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

Simultaneous conduction and valence band quantisation in ultra-shallow, high density doping profiles in semiconductors