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JYX - A software for simulating dispersive properties of multilayered phononic crystal membranes
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Tässä tutkielmassa kehitetty uudenlainen Kalvo-ohjelmisto simuloi monikerroksisten sylinterireikähilaisten fononikidekalvojen dispersioita äärelliselementtimenetelmää (FEM) käyttäen. Havainnollistavan systemaattisen fononikidetutkimuksen simulaatioissa käytettiin neljää erilaista laboratoriossa usein käytettyä materiaalia: piinitridiä (Si3N4), alumiinioksidia (Al2O3), polystyreeniä (PS) ja lyijyä (Pb). Vastaavan laajuista systemaattista tutkimusta ei ole aiemmin kyetty tekemään. Aiemmista simulaatioista tunnetaan, että sylinterireikäisellä Si3N4-fononikiteellä, jonka täyttöaste F = 0.7, hilavakio a = 1000 nm ja kalvonpaksuus hSi3N4 = 400 nm, on spektriaukko, jonka suhteellinen koko w/M ≈ 0.202. Osoittautui, että tätä spektriaukkoa on mahdollista laajentaa lisäämällä kalvoon kerros toista materiaalia. Ohjelmistoa käyttäen löydettiin uusi rakenne, jolla hilan spektriaukon suh- teelliseksi kooksi saatiin simuloitua ≈0.234 (kun F = 0.7) käyttäen Si3N4–Al2O3-kaksikerroskalvoa, jonka hSi3N4 = 340 nm ja hAl2O3 = 130 nm. Tällä materiaalikonfiguraatiolla on spektriaukko vain kun F > 0.58. Tämä spektriaukko laajenee nopeasti täyttöastetta kasvatettaessa, kunnes F > 0.68, minkä jälkeen aukon laajanemistahti hidastuu merkittävästi. Si3N4-kalvon spektriaukkoa ei saatu laajennet- tua polystyreeni- tai lyijykerroksilla. Fononikiteen dispersiorelaatiot muuttuvat, jos toinen kaksikerroskalvon materiaaleista jaetaan kahtia ympäröimään toista materiaalia, eritoten jos jaettava materiaali on jäykempi kahdesta. Esimerkiksi Si3N4–PS- ja PS–Si3N4–PS-kalvoilla on spektriaukko, kun hPS:hSi3N4 = 1:10 ja F = 0.7, mutta vastaavalla Si3N4–PS–Si3N4-kalvolla ei. Ohjelmisto osoittautui hyödylliseksi monikerroksisten fononikiteiden dispersiorelaatioiden systemaattiseen tutkimukseen. ...
This thesis introduces Kalvo, a new type of software developed for simulating the dispersions of multilayered phononic crystal membranes with a cylindrical hole lattice, using the finite element method (FEM). The simulations in a demonstrative systematic study used four different materials commonly used in laboratory: silicon nitride (Si3N4), aluminum oxide (Al2O3), polystyrene (PS) and lead (PS). A systematic study of this scale has not been possible before. It is known from prior simulations that a Si3N4 phononic crystal with cylindrical hole lattice, filling factor F = 0.7, lattice constant a = 1000 nm and Si3N4 membrane thickness hSi3N4 = 400 nm, has a relative band gap w/M ≈ 0.202. Using the software, it was found out that this band gap could be increased to ≈0.234 (for F = 0.7), by using a Si3N4–Al2O3 dual layer membrane with hSi3N4 = 340 nm and hAl2O3 = 130 nm. For this configuration of materials, the band gap exists only when F > 0.58. This band gap widens rapidly as filling factor is increased, until F > 0.68, after which the rate of increasing decreases significantly. The Si3N4 membrane’s band gap could not be widened with layers of polystyrene or lead. The band structure of a phononic crystal is changed if one of the materials in a dual layer membrane is distributed into two layers surrounding the other material, especially if the stiffer of the two materials is distributed. For instance, a band gap exists for a Si3N4–PS and PS–Si3N4–PS membranes with hPS to hSi3N4 ratio of 1:10 and F = 0.7, but not for Si3N4–PS–Si3N4. The software proved to be useful for systematically studying the band structures of multilayered phononic crystals. ...
FEM phononic crystal multilayer silicon nitride Kalvo hajonta fononit tietokoneohjelmat simulointi kiteet kalvot (biologia) rakenne (ominaisuudet) simulaattorit dispersion (mathematics and statistics) phonons computer programmes simulation crystals membranes structure (properties) simulators
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Pro gradu -tutkielmat [24074]
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