Leti on 200 and 300 mm wafers) and, on the other hand by improving the uncertainty of the fluorescence yield of sulfur, which might be a mid-term perspective for PTB or other NMIs in the frame of Fundamental Parameters Initiative.

<table><caption>**Table 4.2:** Comparison between the deposited mass of Sulfur and Molybdenum per unit area determined by inline WDXRF and GIXRF.</caption><thead><tr><th rowspan="2">Sample</th><th colspan="2">WDXRF</th><th colspan="2">GIXRF</th></tr><tr><th>Mo</th><th>S</th><th>Mo</th><th>S</th></tr><tr><td colspan="5" style="text-align: center;">Deposited mass (ng/cm²)</td></tr></thead><tbody><tr><td>A</td><td>454.5</td><td>370.4</td><td>476.3</td><td>362.7</td></tr><tr><td>B1</td><td>451.7</td><td>193.8</td><td>475.7</td><td>267.7</td></tr><tr><td>B2</td><td>456.4</td><td>318.7</td><td>476.8</td><td>336.1</td></tr></tbody></table>

Finally, we compared WDXRF analysis with in-line XPS experiments conducted at CEA-Leti on inline Thermo Scientific Theta 300 tool operated at monochromatized Al-Kα. Although the tool is designed for parallel-angle-resolved XPS experiment, we integrated the photoelectron intensity collected over the wide range of collection angle, from close to normal incidence (22°) to grazing incidence (78°) in order to maximize sensitivity. We used 400 µm spot size and a pass energy of 40 eV that led to a 0.45 eV resolution as measured on Au $4f_{7/2}$.
In the modeling process with Thermo Avantage software, Mo 3d shows that the ratio of the heights of Mo 3d$_{5/2}$ and 3d$_{5/2}$ is different from expected value (0.67). We suggested that this deviation might be caused by a difference in widths for the two spin-orbit components (Coster-Kronig broadening). Therefore, in the fitting of Mo 3d spectra, height and Coster-Kronig broadening were set as parameters for Mo-S states, while keeping area ratios fixed to 0.67, whereas no broadening was included in Mo-O states.

<figure><img src="image_43.png" /><figcaption>**Fig. 4.14:** High-resolution Mo 3d and S 2p XPS core-level spectra of crystallized C sample. The difference in binding energy $\Delta E$ between Mo3d$_{5/2}$ and S2p$_{3/2}$ of Mo-S states can be related to the MoS stoichiometry as suggested by Baker et al.</figcaption></figure>

We used different approaches to evaluate the composition of MoS$_x$ layers. First, we quantified the composition using sensitivity factors from Scofield library$^{23}$ for S 2p and Mo 3d components. We could either include the contribution of MoO$_3$ components to obtain an XRF-like elemental analysis, or decide to focus on Mo-S and S-Mo components in order to provide S/Mo ratio required by process development. Secondly, we used the linear relationship between MoS stoichiometry and the difference in binding energy $\Delta E$ between Mo 3d$_{5/2}$ and S 2p$_{3/2}$ (Fig. 4.14) determined by Baker et al$^{24}$. We applied the first approach to all samples, whereas we focused on crystalline C sample to evaluate the second approach. The Table 4.3 compares WDXRF and XPS composition for C sample. We have completed WDXRF and XPS measurements less than 24 hours after the material deposition in order to limit ageing-related concerns. For XPS, the S/Mo ratio deduced from the relative sensitivity factors (RSF) using Mo-S states is well aligned with the value extracted from the difference in binding energy $\Delta E$ between Mo 3d$_{5/2}$ and S 2p$_{3/2}$. Then, the XPS quantification using relative sensitivity factors for both Mo-S and MoO$_3$ states gives S/Mo irrespective to the binding states, as for WDXRF. In the end, inline monitoring of the mass deposition and the composition of ultrathin Sulfur-based transition metal dichalcogenides can be performed with operator-compatible automated WDXRF recipes along with model-based (all samples) or model-less (crystalline samples, using $\Delta E$) XPS strategies.

<table><caption>**Table 4.3:** Ratio of atomic contents of sulfur and molybdenum deduced from WDXRF and XPS. For XPS, the S/Mo ratio deduced from the relative sensitivity factors using Mo-S states is well-aligned with the value extracted from the difference between Mo 3d$_{5/2}$ and S 2p$_{3/2}$ binding energies. On the other hand, XPS quantification using both Mo-S and MoO$_3$ states gives similar S/Mo ratio as WDXRF</caption><thead><tr><td>Method</td><td>S/Mo ratio</td></tr></thead><tbody><tr><td>XPS - RSF (Mo-S)</td><td>2.0</td></tr><tr><td>XPS - (Mo3d<sub>5/2</sub> - S2p<sub>3/2</sub>)</td><td>2.0</td></tr><tr><td>XPS - RSF (Mo-S + MoO<sub>3</sub>)</td><td>1.8</td></tr><tr><td>WDXRF</td><td>1.8</td></tr></tbody></table>

<footnote>$^{23}$ J. H. Scofield, *Hartree-Slater subshell photoionization cross-sections at 1254 and 1487 eV*, J. Electron Spectrosc. Relat. Phenom., vol. 8, no. 2, pp. 129-137, 1976, https://doi.org/10.1016/0368-2048(76)80015-1</footnote>

<footnote>$^{24}$ M. A. Baker, R. Gilmore, C. Lenardi, W. Gissler, *XPS investigation of preferential sputtering of S from MoS$_2$ and determination of MoS$_x$ stoichiometry from Mo and S peak positions*, Appl. Surf. Sci. 150 (1999) 255, https://doi.org/10.1016/S0169-4332(99)00253-6</footnote>
WDXRF-based compositional analysis was used to support the development of ALD $MoS_2$ deposition process. It permitted to refine the understanding of the deposition process while suggesting an ultrathin Mo-rich buffer layer at the interface between $MoS_2$ and $SiO_2$ substrate (Fig. 4.15).

<figure><img src="image_44.png" /><figcaption>**Fig. 4.15** : High resolution WDXRF spectra of the $MoS_2$ deposits obtained after 2, 3 and 8 ALD cycles followed by thermal annealing at 450 °C under hydrogen; (B) the experimental S/Mo ratio as a function of the number n of ALD cycles (triangles) and model curve S/Mo = (4n - 1)/2n based on the hypothesis of a Mo-rich interfacial buffer layer [N-4.6]</figcaption></figure>

This methodology was extended to support the development of other sulfides materials such as $WS_2$ [N-4.8] and $SnS_2$ [N-4.18], and even to complement XPS to evidence the influence of sulfur based chemical treatments on InGaN materials [N-4-11].
4.4 Quantifying light elements in thin inorganic materials with XRF

In this section, I introduce the challenges we faced to establish XRF-based compositional metrology of nitrogen-doped GeSbTe (GST-N) phase change material. This work was partly included in industrial collaboration, resulting in tight industry-driven specification in terms of accuracy. We had to build reference samples, identify the best reference technique that provides accurate values of nitrogen content in GST-N required for XRF calibration, assess the accuracy of XRF-based compositional metrology, and finally transfer a set of standard and the metrological methodology to the industrial partner. This section is essentially based on the work reported in [N-4.13, cover of JAAS] and in Walter Pessoa's PhD manuscript.

<figure><img src="image_45.png" /></figure>

GST-N materials are already included in phase change memory device produced in fabs. The nitrogen content in the film drives some important properties of the GST-N (crystallization temperature, ...) and must be accurately and non-destructively monitored (within $\le \pm 1\%$ abs) after deposition. WDXRF is a key technique for the analysis of nitrogen content along with overall composition of 100 nm-thick amorphous GST-N films. Alternative solutions come with limitations: i/ XPS would only probe the top surface and would require short Q-time between deposition and analysis in order to limit the impact of oxidation on Ge 3d, Sb 4d and Te 4d region (Section 6.1) ; ii/ FTIR could probe the nitrogen content from the intensity of Ge-N bonds, which are predominant in Ge-rich and Te-rich GST-N films, whereas Sb-N bonds are also present in Sb-rich GST-N (Section 6.1). FTIR is then an alternative solution to access nitrogen content (only) in GST-N with known and stable GeSbTe stoichiometry. At the end, WDXRF is capable to access XRF lines of Ge, Sb, Te and N and should then be able to provide accurate composition of GST-N materials.

However, XRF is complex for low-Z elements, not only because it is low probability (with low net intensities) compared to non-radiative transitions, but also because of the complex XRF background in the soft X-ray region and the greatly enhanced and relatively uncharacterized higher order fluorescence effects, which means that both detection and quantification are both challenging.

Fig. 4.16 illustrates the instrumental difficulty. In the tender and hard X-rays, Ge-Lα, Sb-Lβ₁ and Te-Lα lines feature easy-to-deal background and XRF net intensities compatible with an expanded precision (that is, the uncertainty due largely to counting statistics) of ~ 1%. In addition, the fundamental parameters (FP) related to these XRF lines show only small discrepancy among databases, and the WDXRF instrumental function can be calibrated against Ge, Sb and Te pure targets. On the contrary, it is difficult to extract the N signal out of a WD-XRF spectrum from a GST-N sample: it has a strongly nonlinear background due both to the instrument setup and the analyzer crystal and, also, to the overlap of the Sb and Te Mζ lines. Not only are FP data absent for these lines, they will generate secondary excitation of N-Kα with poorly defined cross sections. More generally, FP in the soft energy region show significant differences among databases (Fig. 4.17), which contribute to the uncertainty budget.
<figure><img src="image_46.png" /><figcaption>**Fig. 4.16: (left)** The WDXRF spectra of Te-rich GST-N film (left) shows the main XRF lines used for quantification. Te-Lα and Sb-Lβ₁ are mostly excited by Rh-K lines and Bremsstrahlung, whereas Ge-Lα and N-Kα lines are mainly excited by Rh-L lines. (**right**) The two different (Rikagu proprietary) synthetic multilayer analysis crystals induce significantly different backgrounds and count ratios in the soft X-ray region [N-4.13].</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>**Fig. 4.17:** Comparison of XRF cross sections in the soft X-ray. The data come from three different databases including Henke<fnref n="25" />, Cullen<fnref n="26" />, and Elam<fnref n="27" /> (practically the same as xraylib<fnref n="28" /> in this case) [N-4.13].</figcaption></figure>

<footnote n="25">²⁵ B. L. Henke, E. M. Gullikson and J. C. Davis, *X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92*, At. Data Nucl. Data Tables, 1993, **54**, 181—342; http://xdb.lbl.gov/</footnote>

<footnote n="26">²⁶ D. E.Cullen, J. H.Hubbell, L.Kissel, University of California Lawrence Livermore National Laboratory, https://www-nds.iaea.org/epd197/</footnote>

<footnote n="27">²⁷ W. T. Elam, B. D. Ravel and J. R. Sieber, *Radiat. Phys. Chem.*, 2002, **63**, 121—128, https://www.nist.gov/mml/csd/inorganic-measurement-science/resources/xrf-downloads</footnote>

<footnote n="28">²⁸ T. Schoonjans, A. Brunetti, B. Golosio, M. Sanchez del Rio, V. A. Solé, C. Ferrero and L. Vincze, *The xraylib library for X-ray-matter interactions. Recent developments*, Spectrochim. Acta, Part B, 2011, **66**, 776—784, http://lvserver.ugent.be/xraylib/(version9/2017)</footnote>
How can we WDXRF quantify the nitrogen content in such samples? Of course, no pure material standards are available to determine instrumental sensitivity factors for N. Moreover, it is not possible to transfer instrumental functions obtained from well-characterized N-containing samples (silicon nitride for example) to GST-N samples. Conversely, WDXRF calibration should rely on a set of GST-N calibration samples, which composition should be accurately determined by reference methods with mastered uncertainties.

GST (including GST225, that is the Ge₂Sb₂Te₅, which is the reference material for many studies) and GST-N films (including GST225-N, that is, nitrogen-doped GST225) were deposited on 300 mm or 200 mm silicon (001) wafers using magnetron sputtering (Applied Materials Endura300 and Evatec CLN200 multi-target PVD chambers). A *calibration sample set* was deposited on 200 mm wafers on the Evatec tool. These were 100 nm thick GeTeN and Ge-rich GST and GST225-N films with various N contents. The films were capped *in situ* with a 5 nm Ta layer to prevent ageing. An exact duplicate of this sample set was grown in the same run in order to routinely calibrate and monitor WD-XRF GST-N samples. The wafers from the *calibration sample set* were cut and 2 cm² samples from (strictly) the same area of each wafer were sent to three organizations that claimed to meet better than 1% accuracy in the measurement of N content in GST-N:

- All organizations determined the mass deposition of Ge and Sb+Te with RBS (Rutherford Back Scattering), which is an analytical method with full metrological traceability capable of very high absolute accuracy

- Organization A (subcontractor) uses two other Ion Beam Analysis methods (IBA) : Particle-Induced X-ray Emission (PIXE) to discriminate Sb and Te, and Nuclear Reaction Analysis (NRA) to determine the nitrogen content

- Organization B (subcontractor) uses WDXRF to discriminate Sb and Te, and NRA to determine the nitrogen content

- Organization C uses Elastic Back Scattering (EBS) to evaluate the nitrogen content.

Fig. 4.18 shows the (unexpected) significant discrepancy in nitrogen contents determined by the three organizations on exactly similar samples, with up to 50 % rel. difference that is of course inadequate to meet industry-driven specification of GST-N metrology. We failed to obtain details on the calibration procedures and explanation of possible sources of uncertainties from Organizations A and B. Conversely, Pr. Chris Jeynes from the Ion Beam Center at the University of Surrey (Organization C) had already got the accreditation of RBS to ISO 17025, and was willing to collaborate in order to establish an IBA protocol with mastered uncertainties and detailed uncertainty budget. Then, we first engaged a collaboration with Pr. Chris Jeynes around IBA, and we secondly included Pr. Michael Mantler in the loop, since he had a long experience in the analysis of low-Z element with XRF.

<figure><img src="image_48.png" /><figcaption>**Fig. 4.18** : IBA of N content of 6 GST-N and 2 GT-N samples. Three IBA laboratories (A, B and C) determine N content. All samples are 100 nm thick duplicates on silicon [N-4.13].</figcaption></figure>
Pr. Mantler confirmed the issues related to XRF-based quantification of GST-N. In addition to the uncertainty related to the secondary fluorescence due to unknown (Mζ) lines, he highlighted the fluorescence by both primary and secondary (photo- and Auger-) electrons, which are both numerous and of relatively high energy as we irradiate the samples with polychromatic Rh source. He also confirmed that FP codes were reasonably reliable for both the fluorescence from the primary beam, and also the secondary self-fluorescence (generated from the primary K & L target fluorescence), whereas they ignore fluorescence by both primary and secondary (photo- and Auger-) electrons, which could be significant in our case.

Then, we decided to calibrate WDXRF against reference samples certified by RBS/EBS with optimized uncertainty, and to limit the use of WDXRF-deduced quantification to ~100 nm-thick GST-N films in order to contain the variability of non-mastered contributions of photo- and Auger high energy electrons. EBS analysis was performed at 3.7 MeV in order to benefit from high cross section due to resonance effect. The EBS analysis was calibrated by RBS using a transfer standard, which was a self-supporting silicon nitride window nominally 200 nm thick. Fig. 4.19 illustrates the sensitivity of EBS at 3.7 MeV (and in contrast the lack of sensitivity of RBS) to nitrogen content in GST-N films.

<figure><img src="image_49.png" /><figcaption>**Fig. 4.19:** 3.7 MeV EBS and 1.5 MeV RBS data from a N-rich GST-N sample with total deposited mass of 55.4 µg/cm². Spectra at two scattering angles are shown: the EBS cross-section for N is much larger for Det1. There is no RBS sensitivity for N. There is very little mass resolution between Sb & Te. There is ~1 at% Ar present in the films, which is consistent with PVD process [N-4.13]</figcaption></figure>

Finally, we assessed the accuracy of IBA-based WDXRF calibration with an evaluation set consisting in 300 mm wafers deposited on the Applied Materials tool. These were 100 nm uncapped GST225-N films with significant variation in the N content. The WD-XRF analysis of this film was performed just after deposition and the IBA analysis about 1 month after. Fig. 4.20 demonstrates that calibrated WDXRF was accurate enough to evidence that the addition of nitrogen in GST225 did not modify the relative content of Ge, Sb and Te. Fig. 4.21 highlights the validity of WDXRF against IBA, as demonstrated on the evaluation set.

Further work could include the careful estimate of the contributions secondary fluorescence and photo- and Auger electrons, either in the frame of NMI "Fundamental parameter initiative" and/or by IBA/WDXRF study of N-doped GST (for instance) with varying thickness.
<figure><img src="image_50.png" /></figure>

**Fig. 4.20:** The GST stoichiometry is not disturbed by the addition of nitrogen. This sort of conclusion is important to understanding the process, and cannot be obtained without a correct calibration of the XRF.

Ge₂Sb₂Te₅ matrix unmodified by N content. "Normalized" {Ge, Sb, Te} is ratio X/(Ge + Sb + Te), that is, ignoring N content [N-4.13].

<figure><img src="image_51.png" /></figure>

**Fig. 4.21:** WDXRF calibration validity demonstrated against IBA. XRF calibrated with Ta-capped samples used to determine N content of 6 uncapped 100 nm thick GST-N samples also measured by IBA. A fit with unity slope is shown. Error bars for IBA show the 0.4 at% precision and the 4% EBS cross-section uncertainty combined in quadrature. Error bars for WD-XRF are shown conservatively as 1% relative but the reproducibility for similar thicknesses and compositions is about 0.5% [N-4.13].
# 5 Elemental Depth-profiling

## Abstract – supervision – collaboration – key papers

The general objective of this research direction was to develop and assess characterization methodologies for the elemental depth-profiling of inorganic layered materials with thickness ranging from the nm-range to ~1 µm. Our first intention was to focus on non-destructive techniques, i.e. X-ray photoemission to address ultrathin materials and the combination of grazing-incidence X-ray fluorescence (GIXRF) and X-ray reflectometry (XRR) to deal with thickness up to 200 nm. Meanwhile, we built a 5-year collaboration with Horiba Jobin to work on their destructive efficient Plasma profiling time-of-flight mass spectrometry tool (PP-TOFMS) that was particularly appropriate for close-to-the-line fast and reliable elemental profiling.

The specific objectives were:

- The introduction of combined GIXRF-XRR analysis at CEA-Leti. As we had access neither to dedicated tool nor to data analysis software, we built collaborations with different institutes: PTB/Berlin in the frame of European metrology programs TReND, ThinErgy and HyMet, Vienna University and FBK/Trento in the frame of B. Caby's PhD, CEA/LNHB in the frame of European metrology programs TReND, ThinErgy and HyMet and of Walter Pessoa's PhD. **Section 5.2** will include details about these collaborations, experimental and modeling work, and applications to depth-profiling of challenging material systems.

- The assessment of non-destructive depth-profiling using XPS, using two complementary paths: i/ parallel-angle XPS in the frame of Blanka Detlefs post doc and Walter Pessoa PhD, ii/ inelastic background analysis during Rose Taylor Bure's PhD. The work about inelastic background analysis benefited from the collaboration with Nicolas Pauly, at the Université Libre of Bruxelles. We present the related scientific highlights in **Section 5.3**.

- The introduction of PP-TOFMS technique at CEA-Leti in the frame of a 5-year collaboration with Horiba Jobin, largely supported by the CDD of Yann Mazel. We worked on the optimization of the process conditions (plasma conditions, evaluation of gas mixtures) and we assessed the performances of the tool, first on model systems by rigorous comparison with TOF-SIMS, then for a large diversity of layered materials. We present the related scientific highlights in **Section 5.4**

**Post docs** : Blanka Detlefs (2013-2015, European program EMRP – TReND *Traceable characterization of nanostructured devices*) ; Hélène Rotella (2015-2016, European program EMRP – ThinErgy *Traceable characterization of thin-film materials for energy applications*) ; Simona Torrengo (2017-2020, European program EMPIR – HyMet *Hybrid Metrology for thin films in energy applications*)

**PhD** : Bérenger Caby (2012-2015) ; Walter Pessoa (2015-2017), Rose Taylor Bure (2019-2023)

**CDD** : Yann Mazel (2016-2018)

**Master training** : Bérenger Caby (2012) ; Gaël Picot (2015) ; Loto Oluwasayo (2015), Amanda Gomes De Carvalho (2017), Rose Taylor Bure (2019)

**Collaboration** with Burkhard Beckoff, Philipp Hönicke (PTB/Berlin) - European metrology programs TReND, ThinErgy and HyMet -transfer of expertise related to reference-free combined GIXRF/XRR with master uncertainties, cross comparison of data analysis, access to PTB Beamline @ Bessy II

Collaboration with Marie-Christine Lépy (CEA/LNHB) - European metrology programs TReND, ThinErgy and HyMet & Walter Pessoa's PhD - access to Métrologie beamline @ Soleil. Interaction about reference-based GIXRF/XRR analysis

Collaboration with Christina Streli and Dieter Ingerle (Vienna University of Technology) and Giancarlo Pepponi (Fondazione Bruno Kessler, Trento) about instrumentation and data analysis
software for reference-based GIXRF/XRR analysis ; access to Lab tool @ Vienna University - in the
frame of Béranger Caby’s PhD.

Collaboration with Daniel Chateigner and Magali Morales from Laboratoire de Cristallographie et Sciences des Matériaux in Caen (CRISMAT) about the use of MAUD software for GIXRF-XRR analysis and perspectives to combine GIXRF-XRR with XRD - in the frame of Béranger Caby’s PhD

Collaboration with Nicolas Pauly (Université Libre of Bruxelles) about inelastic background analysis
with XPS – in the frame of Rose Taylor Burton’s PhD

Collaboration with Horiba Jobin Yvon on PP-TOFMS analytical tool. Horiba decided to install the tool in the cleanroom of CEA-Leti (long-term free loan) and strongly interact with us about hardware, software and methodology improvement and tests. We commonly organized a webmarin dedicated to PP-TOFMS.

**Key publications (metrology-oriented)**

[N-5.1] A. Danel, E. Nolot, S. Lhostis, Y. Campidelli, M.-L. Calvo-Muñoz, T. Decorps, T. Lardin, M. Veillerot, H. Kohno, and M. Yamagami, *Thin Films Characterization by Ultra Trace Metrology*, AIP Conference Proceedings 931, 178 (2007); https://doi.org/10.1063/1.2799366

[N-5.2] Danel, A., Nolot, E., Veillerot, M., Olivier, S., Decorps, T., Calvo-Muñoz, M.-L., Hartmann, J.-M., Lhostis, S., Kohno, H., Yamagami, M., Geoffroy, C., *Thin film characterization by total reflection x-ray fluorescence* ; (2008) Spectrochimica Acta - Part B Atomic Spectroscopy, 63 (12), pp. 1365-1369. ; https://doi.org/10.1016/j.sab.2008.10.024

[N-5.3] Caby, B., Brigidi, F., Ingerle, D., Nolot, E., Pepponi, G., Streli, C., Lutterotti, L., André, A., Rodriguez, G., Gergaud, P., Morales, M., Chateigner, D. ; *Study of annealing-induced interdiffusion in In₂O₃/Ag/ In₂O₃ structures by a combined X-ray reflectivity and grazing incidence X-ray fluorescence analysis* ; (2015) Spectrochimica Acta - Part B Atomic Spectroscopy, 113, art. no. 4968, pp. 132-137; https://doi.org/10.1016/j.sab.2015.09.008

[N-5.4] Hönicke, P., Detlefs, B., Müller, M., Darlatt, E., Nolot, E., Grampeix, H., Beckhoff, B.; Reference-free, depth-dependent characterization of nanolayers and gradient systems with advanced grazing incidence X-ray fluorescence analysis; (2015) Physica Status Solidi (A) Applications and Materials Science, 212 (3), pp. 523-528. ; https://doi.org/10.1002/pssa.201400204

[N-5.5] Ménesguen Y, Boyer B, Rotella H, Lubeck J, Weser J, Beckhoff B, Grötzsch D, Kanngießer B, Novikova A, Nolot E and Lépy MC, *CASTOR, a new instrument for combined XRR-GIXRF analysis at SOLEIL*, X-Ray Spectrom. 2017, 46, 303–308, https://doi.org/10.1002/xrs.2742L

[N-5.6] Rotella H, Caby B., Ménesguen Y., Mazel Y, Valla A., Ingerle D., Detlefs B. , Lepy MC, Novikova A., Rodriguez G., Streli C, Nolot E., *Elemental depth profiling in transparent conducting oxide thin film by X-ray reflectivity and grazing incidence X-ray fluorescence combined analysis*, Spectrochimica Acta Part B: Atomic Spectroscopy, Volume 135, 1 September 2017, Pages 22-28, http://doi.org/10.1016/j.sab.2017.06.011

[N-5.7] Pessoa, W.; Roule, A.; Nolot, E.; et al., *Grazing incident X-ray fluorescence combined with X-ray reflectometry metrology protocol of telluride-based films using in-lab and synchrotron instruments*, Spectrochimica Acta Part B: Atomic Spectroscopy, Volume: 149 Pages: 143-149, Nov 2018, https://doi.org/10.1016/j.sab.2018.07.003

[N-5.8] Nolot, E.; Caby, B.; Gassilloud, R.; et al., *X-ray reflectometry and grazing-incidence X-ray fluorescence characterization of innovative electrodes for tantalum-based resistive random access memories*, Spectrochimica Acta Part B: Atomic Spectroscopy, Volume: 149 Pages: 71-75, Nov 2018, https://doi.org/10.1016/j.sab.2018.07.017

[N-5.9] Hönicke P., Detlefs B., Nolot E., Kayser Y., Mühle U., Pollakowski B., and Beckhoff B.; Reference-free grazing incidence x-ray fluorescence and reflectometry as a methodology for independent validation of x-ray reflectometry on ultrathin layer stacks and a depth-dependent characterization, Journal of Vacuum Science & Technology A 37, 041502 (2019); https://doi.org/10.1116/1.5094891

[N-5.10] E. Nolot, W. Pessoa, S. Torrengo, Y. Mazel, M. Bernard, P. Gergaud, Y. Ménesguen, M.C. Lépy, D. Eichert, Grazing-incidence X-ray fluorescence analysis of thin chalcogenide materials
deposited on Bragg mirrors, Spectrochimica Acta Part B: Atomic Spectroscopy, Volume 168, 2020, 105864, https://doi.org/10.1016/j.sab.2020.105864

[N-5.11] S. Torrengo, D. Eichert, Y. Mazel, M. Bernard, Y. Ménesguen, M.C. Lépy, E. Nolot, *Quantitative depth-profile analysis of transition metal nitride materials with combined grazing-incidence X-ray fluorescence and X-ray reflectometry analysis*, Spectrochimica Acta Part B: Atomic Spectroscopy, Volume 171, 2020, 105926, https://doi.org/10.1016/j.sab.2020.105926

[N-5.12] B. P. Reed, D. J. H. Cant, S. J. Spencer, A. J. Carmona-Carmona, A. Bushell, A. Herrera-Gómez, A. Kurokawa, A. Thissen, A. G. Thomas, A. J. Britton, A. Bernasik, A. Fuchs, A. P. Baddorf, B. Bock, B. Theilacker, B. Cheng, D. G. Castner, D. J. Morgan, D. Valley, E. A. Willneff, E. F. Smith, E. Nolot, F. Xie, G. Zorn, G. C. Smith, H. Yasufuku, J. L. Fenton, J. Chen, J. D. P. Counsell, J. Radnik, K. J. Gaskell, K. Artyushkova, L. Yang, L. Zhang, M. Eguchi, M. Walker, M. Hajdýla, M. M. Marzec, M. R. Linford, N. Kubota, O. Cortazar-Martínez, P. Dietrich, R. Satoh, S. L. M. Schroeder, T. G. Avval, T. Nagatomi, V. Fernandez, W. Lake, Y. Azuma, Y. Yoshikawa, and A. G. Shard., *Versailles Project on Advanced Materials and Standards interlaboratory study on intensity calibration for x-ray photoelectron spectroscopy instruments using low-density polyethylene*, Journal of Vacuum Science and Technology A: Vacuum, Surfaces and Films, 2020, 38(6), 577, https://doi.org/10.1116/6.0000577

[N-5.13] Borrel, J., Hutin, L., Grampeix, H., Nolot, E., Ghegin, E., Rodriguez, P., Tabone, C., Allain, F., Barnes, J.-P., Morand, Y., Nemouchi, F., Gregoire, M., Dubois, E., Vinet, M. ; *Considerations on fermi-depinning, dipoles and oxide tunneling for oxygen-based dielectric insertions in advanced CMOS contacts*, 2016 IEEE Silicon Nanoelectronics Workshop, SNW 2016, art. no. 7578022, pp. 140-141. ; https://doi.org/10.1109/SNW.2016.7578022

[N-5.14] E. Martinez, E. Nolot, J-P Barnes, Y. Mazel, and N. Bernier, *Germanium out diffusion in SiGe-based HfO₂ gate stacks*, Journal of Vacuum Science & Technology B 36, 042902 (2018); https://doi.org/10.1116/1.5027072

[N-5.15] O. Renault, P.-M. Deleuze, J. Courtin, T. R. Bure, N. Gauthier, E. Nolot, C. Robert-Goumet, N. Pauly, E. Martinez and K. Artyushkova, *New directions in the analysis of buried interfaces for device technology by hard X-ray photoemission*, Faraday Discussions, 2022, 236, pp. 288–310, https://doi.org/10.1039/d1fd00110h

[N-5.16] T.R. Bure, O. Renault, E. Nolot, T. Lardin, C. Robert-Goumet, N. Pauly, *Assessing advanced methods in XPS and HAXPES for determining the thicknesses of high-k oxide materials: From ultra-thin layers to deeply buried interfaces*, Applied Surface Science, 2023, 609, 155317, https://doi.org/10.1016/j.apsusc.2022.155317

[N-5.17] Tempez, A., Legendre, S., Barnes, J.-P., Nolot, E.; *Combining plasma profiling TOFMS with TOF-SIMS depth profiling for microelectronic applications*: (2016) Journal of Vacuum Science and Technology B: Nanotechnology and Microelectronics, 34 (3), 03H120; https://doi.org/10.1116/1.4943513

[N-5.18] Mazel, Y., Barnes, J.P., Nolot, E., Tempez, A. and Legendre, S., *Rapid, semi-quantitative depth profiling of ultra-thin films using plasma profiling time-of-flight mass spectrometry*, In 2017 28th Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC) (pp. 285-288). IEEE, https://doi.org/10.1109/ASMC.2017.7969245

[N-5.19] Mazel, A., Nolot, E., Barnes, J.P., Charles, M., Bouveyron, R., Mrad, M., Tempez, A. and Legendre, S., *Multi-technique elemental depth profiling of InAlGaN and InAlN films*, J. Vac. Sci. Technol. B 36(3), May/Jun 2018, https://doi.org/10.1116/1.5019635

[N-5.20] Mrad M., Charles M., Mazel Y., Nolot E. et al., *Understanding and controlling Ga contamination in InAlN barrier layers*, Journal of Crystal Growth Volume: 507 Pages: 139-142 (Feb 2019), https://doi.org/10.1016/j.jcrysgro.2018.10.039

[N-5.21] Nolot, E., Mazel, Y., Barnes, J.-P., Sabbione, C., Navarro, G., Tempez, A., Legendre, S., *Accelerating the development of phase-change random access memory with in-fab plasma profiling time-of-flight mass spectrometry*, Surface and Interface Analysis, 2020, 52(12), pp. 895–899, https://doi.org/10.1002/sia.6823 (Cover SIA Journal)

[N-5.22] Brüner, P., Grehl, T., Brongersma, H., Detlefs, B., Nolot, E., Grampeix, H., Steinbauer, E., Bauer, P.; Thin film analysis by low-energy ion scattering by use of TRBS simulations ; (2015) Journal of Vacuum Science and Technology A: Vacuum, Surfaces and Films, 33 (1), 01A122 ; https://doi.org/10.1116/1.4901451
## 5.1 Introduction

The general objective of this research direction was to develop and assess characterization methodologies for the elemental depth-profiling of inorganic layered materials with thickness ranging from the nm-range to ~1 µm. Our first intention was to focus on non-destructive techniques, i.e. X-ray photoemission to address ultrathin materials and the combination of grazing-incidence X-ray fluorescence (GIXRF) and X-ray reflectometry (XRR) to deal with thickness up to 200 nm. Meanwhile, we built a 5-year collaboration with Horiba Jobin to work on their destructive efficient Plasma profiling time-of-flight mass spectrometry tool (PP-TOFMS) that was particularly appropriate for close-to-the-line fast and reliable elemental profiling. I report in the next sections about the work done around the three techniques (XPS, XRR-GIXRF, PP-TOFMS) that allow probing materials with thickness ranging from nm to µm with nm-like depth resolution, as illustrated below.

<figure><img src="image_52.png" /></figure>
## 5.2 Combined grazing-incidence X-ray fluorescence and X-ray reflectometry

X-ray reflectometry (XRR) and grazing-incidence X-ray fluorescence (GIXRF) are two non-destructive analytical techniques that can be combined on the same tool, which would feature parallel monochromatic incident beam(s). Both techniques use similar measurement procedures and the same fundamental physical principles can be used to analyze the data. In 1954, Parratt<fnref n="29" /> presented the modulation effect of the electromagnetic field as a function of the incident angle based on reflection, refraction and interferences at a flat interface. He proposed a recursive method for the calculation of the reflected part of the beam (XRR). Based on the same recursive method, in 1991, De Boer<fnref n="30" /> presented a theoretical formulation for the fluorescence emitted (GIXRF) from layered samples based on the calculation of the derivative of the Poynting vector through the determination of the reflection and transmission coefficients. The basic concept of GIXRF is to measure the fluorescence signal emitted by the elements present in the sample as a function of angle of incidence of the X-rays. In the grazing angle range, the incident and the reflected beam interfere creating an X-ray standing wave (XSW) field with locally dependent electric field fluctuations<fnref n="31" />. The emitted fluorescence signal is thus amplified by the intensity of the XSW field at a given depth resulting in a strong dependence on the elemental depth profile (i.e. atomic density). Therefore, XRR probes the profile of the electron density in thin layered materials whereas GIXRF analyses the profile of the atomic density. Roughly speaking, the combination of the two techniques feeds XRR with the GIXRF-deduced chemical composition of each layer while providing GIXRF with XRR-deduced thickness information. XRR-GIXRF combined analysis gives access to depth-dependent properties of thin materials with thickness in the 1 to 200 nm range typically: elemental depth-profile along with density, thickness and roughness of individual layers.

In 2012, we had only limited capability to analyze thin materials using XRF in grazing incidence mode:

- We extended the use of inline T-XRF instrument (Rigaku Fab300) dedicated to the monitoring of metallic contamination to the analysis of thin films such as alumina and hafnia high-k dielectrics [N-5.1, N-5.2]. The setup of inline T-XRF was optimized for operation in total reflection mode i.e. below the critical angle for total reflection in order to enhance the sensitivity to metallic contaminants at the surface of silicon substrates. Conversely, the setup was not optimized to perform GIXRF on thin films, due to poor angular resolution and short distance between the wafer to the XRF detector, which led to significant dead time and non-linear detector response when measuring layers thicker than few nm. Then, T-XRF allowed to measure the mass deposition of ultrathin films of the composition of thicker films, but couldn't be used to probe depth-dependent properties

- We extended the use of an inline XRR-XRF tool (Bruker D8 Fabline) so as to irradiate the sample with the XRR primary beam (monochromatized Cu-Kα) and to collect the XRF intensity with the SDD detector of the EDXRF module. We were able to collect GIXRF data related to transparent conductive oxide material (Fig. 5.1), but the geometrical setup did not permit to extract more than the overall mass deposition of indium and silver

- Moreover, we did not have any software to model GIXRF data or combined XRR-GIXRF data

<footnote n="29">²⁹ L. Parratt, Surface studies of solids by total reflection of X-rays, Phys. Rev 95 (1954) 359–369, http://dx.doi.org/10.1103/PhysRev.95.359</footnote>

<footnote n="30">³⁰ D.K.G de Boer, Grazing-incidence X-ray fluorescence of layered materials, Phys. Rev. B 44 (1991) 498–511. http://dx.doi.org/10.1103/PhysRevB.44.498</footnote>

<footnote n="31">³¹ A. von Bohlen, Total reflection X-ray fluorescence and grazing incidence X-ray spectrometry - tools for micro- and surface analysis, Spectrochim. Acta, Part B 64 (2009) 821–832, http://dx.doi.org/10.1016/j.sab.2009.06.012</footnote>
<figure><img src="image_53.png" /><figcaption>**Fig. 5.1** : Thin stacks made of indium oxide and silver of various thickness feature low resistivity and interesting > 80 % optical transmittance in the visible range. GIXRF profile of Ag-La line collected with Cu-Ka primary radiation on Bruker D8-Fabline tool was only sensitive to the variation of the mass deposition (at angle > 1°) whereas no depth-dependent information showed up in the critical angle region.</figcaption></figure>

Then, we investigated two parallel paths to introduce non-destructive XRR-GIXRF at CEA-Leti:

- We built collaborations with different teams in the frame of Bérenger Caby’s PhD (2012-2015). In addition to fruitful scientific interaction and commonly defined experiences :

* The collaboration with Christina Streli and Dieter Ingerle at Vienna University of Technology (VUT) allowed to access to lab-based (home-built) GIXRF instrument and jGIXA (home-built) analysis software

* The collaboration with Giancarlo Pepponi at Fondazione Bruno Kessler, Trento allowed to access GIMPy (home-built) analysis software

* The collaboration with Daniel Chateigner and Magali Morales from Laboratoire de Cristallographie et Sciences des Matériaux in Caen (CRISMAT) allowed to evaluate the use of MAUD software for GIXRF-XRR

* Bérenger Caby spent at least one month in each of this Lab, which was particularly beneficial for the experimental and modelling part of his PhD, then for the transfer of expertise within the collaborative group, then to CEA-Leti

* The goal of this collaborative group was indeed to share expertise, instruments and analysis software on combined XRR and GIXRF to accelerate the development of the technique.

- We built collaboration with NMIs in the frame of different European metrology program funded by Euramet:

* A long-term collaboration with Burkhard Beckoff and Philipp Hönicke (PTB/Berlin, experts in reference-free XRR-GIXRF analysis) was established within the European metrology programs TReND, ThinErgy and HyMet. TReND was particularly interesting as Euramet encouraged and financed 5-month stay of Blanka Detlefs (post doc) at PTB/Berlin, who was part of GIXRF-XRR experiments on PTB beamline at Bessy II, and could closely interact with PTB team about the challenges in data modelling of combined XRR-GIXRF data

* A long-term collaboration with Marie-Christine Lépy (CEA/LNHB) in the same metrology programs and during Walter Pessoa’s PhD, which allowed us to access to the Métrologie beamline @ Soleil, where a duplicate of PTB XRR-GIXRF instrument had been installed [N-5.5].

We conducted the following activities on XRR-GIXRF analysis:

- Evaluation of the influence of the instrumental setup and of the data reduction software in the analysis of combined XRR-GIXRF data collected in the lab or at synchrotron beamlines

- Writing and assessment of a Python-based open source code for the modelling of XRR-GIXRF data

- Assessment of reference-based XRR-GIXRF analysis
**First** [N-5.3], we measured XRR and GIXRF data of the thin layered presented in Fig. 5.1, with optimal silver thickness equal to 6 nm and sample differences in terms of thickness of the top indium oxide and annealing step (Table 5.1).

<table><caption>Table 5.1 : Definition of top layer thickness and annealing conditions for In₂O₃ (top)/Ag (6 nm)/In₂O₃ (40 nm) stack grown by PVD on 500 nm-thick thermal SiO₂ [N-5.3]</caption><thead><tr><td>Sample</td><td>Top layer</td><td>Annealing</td></tr></thead><tbody><tr><td>A</td><td>40nm</td><td></td></tr><tr><td>B</td><td>40nm</td><td>200°C for 1h</td></tr><tr><td>C</td><td>15nm</td><td></td></tr><tr><td>D</td><td>15nm</td><td>200°C for 1h</td></tr></tbody></table>

We measured XRR and GIXRF data at Cu-Kα primary energy on VUT lab-tool. However, In-L and Ag-L fluorescence lines as well as Si pile-up peak overlap in the 3 keV range (Fig. 5.2). As for all the future analysis, we first extracted the net XRF intensities at each incident angle with PyMCA<fnref n="32" /> software before modelling combined XRR-GIXRF angle-dependent data (Fig. 5.3, Fig. 5.4). We complemented the lab data with GIXRF data measured at high energy on Gilda beamline at ESRF, more specifically Ag-Kα intensity collected at 26.4 keV, below In-K edge. jGIXA modelling of the data set consisting of lab XRR-GIXRF data and synchrotron GIXRF data (Fig. 5.5) clearly highlighted the following points [N-5.8]:

- To account for the instrumental function was important for XRR and crucial for GIXRF analysis

- Thinning the top indium oxide layer significantly increased the sensitivity of GIXRF to small annealing-induced modification in the depth of the stack.

- XRR-GIXRF revealed unambiguous modification of the depth-dependent properties after annealing, suggesting annealed-induced interdiffusion between the Ag and the In₂O₃ layers

- The precise quantification of the elemental depth-profile should be supported by dedicated reference samples.

<figure><img src="image_54.png" /><figcaption>**Fig. 5.2.** : Decomposition of the XRF spectra of sample A collected in the Lab at 1.2° [N-5.3]</figcaption></figure>

<figure><img src="image_55.png" /><figcaption>**Fig. 5.3.** : Ag-Lα GIXRF measurements (open circles) and fits (solid lines) of the as-deposited samples A and C in the Lab at 8.05 keV [N-5.3]</figcaption></figure>

<footnote n="32">³² V.A. Solé, E. Papillon, M. Cotte, P. Walter, J. Susini, *A multiplatform code for the analysis of energy-dispersive X-ray fluorescence spectra*, Spectrochim. Acta, 62 (2007), p. 63-68, https://doi.org/10.1016/j.sab.2006.12.002</footnote>
<figure><img src="image_56.png" /><figcaption>**Fig. 5.4.:** XRR measurements (open circles) and fits (solid lines) of the as-deposited sample A at 8.05 keV with and without the introduction of the low-density $In_2O_3$ top layer in the model [N-5.3]</figcaption></figure>

<figure><img src="image_57.png" /><figcaption>**Fig. 5.5.:** XRR and GIXRF measurements of the sample D with reflectivity measured at 8.05 keV and fluorescence at 26.4 keV. Inter-diffusion had to be taken into account in the modelling with jGIXA [N-5.3]</figcaption></figure>

Secondly, we assessed XRR-GIXRF against TOF-SIMS to evidence process-induced elemental depth-profiles in thin materials. For instance [N-5.8], we performed XRR-GIXRF experiment on the Fluorescence beamline at Elettra synchrotron to probe $Ta_2O_5$/metal structure, titanium nitride and nickel being investigated as bottom electrode material as they are good candidates for the replacement of noble materials by low-cost fab-friendly abundant electrodes for Resistive random access memory (ReRAM). In order to evaluate low-cost fab-friendly abundant electrodes that could replace noble metals for $Ta_2O_5$ ReRAM, the sample set included layered stacks consisting in 15 nm $Ta_2O_5$ layer deposited on 10 nm-thick electrode material grown on 300 nm Si(001) substrate. Titanium nitride and nickel were both evaluated as potential electrode materials. Nickel and titanium nitride layers were deposited via Physical Vapor Deposition (PVD), whereas tantalum oxide material was grown by Plasma Enhanced Atomic Layer Deposition (PE-ALD).

We varied the PE-ALD conditions in order to minimize $Ta_2O_5$-metla inter-diffusion. The first PE-ALD experimental condition consists in successive cycling of deposition of TBTDET precursor (for $Ta_2O_5$ deposition) followed by the use of O\* plasma. O\* plasma is known to have a strong impact on the sample, often leading to a large oxidation of the substrate or layer on which the tantalum layer is deposited. Therefore, alternative PE-ALD conditions have been considered, consisting in adding H\* in the plasma prior to O\*, as this former is supposed to result in deoxidation at each deposition cycle.

PyMCA software was used to determine the XRF intensities at each angle. Dedicated samples (thin nickel layer on silicon and thin tantalum oxide film on silicon) were used to estimate the instrumental function of the XRF detector and then improve the accuracy of Ta-Lα intensities by appropriate deconvolution from Ni-Kβ₁. Angle-dependent XRF intensities of Ta-Lα (after deconvolution) and Ta-Lβ₁ (less intense but isolate XRF line) were then compared as a sanity check. Angle-dependent GIXRF data and XRR data were then processed using Jgixa software. The instrumental parameters of GIXRF and XRR (i.e. detected zone, beam width and divergence) were calculated from the analysis of GIXRF/XRR data of a thin, smooth nickel material deposited on silicon. Finally, best multilayer model of samples of interest was estimated by simultaneously fitting of XRR/GIXRF with differential algorithm, using fixed pre-determined instrumental function.
<figure><img src="image_58.png" /><figcaption>**Fig. 5.6.** : TOF-SIMS and XRR-GIXRF analysis of the elemental-depth profiles related to the different PE-ALD conditions [N-5.8]</figcaption></figure>

TOF-SIMS and GIXRF/XRR both unambiguously demonstrate (Fig 5.6) the significant TiN-Ta intermixing in Ta₂O₅/TiN stacks, even with optimized Ta₂O₅ process conditions. On the contrary, TOF-SIMS profiles reveal that the introduction of H* plasma step in PE-ALD Ta₂O₅ process drastically reduces both the oxidation of nickel electrode material and the Ta₂O₅/Ni intermixing, therefore confirming that nickel is a good candidate for Ta₂O₅ based ReRAM. The influence of H* plasma on nickel-based samples was also evidenced by GIXRF/XRR technique, first qualitatively, then quantitatively by the use of model-based multilayer combined analysis, therefore demonstrating the performances of GIXRF/XRR as highly-sensitive, non-destructive chemical depth-profile technique suitable to support process development, either in lab or even in fabs.

**At that point,** we had a rather clear idea that quantitative depth-profile using combination of XRR-GIXRF could be conducted in two different ways :

- The reference-free approach that PTB had developed for a long time (over 15 years) and that lies on two main pillars : i/ the use of a radiometrically calibrated instrumentation of the PTB and ii/ a fundamental parameter-based reference-free quantification approach. The preparation of the experiment must careful control of the geometrical parameters (beam and sample alignment, detector positioning), the monitoring of the incident photon flux using calibrated photodiodes, and the calibration of the detector response functions and detection efficiency of the silicon drift detector (SDD) for the measurement of the emitted fluorescence radiation. Such approach is elegant but difficult to adapt to any instrumental setup. For instance, it would be difficult or even impossible to carry the calibration of instrumentation of an automated tool dedicated to production lines.

- A reference-based approach, that would i/ describe the instrumental function with a limited number of parameters, from the measurement of stable, easy-to-produce thin materials, ii/ include available database for fundamental parameters (xraylib for instance) and iii/ refine absolute quantification by the measurement of standards (thin layers or substrates) that would include the materials of interest for the experiment.

We designed the open-source code MEDePY (Material Elemental Depth profiling using Python) to support the reference-based approach. MEDePY was developed by Blanka Detlefs with the help of Gaël Picot for robust implementation of the GUI. It is based on Parrat and de Boer formalism and uses xraylib library. A careful implementation of a reduced instrumental function (Fig. 5.7) was performed by Hélène
Rotella, using results from Bérenger Caby's PhD collaborative group to extend the geometrical factor correction presented by Li et al.<fnref n="33" />. For instance, the evaluation of the solid angle of detection (considered as constant during the GIXRF by Li) was implemented in MEdPY (Fig. 5.8).

<figure><img src="image_59.png" /><figcaption>**Fig. 5.7.** : Schematic of the geometry for the fluorescence X-ray detection in a GIXRF experiment with an X-ray fluorescence detector tilted compared to the sample surface in a theta-theta configuration. The reduced instrumental function refined in MEdPY includes the following parameters : sample-collimator distance, pinhole diameter and height, along with beam divergence [B. Caby's PhD manuscript]</figcaption></figure>

<figure><img src="image_60.png" /><figcaption>**Fig. 5.8.** : Schematic representation used for the calculation of the solid angle of detection. In the region marked as l₂, the solid angle is subtended by a circle since the whole area of the detector not covered by the collimator is accessible. In the region marked as l₁, the solid angle is not subtended by a circle any more, but from an ellipse that becomes smaller moving far from the center of the detector [B. Caby's PhD manuscript].</figcaption></figure>

MEdPY permits to evaluate the impact of instrumental parameters on XRR and GIXRF angle-dependent data, then to optimize (when possible), the experimental setup to probe a specific thin material system (Fig. 5.9).

**At the end,** Simona Torrengo assessed MEdPY for reference-based XRR-GIXRF analysis of TiNW thin materials on the Métrologie beamline at Soleil [N-5.11], using stable thin nickel film to calculate the reduced instrumental function and individual TiN and WN layers to refine the quantification of TiNW alloys. The mass deposition of Ti and W deduced from MEdPY analysis was aligned with WDXRF results within 1% abs, whereas the elemental depth-profiles in TiNW samples matched TOF-SIMS analysis.

Li presented a geometrical factor correction which takes into account both the spatial intensity distribution of the primary X-ray beam (i.e. the shape of the beam) and the instrumental geometry (such as the collimator geometry of the fluorescence detector, the size of the X-ray source and the imprint beam size on the sample).

As the detected fluorescence intensity $I_x(\theta)$ depends on the geometrical factor, it can be expressed by :

$$I_x(\theta) = F_x(\theta)G(\theta) = F_x(\theta) \frac{\Delta\Omega}{4\pi} I_0 S(\theta) \varepsilon_{det} T_{air}$$

where $F_x(\theta)$ is the total emitted fluorescence intensity by atoms of element x, $\Delta\Omega$ is the solid angle contained by the detector surface, $I_0$ is the incident beam intensity which is generally non-uniform along the beam thickness perpendicular to the incident direction, $S(\theta)$ is the sample surface area which is illuminated by the incident beam and detected by the fluorescence detector. $\varepsilon_{det}$ and $T_{air}$ represent the detector efficiency and the transmission efficiency of the X-ray fluorescence through the air path between the sample and the fluorescence detector. These two last factors are independent on the incident angle will be considered as constants.

<footnote n="33">³³ W. Li, J. Zhu, X. Ma, H. Li, H. Wang, K. J. S. Sawhney, and Z. Wang, "Geometrical factor correction in grazing incident x-ray fluorescence experiment," Rev. Sci. Instrum., vol. 83, no. 5, p. 053114, May 2012, https://doi.org/10.1063/1.4722495</footnote>
<figure><img src="image_61.png" /><figcaption>**Fig 5.9:** Influence of the sample-collimator distance (left) and pinhole diameter (right) on the angular dependent of Ni-Kα intensity from 50 nm-thick Ni film deposited on silicon with various distance sample-collimator. MEdEpy simulation considers the simple case of an XRF detector placed at 90° above the surface of the sample in theta-theta spectrometer. For the following simulations of the correction function, we considered a beam width $b_0$ of 50 µm and a sample length $L_s$ of 20 cm (larger than the illuminated area or the detected area) [B. Caby's PhD manuscript]</figcaption></figure>

A key feature of reference-free XRR-GIXRF analysis at PTB/Berlin is the ability to estimate the uncertainty budget. We measured complex stacks of ultrathin alumina and hafnia high-k dielectrics, first using inline XRR at CEA-Leti (Bruker D8 Fabline at Cu-Kα), then on PTB beamlines at Bessy II, where samples were analyzed using two different primary energy: 1.622 keV for the quantification of Al and O, and 10 keV for the quantification of Hf [N-5.9].

On the one hand, we modelled the XRR data using two different software, Bruker Leptos<fnref n="34" /> and GenX<fnref n="35" />, which resulted in small discrepancy in the deduced thickness and density of individual layers. Reference-free GIXRF analysis performed at PTB provided the mass deposition of Al, O and Hf (Fig. 5.10) with related uncertainties, which highlights the limitations of XRR-only analysis of such challenging materials. Complementary combined XRR-GIXRF analysis at PTB highlighted that annealing step at high temperature (800°C) led to inter-diffusion in the thin layered stack.

<figure><img src="image_62.png" /><figcaption>**Fig 5.10:** Comparison of quantified elemental mass depositions for Al (center) and Hf (right) in various thin materials stacks (left) versus the calculated data using both the Bruker Leptos and the GenX modeling results of the LETI-XRR data. The reference-free GIXRF quantification was performed for incident angles above 4° [N-5.9]</figcaption></figure>

<footnote n="34">³⁴ A. Ulyanenkov, Proc. SPIE 5536, 1 (2004)</footnote>

<footnote n="35">³⁵ M. Bjorck and G. Andersson, J. Appl. Cryst. 40, 1174 (2007)</footnote>
The resolution of GIXRF decreases with depth as the **XSW-induced amplification** of XRF is no more present. We conducted a first experiment to overcome this difficulty, deposited 25 nm-thick layer stacks of GeSe and GeSeSb on top of silicon or (Mo/Si)₄₀ superlattice substrates, the latter being optimized to generate XSW amplification at different depth in the 25 nm stack [N-5.10]. This first XRR-GIXRF experiment produced same elemental depth-profiles as TOF-SIMS and was an encouraging step towards substrate-enhanced XRR-GIXRF analysis (Fig. 5.11).

<figure><img src="image_63.png" /><figcaption>**Fig. 5.11** : We deposited GeSe-based layers by PVD on silicon substrate or on top of (Mo/Si)₄₀ superlattice in order to optimize XSW amplification, as calculated using MEdPY. Elemental depth-profiles deduced from XRR-GIXRF were aligned with TOF-SIMS analysis.</figcaption></figure>

XRR-GIXRF activity has slowed down since 2020 due to the lack of supporting programs and, above all, to the lack of XRR-GIXRF instrument at CEA-Leti. We have just invested in a new inline tool that will feature XRR and XRF capability using 3 different primary energy and grazing incidence capability (Rigaku MFM 310). XRR-GIXRF activity will therefore be extended in 2024.
## 5.3 X-ray photoemission

There are different ways to access depth-dependent information from surface sensitive XPS technique, as summarized hereafter. Our research in this field was oriented to non-destructive analysis, either based on p-ARXPS (Walter Pessoa and Rose Taylor Bure's PhD) and on inelastic background analysis (Rose Taylor Bure's PhD). We used existing XPS tools and existing XPS analysis software to assess the accuracy of non-destructive XPS depth-profiles against different techniques.

<table><tr><td><p>These surface morphologies all give the same XPS-peak intensity</p><p><strong>Figure 5.1: XPS spectra of a 1.1Å thick Au film on SiO<sub>2</sub> substrate.</strong></p><p>Figure 5.2: XPS spectra of a 20Å thick Au film on SiO<sub>2</sub> substrate.</p><p>Figure 5.3: XPS spectra of a 30Å thick Au film on SiO<sub>2</sub> substrate.</p><p>Figure 5.4: XPS spectra of a 25Å thick Au film on SiO<sub>2</sub> substrate.</p><p>Figure 5.5: XPS spectra of a 50Å thick Au film on SiO<sub>2</sub> substrate.</p><p>Figure 5.6: XPS spectra of a 10Å thick Au film on SiO<sub>2</sub> substrate.</p><p>Figure 5.7: XPS spectra of a 20Å thick Au film on GaAs substrate.</p><p>Figure 5.8: XPS spectra of a 30Å thick Au film on GaAs substrate.</p><p>Figure 5.9: XPS spectra of a 50Å thick Au film on GaAs substrate.</p><p>Figure 5.10: XPS spectra of a 10Å thick Au film on GaAs substrate.</p><p>Figure 5.11: XPS spectra of a 20Å thick Au film on GaAs substrate.</p><p>Figure 5.12: XPS spectra of a 30Å thick Au film on GaAs substrate.</p><p>Figure 5.13: XPS spectra of a 50Å thick Au film on GaAs substrate.</p><p>Figure 5.14: XPS spectra of a 10Å thick Au film on GaAs substrate.</p><p>Figure 5.15: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.16: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.17: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.18: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.19: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.20: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.21: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.22: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.23: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.24: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.25: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.26: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.27: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.28: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.29: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.30: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.31: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.32: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.33: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.34: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.35: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.36: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.37: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.38: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.39: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.40: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.41: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.42: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.43: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.44: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.45: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.46: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.47: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.48: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.49: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.50: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.51: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.52: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.53: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.54: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.55: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.56: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.57: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.58: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.59: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.60: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.61: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.62: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.63: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.64: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.65: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.66: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.67: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.68: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.69: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.70: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.71: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.72: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.73: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.74: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.75: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.76: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.77: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.78: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.79: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.80: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.81: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.82: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.83: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.84: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.85: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.86: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.87: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.88: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.89: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.90: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.91: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.92: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.93: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.94: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.95: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 5.96: XPS spectra of a 30Å thick Au film on PbS substrate.</p><p>Figure 5.97: XPS spectra of a 50Å thick Au film on PbS substrate.</p><p>Figure 5.98: XPS spectra of a 10Å thick Au film on PbS substrate.</p><p>Figure 5.99: XPS spectra of a 20Å thick Au film on PbS substrate.</p><p>Figure 6.00: XPS spectra of a 30Å thick Au film on PbS substrate.</p></td><td>The electron inelastic mean free path (IMFP) is a convenient (inverse) measure of the probability of inelastic scattering for the detected photoelectrons. The IMFP is a function of material and photoelectron energy. Plots of electron inelastic mean free paths as a function of electron energy for SiO<sub>2</sub>, GaAs, InP, and PbS<sup>36</sup> show that:<ul><li>The use of XPS lines with different kinetic energies is a way to access depth-dependent information</li><li>The use of X-ray source in the hard X-ray (HAXPES) instead of Al-Kα extends the information depth of XPS</li></ul></td></tr><tr><td>The inelastic background of XPS spectra contains valuable depth-dependent information, as largely exposed by S. Tougaard<sup>37</sup>. Left panel: four widely different surface and near-surface distributions of Cu atoms in and on Au that give identical Cu XPS peak intensities, but quite different inelastic backgrounds. Right panel: Au4d spectra from samples where the same 1 nm thick Au film is placed at increasingly larger depths in a Cu matrix. In addition, the inelastic background contains information for depths up to 8*IFMP instead of 3*IFMP for core levels.</td><td></td></tr></table>

<footnote n="36"><sup>36</sup> C. J. Powell, S. Tanuma, “Inelastic Mean Free Paths, Mean Escape Depths, Information Depths, and Effective Attenuation Lengths for Hard X-ray Photoelectron Spectroscopy”, in book Hard X-ray Photoelectron Spectroscopy (HAXPES), 2016, https://doi.org/10.1007/978-3-319-24043-5_5</footnote>

<footnote n="37"><sup>37</sup> S. Tougaard, Energy loss in XPS: Fundamental processes and applications for quantification, non-destructive depth profiling and 3D imaging, Journal of Electron Spectroscopy and Related Phenomena, Vol 178–179, 2010, https://doi.org/10.1016/j.elspec.2009.08.005</footnote>
<table><tr><td><img src="image_0.png" alt="A classical way to probe elemental depth-profiles with XPS is to measured XPS signal along the sputtering of the thin material with Ar<sup>+</sup> ions or clusters. We did not investigate this destructive option."></td><td>A classical way to probe elemental depth-profiles with XPS is to measured XPS signal along the sputtering of the thin material with Ar<sup>+</sup> ions or clusters. We did not investigate this destructive option.</td></tr><tr><td><img src="image_1.png" alt="Angle-dependent analysis permits to vary the information depth of XPS. This can be realized either by titling the sample, which is difficult to consider for 300 mm wafers, or (better) by virtue of parallel collection of angle-resolved photoelectrons (p-ARXPS). We investigated the use of non-destructive p-ARXPS depth profiling on Thermo Theta 300 tool, which two-dimensional detector at the output plane has photoelectron energy dispersed in one direction and the angular distribution dispersed in the other direction<sup>38</sup>. Such arrangement provides an angular range of ~60° (from 20° to 78° relative to the normal of the sample) with a resolution close to 1°."></td><td>Angle-dependent analysis permits to vary the information depth of XPS. This can be realized either by titling the sample, which is difficult to consider for 300 mm wafers, or (better) by virtue of parallel collection of angle-resolved photoelectrons (p-ARXPS). We investigated the use of non-destructive p-ARXPS depth profiling on Thermo Theta 300 tool, which two-dimensional detector at the output plane has photoelectron energy dispersed in one direction and the angular distribution dispersed in the other direction<sup>38</sup>. Such arrangement provides an angular range of ~60° (from 20° to 78° relative to the normal of the sample) with a resolution close to 1°.</td></tr></table>

## About the use of XPS lines with different kinetic energies

We mostly worked on the Thermo Theta 300 XPS tool, as this instrument was the only one available in the cleanroom and compatible with measurement on up to 300 mm wafers. This instrument is equipped with a monochromatic Al-Kα source, which limits the use of XPS lines with different kinetic energies when compared to HAXPES. Nevertheless, we demonstrated this use on different materials, for instance containing germanium (in epitaxial SiGe, in phase change GeSbTe, etc.) as Ge 2p and Ge 3d electrons feature significantly different kinetic energy (~1450 eV for Ge 3d, ~260 eV for Ge 2p) resulting in different IMFP and information depth (ID).

For instance, in [5-14], we combined the use of Ge 2p and Ge 3d with angular information in order to highlight the out diffusion of elemental germanium from SiGe pseudo-substrate into ultrathin HfO₂ dielectrics (Fig. 5.12).

<footnote n="38">³⁸ John F. Watts, John Wolstenholme, *An Introduction to Surface Analysis by XPS and AES*, Second edition, Wiley, 2020, ISBN 9781119417620</footnote>
<figure><img src="image_64.png" /><figcaption>**Fig. 5.12** : Ge 3d provides bulk-like sensitivity when Ge 2p provides surface-like sensitivity in the thin HfO₂/SiON/SiGe stack. The surface sensitivity of Ge 2p is enhanced at grazing angles (> 55°). **Left**: Ge 2p₃/₂ core level spectra measured by p-ARXPS for all the samples ; **Right**: decomposition of the Ge 3d spectrum measured for sample Si-rich1 [5-14].</figcaption></figure>

Estimation of the instrumental function prior to p-ARXPS analysis

The accuracy in p-ARXPS reconstruction relates to the intensity calibration and to the angular signature of the XPS tool. We engaged with NPL (English NMI) who conducted a VAMAS interlaboratory study on intensity calibration for XPS instruments using low-density polyethylene [N-5.12]. In addition, we routinely estimate the angular-dependence of the energy resolution (via Fermi edge width and Au 4f<sub>7/2</sub> FWHM on clean gold target) and value (Au 4f<sub>7/2</sub> binding energy) as illustrated in Fig. 5.13. We also track the distance to cos-like dependence of the integrated intensity of Au 4f<sub>7/2</sub> from clean gold target as a function of the selected number of angular channels in the 20-78° range (Fig. 5.14).

<figure><img src="image_65.png" /><figcaption>**Fig. 5.13** : Angular dependence of the Au 4f<sub>7/2</sub> binding energy and FWHM measured with Thermo
Theta 300 tool on clean gold target</figcaption></figure>
<figure><img src="image_66.png" /><figcaption>**Fig. 5.14** : Deviation from cos-like function of the angular response of Thermo Theta 300 tool as a function of angular sectoring (8 to 96 channels) and acquisition time (number of scans)</figcaption></figure>

<table><thead><tr><td>Channels</td><td>Scans</td><td>deviation(%)</td></tr></thead><tbody><tr><td>8</td><td>1</td><td>-27.5 / +6.5</td></tr><tr><td>8</td><td>64</td><td>-16.8 / +5.6</td></tr><tr><td>96</td><td>128</td><td>-31.2 / +15.1</td></tr></tbody></table>

p-ARXPS data collected on Thermo Theta 300 tool were analyzed using Thermo Avantage software, more specifically using the sharp interfaces multi-overlayer model. A 20-60° angular range was used in order to get rid of elastic-scattering effects. We used this method quite extensively, for instance to evidence the efficiency of a plasma cleaning step to the native oxide of thin tungsten films (Fig. 5.15), but we did not have an exact idea of the *accuracy* of the provided thickness information.

<figure><img src="image_67.png" /><figcaption>**Fig. 5.15** : W 4f spectra of thin tungsten films grown by PDV on thermal SiO₂. p-ARXPS was used to estimate the thickness of the residual oxide after chemical mechanical polishing (CMP), then after different plasma. The aim was to get bonding-compatible almost un-oxidized surface (unpublished).</figcaption></figure>

In the frame of Rose Taylor Bure's PhD, we assessed the accuracy of p-ARXPS and Inelastic background analysis conducted on XPS and HAXPES lab-tools for determining the thicknesses of high- k oxide materials [N-5.16]. We selected these technological-relevant materials because due to their validated Atomic Layer Deposition conditions that come with layer/substrate interface management and atomic level control of thin film deposition. We summarize the main findings of this work in the next pages.

Layers of Al₂O₃ and HfO₂ with individual thicknesses in the sub-nanometer to 25 nm range were deposited on 300 mm silicon (001) wafers by ALD. The layer thickness is determined by the number of
ALD cycles. Water vapor was used as the oxygen source for both metal-oxides, while Trimethylaluminium and HfCl₄ were used as precursors. The deposition temperature was 300 °C. Three classes of ALD samples were examined in this work (Fig 5.16) : (a) ultrathin samples of Al₂O₃ with sub-nanometer thicknesses, (b) a stack of SiO₂, HfO₂, and Al₂O₃ layers of 1–2 nm, (c) thin buried Al₂O₃ or HfO₂ layers underneath a thick layer (9–25 nm) of HfO₂ or Al₂O₃, respectively. The samples from the first class were deposited either over the native oxide, or after HF surface preparation. The sample in the second class was prepared according to the experimental specifications found in [N-5.9, see Section 5.2]. A 1 nm chemical oxide was formed prior to the HfO₂ ALD layer deposition. The third class of ALD samples used HF surface preparation, and features two sets of three bilayer samples in which a HfO₂ or Al₂O₃ overlayer of approximately 10, 15, and 25 nm was deposited over an approximately 2.5 nm layer of either Al₂O₃ or HfO₂, respectively.

<figure><img src="image_68.png" /><figcaption>**Fig. 5.16:** The schematic representation of the structure of (a) the sub-nanometer ultrathin class of samples (with or without native oxide); (b) trilayer of thin metal oxide layers and (c) bilayers with deeply buried layer of HfO₂ or Al₂O₃ and overlayer of approximately 10, 15, and 25 nm composed of the opposing metal-oxide [N-5.16].</figcaption></figure>

**p-ARXPS analyses** were carried out with a Thermo Scientific Theta 300 spectrometer using a monochromatic Al Kα source. High-resolution spectra were collected using an analysis area of ~ (400 µm)² and a 40 eV pass energy. The energy resolution was 0.45 eV as determined from the Fermi cutoff of a gold reference sample. p-ARXPS data were analyzed using Thermo Avantage software (version 5.9902), more specifically using the sharp interfaces multi-overlayer model. A 20-60° angular range was used in order to get rid of the contributions of elastic interactions.

**XPS measurements** (PHI 5000 VersaProbe II) were using monochromated Al-Kα radiation and a takeoff angle of 45° at a pass energy of 117 eV. The FWHM for Ag 3d<sub>7/2</sub> is 1.5 eV for this pass energy. The analyses were done with and without surface preparation by argon gas-cluster ion beam (GCIB) with a cluster size of 2500 atoms at 10 keV for 4 eV per atom of argon and a dose of 1.25nA per mm².

**HAXPES measurements** were acquired using an X-ray monochromatic Cr-Kα source (hν = 5414.9 eV) as excitation and an analyzer pass energy of 280 eV, provided by the PHI Quantes instrument. The FWHM for Ag 3d<sub>7/2</sub> is 2.3 eV for this pass energy. The photoelectron emission angle (sample-analyzer angle) was varied between 30° – 80°. The spectra were recorded over an extended energy range suitable for inelastic background analysis (IBA). The spectra included Al 1s at 1559.6 eV BE, Hf 3d at 1662 eV BE, and Si 1s at 1839 eV BE in the high binding energy region, and O 1s at 531 eV BE in the low binding energy region. Additional scans were taken in the 518 eV kinetic energy region in order to record the O KLL Auger signal for IBA.

Inelastic background analysis (IBA) of the photoemission spectra was effectuated using the QUASES-Analyze software from the QUASES-Tougaard software package<fnref n="39" />.

For the best illustration on how IBA works, we present an example of HAXPES-IBA in Fig. 5.17, which depicts background analysis performed in QUASES-Analyze for Hf 3d in a pure, 3 mm HfO₂ sample.

<footnote n="39">³⁹ S. Tougaard, Software Packages to Characterize Surface Nano-Structures by Analysis of Electron Spectra, 2021. <http://www.quases.com/></footnote>
The inelastic background (red line) is subtracted from the measured spectrum (J(E), black line), leaving the no-loss spectrum (F(E), blue line). The inelastic background modeled for the depth distribution of the element is obtained by varying step by step, in the software, the thickness and buried depth of the layer from which the photoelectron originates, until a good match between J(E) and the modeled background is reached over the widest possible kinetic energy range. The result is appreciated by visual inspection of the spectra, in which the closeness of the fit between the simulated and measured background is evaluated in the kinetic energy range 30–100 eV after the peak (Fig. 5.17 (a)). The exact peak shape in the energy region close to the peak energy up to ~10–20 eV below the peak energy is not accounted for by the model since it is largely determined by the chemical bond, lifetime broadening, and intrinsic excitations in the photoemission process, which all may depend on the local chemical environment. Fig. 5.17 (b) demonstrates a poor fit where the modeled HfO₂ distribution of 5–10 nm is incorrect. The simulated inelastic background is poorly fitted to the measured background, and the subsequent no-loss spectrum does not lie at zero.

<figure><img src="image_69.png" /><figcaption>**Fig. 5.17.** QUASES-Analyze IBA of Hf 3d in bulk HfO₂ recorded with Cr Kα source. The black line is the raw measured data, and the red line is the inelastic background calculated by the software. The blue line is the spectrum, which has been corrected for inelastic losses by subtracting the red line. A good fit between measured and calculated inelastic backgrounds is seen in (a) where the depth distribution of an infinite medium is accurate. A poor fit is seen in (b) where the depth distribution of 5–10 nm is incorrect [N-5.16]</figcaption></figure>

There are few parameters required from the user, since the principle source of information is the background shape. An effective inelastic mean free path (IMFP<sub>eff</sub>) is calculated as the weighted average over the individual IMFP for each layer determined by the TPP-2M formula<sup>40</sup>. The weighted contribution is taken based on the thickness of each layer within the path the photoelectron travels out of the material, with a half-contribution from the layer from which the photoelectron originates. The half-contribution accounts for the probability of the photoelectron to originate at any depth within the layer and the choice of IMFP<sub>eff1/2</sub> for materials with similar inelastic scattering cross-sections has been extensively published upon. A weighted IMFP ensures that the relatively high photoelectron transport in Al<sub>2</sub>O<sub>3</sub> versus HfO<sub>2</sub> was accounted for in the inelastic background analysis.

The second parameter required by the software is the differential energy loss cross-section K(E, T). K(E, T) is the probability for an electron of energy E to lose energy T per unit energy loss and path length traveled, and is essentially a delineation of the background after the no-loss peak.

<footnote n="40"><sup>40</sup> S. Tanuma, C.J. Powell, D.R. *Penn Calculation of electron inelastic mean free paths (IMFPs) VII. Reliability of the TPP-2M IMFP predictive equation*, Surf. Int Anal., 35 (2003), pp. 268-275, https://doi.org/10.1002/sia.1526</footnote>
A universal cross-section of two mathematical parameters is available which accurately describes the background for most transition metals and their alloys and oxides<fnref n="41" />. The equation is as follows:

$$ \lambda(E)K(E,T) = \frac{BT}{(C + T^2)^2} $$

$B \approx 3000 \text{ eV}^2$ and $C = 1643 \text{ eV}^2$. $B$ is normalized to $2C$, while $C$ was determined via a dielectric-response calculation.

We found that the **accuracy of the three XPS analysis strategy** (p-ARXPS, IBA-XPS and IBA-HAXPES) in the determination of the thickness of ALD materials strongly depends on the ratio of the layer thickness to the information depth.

The modification of the inelastic background in XPS-IBA and HAXPES-IBA induced by the **first class of samples** (ultrathin $Al_2O_3$) was too low to permit any related metrology. Conversely, we evaluated the performances of p-ARXPS, using the following methodology:

- Assessment of non-destructive WDXRF analysis against destructive LPD-ICPMS (Liquid Phase Decomposition coupled to Inductively Coupled Plasma Mass Spectrometry). LPD-ICPMS was used as a destructive, whole surface and reference technique since calibrated with certified standards for the quantification of Al dose, resulting in better than 10% abs accuracy (Fig. 5.18).

- Modelling of p-ARXPS data (Fig. 5.19) and systematic comparison of the calculated thickness with WDXRF<fnref n="42" />, both at the same position on the sample in order to get rid of (limited) process non-uniformity over the wafer. The very good agreement between the two techniques (Fig. 5.20) allowed using p-ARXPS to evidence the influence of substrate management on the ALD deposition and, for instance, to highlight the nucleation delay in the case of HF-prepared surface (Fig. 5.21).

<figure><img src="image_70.png" /><figcaption>**Fig. 5.18** : comparison between the Al dose measured by LPD-ICPMS and evaluated by WDXRF, using fundamental parameters and calibration against Al pure metal target [N-5.16]</figcaption></figure>

<figure><img src="image_71.png" /><figcaption>**Fig. 5.19** : Non-destructive depth profile of the ultrathin $Al_2O_3$ sample with carbon contamination and native $SiO_2$ layer. The p-ARXPS simulation values (dotted line) correspond well to the experimental values of the intensity ratio (symbols) [N-5.16].</figcaption></figure>

<footnote n="41">⁴¹ S. Tougaard, *Universality classes of inelastic electron scattering cross-sections*, Surf. Interface Anal., 25 (1997), pp. 137-154, https://doi.org/10.1002/(SICI)1096-9918(199703)25:3<137::AID-SIA230>3.0.CO;2-L</footnote>

<footnote n="42">⁴² The layer thickness was determined based on assumptions on the material stoichiometry ($Al_2O_3$) and mass density (3.9 g/cc).</footnote>
<figure><img src="image_72.png" /><figcaption>**Fig. 5.20** : Al₂O₃ thickness as a function of the number of ALD cycles for chemical SiO₂ and HF-last sample preparation as determined by p-ARXPS and WDXRF [N-5.16].</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>**Fig. 5.21** : p-ARXPS thickness determinations as a function of ALD cycle for an ultrathin Al₂O₃ sample with a HF-last surface preparation. Linear growth is seen after approximately 12 cycle [N-5.16]s.</figcaption></figure>

In the case of the (slightly) thicker **sample of the second class**, we evaluated the accuracy of p-ARXPS and XPS-IBA against Al and Hf mass deposition determined by reference-free GIXRF conducted at PTB (Section 5.2). Comparison with layer thickness was based on assumptions on the material stoichiometry (HfO₂, Al₂O₃) and mass density (9.6 and 3.9 g/cc resp.). GIXRF gives a value of 3.14 ± 0.24 ng/mm² for the mass deposition of Al, while the ARXPS calculation yields 2.90 ng/mm². Hf mass deposition is 7.4 ± 0.6 ng/mm² according to GIXRF, and 9.0 ng/mm² by ARXPS. The proximity in these values further supports ARXPS as a quantitative method for depth profiling in high-k ALD samples. The quantitative analysis of XPS-IBA survey spectra using Quases software is a manual process, which requires careful (visual) estimate of the difference between the measured spectrum and the modelled background. So far, we failed to automatize this baseline determination step. We found that the range of acceptable thicknesses in the IBA model was reduced for XPS spectral with limited noise. Consequently, we used Gas Cluster Ion Beams (GCIB) in the XPS tool as gentle in situ surface cleaning step for removing adventitious carbon contamination, which resulted in “IBA-compatible” XPS spectra (Fig. 5.22). Another restriction in the use of XPS-IBA is that the background spectra must be approximately 100 eV long and free of peaks from other elements in order to prevent interference in the background signal. This prevents the use of Al 2p background as Al 2p is too close to Si 2p and Si 2s peak. Then, the depth distribution of oxygen was taken to represent the overall thickness of the stack comprised of HfO₂, Al₂O₃, and SiO₂. The depth distribution of Hf, from Hf 4p₃/₂ IBA, was then taken to indicate the HfO₂ layer, the subtraction of which enabled inferring Al₂O₃ and SiO₂ overall thickness. For such samples, p-ARXPS appears more precise than XPS-IBA (Fig. 5.23). However, as material layers get too thick for p-ARXPS, IBA becomes the more relevant depth profiling technique for depth profiling. This was demonstrated for the third class of samples.
<figure><img src="image_74.png" /><figcaption>**Fig. 5.22** : QUASES-Analyze IBA for the ALD bilayer stack: HfO₂ (1.5 nm) buried under Al₂O₃ (2 nm) before and after GCIB treatment. The black line is the raw measured spectrum, the red line is the calculated inelastic background, and the blue line is the spectrum corrected for inelastic losses by subtracting the red line.</figcaption></figure>

<figure><img src="image_75.png" /><figcaption>**Fig. 5.23.** Comparison of thickness determinations by IBA, p-ARXPS, and GIXRF. IBA distributions are shown for before and after a GCIB surface treatment in order to remove contamination.</figcaption></figure>

The third class of samples was too thick for p-ARXPS or XPS-IBA, but was appropriate for HAXPES-IBA, which was assessed against XRR for the whole sample set. HAXPES spectra with Cr-Kα source contained deeper Si 1s, Hf 3d, and Al 1s core levels, which are well suited for analysis because of no peak overlap, unlike the XPS case. These transitions were necessary for a complete depth profiling of the samples incorporating each element present in the material. An example of HAXPES-IBA analysis of Al₂O₃ overlayer sample using Al 1s and Hf 3d is shown in Fig. 5.24. We found HAXPES-IBA very accurate (within few tenths of nm) for the thickness determination in Al₂O₃ overlayer samples. The accuracy was slightly degraded for HfO₂ overlayer samples. This is due in part to the weak signal of Al 1s as it travels through the dense HfO₂ layer, but also because of the especially strong Hf 3d₅/₂ signal, which follows just 100 eV behind. The thickness of Al 1s was therefore determined by the relative end depth of Hf 3d₅/₂ and start depth of Si 1s. Sensitivity of the technique was lower in the HfO₂ overlayer series due to the density of HfO₂ and its contribution to the reduced inelastic mean free path of the buried species. To sum up, HAXPES-IBA with Cr-Kα source was able to probe dielectric layer thicknesses in the 10–25 nm range and < 3 nm-thick buried layers with resulting thickness values in excellent agreement with XRR for both the surface and buried layers. The thickness determination is accurate with an uncertainty below 6% for the surface layer with an expected increased uncertainty in the buried layer.

One of the key advantages of XPS when compared to XRR-GIXRF for instance lies in the spot size, which is compatible with non-destructive depth-profile in small measurement box (100 µm down to 50 µm) on product wafers.
<figure><img src="image_76.png" /><figcaption>**Fig. 5.24.** QUASES-Analyze IBA for sample with HfO₂ (2.4 nm) buried under Al₂O₃ (9.9 nm). The elemental distributions for the Al 1s and Hf 3d peaks support anticipated thickness of the sample.</figcaption></figure>
## 5.4 Plasma profiling time-of-flight mass spectrometry

In 2015, I worked closely with CEA-Leti material deposition lab who highlighted the need for fast elemental depth-profiling to support their development. In the cleanroom XPS-based profiling was limited to parallel-angle XPS solution with probing depth ~ 5 nm. At that time, we did not have access to inline combined XRR-GIXRF setup. Then, we looked for a solution that would complemented destructive lab analysis.

A short demo of Plasma profiling time of flight mass spectrometry (PP-TOFMS) tool produced by Horiba Scientific suggested that this technique could meet our needs. I first failed in the application of an “ANR chercheur étranger” around this technique (2015). Then, I motivated a collaboration with Horiba, where the instrument was installed in CEA-Leti as part of a free loan contract, whereas CEA-Leti hired Yann Mazel for a 3-year non-permanent position fully dedicated to the collaborative program. At the end, we had a 5-year collaboration with Horiba around this technique, but most of the scientific results were obtained during the first three years, when Yann was fully dedicated to the program. The overall output of the collaboration include 15 peer-review papers (including the cover of Surface and Interface Analysis SIA in 2020), 14 oral presentations at conferences and a commonly-prepared webinar dedicated to PP-TOFMS in 2017.

<figure><img src="image_77.png" /><figcaption>**Fig. 5.25:** Schema of Plasma profiling time of flight spectrometer (PP-TOFMS) instrument illustrating its three different parts: the plasma source, the interface and the Time of flight mass spectrometer [A. G. Carvalho's master report].</figcaption></figure>

Few words about the main features of PP-TOFMS (Fig 5.25). PP-TOFMS is a sputtering based depth profiling technique [N-5.17]. Sputtering is ensured by a glow discharge (GD) plasma of ultra-pure Argon. The plasma is generated between the sample surface and a cylindrical anode usually made of copper. Ar ions created in the plasma bombard the sample surface, the sputtered species are ionized and the ionized species are detected by an orthogonal time-of-flight mass spectrometer. The pulsed RF excitation allows analysis of conductive and non-conductive materials as well as semiconductors. The sample is used to close the plasma chamber and therefore does not need to be transferred into a UHV chamber. The lateral resolution of the technique is defined by the diameter of the anode used and is typically of a few millimeters, prohibiting imagery. Such plasma works with a few mbar and the energy of the ions in the plasma is 50 eV. The low energy minimizes the surface damage (versus traditional SIMS) and high current ensures high sputtering rate, up to few tens of nanometer per second. Unlike SIMS where the analytical ion signals are from ions escaping the sample surface, PP-TOFMS signals are generated from sputtered neutrals diffusing out and ionized in the GD plasma. This decoupling between the sputtering and the ionization processes makes PP-TOFMS much less matrix dependent