Heat spreading revisited – effective heat spreading angle

There is probably no thermal engineer who has not yet developed his or her own spreadsheet to calculate the thermal resistance of a layered structure such as the chip / die-attach / lead-frame stack in a power semiconductor. The more sophisticated versions of such spreadsheets consider also the effect of heat-spreading inside the layers, usually assuming a constant spreading angle which is often chosen to be 45°. As simple as this approach is as poor are often the results compared to Finite Element simulations or measurements. Herein we propose a definition of the effective heat-spreading angle which is based on the local variation of the heat-flux density along the heat-flow path. Using this definition it is possible to accurately calculate the heat-spreading angle inside a given structure and thus to develop more accurate heat spreading models e.g. for spreadsheet calculations.