edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 4 8 bremsstrahlung radiation and through inelastic scattering that excites atomic electrons, which then relax by emitting characteristic fluorescence radiation. Any x-rays emitted in the forward direction pass through a narrow spacer layer of silicon and then through the IC of interest, to be imaged by the TES array. Two-dimensional images over larger areas are generated by moving the sample laterally relative to the source and detector array, while the third (depth) dimension is explored by rotating the sample so that x-rays cross it at a variety of angles. The Tomcat CT instrument requires specially prepared—but reusable—IC samples. For the first demonstration, we removed the circuit’s largest, back-end-of-line wiring layers by spin-milling the IC in a plasma focused ion beam. Tomcat would still work with the larger wiring layers intact, but their presence would have slowed down imaging of the smallest features that were of primary interest in the initial demonstration. After the thinning step, three wiring and three dielectric layers of silicon dioxide remained in the sample circuit. A carbon wafer transparent to x-rays was then epoxied to the sample to stiffen it for the remaining preparation work. One critical design challenge that Tomcat faces is that of achieving high resolution in a compact, laboratory-sized system. The smallest features of interest, only 160 nm wide, must be magnified onto the surface of the imaging detector so that they are larger than the typical spacing of the pixels, which is 500 μm in the TES array. The magnification requirement could have been met by placing the detectors very far from the sample, but this choice would strain the limits of a “compact” system and also reduce the all-important photon yield. To achieve a lab-scale and high-efficiency instrument, we instead chose to locate the conversion target very close to the sample. IC wafers are far too thick to meet this requirement without further processing— the platinum thin-film electron-conversion target must be placed within micrometers of the transistor layers, in the middle of the wafer itself. Thus, the next step in preparation was to thin the carrier wafer. The great majority of the wafer was removed by lapping and polishing, leaving a spacer layer of silicon only 8.5 μm thick behind the transistor region of the circuit. The 100 nm film of platinum, the conversion target, was then deposited on the remaining spacer. This step fixed the system geometry with a high and, importantly, a constant optical magnification. The spacer thickness was chosen because the imaging array could be no closer than 75 mm from the sample, and because of the minimum feature sizes of this specific IC sample. The choice of platinum as a target material involved several factors; most critically, platinum efficiently emits fluorescence lines at energies that maximize the x-ray absorption contrast between the copper wiring and dielectric in the IC. For CT measurements, the prepared sample is held in a complex stack of positioning instruments that enable 3D placement with 10 nm precision, as well as rotation about a vertical axis. The IC region of interest (ROI) is measured in a raster-scan pattern across a rectangular area, with discrete steps no more than a fraction of the roughly 1 μm viewable by the TES array at any one instant. The ROI is then rotated about the vertical axis and scanned again to access information about the third, depth, dimension. The two 3D-reconstruction algorithms used are based on Bayesian and maximum-entropy methods. We adopt a Bayesian prior that penalizes absolute gradients in the reconstructed image, favoring smoother reconstructions. Maximum-entropy methods are well suited to a problem where we have a set of measurements covering only a limited range of angles. In contrast, filtered backprojection, which reigned in medical tomography for four decades,[17] requires that the data be collected in a complete and regular array of angles, then Fourier transformed. Relying on fast Fourier transforms, filtered backprojection is indeed very fast. The speeds of algorithms are becoming less of a concern, however, and the focus today is on obtaining the best reconstructed images for any given data collection. Fig. 6 Comparison of reconstructions (top) and the design file (bottom). The left images show a single slice; the right images show a 3D view. The finest lines are 160 nm wide and the scale bar is 2 µm. Figure reprinted from Ref. 16 with permission.
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