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

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.,
$k$
. This consistently underestimates the junction temperature. Typically, the maximum temperature is calculated using the expression
$T_{m} = T_{o} + \Delta T_{\rm lin}$
, where
$T_{o}$
is the base-plate temperature, and
$\Delta T_{\rm lin}$
is the linear temperature rise. This paper derives a new expression, i.e.,
$T_{m} = T_{o}\ \hbox{exp}( \Delta T_{\rm lin}/T_{o})$
, 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
$k$
, 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 can 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-element simulations and experimental observations from GaAs heterojunction bipolar transistors and GaN HEMTs.