cONSTRICTION/SPREADING RESISTANCE MODEL FOR ELECTRONICS PACKAGING

k thermal conductivity, W/mK An analytical model is developed for predicting constriction and spreading resistances associated with heat transfer from various electronic components under different modes of cooling. The model assumes a heat source in contact with a larger cold plate which is in turn cooled with a convective heat transfer coefficient specified over the sink surface. Unlike existing models that mostly assume limiting boundary conditions, such as isothermal conditions, at the sink surface, the present solution allows one to accurately determine the constriction and spreading resistances in a plate with a full range of cooling conditions varying from an isothermal condition in one limit to a uniform heat-flux condition in the other limit. Dimensionless expressions in the form of infinite series are provided for computing the average and maximum constriction resistances as a function of relative contact size, plate thickness and the Biot number. The results are compared with published numerical data, and the agreement is excellent over a wide range of parameters typically found in microelectronics applications. r, z T T, t rate of heat transfer, W heat flux at the source surface, W / m2 constriction resist ante, C/ W external resist ante, ‘ c / w material resistance, ‘ c / w cylindrical coordinates, m temperature excess over ambient temperature, ‘C temperature at the source, 0 C plate thickness, m Greek Symbols 7)( dimensionless coordinates, r/b, z/b e dimensionless contact radius, a/b A, empirical parameter given by Eq. (27) An eigenvalue T dimensionless plate thickness, t/b a. dimensionless parameter defined by Eq. (26) a. dimensionless parameter defined by Eq. (21) @ dimensionless constriction resistance