Optimum Aspect Ratio of Superjunction Pillars Considering Charge Imbalance
K. Akshay, Shreepad Karmalkar
Abstract
Development of Superjunction (SJ) technology has striven to raise the pillar aspect ratio, r, believing that this is the key to progressively reduce the specific ON-resistance, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> , for a target breakdown voltage ( V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> ). We study the variation of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> with r and show the following analytically. The minimum R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> of practical Si and 4H-SiC SJs is attained at an optimum r = r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> which is as low as 8-15 for V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> = 0.1-10 kV and charge imbalance, k = 5%-20%. Moreover, an advantage is that the r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is not sharply defined, as even ±30% change in r around r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> raises R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> by <; 10% above the minimum, the raise being lower for lower k and higher V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> . In general, for k ≥ 2.5/r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> increases logarithmically with ( V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> /Bandgap). In contrast, the r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> of a balanced SJ increases super-linearly with ( V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> /Bandgap) and is several times higher, calling for caution while using balanced SJ theory to design practical SJs. We give a generic closed-form solution valid across materials for designing SJs based on these insights. We verify our results by technology computer-aided design (TCAD) simulation and compare them with prior experimental and theoretical data.