μ-Raman spectroscopy and FE-modeling for TSV-Stress-characterization

Relation between Raman frequency and triaxial stress in Si for surface and cross-sectional experiments in microelectronics components

“…ÀDx(cm À1 )/ r 11 (Pa) be neglected, as shown by Ryu et al 10 and Saettler et al 11 The variation of this vertical stress component with depth highly depends on processing conditions, and the above discussed results clearly show that care has to be taken when assuming uniaxial or biaxial stress. In general, Eqs.…”

“…Most simulations predict very low values of the shear stress components near a TSV compared to the axial components. [9][10][11] If shear stress components can be neglected, one can assume the three major stress components along the X, Y, and Z-axes to be non-zero near a TSV. This is a typical example of a triaxial stress assumption.…”

“…(19), the third stress component r c 33 , that is, the axial compressive stress, will dominate the Raman frequency shift measured near the TSVs. When using a longer wavelength of the probing laser, the axial stress can mostly not be neglected 11,12,37 and the assumption r c 33 ¼ 0 is not correct. This is confirmed by the experiment shown in Fig.…”

“…Several recent publications indeed correlate micro-Raman spectroscopy (lRS) results measured in the Si near TSVs or micro-bumps with results from models and electrical measurements. [2][3][4][5][6][7][8][9][10][11][12][13] Nearly, all these studies, with a few exceptions, 9,11,13 however have one assumption in common: They neglect the stress component along the length axis of the TSV in their calculation of stress from the Raman frequency shift and assume uniaxial or biaxial stress in the Si surface plane. This assumption has to be applied with care: It is often incorrect and can lead to erroneous conclusions.…”

“…A possible approach is to use an analytical model or finite element modelling (FEM) to predict the strain tensor elements in the silicon and then calculate the expected Raman shift taking into account all the stress/strain tensor elements. This "predictive Raman spectroscopy" approach was originally developed for Si isolation structures 14 and was successfully applied to Cu TSVs [9][10][11]13,15,16 but can be very time-consuming. It also does not offer easy insight into the various stress components.…”