The quadratic Zeeman effect used for state-radius determination in neutral donors and donor bound excitons in Si:P

We have measured the near-infrared photoluminescence spectrum of phosphorus doped silicon (Si: P) and extracted the donor-bound exciton (DX) energy at magnetic fields up to 28 T. At high field the Zeeman effect is strongly nonlinear because of the diamagnetic shift, also known as the quadratic Zeeman effect (QZE). The magnitude of the QZE is determined by the spatial extent of the wave-function. High field data allows us to extract values for the radius of the neutral donor (D) ground state, and the light and heavy hole DX states, all with more than an order of magnitude better precision than previous work. Good agreement was found between the experimental state radius and an effective mass model for D. The DX results are much more surprising, and the radius of the mJ=±3/2 heavy hole is found to be larger than that of the mJ=±1/2 light hole.