Dependence of the ionization energy of shallow donors and acceptors in silicon on the host isotopic mass

A comparison of the infrared absorption spectra of isotopically pure ²⁸Si and ³⁰Si reveals small shifts in the transition energies for both the shallow donor phosphorus and the shallow acceptor boron. The impurity binding energies for both species are slightly larger in ³⁰Si than in ²⁸Si. A similar effect was earlier observed for the boron acceptor in ¹³C vs ¹²C diamond, and later explained as resulting from a change in the ground and excited state binding energies due to the dependence of the hole effective mass on the host isotopic composition. Here we show that the results for both donors and acceptors in Si can be explained by the same mechanism, with the additional inclusion of the isotopic dependence of the dielectric constant.