  Quantum bits, or qubits, are an example of coherent circuits envisioned for
next-generation computers and detectors. A robust superconducting qubit with a
coherent lifetime of $O$(100 $\mu$s) is the transmon: a Josephson junction
functioning as a non-linear inductor shunted with a capacitor to form an
anharmonic oscillator. In a complex device with many such transmons, precise
control over each qubit frequency is often required, and thus variations of the
junction area and tunnel barrier thickness must be sufficiently minimized to
achieve optimal performance while avoiding spectral overlap between neighboring
circuits. Simply transplanting our recipe optimized for single, stand-alone
devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer)
initially resulted in global drifts in room-temperature tunneling resistance of
$\pm$ 30%. Inferring a critical current $I_{\rm c}$ variation from this
resistance distribution, we present an optimized process developed from a
systematic 38 wafer study that results in $<$ 3.5% relative standard deviation
(RSD) in critical current ($\equiv \sigma_{I_{\rm c}}/\left\langle I_{\rm c}
\right\rangle$) for 3000 Josephson junctions (both single-junctions and
asymmetric SQUIDs) across an area of 49 cm$^2$. Looking within a 1x1 cm moving
window across the substrate gives an estimate of the variation characteristic
of a given qubit chip. Our best process, utilizing ultrasonically assisted
development, uniform ashing, and dynamic oxidation has shown $\sigma_{I_{\rm
c}}/\left\langle I_{\rm c} \right\rangle$ = 1.8% within 1x1 cm, on average,
with a few 1x1 cm areas having $\sigma_{I_{\rm c}}/\left\langle I_{\rm c}
\right\rangle$ $<$ 1.0% (equivalent to $\sigma_{f}/\left\langle f
\right\rangle$ $<$ 0.5%). Such stability would drastically improve the yield of
multi-junction chips with strict critical current requirements.
