  The ability to tune quantum tunneling is key for achieving selectivity in
manipulation of individual particles in quantum technology applications. In
this work we count electron escape events out of a time-dependent confinement
potential, realized as a dynamic quantum dot in a GaAs/AlGaAs heterostructure.
A universal scaling relation of the escape probability as a function of
potential barrier risetime and depth is established and developed as a method
to probe tunneling rates over many orders of magnitude reaching limits of WKB
approximation as the anharmonicity of shallow confinement becomes relevant.
Crossover to thermally activated transport is used to estimate the single
time-energy scale of the universal model. In application to metrological single
electron sources, in-situ calibrated control signals greatly extend the
accessible dynamical range for probing the quantization mechanism. Validation
of the cubic potential approximation sets a foundation for microscopic modeling
of quantum tunneling devices in the shallow confinement regime.
