Transform domain techniques for efficient extraction of substrate parasitics

A semi-analytical technique for computation of the frequency- behavior of silicon substrates is demonstrated. The technique uses a boundary element approach, that utilizes the complex substrate Green Function and the two-dimensional Fast Fourier Transform. The resultant dense system matrix is sparsified by application of orthogonal transform operators on the matrix representing the system. Three transform operators are evaluated for this purpose - the Discrete Cosine Transform (DCT), the Discrete Wavelet Transform (DWT) and the Discrete Hadamard Transform (DHT). The application of any one of these operators provides a rigorous sparsification technique, which significantly reduces the computation time. The Green Function is computed in the two layers at the top of the substrate. This is done so that contacts in the oxide layer can be included in the substrate model, along with contacts in the silicon substrate. Hence, substrate loss terms in metal interconnect lines and in line-to- line interaction models, can be evaluated using this technique. Extraction of a simple circuit-simulator compatible model from frequency-domain data is discussed.