Enhanced Theoretical Lower Limit for the Specific On-Resistance of a Silicon Balanced Superjunction

We propose a simple yet highly effective analytical model for the electric field distribution along the critical path in a balanced superjunction (SJ) power device. Using this electric field model for silicon SJ devices, we relate the breakdown voltage (
${V}_{\text {Br}}$
) to the pillar parameters, namely width (2W), length (L), and doping (N). Furthermore, we derive simple closed-form expressions for the optimum design parameters,
${L}_{\text {opt}}$
and
${N}_{\text {opt}}$
, which minimize the specific ON-resistance (
${R}_{{\text {ON}},\text {sp}}$
) for a target
${V}_{\text {Br}}$
and a given W. Analytical formulas for the optimum
${R}_{{\text {ON}},\text {sp}}$
and critical electric field are also provided. We show that our predictions of optimum
${R}_{{\text {ON}},\text {sp}}$
are lower than the lowest predictions made till date. Moreover, our model achieves the ideal relations of SJ, i.e.,
${L}_{\text {opt}}\propto {V}_{\text {Br}}$
, and
${N}_{\text {opt}}$
independent of
${V}_{\text {Br}}$
, leading to
${R}_{{\text {ON}},\text {sp}} \, \propto \, {V}_{\text {Br}}$
, except at high
${V}_{\text {Br}}$
in low W devices. Our theory unveils a crucial insight that the total charge (
${{\textit {qN}_{\text {opt}} \times 2 W L_{\text {opt }}}}$
) of an optimum device remains constant for a target
${V}_{\text {Br}}$
, regardless of W. Our results greatly simplify the design process, avoiding the need of using iterative solvers. We validate our model using 2-D numerical simulations.