Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, ItalyAs reported previously, the gap is generated from thebending of the branches #2 and #3. We have investigated thedistribution of the eigenmodes inside the unit cell for thesetwo branches, at the points A and B of the dispersion curvesin Fig. 1c (h=0.6µm, e=0.1µm). The displacement fields ofWe have also investigated the persistence of this gapagainst different combinations of the materials constitutingthe dot and the plate among a set of five materials (tungsten,steel, silicon, aluminum and epoxy). In Fig. 4a, we show thegap by changing the material of the plate when the dots arethe corresponding eigenmodes (k A =k B =(π/a, 0, 0); made of steel. Similarly, Fig. 4b displays the gap for variousf A =0.233GHz and f B =0.1806GHz) have been calculatedusing the Finite Element method and are plotted in Fig. 3.For the point A (Fig. 3a), we clearly observe an oscillation ofthe dot in the y direction associated with a bending of theplate. For the point B (Fig. 3b) we observe an oscillation ofthe dot in the z direction correlated to a strong bending of theplate. In both cases, the displacement fields are distributed inthe dot as well in the plate, in agreement with thedependence of the branches #2 and #3 with both parametersmaterials in the dots and the plate being made of silicon. Onecan notice the persistence of this gap even if the constitutingmaterials are identical. This supports the origin of the gap asbeing related to the geometrical rather than physicalparameters of the structure. On the other hand, the centralfrequency of the gap is very dependent upon the choice ofthe materials and happens at lower frequencies when wecombine a high density material (tungsten) in the cylinderswith a low density material (epoxy) in the plate.e and h. Moreover, the stronger dependence of the branch #3with the thickness of the plate observed in the previous(a) Steel cylinders on various platesection can be related to a higher deformation in the platethan in the dot.0.50.4Mode 2 (A)f A = 0.233 GHzFrequency (GHz)0.30.20.10.0Mode 3 (B)f B = 0.1806 GHzyz(b)0.50.4WSteelSiAlEpoxyVarious cylinders on Si platefrequency (GHz)0.30.2Fig.3. Displacement field of the eigenmode at the boundary of the Brillouinzone (X) inside one unit cell for e=0.1 µm, h=0.6 µm at the eigenfrequencies(a) 0.233.0 GHz and (b) 0.180.6 GHz (points A and B in Fig. 1.c). In thesefigures, the dashed lines correspond to the rest position of the structurexz0.10.0WSteelSiAlEpoxyFig. 4. Evolution of the lower gap for various combinations of the materialsconstituting the dots and the plate (a) Various cylinders on a silicon plate.(b) Steel cylinders on various plates.©EDA Publishing/THERMINIC 2008 165ISBN: 978-2-35500-008-9