Analysis of photoelastic properties of monocrystalline silicon
<p>Photoelasticity is considered a useful measurement tool for the non-destructive and contactless determination of mechanical stresses or strains in the production of silicon wafers. It describes a change in the indices of refraction of a material when the material is mechanically loaded. As...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2020-07-01
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| Series: | Journal of Sensors and Sensor Systems |
| Online Access: | https://jsss.copernicus.org/articles/9/209/2020/jsss-9-209-2020.pdf |
| _version_ | 1811340196880318464 |
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| author | M. Stoehr G. Gerlach T. Härtling S. Schoenfelder |
| author_facet | M. Stoehr G. Gerlach T. Härtling S. Schoenfelder |
| author_sort | M. Stoehr |
| collection | DOAJ |
| description | <p>Photoelasticity is considered a useful measurement tool for the non-destructive and contactless determination of mechanical stresses or strains in the production of silicon wafers. It describes a change in the indices of refraction of a material when the material is mechanically loaded. As silicon has a diamond lattice structure, the stress-dependent change in the refractive indices varies with the loading direction. In this work, an anisotropic stress-optic law is derived, and the corresponding stress-optical parameters are measured using a Brazilian disc test. The parameters were determined to be <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>(</mo><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">11</mn></msub><mo>-</mo><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">12</mn></msub><mo>)</mo><mo>=</mo><mn mathvariant="normal">14.4</mn><mo>⋅</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="114pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="73f78fd9f4f70b6d679a30b05037b11b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jsss-9-209-2020-ie00001.svg" width="114pt" height="15pt" src="jsss-9-209-2020-ie00001.png"/></svg:svg></span></span> MPa<span class="inline-formula"><sup>−1</sup></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">44</mn></msub><mo>=</mo><mn mathvariant="normal">9.4</mn><mo>⋅</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="74pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="07fb3e6ffb9fda80dab331b044aa14b1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jsss-9-209-2020-ie00002.svg" width="74pt" height="15pt" src="jsss-9-209-2020-ie00002.png"/></svg:svg></span></span> MPa<span class="inline-formula"><sup>−1</sup></span>. The results of this work are compared to previous works found in the literature, and the deviations are discussed.</p> |
| first_indexed | 2024-04-13T18:38:21Z |
| format | Article |
| id | doaj.art-d2353c07a2764eae93674c5d29d2dc11 |
| institution | Directory Open Access Journal |
| issn | 2194-8771 2194-878X |
| language | English |
| last_indexed | 2024-04-13T18:38:21Z |
| publishDate | 2020-07-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Journal of Sensors and Sensor Systems |
| spelling | doaj.art-d2353c07a2764eae93674c5d29d2dc112022-12-22T02:34:49ZengCopernicus PublicationsJournal of Sensors and Sensor Systems2194-87712194-878X2020-07-01920921710.5194/jsss-9-209-2020Analysis of photoelastic properties of monocrystalline siliconM. Stoehr0G. Gerlach1T. Härtling2S. Schoenfelder3Leipzig University of Applied Sciences, Faculty of Engineering Sciences, Leipzig, GermanyTechnische Universität Dresden, Department of Electrical and Computer Engineering, Institute of Solid State Electronics, Dresden, GermanyTechnische Universität Dresden, Department of Electrical and Computer Engineering, Institute of Solid State Electronics, Dresden, GermanyLeipzig University of Applied Sciences, Faculty of Engineering Sciences, Leipzig, Germany<p>Photoelasticity is considered a useful measurement tool for the non-destructive and contactless determination of mechanical stresses or strains in the production of silicon wafers. It describes a change in the indices of refraction of a material when the material is mechanically loaded. As silicon has a diamond lattice structure, the stress-dependent change in the refractive indices varies with the loading direction. In this work, an anisotropic stress-optic law is derived, and the corresponding stress-optical parameters are measured using a Brazilian disc test. The parameters were determined to be <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>(</mo><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">11</mn></msub><mo>-</mo><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">12</mn></msub><mo>)</mo><mo>=</mo><mn mathvariant="normal">14.4</mn><mo>⋅</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="114pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="73f78fd9f4f70b6d679a30b05037b11b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jsss-9-209-2020-ie00001.svg" width="114pt" height="15pt" src="jsss-9-209-2020-ie00001.png"/></svg:svg></span></span> MPa<span class="inline-formula"><sup>−1</sup></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">π</mi><mn mathvariant="normal">44</mn></msub><mo>=</mo><mn mathvariant="normal">9.4</mn><mo>⋅</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="74pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="07fb3e6ffb9fda80dab331b044aa14b1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jsss-9-209-2020-ie00002.svg" width="74pt" height="15pt" src="jsss-9-209-2020-ie00002.png"/></svg:svg></span></span> MPa<span class="inline-formula"><sup>−1</sup></span>. The results of this work are compared to previous works found in the literature, and the deviations are discussed.</p>https://jsss.copernicus.org/articles/9/209/2020/jsss-9-209-2020.pdf |
| spellingShingle | M. Stoehr G. Gerlach T. Härtling S. Schoenfelder Analysis of photoelastic properties of monocrystalline silicon Journal of Sensors and Sensor Systems |
| title | Analysis of photoelastic properties of monocrystalline silicon |
| title_full | Analysis of photoelastic properties of monocrystalline silicon |
| title_fullStr | Analysis of photoelastic properties of monocrystalline silicon |
| title_full_unstemmed | Analysis of photoelastic properties of monocrystalline silicon |
| title_short | Analysis of photoelastic properties of monocrystalline silicon |
| title_sort | analysis of photoelastic properties of monocrystalline silicon |
| url | https://jsss.copernicus.org/articles/9/209/2020/jsss-9-209-2020.pdf |
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