Semiconductor Si-based qubits have been realized in various lithographically-defined Si/SiGe heterostructures and validated only for milli-Kelvin temperature operation. Germanium (Ge) QD qubits systems are envisaged to have high scalabilty and operate at higher temperatures. We report the unique scalability and size tunability of Ge spherical-shaped QDs that are controllably located, closely coupled between each another, and self-aligned with control electrodes, using a coordinated combination of lithographic patterning and self-assembled growth. The core experimental design is based on the thermal oxidation of SiGe spacer islands located at each sidewall corner of Si₃N₄/Si fanout-ridges with specially designed fanout structures. Spherical-shaped Ge QDs are closely coupled to each other via coupling barriers of Si and to self-aligned Si-based electrodes via Si₃N₄ tunneling barriers. Our ability to place size-tunable spherical Ge QDs at any desired location, therefore, offers a large parameter space within which to design novel quantum electronic devices.

     Physically-defined QDs promise higher temperature operation and better immunity to quantum leak thanks to the fact that hard-wall barriers primarily result in strong quantum confinement and enlarge energy scales. However, tunneling current through physically-defined QD qubits is typically small in magnitude (~ pA or smaller) due to strong confinement of carriers within physically-defined QDs, leading to the difficulty in resolving charge-states and their in-between transition lines simply using direct current measurement. Thereby, intricate readout techniques such as RF-reflectometry are necessary.
Our study reports that using a direct current measurement, photo-current spectroscopy of Ge DQDs not only offers a quick estimation of charging energies of the individual QDs, but also provides approximate operating conditions of charge states for further manipulation of DQD occupancy.