Top-down method to introduce ultra-high elastic strain

Abstract

Abstract

Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators

“…To overcome these limitations, several techniques for stress engineering have been pursued, 19 including bending of the chip, 20 phononic crystal patterning, 21 loss dilution, 21 clamp widening, 22 hierarchical structuring, 23 clamp tapering, 24 or altering the resonator design. 25,26 Here, we present a novel method to geometrically tune the stress of nanomechanical structures, 27 adding a new degree of freedom for e.g. applications demanding resonators with controllable resonance frequency.…”

“…Finally, different deposition parameters may result in different amounts of defects, making a systematic study of the stress dependence of the dissipation challenging. To overcome these limitations, several techniques for stress engineering have been pursued, including bending of the chip, phononic crystal patterning, loss dilution, clamp widening, hierarchical structuring, clamp tapering, or altering the resonator design. , …”

Generalized dissipation dilution in strained mechanical resonators

“…Using this theory we show how a non-uniform width can be used to enhance Q with three strategies: mode localization with phononic crystals [18], both alone and in combination with adiabatic tapering [19] and "thin clamping", introduced here. We show that in a number of cases engineering dissipation dilution is related to geometric strain engineering [22,23]. We also derive the ultimate limit of dissipation dilution set by the material yield strain.…”

“…Here s = x/l is the scaled coordinate along the beam, u n (s) is the mode shape, v(s) = w(s)/w avg is the beam width variation normalized to its average width and quantities with subscript "cl" are computed near the clamps (see SI). Dissipation dilution of a non-uniform beam can be discussed entirely in terms of the reduction of the α n and β n coefficients by varying the beam shape w(x); however, some results are more intuitively interpreted from the prospective of geometric strain engineering [19,22,23], a technique that exploits relaxation of a suspended film to locally enhance the strain. Formally, the treatment in terms of the transverse beam shape, w(x), or the static strain distribution along the beam, (x), is equivalent as these quantities are uniquely related as (see SI for details) (x)/ avg = w avg /w(x), (18) through the condition that the tension force must be constant along the beam.…”