Dissipation in ultrahigh quality factor SiN membrane resonator
S. Chakram, Y. S. Patil, L. Chang, and M. Vengalattore
Physical Review Letters, 112, 127201 (2014)
arXiv:1311.1234 (2013)

Abstract

We study the mechanical properties of stoichiometric SiN resonators through a combination of spectroscopic and interferometric imaging techniques. At room temperature, we demonstrate ultrahigh quality factors of 5 × 10^7 and a f × Q product of 1 × 10^14 Hz. To our knowledge, these correspond to the largest values yet reported for mesoscopic flexural resonators. Through a comprehensive study of the limiting dissipation mechanisms as a function of resonator and substrate geometry, we identify radiation loss through the supporting substrate as the dominant loss process. In addition to pointing the way towards higher quality factors through optimized substrate designs, our work realizes an enabling platform for the observation and control of quantum behavior in a macroscopic mechanical system.

Bibtex

@article{chakramDissipation2014,
title = {Dissipation in Ultrahigh Quality Factor SiN Membrane Resonators}, author = {Chakram, S. and Patil, Y. S. and Chang, L. and Vengalattore, M.},
journal = {Phys. Rev. Lett.},
volume = {112},
issue = {12},
pages = {127201},
numpages = {5},
year = {2014},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.112.127201},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.127201}
}

Figure 1

Peak mechanical quality factors of a L=5 mm, h=100 nm SiN membrane versus frequency (filled square). The solid line corresponds to f×Q = kB/h×300 K. For low mode frequencies (νjk < 300 kHz) , the quality factors can be improved by an order of magnitude (filled diamond) simply by reducing the contact region between the substrate and the in-vacuum mount. The weak frequency dependence of the measured Qs at high frequencies is further reduced for h=30 nm (opened square) (see text for discussion). Inset: characteristic mechanical ringdown of the (5,5) mode at ν55 = 407 kHz.

Figure 2

Peak mechanical quality factors versus film geometry parametrized by the ratio of membrane width (L) to membrane thickness (h). For L/h<10^5, we observe a scaling consistent with Q∼(L/h)^2. A linear scaling is also shown for reference.

Figure 3

Interferometric imaging of the mechanical modes: in situ images of the (a) (1,10) mode and (b) (9,9) mode (color scale for displacement shown). Substrate-induced coupling between proximal asymmetric eigenmodes results in hybridization into more symmetric structures. (c),(d) The modal structures corresponding to ϕ10,6 ± ϕ6,10 hybridized modes. These can be compared to the calculated mode profiles for this hybridization (e),(f).

Figure 4

(a) Predicted quality factors versus mode indices based on asymptotic limits of our anchor loss model (see the Supplemental Material [25] for details), (b) Predicted quality factors versus ϕ ≡ arctan(j/k) for mode indices sqrt(j2+k2) = 12 with (without) substrate-mediated hybridization are shown as filled square (filled circle). Also shown is the asymptotic expression for the quality factors from our model (dashed line). (c) Measured Qs for mode indices indicated by the green arc in (a). (d) The angle-averaged measurements from (c) are compared to our predictions from (b).