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<h1>Activity 7: Large clusters and path filtering</h1>
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-number-of-scattering-paths">The number of scattering paths</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#paths-filtering-in-msspec">Paths filtering in MsSpec</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#application-to-a-deep-plane-in-a-si-001-sample">Application to a deep plane in a Si(001) sample</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="activity-7-large-clusters-and-path-filtering">
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<span id="path-filtering"></span><h1>Activity 7: Large clusters and path filtering<a class="headerlink" href="#activity-7-large-clusters-and-path-filtering" title="Link to this heading">#</a></h1>
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<p>So far you have seen that multiple scattering calculations with MsSpec can use two different algorithms: <em>matrix inversion</em> or <em>Rehr Albers series expansion</em>. When matrix inversion becomes impossible because the kinetic energy is too high and the number of atoms is too large, serial expansion is the alternative. This algorithm requires very little memory but it processes the scattering paths sequentially, which can lead to very long calculation times.</p>
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<p>In this activity, we will explore how to configure MsSpec to reduce this calculation time to compute the signal from a deep emitter in Si(001).</p>
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</div>
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<section id="the-number-of-scattering-paths">
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<h2>The number of scattering paths<a class="headerlink" href="#the-number-of-scattering-paths" title="Link to this heading">#</a></h2>
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<p>To fix the idea, we will first evaluate how many scattering paths we need to compute for an emitter in the subsurface (2<sup>nd</sup> plane) or in the bulk (7<sup>th</sup> plane) of a Si(001) cluster.</p>
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<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
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<p>Create a cluster of Si(001) with the emitter in the subsurface, 40 Å diameter with 2 planes (since atoms below the emitter can be ignored at high kinetic energies).</p>
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<ol class="arabic simple">
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<li><p>For an emitter in the subsurface, we can use single scattering (see <a class="reference internal" href="../Activity05/Activity05.html#forward-scattering"><span class="std std-ref">Activity 5: Multiple scattering in the forward scattering regime</span></a>). How many paths would be generated for this calculation ?</p></li>
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<li><p>Same question for an emitter in the 7<sup>th</sup> plane. If we were able to treat each scattering path within only 1 µs. How long would be such calculation ?</p></li>
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</ol>
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<p class="admonition-title">Note</p>
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<p>Remember that</p>
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<ol class="arabic simple">
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<li><p>for an emitter in plane <span class="math notranslate nohighlight">\(p\)</span>, the scattering order has to be at least the number of planes <code class="docutils literal notranslate"><span class="pre">above</span></code> the emitter</p></li>
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<li><p>The number of scattering paths of order <span class="math notranslate nohighlight">\(n\)</span> corresponds to the number of possibilities of arranging up to <span class="math notranslate nohighlight">\(n\)</span> atoms (taking order into account).</p></li>
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<div class="toggle docutils container">
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<p>To get the total number of paths generated by a cluster of <span class="math notranslate nohighlight">\(N\)</span> atoms up to order <span class="math notranslate nohighlight">\(M\)</span>, use the following formula:</p>
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<div class="math notranslate nohighlight" id="equation-eq-nbpaths">
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<span class="eqno">(3)<a class="headerlink" href="#equation-eq-nbpaths" title="Link to this equation">#</a></span>\[\sum_{i=0}^{i=M} (N-1)^i\]</div>
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<figure class="align-default" id="nbpaths-fig">
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<a class="reference internal image-reference" href="../_images/fig1.jpg"><img alt="path filtering" class="align-center" src="../_images/fig1.jpg" style="width: 600px;" />
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</a>
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<figcaption>
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<p><span class="caption-number">Fig. 16 </span><span class="caption-text">The time for computing all scattering path for increasing cluster size and scattering order (up to 6<sup>th</sup> order with 739 atoms. (One path is assumed to be calculated within 1 µs)</span><a class="headerlink" href="#nbpaths-fig" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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</div>
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<div class="docutils">
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</div>
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</section>
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<section id="paths-filtering-in-msspec">
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<h2>Paths filtering in MsSpec<a class="headerlink" href="#paths-filtering-in-msspec" title="Link to this heading">#</a></h2>
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<p>As you may expect, not all paths contribute significantly to the total intensity. This is why we can filter out some scattering paths and drastically reduce the computation time. MsSpec offers several filters for this. The 3 most common filters are:</p>
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<ol class="arabic simple">
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<li><p>the <code class="docutils literal notranslate"><span class="pre">forward_scattering</span></code> filter which allows all paths where each scattering angle is within a cone of defined aperture</p></li>
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<li><p>the <code class="docutils literal notranslate"><span class="pre">backward_scattering</span></code> filter which is similar to the previous one but for backscattering direction</p></li>
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<li><p>the <code class="docutils literal notranslate"><span class="pre">distance</span></code> filter which rejects all paths longer than a threshold distance</p></li>
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</ol>
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<p>The following figure illustrate the effect of theses filters on scattering paths</p>
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<figure class="align-default" id="filters-fig">
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<a class="reference internal image-reference" href="../_images/filters.jpg"><img alt="path filtering" class="align-center" src="../_images/filters.jpg" style="width: 600px;" />
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</a>
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<figcaption>
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<p><span class="caption-number">Fig. 17 </span><span class="caption-text">Some examples of scattering paths with <code class="docutils literal notranslate"><span class="pre">forward_scattering</span></code>, <code class="docutils literal notranslate"><span class="pre">backward_scattering</span></code> and <code class="docutils literal notranslate"><span class="pre">distance</span></code> filters selected. The accepted forward angle is 45°, the accepted backscattering angle is 20° and the threshold distance is <span class="math notranslate nohighlight">\(6a_0\)</span> where <span class="math notranslate nohighlight">\(a_0\)</span> is the lattice parameter. Note that the yellow path is rejected but if the <code class="docutils literal notranslate"><span class="pre">off_cone_events</span></code> option is set to a value > 1, then it could have been accepted.</span><a class="headerlink" href="#filters-fig" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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</section>
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<section id="application-to-a-deep-plane-in-a-si-001-sample">
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<h2>Application to a deep plane in a Si(001) sample<a class="headerlink" href="#application-to-a-deep-plane-in-a-si-001-sample" title="Link to this heading">#</a></h2>
|
|
<p>The following script will compute contribution of all the planes of a Si(001) substrate to get the total photoelectron intensity of a Si(2s) polar scan.</p>
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<div class="sd-tab-set docutils">
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<input checked="checked" id="sd-tab-item-1" name="sd-tab-set-1" type="radio">
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<label class="sd-tab-label" for="sd-tab-item-1">
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<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
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<p>The script is almost completed, try to define path filtering options and compare results with and without filtering for emitter in plane n° 3 at scattering order 2.</p>
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<p>Compute the contribution of plane n° 7</p>
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</div>
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</div>
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</section>
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