Graphical based characterisation and modelling of material gradients in porosified LTCC

The chemical composition of low temperature cofired ceramics (LTCC) allows to locally embed air into sintered substrates by a selective wet chemical etch process. Therefore, LTCC substrate with areas of low permittivity can be created without material combination. The presented graphical method of material component contrast images enables the evaluation of their most important material properties which are their component distribution, their porosification gradient and their residual bearing surface. The graphical method, including focused ion beam and scanning electron microscopy analyses, is applied to different commercially available LTCC types having two porosification states each. Derived mathematical models, which are suitable for finite element method implementation, allow the characterisation of the effective permittivity reduction while keeping a maximum residual surface area for, e.g., metallisation purposes. The shape of the optimum material distribution function features an ‘air pocket’ of small width and a depth being dependent on the application specific operating frequency.