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<p>Greetings from new science-loving friends and welcome to my new installment of materials characterization, where I share my knowledge and experiences in the area of materials physics, especially semiconductor compounds.</p>

<p>This would be publication number 8 concerning the electrical characterization of materials. I have decided to divide it into several sections due to the extensive content, since in order to study the electrical properties of a semiconductor material different experimental techniques are needed, some with which you feel familiar, especially chemists, physicists and engineers and others that perhaps had never been mentioned that are generally novel techniques which are based on old techniques already known. The ideal is to perfect each experimental method in order to obtain viable results in the measurements.</p>

<center> <img src="https://cdn.steemitimages.com/DQmZxM37M3FvVftSsVEcz8nqtPC1DbC1jx33n5mFkqnWjCS/image.png"></center>

<p>Before starting this eighth installment I recommend you to review my previous publications.</p>

<p>Here I will leave you the links:</p>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1557107600">Part 1</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/material-characteriz-1557793862">Part 2</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1564358361">Part 3</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1570158372">Part 4</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1571241375">Part 5</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1573947271">Part 6</a>

<a href="https://www.steemstem.io/#!/@carloserp-2000/methods-of-character-1575069665">Part 7</a>

<p>In this installment I will continue with the development of Van der Pauw's technique explaining its experimental configuration, following by the analytical method to calculate the electrical resistivity in a semiconductor plate and some important tips to be able to obtain reliable measurements.</p>

<p>Let's remember that currently different techniques to calculate one of the properties in a semiconductor, such as "electrical resistivity", all have basically the same purpose, which is to find mobility, the concentration of charge carriers of a material, where we involve different terms such as electrical conductivity, hall coefficient, energy gap, and so on.</p>

<p>That is why this tool is fundamental for the creation of various optoelectronic devices and other technological applications, so it is important to study the physical properties of these materials and for this purpose different methods of experimental analysis are needed to give us results of its possible application in the technological field.</p>

<blockquote>Van der Pauw's technique is another used to find the electrical resistivity, mobility and concentration of charge carriers in a semiconductor material... It bears the name of its creator, and unlike the techniques explained above, "Van der Pauw" uses the surface resistance of the sample to determine the values of mobility and concentration in the material, remembering that in the first we use the hall coefficient and conductivity at room temperature.</blockquote>

<p>The main advantage of this technique is that it is possible to obtain mobility measurements of load carriers at different temperatures, while in the previous one we can only do it at room temperature.</p>

<p>Now, showing both diagrams of my previous publication and using the same configuration we can define the calculation of the measurement of electrical resistivity using the Van der Pauw technique.</p>

<center> <img src="https://cdn.steemitimages.com/DQmTsyzbFzTeXDwuDHStri8Z16cy5dwa7VrFM69DuKgMzpn/image.png"><br><sup><b>Figure 1: Experimental configuration of the Van der Pauw technique for the determination of electrical resistivity in a semiconductor material</b></sup></center>

<center> <img src="https://cdn.steemitimages.com/DQmYk6xmWa8rVRNQkCAtvzx95SG8bArTLCp5honzxZmPCyM/image.png"><br><sup><b>Figure 2: Real assembly of a semicondcutora sample</b></sup></center>

<p>After preparing correctly the sample of the semiconductor material on the bakelite we proceed to connect the ohmic cables in the sample, these cables are preferably of very fine copper wire which adheres to the sample by means of a very small spot of tin solder. Label 1, 2, 3, and 4 counterclockwise as shown in Figure 1.</p>

<p><i>It is recommended to use the same quantity of copper wire for each contact in order to minimize the error of any thermolectric effect.</i></p>

<p>We must define certain very important parameters to perform the measurement process which are as follows:</p>

<p><b><i>ρ</i></b> = electrical resistivity (at Ω-cm).</p>

<p><b><i>d</i></b> = sample thickness (cm).</p>

<p><b><i>I<sub>12</sub></i></b> = positive direct current enters into contact 1 and exits through contact 2. <i>I<sub>23</sub></i>, <i>I<sub>34</sub></i>, <i>I<sub>41</sub></i>, <i>I<sub>21</sub></i>, <i>I<sub>14</sub></i>, <i>I<sub>43</sub></i>, <i>I<sub>32</sub></i>, <i>I<sub>23</sub></i> (in amperes, A).</p>

<p><b><i>V<sub>12</sub></i></b> = direct current voltage measured between contacts 1 and 2 <b><i>V<sub>1</sub></i></b> - <b><i>V<sub>2</sub></i></b>, without the applied magnetic field (B = 0). Equally for <b><i>V<sub>23</sub></i></b>, <b><i>V<sub>34</sub></i></b>, <b><i>V<sub>41</sub></i></b>, <b><i>V<sub>21</sub></i></b>, <b><i>V<sub>14</sub></i></b>, <b><i>V<sub>43</sub></i></b> and <b><i>V<sub>32</sub></i></b> (in volts, V).</p>

<div class="pull-right">

<center> <img src="https://cdn.steemitimages.com/DQmdEy2dVo1ePQLgc8oJR9DDjSgDZmNuEbrxKXDuhjdGiUK/image.png"><br><sup><b>Figure 3: Real picture of the linear graph in the ohmic contacts of the sample</b></sup></center>
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<p>Before starting the measurement process, it is always recommended to check the ohmic contacts (current circulating linearly over the entire sample). The data must be verified for internal consistency, for the quality of the ohmic contact, and for the uniformity of the sample.</p>

<p>We prepare the direct current in the sample and have a range around 1mW. Then we measure the resistance in the material between any of the contacts, but these must be opposite, i.e. from contact 1 to 3 or from contact 2 to 4 and that <b><i>I &lt; (200R)-0.5</i></b>.</p>

<p>Then we apply current in <b><i>I<sub>21</sub></i></b> and we measure the voltage in <b><i>V<sub>34</sub></i></b>.</p>. We invert the polarity of the current in the semiconductor sample. <b><i>I<sub>12</sub></i></b> and we measure the voltage in <b><i>V<sub>43</sub></i></b>. The procedure is repeated for the rest.<p></p>

<p>In this step the voltage measurements produce 8 resistance values, which should always be positive and are as follows:</p>

<center> <img src="https://cdn.steemitimages.com/DQmW3fJC6tyHHdeN8X5M8QnaCfRv1ADSbg6EKbThMo3WCbc/image.png"></center>

<center> <img src="https://cdn.steemitimages.com/DQmRGuFiEcsZWrCdfi2FqEvjFrAe3sVuZUnEkZP3HRrJPJY/image.png"></center>

<p><b>Important:</b> When we perform the experimental configuration of the measurement system as shown in the previous image, we must take into account that the voltage meter only takes the positive voltages, therefore it must be set to zero subtly so as not to affect the system due to any sudden movement or external agent. In the same way the quality of the ohmic contacts play a fundamental role in the measurement and of course the uniformity of the sample.</p>

<p>The measures must be consistent and at the moment of reversing their polarity they must comply with the following condition:</p>

<p><b><i>R<sub>21,34</sub></i></b> = <b><i>R<sub>12,43</sub></i></b></p>
<p><b><i>R<sub>43,12</sub></i></b> = <b><i>R<sub>34,21</sub></i></b></p>
<p><b><i>R<sub>32,41</sub></i></b> = <b><i>R<sub>23,14</sub></i></b></p>
<p><b><i>R<sub>14,23</sub></i></b> = <b><i>R<sub>41,32</sub></i></b></p>

<p>Finally to perform the electrical resistivity calculations and determine the surface resistance which I explained in my previous publication the following is done:</p>

<center> <img src="https://cdn.steemitimages.com/DQmYsNVEGh6fwRjCxubWkT9wfzZccWnpXuMcePonwrJvLuD/image.png"></center>

<p>Subsequently by means of the Van der Pauw equation described in my previous publication we solve:</p>

<center> <img src="https://cdn.steemitimages.com/DQmUzYv7D5uBogE1ds1EXKv7exxdRkRkQNEMUwVSZtmejMT/image.png"></center>

<p>If the thickness of the sample is known we can also determine the resistivity from:</p>

<center> <img src="https://cdn.steemitimages.com/DQmYyZWjHRHyYRvcqLNQwuMrup9ycQsGMxN18Cp9kzDvQQ1/image.png"></center>

<p><b>Recommendation:</b> In most cases when we practice this technique can present various errors in the measures, generally these errors can be caused to bad contacts, parasitic capacitances and non-uniformity of the sample. It is for that reason that it is necessary to check at every moment the assembly of the system of measurements and to verify the linearity of the current.</p>

<p>There may also be other effects that may distort the measurements which may be: Righi-Leduc effect, Seebeck, Peltier or Ettinghausen-Nernst. Also bad preparation of the sample, impurities, corrosion, bad positioning of the cables.</p>

<p>The images are property of @carloserp-2000 and are for free use. For any extra information or questions you can leave your comment.</p>

<p>See you in the next installment where I will explain more about the electrical properties in a semiconductor.</p>

<h3> Sources </h3>

<p></p><li><sup>L. J. van der Pauw, "A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitrary Shapes," Philips Res. Repts. 13, 1-9 (1958).</sup></li><p></p>

<p></p><li><sup>L. J. van der Pauw, "A Method of Measuring the Resistivity and Hall Coefficient on Lamellae of Arbitrary Shape," Philips Tech. Rev. 20, 220-224 (1958).</sup></li><p></p>

<p></p><li><sup>E.H. Hall: "On a New Action of the Magnet on Electric Currents". American Journal of Mathematics vol 2, 1879, p.287-292.</sup></li><p></p>

<p></p><li><sup>Marín, G.(1996). Síntesis y crecimiento del compuesto CuInTe2 por el método de Bridgman horizontal con tres zonas y sus características. Trabajo para optar al título de licenciado en física. Maracaibo. Universidad del Zulia</sup></li><p></p>

<p></p><li><sup>NIST National Institute of Standards and technology. Hall Effect Measurements.</sup></li><p></p>

<p></p><li><sup><a href="http://www.four-point-probes.com/ecopia.html">Van der Pauw Ecopia HMS-3000 Hall Measurement System.</a></sup></li><p></p>

<p></p><li><sup><a href="http://www.phywe.com">PHYWE series of publications. Hall effect in n-germanium, Hall effect in p-germanium.</a></sup></li><p></p>

<p></p><li><sup><a href="https://vlab.amrita.edu/?sub=1&amp;brch=282&amp;sim=879&amp;cnt=1">Hall effect experiment:- Determination of charge carrier density</a></sup></li><p></p>

<p></p><li><sup><a href="https://www.academia.edu/20228485/Measurement_of_Semiconductor_Parameters">Measurement of Semiconductor Parameters. Muhammad EL-SABA</a></sup></li><p></p>

<p></p><li><sup><a href="https://www.iiserkol.ac.in/~ph324/StudyMaterials/ResistivityTdep.pdf">Temperature Dependence of Semiconductor Conductivity. (Originally contributed by Professor E.D.H. Green)</a></sup></li><p></p>

<p></p><li><sup><a href="https://en.wikipedia.org/wiki/Hall_effect">Hall effect</a></sup></li><p></p>

<p></p><li><sup><a href="https://www.sciencedirect.com/topics/chemistry/hall-effect">Hall Effect</a></sup></li><p></p>

<p></p><li><sup><a href="https://link.springer.com/chapter/10.1007/978-3-319-48933-9_2">Electrical Conduction in Metals and Semiconductors</a></sup></li><p></p>

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