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<h1>Activity 8: Inequivalent emitters and the XPD of a substrate</h1>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-aluminium-nitride-aln-polarity">The Aluminium Nitride (AlN) polarity</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="activity-8-inequivalent-emitters-and-the-xpd-of-a-substrate">
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<h1>Activity 8: Inequivalent emitters and the XPD of a substrate<a class="headerlink" href="#activity-8-inequivalent-emitters-and-the-xpd-of-a-substrate" title="Link to this heading">#</a></h1>
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<p>XPD can be used to study the adsorption of atoms or molecules on surfaces (<a class="reference internal" href="Activity03_light.html#ssc"><span class="std std-ref">Activity 3</span></a>), or atomic substitutions on surfaces (<a class="reference internal" href="Activity02_light.html#exp-setup"><span class="std std-ref">Activity 2</span></a>). In this case, modeling is relatively straightforward, since only one emitter atom is involved.</p>
|
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<p>We have seen from previous examples that, for kinetic energies <span class="math notranslate nohighlight">\(\gtrsim\)</span> 500 eV, the use of Rehr-Albers series expansion and scattering path filtering give access to the intensity of deeper emitter atoms (<a class="reference internal" href="Activity07_light.html#path-filtering"><span class="std std-ref">Activity 7</span></a>).
|
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This is the key to computing the total photodiffraction signal of a <em>substrate</em>. As emitted photoelectrons originate from highly localized core levels around the atoms, the total signal corresponds to the (incoherent) sum of the intensities of all inequivalent emitters in the probed volume.</p>
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<p>Let’s take a look at how this is done on the following example.</p>
|
||
<section id="the-aluminium-nitride-aln-polarity">
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||
<h2>The Aluminium Nitride (AlN) polarity<a class="headerlink" href="#the-aluminium-nitride-aln-polarity" title="Link to this heading">#</a></h2>
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<p>In this example, we will compute polar diagrams of an aluminum nitride substrate.</p>
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||
<p>In a work published in 1999, Lebedev <em>et al.</em> demonstrated that Photoelectron diffraction can be used as a non invasive tool to unambiguously state the polarity of an AlN surface. Aluminium nitride cristallizes in an hexagonal cell and the authors experimentally showed that the polarity of the surface can be controlled by the annealing temperature during the growth. Both polarities are sketched in the <a class="reference internal" href="#aln-fig1"><span class="std std-ref">figure</span></a> below.</p>
|
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<div class="admonition seealso" id="aln-paper">
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<p class="admonition-title">See also</p>
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<p>based on this paper from V. Lebedev <em>et al.</em>
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||
<a class="reference external" href="https://doi.org/10.1016/S0022-0248(99)00375-9">J. Cryst. Growth. <strong>207(4)</strong> p266-72 (1999)</a></p>
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</div>
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<figure class="align-default" id="aln-fig1">
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<a class="reference internal image-reference" href="light/AlN-fig1.jpg"><img alt="AlN crystal direction" class="align-center" src="light/AlN-fig1.jpg" style="width: 600px;" />
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</a>
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<figcaption>
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<p><span class="caption-text">AlN hexagonal lattice. Left) N polarity with nitrogen terminated surface and AlN<sub>4</sub> tetrahedrons pointing downward. Right) Al polarity with aluminium terminated surface and AlN<sub>4</sub> tetrahedrons pointing upward</span><a class="headerlink" href="#aln-fig1" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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<p>The AlN(0001) and (00.-1) faces share the same crystallograpphic symmetry and the Al and N atoms have the same geometrical surrounding differing only in the exchange of Al and N atoms (<code class="xref std std-numref docutils literal notranslate"><span class="pre">Fig.</span> <span class="pre">%s</span></code>).</p>
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<p>It is thus expected that Al(2p) and N(1s) XPD patterns exhibit almost the same features with only small differences due to the contrast between Al and N scattering amplitudes.</p>
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||
<figure class="align-default" id="aln-fig2">
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<a class="reference internal image-reference" href="light/AlN-fig2.jpg"><img alt="AlN crystal direction" class="align-center" src="light/AlN-fig2.jpg" style="width: 600px;" />
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</a>
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<figcaption>
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||
<p><span class="caption-text">Side views of N- or Al- terminated surfaces showing nearest neighbours main polar crystallographic directions. The inset shows the experimental Al(2p)/N(1s) ratio versus polar angle for both AlN polarities (taken from <a class="reference internal" href="#aln-paper">Lebedev <em>et al.</em></a>).</span><a class="headerlink" href="#aln-fig2" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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<p>The strongest differences in photoemission intensities suitable for a quick and unambiguous determination of polarity were found in the (10-10) azimuthal plane at <strong>32°</strong> and <strong>59°</strong> (polar scans in the inset of <code class="xref std std-numref docutils literal notranslate"><span class="pre">Fig.</span> <span class="pre">%s</span></code>).</p>
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<p>These are the directions of short neighbor distances between the atoms of the same element (32°) and between Al and N atoms (58.5°), respectively.</p>
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<p>Using the crystal view in <code class="xref std std-numref docutils literal notranslate"><span class="pre">Fig.</span> <span class="pre">%s</span></code> and assuming that we want to compute Al(2p) and N(1s) intensities for emitters located in 3 different planes to get a <em>substrate</em> signal. How many clusters do we need to build ?</p>
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<p>Download <a class="reference internal" href="#AlN.py"><span class="xref myst">this script</span></a> and fill in the lines indicated by the comments “FILL HERE”. Run the calculation and check that you are reproducing polar scan of <code class="xref std std-numref docutils literal notranslate"><span class="pre">Fig.</span> <span class="pre">%s</span></code>.</p>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-aluminium-nitride-aln-polarity">The Aluminium Nitride (AlN) polarity</a></li>
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