Extraction of True Finger Temperature From Measured Data in Multifinger Bipolar Transistors

Abstract

In this brief, we propose a step-by-step strategy to accurately estimate the finger temperature in a silicon-based multifinger bipolar transistor structure from conventional measurements. First we extract the nearly zero-power self-heating resistances (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th,ii</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> )) and thermal coupling factors ( <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cij</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> )) at a given ambient temperature. Now, by applying the superposition principle on these variables at nearly zero-power, where the linearity of the heat diffusion equation is preserved, we estimate an effective thermal resistance (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th,i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> )) and the corresponding revised finger temperature T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ). Finally, the Kirchhoff's transformation on T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ) yields the true temperature at each finger (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a,</sub> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> )). The proposed extraction technique automatically includes the effects of back-end-of-line metal layers and different types of trenches present within the transistor structure. The technique is first validated against 3-D TCAD simulation results of bipolar transistors with different emitter dimensions and then applied on actual measured data obtained from the state-of-the-art multifinger SiGe HBT from STMicroelectronics B5T technology. It is observed that the superposition of raw measured data at around 40 mW power underestimates the true finger temperature by around 10%.