Abstract
The drive for smaller, faster, and higher output power integrated circuits continues to push the device junction (channel) temperature to higher levels. An accurate estimate of the maximum junction temperature is necessary for ensuring proper and reliable operation. In most cases, for simplicity, the thermal resistance within the device is calculated or measured assuming constant thermal conductivity, i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$k$</tex></formula> . This consistently underestimates the junction temperature. Typically, the maximum temperature is calculated using the expression <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{m} = T_{o} + \Delta T_{\rm lin}$</tex></formula> , where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{o}$</tex></formula> is the base-plate temperature, and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta T_{\rm lin}$</tex></formula> is the linear temperature rise. This paper derives a new expression, i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{m} = T_{o}\ \hbox{exp}( \Delta T_{\rm lin}/T_{o})$</tex></formula> , replacing the common expression. It is shown that this new expression, which is reported for the first time, accounts for most of the resultant effect due to the nonlinearity of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex></formula> , converges to the common expression for small <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta T_{\rm lin}$</tex></formula> , and is independent of the semiconductor material used in the device. Hence, an improved assessment of the junction temperature can be established even in cases where the temperature dependence of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex></formula> is not known. The expression's validity is verified by comparing its results with those from finite-element simulations and experimental observations from GaAs heterojunction bipolar transistors and GaN HEMTs.
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