  By creating a sharp and dense dopant profile of phosphorus atoms buried
within a silicon host, a two-dimensional electron gas is formed within the
dopant region. Quantum confinement effects induced by reducing the thickness of
the dopant layer, from $4.0$\,nm to the single-layer limit, are explored using
angle-resolved photoemission spectroscopy. The location of theoretically
predicted, but experimentally hitherto unobserved, quantum well states known as
the $\Delta$-manifold is revealed. Moreover, the number of carriers hosted
within the $\Delta$-manifold is shown to be strongly affected by the
confinement potential, opening the possibility to select carrier
characteristics by tuning the dopant-layer thickness.
