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A four-terminal donor quantum dot (QD) is used to characterize potentialbarriers between degenerately doped nanoscale contacts. The QD is fabricated byhydrogen-resist lithography on Si(001) in combination with $n$-type doping byphosphine. The four contacts have different separations ($d$ = 9, 12, 16 and 29nm) to the central 6 nm $\times$ 6 nm QD island, leading to different tunneland capacitive coupling. Cryogenic transport measurements in theCoulomb-blockade (CB) regime are used to characterize these tunnel barriers. Wefind that field enhancement near the apex of narrow dopant leads is animportant effect that influences both barrier breakdown and the magnitude ofthe tunnel current in the CB transport regime. From CB-spectroscopymeasurements, we extract the mutual capacitances between the QD and the fourcontacts, which scale inversely with the contact separation $d$. Thecapacitances are in excellent agreement with numerical values calculated fromthe pattern geometry in the hydrogen resist. We show that by engineering thesource-drain tunnel barriers to be asymmetric, we obtain a much simplerexcited-state spectrum of the QD, which can be directly linked to the orbitalsingle-particle spectrum.

Tunnel barrier design in donor nanostructures defined by hydrogen-resist lithography