# Characterizing Critical Buried Interfaces by Inelastic Background Analysis (IBA) using Lab-Scale Hard X-ray Spectroscopy

T. R. Bure<fnref n="1" />, C. Robert-Goumet<fnref n="1" />, O. Renault<fnref n="2" />, E. Nolot<fnref n="2" />, T. Conard<fnref n="3" />, N. Pauly<fnref n="4" />

**ABSTRACT:** devices are shrinking while increasing in complexity. The buried interfaces in electronic materials are critical to their functionality but notoriously difficult to characterize. This work aims to expand an existing approach to non-destructive depth profiling of deeply buried interfaces by developing a generic and semi-automated method analyzing the inelastic background of XPS spectra

## Objectives

1. Apply IBA to lab-based HAXPES spectra for the characterization of interfaces and buried layers

2. Develop a generalized, semi-automatic method for evaluating results and fitting uncertainty in the IBA solution

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

**Final Objective:**

Bring offline HAXPES analysis to inline metrology for semiconductor technologies

2000: « The interface is the device »
Herbert Kroemer, Nobel Lecture

## XPS

* Non-destructive core-level analysis

* Minimal sample preparation

* Limited probing depth

## Inelastic Background Analysis (IBA)

* QUASES software package

* 10 nm probing depth with traditional XPS

* no additional instrumentation needed

* Limitations: peak interference in background

$$ \text{HAXPES} + \text{IBA} $$

* Up to 150 nm probing depth when combined with background analysis

* Expand collection of available peaks

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## Objective 1(a) Al₂O₃ / HfO₂

3 bilayer samples of High-k metal oxides with $d(HfO2)=2.5$ nm

* ☐ Compare Cr Kα and Ga Kα HAXPES results

<figure><img src="image_4.png" /></figure>

<table><thead><tr><th>Surface layers</th><th>Name</th><th>Surface Layer Thickness (nm)</th></tr></thead><tbody><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>A1</td><td>9.9</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>A2</td><td>14.8</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>A3</td><td>24.4</td></tr></tbody></table>

* Cr Kα $\hbar v = 5414.72$ eV
IMFP Hf3d = 6.6 - 6.7 nm

* Ga Kα $\hbar v = 9251.74$ eV
IMFP Hf3d = 11.8 - 12.2 nm

### Comparison of Interface Positions

<figure><img src="image_5.png" /></figure>

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<figure><img src="image_7.png" /></figure>

* Hf3d is not in accordance with Al1s interface position and Ga Kα HAXPES energy did not improve IBA model

* Increasing source energy increases inelastic losses in the kinetic energy range further from the peak (Hf3d), which is interrupted by other peaks (Si1s) in these spectra

* Must carefully choose source energies for individual sample (peak overlap and buried layer thickness)

## Objective 1(b) Al₂O₃ / GaN

5 bilayer samples representative of HEMT device

* ☐ Apply QUASES-Generate reference spectra

<figure><img src="image_8.png" /></figure>

3 - 30 nm

* Start Depth of buried Ga2p too close to surface

* Creates broad interface with Al₂O₃

<figure><img src="image_9.png" /></figure>

* Start Depth of buried Ga2p is in accordance with anticipated interface with Al₂O₃ obtained by IBA of Al1s and O1s

* Al1s and O1s were best modeled with QUASES-Analyze and the Universal cross-section

### QUASES-Analyze - no reference

<figure><img src="image_10.png" /></figure>

### QUASES-Generate - GaN bulk reference spectrum

<figure><img src="image_11.png" /></figure>

$$ MSE = \frac{1}{n} \sum_{i=1}^{n} (Y_i - \hat{Y}_i)^2 $$

## Objective 2. Error Calculation for Evaluation of IBA Solution

Calculate the error between a range of points on the x-axis, and look for the lowest error in possible solutions

Problem: The size and location of the background region for comparison changes with:

$Y_i$ = Recorded Spectrum

$\hat{Y}_i$ = Modeled inelastic background

<figure><img src="image_12.png" /></figure>

Photon Energy

<figure><img src="image_13.png" /></figure>

☐ Restrict energy range

Buried depth of layer

<figure><img src="image_14.png" /></figure>

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☐ Restrict possible solution

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* Hf3d is not in agreement with Al1s interface position and Ga Kα HAXPES energy did not improve IBA model

* HAXPES-IBA solutions from visual inspection and error calculation agree

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

* HAXPES-IBA solutions from visual inspection and error calculation agree

* Visual inspection overestimates start depth

More elegant algorithms are needed for a general error calculation but it could be a useful tool for avoiding user bias in IBA

<footnote n="1">¹Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, F-63000 Clermont-Ferrand, France</footnote>

<footnote n="2">²Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France</footnote>

<footnote n="3">³IMEC, Kapeldreef 75, B-3001, Leuven, Belgium</footnote>

<footnote n="4">⁴Université Libre de Bruxelles, Service de Métrologie Nucléaire (CP 165/84), 50 av. F. D. Roosevelt, B-1050 Brussels, Belgium</footnote>

<footnote>[1] S. Tougaard, Practical guide to the use of backgrounds in quantitative XPS, J. Vac. Sci. Technol. A. 39 (2021) 011201.</footnote>

<footnote>[2] 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. Appl. Surf. Sci. 609 (2023) 155317.</footnote>

<footnote>[3] O. Renault, P. Deleuze, J. Courtin, R. T. Bure, N. Gauthier, E. Nolot, C. Robert-Goumet, N. Pauly, E. Martinez, K. Artyushkova. New directions in the analysis of buried interfaces for device technology by hard X-ray photoemission. Faraday Discuss., 236 (2022) 288.</footnote>