Optical imaging and image analysis for high aspect ratio NEMS

Abstract

A strategy for optical microscopy of high-aspect-ratio (HAR) nanoelectromechanical systems (NEMS) that combine large feature spacing and large height with subwavelength width is presented. Line images are simulated using a 2D model of incoherent imaging based on modal diffraction theory. Beyond a sufficient depth, it is shown that sub-wavelength features appear as dark lines, while wider features are visible as their edges. The results suggest NEMS and MEMS may be separated from background in images by detection of valleys in brightness. Results are confirmed by imaging of Si NEMS containing 100 nm wide features in a bright-field microscope. Algorithms for separation of NEMS, MEMS and background in microscope images based on valley detection, thresholding and masking are demonstrated.

Dark-field optical fault inspection of ∼10 nm scale room-temperature silicon single-electron transistors

“…Previous work on nanoelectromechanical systems (NEMS) structures has shown that sub-wavelength features can be imaged by non-invasive optical microscopic imaging. The observed line scans can be predicted by applying a rigorous modal diffraction theory [34][35][36][37][38] to transverse electric (TE) white light, extending the work by Hopkins [39], Nyssonen [40,41], Sheridan [42][43][44] and Syms [38,45]. Of particular interest, etched NEMS structures [45] have shown high contrast in dark-field (DF) optical imaging.…”

Improved optical imaging of high aspect ratio nanostructures using dark-field microscopy

“…Models of bright-and dark-field imaging are shown in figures 1(a) and (b), respectively, the first being previously described in [11]. The surface for imaging is modeled as a relief structure of period Λ, consisting of a semi-infinite substrate of relative dielectric constant ε r3 (Layer 3) carrying a set of vertical ribs of width w and depth d formed in a material with ε r =ε r2a surrounded by air (ε r2b ) (Layer 2) and capped by further semi-infinite layer of air (Layer 1; ε r1 =ε r2b ).…”

“…The visibility of widely spaced sub-micron features in an optical microscope [10] suggests an obvious approach. We have previously shown that HAR NEMS are visible in bright field with white light illumination [11]. Nanostructures cannot be properly resolved, but appear as wider dark lines; microstructures appear as dark lines at feature edges.…”

“…In Section 3, we verify the predictions experimentally using silicon NEMS, and show that feature extraction with improved tolerance to substrate variations is obtained in dark field. Conclusions are drawn in Section 4. respectively, the first being previously described in [11]. The surface for imaging is modeled as a relief structure of period , consisting of a semi-infinite substrate of relative dielectric constant r3 (Layer 3) carrying a set of vertical ribs of width w and depth d formed in a material with r = r2a surrounded by air (r2b) (Layer 2) and capped by further semi-infinite layer of air (Layer 1; r1 = r2b).…”

“…Unfortunately, this region also contains the shoulders of nanoscale features. To suppress these regions, we have used a strategy proposed in [11]. The nanoscale pattern is extracted first, and then convolved with a small, uniform, square matrix to broaden any features therein.…”