Fabrication of graphene-based quantum Hall networks and influences of partial star-mesh recursion

This work presents a substantial advancement on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. More specifically, this work introduces a generalized mathematical reconciliation to recover exact effective quantized resistances found by simulation and measurement. Furthermore, this work explores the concept of fractal dimension, clarifying the benefits of both full and partial recursions in QHARS devices. Three different partial recursion cases are visited for a near-1 $\text{G}\Omega$ QHARS device. These partial recursions, analyzed in the context of their fractal dimensions, offer increased flexibility in accessing desired resistances within a specific neighborhood of values compared to full recursion methods, though at the cost of the number of required elements.