Visualizing nanometric structures with sub-millimeter waves

Abstract

The resolution along the propagation direction of far field imagers can be much smaller than the wavelength by exploiting coherent interference phenomena. We demonstrate a height profile precision as low as 31 nm using wavelengths between 0.375 mm and 0.5 mm (corresponding to 0.6 THz–0.8 THz) by evaluating the Fabry-Pérot oscillations within surface-structured samples. We prove the extreme precision by visualizing structures with a height of only 49 nm, corresponding to 1:7500 to 1:10000 vacuum wavelengths, a height difference usually only accessible to near field measurement techniques at this wavelength range. At the same time, the approach can determine thicknesses in the centimeter range, surpassing the dynamic range of any near field measurement system by orders of magnitude. The measurement technique combined with a Hilbert-transform approach yields the (optical) thickness extracted from the relative phase without any extraordinary wavelength stabilization.

Emulating a broadband frequency sweep for Terahertz thin-film imaging

“…3(b) with enhanced clarity, evaluated employing such postprocessing techniques. To test the limits of this zero-padding enhanced thickness resolution technique, we further image two HR-Si samples with silicon nitride of thicknesses of 240 nm (SS240) and 350 nm (SS350) (corresponding to optical thicknesses of 490 and 714 nm [2], respectively) deposited atop using chemical vapour deposition. Zero-padding of order 8000 and 2000 are used, respectively, to reconstruct the images of SS240 and SS350.…”

“…Additional image extraction and enhancement steps are necessary to evaluate these nanometric structures for two reasons. Firstly, the thickness of polished wafer is not uniform throughout and has a surface warping of about 4 − 5 µm [2]. This, along with the overall frequency drift of the lasers, overshadows the Siemens star, which is orders of magnitude thinner.…”

“…erahertz (THz) imaging can be used in a plethora of applications in diverse domains like security, biomedicine, material analysis, etc [1]. Recently, we demonstrated nanometric imaging capabilities with a precision of only 28 nm from a continuous-wave (CW) frequency scan conducted between 0.6 − 0.8 THz [2]. This technique, as well as other conventional thickness measurement algorithms, relies on the Fabry-Pérot oscillations generated in a relatively thick host wafer, attached to these thin structures to be imaged.…”

“…For the homodyne CW system, the homodyne oscillations of the receiver current (𝐼 𝑅𝑥 ) is proportional to the optical path length difference between the received terahertz field and the laser signal at the receiver. It is expressed as [2]…”

Current tuned slotted Y‐branch laser for wafer thickness measurements with THz radiation

“…The reference interpolant is evaluated at the identified sample peak positions and used to calculate the sample transmission. An alternative approach for data analysis uses the Hilbert transform in order to access the amplitude and phase information [11], followed by fitting the Fabry Pérot interference pattern either to the phase or amplitude spectrum. However, this approach requires larger frequency spans with low noise to achieve high fitting accuracy.…”