Optical coherence tomography using broad-bandwidth XUV and soft X-ray radiation
- 1.4k Downloads
We present a novel approach to extend optical coherence tomography (OCT) to the extreme ultraviolet (XUV) and soft X-ray (SXR) spectral range. With a simple setup based on Fourier-domain OCT and adapted for the application of XUV and SXR broadband radiation, cross-sectional images of semiconductors and organic samples becomes feasible with current synchrotron or laser-plasma sources. For this purpose, broadband XUV radiation is focused onto the sample surface, and the reflected spectrum is recorded by an XUV spectrometer. The proposed method has the particular advantage that the axial spatial resolution only depends on the spectral bandwidth. As a consequence, the theoretical resolution limit of XUV coherence tomography (XCT) is in the order of nanometers, e.g., 3 nm for wavelengths in the water window (280–530 eV). We proved the concept of XCT by calculating the reflectivity of one-dimensional silicon and boron carbide samples containing buried layers and found the expected properties with respect to resolution and penetration depth confirmed.
KeywordsOptical Coherence Tomography Coherence Length Boron Carbide Optical Coherence Tomography Signal Optical Coherence Tomography Device
Within the last decade and in conjunction with the quickly developing sector of advanced material design, the scale length of interest has dropped from micrometers to a few nanometers. Both the semiconductor circuit industry, aiming at fast and power-saving solutions, as well as structural biology and environmental chemistry with their enormous interest in nanostructures, call for resolutions in the nanometer regime. The ideas presented here take advantage of the fact that the coherence length can be significantly reduced if broadband XUV and SXR radiation is used.
Microscopy using XUV and SXR radiation has regularly ineluctable practical restrictions imposed by the optics and sources available in this regime. Coherence tomography with short wavelengths can circumvent some of these limitations in principle. A major limitation of XUV radiation is the absorption within a few tens or hundreds of nanometers  depending on the actual composition of the material and the wavelength range. Consequently, XUV coherence tomography (XCT) can only display its full capabilities when used in the transmission windows of the sample materials. For instance, the silicon transmission window (30–99 eV) corresponds to a coherence length of about 12 nm assuming a rectangular spectrum and an absorption length of about 200 nm, thus suggesting applications for semiconductor inspection. In the water window at 280–530 eV as defined by the K absorption edges of carbon and oxygen, respectively, a coherence length as short as 3 nm can be achieved and highlights possible applications of XCT for life sciences.
2 Theory of XUV coherence tomography
In most cases of Michelson-type OCT, the reflectivity of the reference mirror is much higher than the reflectivities of the sample layers. Therefore, the amplitudes of the autocorrelation terms are weak as compared to the cross-correlation terms. Hence, the autocorrelation terms are usually not evaluated and only the cross-correlation components are used to reconstruct the depth structure.
Unfortunately, the wave number k=nω/c cannot be calculated without uncertainties, due to the unknown refractive index n(ω,z S ) of the sample. In the simplest case, one could approximate the sample as an ideal non-dispersive object and calculate the Fourier transform. However, accuracy and precision will decrease, if the media is dispersive. Therefore, the absolute values of the depths of the buried layers as computed by the Fourier frequencies have an uncertainty due to the inaccurate assumptions about the refractive index and the optical path lengths in the sample, respectively. In order to reduce these inaccuracies, we assume a dispersion given by the material that is dominant in the sample. In practice, the dominant substance is known for most nano-scale samples of interest. For the present case of XCT, knowledge of the dominant substance is a prerequisite for determining the transparency window anyhow.
3 Simulated reflected signals of a layer structure based on a matrix method algorithm
In order to test the ideas outlined above, a simulation of the reflectivity of a multilayer structure is essential. For this purpose, we developed a computational model based on the matrix method algorithm  and using the refractive index database from . Molybdenum (Mo) and Lanthanum (La) layers buried under a silicon layer were investigated as a sample for proof-of-principle studies in the silicon transmission window. These materials have a well-pronounced absorption contrast with respect to the silicon substrate. Further, layer combinations of different materials, e.g., B4C and SiO2 were investigated for the water window. The simulations of the sample reflectivity in both spectral ranges show strong modulations in the reflected spectrum, as predicted by the theory of coherence tomography.
Let us perform a rough estimation to show that such an experiment is indeed possible: The simulations show a reflectivity of the used materials of about 10−2 in the XUV range and about 10−5 in the SXR range. The efficiency of a typical XUV spectrometer consisting of a toroidal mirror and a gold transmission grating  or a reflection grating  depends strongly on the photon energy and is on the order of 10−2 at 50 eV. A typical XUV CCD camera needs about 104–105 photons for saturation. With a synchrotron undulator source, photon fluxes of about 1012 photons/s at 0.1% bandwidth are possible. This means that exposure times of a few microseconds in the XUV regime and some seconds in the SXR are required, proving the feasibility of the scheme. A proof-of-principle experiment was performed at synchrotron radiation sources at DESY (Deutsches Elektronen-Synchrotron) and BESSY (Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung), which produce the required photon flux. The broad spectrum could be achieved by changing the undulator gap over time. The results will be published soon.
Furthermore, the broadband XUV radiation from laser plasmas could be a suitable source. Using a calibrated spectrometer, we observed photon fluxes at the entrance of the spectrometer of about 1011 photons per laser shot at 0.1% bandwidth  in experiments irradiating solid density targets with intensities of approximately 1019 W/cm2. The corresponding spectrum is very broad and smooth and the source dimension is small, i.e., very suitable for XCT.
We have presented calculations for a proof-of-principle experiment of optical coherence tomography using broad bandwidth XUV and SXR radiation (XCT). Evidence has been given that synchrotron and laser plasma XUV and soft X-ray sources offer sufficient flux for XCT. This strongly suggests its application as a new non-invasive tomographic method to investigate nanometer-scale structures of layered systems and simple three-dimensional samples by lateral raster scanning. We emphasize in particular the opportunities offered by the silicon and water spectral windows. The former is highly relevant for a new non-destructive method of imaging semiconductor devices. The water window, on the other hand, is known for its significance in the life sciences. The remarkable contrast of carbonic and oxygenic materials in the SXR range promises high-quality images of biological samples. The axial resolution of the imaged structures is only affected by the dynamic range of the spectrometer’s detector and the width and wavelength of the used transmission.
This work was partially supported by Deutsche Forschungsgemeinschaft (project SFB/TR 18) and the German Federal Ministry for Education (BMBF) (project FSP 301-FLASH). C.R. acknowledges support from the Carl Zeiss Stiftung.
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.