A two-dimensional low pass filter model for die-level topography variation resulting from chemical mechanical polishing of ILD films

This paper presents a new two-dimensional (2-D) low pass filter model for the prediction of post-chemical-mechanical polishing (CMP) die level wafer topography variation caused by the interconnect metal density of a circuit layout. It is demonstrated that the local smoothing and planarization effects of an ILD polishing process can be characterized accurately (in the frequency domain) by a polynomial equation with a small number of fitted parameters. In this method, the design specific metal density patterns with millions of shapes are first captured in the frequency domain using a 2-D Fast Fourier Transform (FFT). A fitted low pass filter CMP model is then applied to filter/remove short range pattern variation. (Die level topography variations are not removed by CMP effectively). Finally, the post-CMP smoothed topography in the spatial domain is computed from inverse FFT. Model predictions and experimental data are compared in three examples (a) a test structure, (b) a die with shallow trench isolation (c) cumulative topography of a die after ILD1, 1LD2 and ILD3 polishing.