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 RONSPwith r and show the following analytically. The minimum RONSPof practical Si and 4H-SiC SJs is attained at an optimum r = r0which is as low as 8-15 for VBR= 0.1-10 kV and charge imbalance, k = 5%-20%. Moreover, an advantage is that the r0is not sharply defined, as even ±30% change in r around r0raises RONSPbyBR. In general, for k ≥ 2.5/r2, the r0increases logarithmically with ( VBR/Bandgap). In contrast, the r0of 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.