has been performed at Cornell in which it was found that different mode shapes may experience different support-related clamping losses [58]. What we have found is that the result shown in Figure 4.7 varies widely depending on the details of the membrane window and membrane chip geometry, as well as the way that the chip is attached to the etalon. A large collection of measurements of the sort shown in Figure 4.7 was taken in order to sort out this behavior phenomenologically. We discuss this study in the next section.
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chip clamped chip free standing single trial glue two corners glue three corners glue full chip surface
Figure 4.8: Compilation of mechanical Q measurements for different chip mounting methods.
Here we have fixed the chip and membrane dimension at {dm, wmem} = {50 nm,500µm} and {dchip, wchip} = {0.2 mm,5 mm}, respectively. A variety of methods were investigated, including adhesive bonding and rigid mechanical clamping, denoted as open or closed black circles. Three examples are illustrated with black lines. These consist of adhesively bonding the entire chip surface to a planar surface, bonding three corners, and bonding two corners, respectively. We compare these results to the case for which the membrane rests “free standing” under its own weight on a planar surface, corresponding to red points.
4.7.1 Influence of Chip Mounting
Practically speaking, we must somehow attach the membrane chip to a separate device (e.g., a mir- ror) in order to conduct simple tests or to perform the more complicated optomechanics experiment described in the rest of this dissertation. We at first did not anticipate that this would have a substantial effect on the membrane mechanics. We were wrong. For the measurements described in this chapter, we had to somehow attach the chip to the etalon mirror substrate. Originally the entire setup was oriented vertically rather than horizontally (membrane surface normal to gravity);
for these earlier iterations we used a small dab of glue or carbon sticky tape to secure the membrane chip against the mirror. Those initial trials were performed on large (1 mm), low-stress (∼ 100 MPa) films, which exhibitedQm∼105− −106, as large as we expected from the work done at Yale and Cornell [13, 40]. When we started studying high-stress Norcada films of nominal dimensions {dm, wmem} = {50 nm,500µm}, we discovered a trend whereby the lower order membrane modes, particularly the fundamental, exhibited significantly deterioratedQ-values relative to higher order membrane modes, and that the quality factor of the lower order modes varied widely from chip
to chip. We made various attempts at alleviating the problem. We tried varying the type of glue from soft silicon adhesive (VacSeal, RTV) to hard epoxy (Masterbond EPLTE-LO) to hard-ceramic (Ceramabond 835). We tried bonding the chip rigidly over its entire surface using a flowable UV epoxy (Norland 81). We tried using minuscule dabs of cyanoacrylic adhesive (Krazy Glue) at the corners. We also tried mechanically clamping the chip between two flat metal surfaces. More re- cently, we’ve investigated optical contacting of the chip to the mirror. Without exception, the best results we’ve observed are for a vertically oriented setup in which the chip simply rests under its own gravity (“free-standing”) on the surface of a smooth mirror, or on three points provided by resting on a curved mirror or a washer ring (see left side of Figure 4.3, each geometry gives similar results).
We’ve found the “next best” alternative to be a single dab of adhesive at one corner, then two corners, three corners, and so on. The extent to which theQis affected depends on the size of the chip and the membrane, being more sensitive for thin membranes and chips. In Figure 4.8, we focus on the results of testing a batch of chips with the nominal membrane/substrate dimensions given above for different mounting techniques. These results illustrate the qualitative behavior described in this paragraph.
4.7.2 Influence of Membrane Thickness and Substrate Thickness
We have purchased chips from Norcada with varying film thickness (dm= 30 nm, 50 nm, and 100 nm) and chip thickness (dchip = 200 µm and 500 µm). By fixing the square dimensions of the membrane (wm= 500µm) and chip (wchip= 5 mm), we were able to study the role ofdmanddchip
onQm. An exhaustive set of measurements was carried out by one of our SURF students, Jetson- Leder-Louis, in the summer of 2010. Those results are shown in Figure 4.9. For each measurement, the membrane was allowed to rest on four corners under its own weight atop a piezo-electric spacer, as shown at top left in Figure 4.3. Jetson’s results suggest that the quality factors of low-order membrane modes increase roughly linearly with decreasing membrane thickness, and that for each membrane thickness, theQs obtained for a 500−µm-thick substrate are∼25− −50% better than the results obtained for a 200−µm-thick substrate.
4.7.3 Influence of Membrane Window Size
We have for some time been interested in using smaller membranes with larger fundamental reso- nance frequencies, lower effective masses, and larger thermal displacement amplitudes for our op- tomechanics experiment. To date, we have tested high-stress membranes with square dimensions varying from 1 mm to 200 µm, the latter having been developed at the KNI facility at Caltech by Richard Norte and Kang-Kuen Ni. When all other membrane and chip dimensions are fixed, we have found evidence that suggests that membranes with smaller square dimensions exhibit lowerQ×f
8 6 4 2 0 Qua lit y fa ct or (x 10
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dm = 30 nm dm = 50 nm dm = 100 nm dchip
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= 0.5
= 0.2
d wm
dchip wchip
m
Figure 4.9: Compilation of Q measurements for different membrane and chip thicknesses. Here we have fixed the square chip and membrane dimensions at wm = 500µm and wchip = 5 mm, respectively. The thickness of the film is varied between dm = 30 nm, 50 nm, and 100 nm. The thickness of the chip is varied betweendchip= 200 µm and 500µm. For a given membrane mode, the quality factor scales roughly inversely with membrane thickness. Marginal improvement is also seen for thicker chips. In all cases, the membrane is mounted by resting on a planar surface under its own weight.
products. For free-standing chips, most of our study as been limited towm= 0.25 mm and 0.5 mm membrane windows. We have found that at similar mechanical frequencies, Qm for the modes of thewm= 0.25 mm membrane are roughly half that of the wm = 0.5 mm membrane. A subset of results fordm= 50 nm membranes in which the chip dimensions has been fixed atdchip= 0.2 mm thick andwchip= 5 mm wide is shown in Figure 4.10.