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(a) Sketch of a coplanar waveguide structure. Here, G denotes the gap between the ground plane and the centerstrip, W the width of the center strip, D the depth of the trench, and T the thickness of the TiN film. The inset shows the top corner of the CPW center strip and illustrates the position of substrate-vacuum (S-V), conductor-vacuum (C-V), and conductor-substrate (C-S) interfaces in the cross-section of the CPW. (b) Extracted internal loss as a function of internal voltage of the resonators described in Table II. The different markers represent the different resonators: () F1, () F2,() Cl1, () Cl2, () Cl3, and () IM. The lines are fits of Eq. (1) by the use of the calculated electric field in region S-V (solid) and region C-S (dashed).
SEM images of different etched samples. (a) Trenched F-etch F1. (b) Trenched Cl-etch Cl1. (c) Non trenched Cl-etch Cl3. (d) Trenched ion milled IM. From the cross sections, it is clear that the F-etched resonator has an undercut profile that is not observed for the Cl-etched resonators. It can also be seen that the ion-milled profile has re-deposited material on the top and sides of the TiN film.
Calculated filling factors of the substrate-vacuum (S-V), conductor-vacuum (C-V), and conductor-substrate (C-S) interfaces for resonators F1, F2, Cl1, Cl2, and Cl3. Only a minor part of the total electric energy is stored at the interfaces with ∼90% of the total electric energy is stored in the bulk of the Si substrate and only ∼10% is stored in the vacuum. The difference in measured loss between the two Cl-etched resonator Cl1 and Cl3 is well explained by the difference in filling factors of the S-V and C-S interfaces.
Parameters for the different etches used in the experiment. An 8 in. ion gun was used for the ion mill.
Extracted parameters for the different resonators (see Fig. 1(a)). The parameters of the different etches are given in Table I. The geometric inductance L g and kinetic inductance L k are calculated through the method of Sheen et al. 21 The best fit is obtained assuming a penetration depth of 245 nm, close to that previously obtained for TiN films.13 The capacitance is obtained from FEM calculations.
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