  The most commonly used physical realization of superconducting qubits for
quantum circuits is a transmon. There are a number of superconducting quantum
circuits applications, where Josephson junction critical current
reproducibility over a chip is crucial. Here, we report on a robust chip scale
$Al/AlO_x/Al$ junctions fabrication method due to comprehensive study of shadow
evaporation and oxidation steps. We experimentally demonstrate the evidence of
optimal Josephson junction electrodes thickness, deposition rate and deposition
angle, which ensure minimal electrode surface and line edge roughness. The
influence of oxidation method, pressure and time on critical current
reproducibility is determined. With the proposed method we demonstrate
$Al/AlO_x/Al$ junction fabrication with the critical current variation
($\sigma/I_c$) less than 3.9% (from $150\times200$ to $150\times600$ $nm^2$
area) and 7.7% (for $100\times100$ $nm^2$ area) over $20\times20$ $mm^2$ chip.
Finally, we fabricate separately three $5\times10$ $mm^2$ chips with 18
transmon qubits (near 4.3 GHz frequency) showing less than 1.9% frequency
variation between qubit on different chips. The proposed approach and
optimization criteria can be utilized for a robust wafer-scale superconducting
qubit circuits fabrication.
