Calculation of the Nonlinear Junction Temperature for Semiconductor Devices Using Linear Temperature Values


The drive for smaller, faster, and better output power integrated circuits continues to push the device junction (channel) temperature to higher levels. An correct estimate of the maximum junction temperature is critical for ensuring correct and reliable operation. In most cases, for simplicity, the thermal resistance at intervals the device is calculated or measured assuming constant thermal conductivity, i.e., $k$. This consistently underestimates the junction temperature. Typically, the utmost temperature is calculated using the expression $T_m = T_o + Delta T_rm lin$, where $T_o$ is the bottom-plate temperature, and $Delta T_rm lin$ is the linear temperature rise. This paper derives a new expression, i.e., $T_m = T_o hboxexp( Delta T_rm lin/T_o)$, replacing the common expression. It's shown that this new expression, which is reported for the first time, accounts for many of the resultant effect due to the nonlinearity of $k$, converges to the common expression for small $Delta T_rm lin$, and is independent of the semiconductor material used in the device. Hence, an improved assessment of the junction temperature will be established even in cases where the temperature dependence of $k$ is not known. The expression's validity is verified by comparing its results with those from finite-part simulations and experimental observations from GaAs heterojunction bipolar transistors and GaN HEMTs.

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