Ta2O5 Young's modulus is quoted to be 140 GPa from this paper Martin1993, but that is the value of Ta2O5 deposited on Silicon substrate cf fig5, top plot. The deposition technique is IAD. I'm not sure if it is the same as ion beam sputtering or not. I'm looking into it.
Anyway, the Young's modlus of Ta2O5 can be down to 70 GPa for IAD technique on glass substrate, as the paper says in the conclusion section.
Note that Crooks2006 mentions other papers measure YTa2O5 to be around 100-110 GPa as well. I'm looking into it.
I just talked to Matt and learned that:
- The measurement from the above paper (that everybody quotes) is wrong, they just measured the Young's moduli of the substrate. However, the actual value of Y_Ta2O5 is ~ 140 GPa (use +/- 30% for conventional uncertainty) (Abernathy's from 500 nm sample) and the measurement for Y_SiO2 is ~ 70 GPa ( from 2 um sample)
- The term ion beam sputter (IBS) for our coating is actually IAD.
- Note about coating loss in Penn2003
The measurement from Penn extracts phi1 and phi2 from
phi_c = (Y1 *d1*phi1 + Y2*d2*phi2) / (d1*Y1 + d2*Y2).
Phi_c is calculated from the total phi of the ring down system.
The dissipated energy comes from two part, the substrate and the coating. With the assumption that phi sub is much smaller than phi coat, we can write
phi_total (measured from ring down) = |energy in coating| / |Energy in substrate| * coating loss, and the ratio Ec/Es can be obtained from FEA. For drum head mode it is ~ 1500 (From Penn paper), see the picture, top panel.
This Ec/Es also depends on the Young's moduli, so the calculated phi_c also has Y as a parameter. The calculation I did before takes phi_c from the reported values, so it is not correct.
To get the correct phi_c, the ratio of Ec/Es has to be changed with Y. Crooks PDH thesis has an analytical expression for the drum head mode of a cylindrical substrate. The analytical result is comparable to the FEA result used in Penn2003 within 5%. Note that the young's modulus of the coating is the volume average (Yc tc = y1*t1 +y2*t2) where tc is the total thickness, tx = thickness of material x. See the middle panel in the picture above.
For the next step, instead of using the report value of phi1,phi2 and Y1,Y2 to reconstruct phi_c (Penn2003). I will use the measured phi_tot (for drum mode) then use that as a constraint on Y1, Y2, phi1, and Phi2 instead, see bottom panel in the picture. This should give a correct dependent among these variables.