THERMAL-ANALYSIS AND OPTIMIZATION OF SUBSTRATES WITH DIRECTIONALLY ENHANCED CONDUCTIVITIES

An approximate analytical solution for the thermal resistance of the a xisymmetric chip-on-substrate problem is presented for a substrate wit h a direction dependent (orthotropic) thermal conductivity. The substr ate may be convectively cooled on either, or both, of its planar surfa ces. The solution reveals substrate geometries with law maximum substr ate temperatures. These optimal substrate sizes are mapped for Blot nu mbers typical of microelectronic applications. The effects of varying the radial and axial substrate conductivities are investigated. In gen eral, radial conductivity enhancement is beneficial for bottom-side an d both-side convective cooling of thin substrates, and for top-side co oling of all substrates. For thin substrates, radial conductivity enha ncement provides comparable thermal performance to an equivalent isotr opic conductivity enhancement. For electronic packaging applications t hin substrates are desirable and radial conductivity enhancement is mo re beneficial than axial conductivity enhancement.