Strain versus Tunable Terahertz Nanogap Width: A Simple Formula and a Trench below

Abstract

A flexible zerogap metallic structure is periodically formed, healing metal cracks on a flexible substrate. Zerogap is continuously tunable from nearly zero to one hundred nanometers by applying compressive strains on the flexible substrate. However, there have been few studies on how the gap width is related to the strain and periodicity, nor the mechanism of tunability itself. Here, based on atomic force microscopy (AFM) measurements, we found that 200 nm-deep nano-trenches are periodically generated on the polymer substrate below the zerogap owing to the strain singularities extant between the first and the second metallic deposition layers. Terahertz and visible transmission properties are consistent with this picture whereby the outer-bending polyethylene terephthalate (PET) substrate controls the gap size linearly with the inverse of the radius of the curvature.

Trench Formation under the Tunable Nanogap: Its Depth Depends on Maximum Strain and Periodicity

“…and confirmed by experiments [23]. Obviously, to stretch the gap region by orders of magnitudes, damage is expected to occur because for bulk PDMS, it is hard to endure more than 200% of the tensile strain.…”

“…This deformation induces substantial stress, which can lead to surface damage and the formation of trenches below the nanogap. The presence of these trenches beneath the nanogap has been reported in several studies [22,23]. It is noteworthy that these trenches are not mere degradation; they serve as an effective method to enhance the device's robustness by relieving the strain singularity.…”

“…When applying tensile strain to stretchable nanogap devices, the width of the nanogap can be expected to change by a few orders of magnitude: for example, assuming the yield strength of PDMS to be 10 MPa, a 100 µm period nanogap can be expanded from the 10 nm of the initial width to 3.6 µm. In fact, the 10 nm initial width is somewhat arbitrary and can be of sub-nanometer range as in zerogap technologies [19,20,23], making the range even larger. Due to the relatively high elastic modulus of gold compared to the substrate, most of the stretching occurred at the PDMS under the nanogap region.…”

“…When the notches are designed on the top film, external strain can initiate crack propagation within the substrate along the path connecting those notches, leading to the formation of sub-micrometer-depth trenches; a 50 µm width film created by this crack development showed no random cracks even at 35% tensile strain [27]. Recently, trenches below zerogaps were observed using AFM scanning and optical diffraction [23].…”