We perform high-resolution photocurrent (PC) spectroscopy to investigate resonantly the neutral exciton ground-state (X0) in a single InAs/GaAs self-assembled quantum dot (QD) embedded in the intrinsic region of an n-i-Schottky photodiode based on a two-dimensional electron gas (2DEG), which was formed from a Si delta-doped GaAs layer. Using such a device, a single-QD PC spectrum of X0 is measured by sweeping the bias-dependent X0 transition energy through that of a fixed narrow-bandwidth laser via the quantum-confined Stark effect (QCSE). By repeating such a measurement for a series of laser energies, a precise relationship between the X0 transition energy and bias voltage is then obtained. Taking into account power broadening of the X0 absorption peak, this allows for high-resolution measurements of the X0 homogeneous linewidth and, hence, the electron tunnelling rate. The electron tunnelling rate is measured as a function of the vertical electric field and described accurately by a theoretical model, yielding information about the electron confinement energy and QD height. We demonstrate that our devices can operate as 2DEG-based QD photovoltaic cells and conclude by proposing two optical spintronic devices that are now feasible.