Redetermination of the valley-orbit (chemical) splitting of the 1<i>s</i>ground state of group-V donors in silicon

Abstract

The sixfold degeneracy of the 1s(${\mathit{A}}_{1}$+E+${\mathit{T}}_{2}$) ground state of substitutional group-V donors in Si, originating from the six \ensuremath{\Delta} conduction-band minima, is lifted by the valley-orbit (chemical) splitting, with 1s(E) and 1s(${\mathit{T}}_{2}$) remaining close to the effective-mass position and 1s(${\mathit{A}}_{1}$) depressed significantly. The binding energies of 1s(${\mathit{A}}_{1}$), 1s(E), and 1s(${\mathit{T}}_{2}$) are accessible to an experimental determination through the observation of the 1s(${\mathit{A}}_{1}$),1s(E),1s(${\mathit{T}}_{2}$)\ensuremath{\rightarrow}${\mathit{np}}_{0}$,${\mathit{np}}_{\ifmmode\pm\else\textpm\fi{}}$ transitions in the Lyman spectrum of the neutral donors, where the ${\mathit{p}}_{0}$ and ${\mathit{p}}_{\ifmmode\pm\else\textpm\fi{}}$ levels are accurately described in the effective-mass theory. We have remeasured the excitation spectrum of Si(P, As, Sb, or Bi) in the temperature range 1.8--100 K under high resolution and signal-to-noise ratio; while only the 1s(${\mathit{A}}_{1}$)\ensuremath{\rightarrow}${\mathit{np}}_{0}$, ${\mathit{np}}_{\ifmmode\pm\else\textpm\fi{}}$ transitions are observed at the lowest temperature, the 1s(E),1s(${\mathit{T}}_{2}$)\ensuremath{\rightarrow}${\mathit{np}}_{0}$,${\mathit{np}}_{\ifmmode\pm\else\textpm\fi{}}$ transitions appear on thermally populating 1s(E) and 1s(${\mathit{T}}_{2}$).In this manner we have recorded the 1s(E),1s(${\mathit{T}}_{2}$)\ensuremath{\rightarrow}2${\mathit{p}}_{0}$,2${\mathit{p}}_{\ifmmode\pm\else\textpm\fi{}}$ transitions in Si(P, As, and Sb) at optimum temperatures in the range 20--80 K. In Si(Sb), the transitions which originate from 1s(${\mathit{T}}_{2}$) are doublets but not those from 1s(E). This feature arises from the inclusion of the spin-orbit interaction which lifts the sixfold degeneracy of 1s(${\mathit{T}}_{2}$:${\mathrm{\ensuremath{\Gamma}}}_{5}$) resolving it into a doublet 1s(${\mathit{T}}_{2}$:${\mathrm{\ensuremath{\Gamma}}}_{7}$) and a quadruplet 1s(${\mathit{T}}_{2}$:${\mathrm{\ensuremath{\Gamma}}}_{8}$); the latter has a smaller binding energy implying a positive value for the spin-orbit coupling parameter. The corresponding observations in Si(Bi) reported here show the spin-orbit splitting of 1s(${\mathit{T}}_{2}$:${\mathrm{\ensuremath{\Gamma}}}_{5}$) in Bi and yield a binding energy of 30.1 meV for 1s(E:${\mathrm{\ensuremath{\Gamma}}}_{8}$).