Atomically precise donor-based quantum devices are a promising candidate for scalable solid-state quantum computing. Atomically precise design and implementation of the tunnel coupling in these devices is essential to realize gate-tunable exchange coupling, and electron spin initialization and readout. Current efforts in atomically precise lithography have enabled deterministic placement of single dopant atoms into the Si lattice with sub-nm precision. However, critical challenges in atomically precise fabrication have meant systematic, atomic-scale control of the tunneling coupling has not been demonstrated. Here using a room-temperature grown locking layer and precise control over the entire atomic-scale fabrication process, we demonstrate atomic-scale control of the tunnel coupling in atomically precise single-electron transistors (SETs). Using the naturally occurring Si (100) 2x1 surface reconstruction lattice as an atomically-precise ruler, we systematically vary the number of lattice counts within the tunnel junction gaps and demonstrate exponential scaling of the tunneling resistance at the atomic limit. Using low-temperature transport measurements, we characterize the tunnel coupling asymmetry in a pair of nominally identical tunnel gaps that results from atomic-scale variation in the tunnel junction and show a resistance difference of four that corresponds to half a dimer row pitch difference in the effective tunnel gap distances - the intrinsic limit of hydrogen lithography precision on Si (100) 2x1 surfaces. Our results demonstrate the key capability to do atom-scale design and engineering of the tunnel coupling necessary for solid-state quantum computing and analog quantum simulation.
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