  Quantum computation based on semiconductor electron-spin qubits requires high
control of tunnel-couplings, both across quantum dots and between the quantum
dot and the reservoir. The tunnel-coupling to the reservoir sets the qubit
detection and initialization bandwidth for energy-resolved spin-to-charge
conversion and is essential to tune single-electron transistors commonly used
as charge detectors. Potential disorder and the increasing complexity of the
two-dimensional gate-defined quantum computing devices sets high demands on the
gate design and the voltage tuning of the tunnel barriers. We present a Green's
formalism approach for the calculation of tunnel-couplings between a quantum
dot and a reservoir. Our method takes into account in full detail the
two-dimensional electrostatic potential of the quantum dot, the tunnel barrier
and reservoir. A Markov approximation is only employed far away from the tunnel
barrier region where the density of states is sufficiently large. We calculate
the tunnel-coupling including potential disorder effects, which become
increasingly important for large-scale silicon-based spin-qubit devices.
Studying the tunnel-couplings of a single-electron transistor in Si/SiGe as a
showcase, we find that charged defects are the dominant source of disorder
leading to variations in the tunnel-coupling of four orders of magnitude.
