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This invention provides a silicon nitride substrate, which has a high coefficient of thermal conductivity in the thickness-wise direction and has high fracture toughness in the thickness-wise direction, a silicon nitride wiring board using the silicon nitride substrate, which has low heat resistance and is highly reliable, and a semiconductor module using this silicon nitride wiring board, which has low heat resistance and is highly reliable. The silicon nitride substrate comprises β-type silicon nitride and at least one rare earth element. The degree of in-plane orientation fa of the silicon nitride substrate is 0.4 to 0.8. In this case, the degree of in-plane orientation fa refers to the proportion of orientation in a plane perpendicular to the thickness-wise direction determined based on the proportion of each X-ray diffraction line intensity for a predetermined lattice plane of β-type silicon nitride.
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