Optimum Aspect Ratio of Superjunction Pillars Considering Charge Imbalance

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, RONSP, for a target breakdown voltage (VBR). We study the variation of RONSP with r and show the following analytically. The minimum RONSP of practical Si and 4H-SiC SJs is attained at an optimum r = r0 which is as low as 8-15 for VBR = 0.1-10 kV and charge imbalance, k = 5%-20%. Moreover, an advantage is that the r0 is not sharply defined, as even ±30% change in r around r0 raises RONSP by < 10% above the minimum, the raise being lower for lower k and higher VBR. In general, for k ≥ 2.5/r2, the r0 increases logarithmically with (VBR/Bandgap). In contrast, the r0 of a balanced SJ increases super-linearly with (VBR/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.