A four-terminal donor quantum dot (QD) is used to characterize potential barriers between degenerately doped nanoscale contacts. The QD is fabricated by hydrogen-resist lithography on Si(001) in combination with $n$-type doping by phosphine. The four contacts have different separations ($d$ = 9, 12, 16 and 29 nm) to the central 6 nm $times$ 6 nm QD island, leading to different tunnel and capacitive coupling. Cryogenic transport measurements in the Coulomb-blockade (CB) regime are used to characterize these tunnel barriers. We find that field enhancement near the apex of narrow dopant leads is an important effect that influences both barrier breakdown and the magnitude of the tunnel current in the CB transport regime. From CB-spectroscopy measurements, we extract the mutual capacitances between the QD and the four contacts, which scale inversely with the contact separation $d$. The capacitances are in excellent agreement with numerical values calculated from the pattern geometry in the hydrogen resist. We show that by engineering the source-drain tunnel barriers to be asymmetric, we obtain a much simpler excited-state spectrum of the QD, which can be directly linked to the orbital single-particle spectrum.
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