  We demonstrate simultaneous quantisation of conduction band (CB) and valence
band (VB) states in silicon using ultra-shallow, high density, phosphorus
doping profiles (so-called Si:P $\delta$-layers). We show that, in addition to
the well known quantisation of CB states within the dopant plane, the
confinement of VB-derived states between the sub-surface P dopant layer and the
Si surface gives rise to a simultaneous quantisation of VB states in this
narrow region. We also show that the VB quantisation can be explained using a
simple particle-in-a-box model, and that the number and energy separation of
the quantised VB states depend on the depth of the P dopant layer beneath the
Si surface. Since the quantised CB states do not show a strong dependence on
the dopant depth (but rather on the dopant density), it is straightforward to
exhibit control over the properties of the quantised CB and VB states
independently of each other by choosing the dopant density and depth
accordingly, thus offering new possibilities for engineering quantum matter.
