  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.
