Nonlinear microscopy for failure analysis of CMOS integrated circuits in the vectorial focusing regime
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This thesis focuses on the development of techniques for enhancing the spatial resolution and localisation precision in the sub-surface microscopy for failure analysis in semiconductor integrated circuits (ICs). Highest spatial resolutions are obtained by implementing solid immersion lenses (SIL), which provide unsurpassed numerical aperture (NA) for sub-surface microscopy. These high NA conditions mean that scalar diffraction theory is no longer valid and a vectorial focusing description should be applied to accurately describe the focal plane electric field distribution. Vectorial theory predicts that under high NA conditions a linearly polarised (LP) light focuses to a spot that is extended along the electric field vector, but radially polarised (RP) light is predicted to form a circular spot whose diameter equals the narrower dimension obtained with linear polarisation. By implementing a novel liquid-crystal (LC) radial polarisation converter (RPC) this effect was studied for both two-photon optical-beam-induced current (TOBIC) microscopy and two-photon laser assisted device alteration (2pLADA) techniques, showing a resolution and localisation improvement using the RP beam. By comparing images of the same structural features obtained using linear, circular and radial polarisations imaging and localisation resolutions both approaching 100 nm were demonstrated. The obtained experimental results were in good agreement with modelling and were consistent with theoretically predicted behaviour. Certain artefacts were observed under radial polarisation, which were thought to result from the extended depth of focus and the significant longitudinal field component. In any application these effects must be considered alongside the benefits of the symmetric field distribution in the focal plane. While SIL sub-surface microscopy offers unmatched spatial resolutions, it is prone to being severely degraded by aberrations arising from inaccurate dimensions of the SIL, imprecise substrate thickness or imperfect contact between SIL and substrate. It is in this context that techniques to identify and even mitigate aberrations in the system are important. A simple approach is demonstrated for revealing the presence of chromatic and spherical aberrations by measuring the two-photon autocorrelation of the pulses at the focal plane inside the sample. In the case of aberration free imaging, it was shown both theoretically and experimentally that the planes of the maximum autocorrelation amplitude and shortest pulse duration always coincide. Therefore, the optics of the imaging system can be first adjusted to obtain the minimum autocorrelation duration and then the wavefront of incident light modified to maximise the autocorrelation intensity, iterating this procedure until the positions of minimum pulse duration and maximum autocorrelation amplitude coincide.