Redetermination of the valley-orbit (chemical) splitting of the 1sground state of group-V donors in silicon

The sixfold degeneracy of the 1s(A₁+E+T₂) ground state of substitutional group-V donors in Si, originating from the six {Δ} conduction-band minima, is lifted by the valley-orbit (chemical) splitting, with 1s(E) and 1s(T₂) remaining close to the effective-mass position and 1s(A₁) depressed significantly. The binding energies of 1s(A₁), 1s(E), and 1s(T₂) are accessible to an experimental determination through the observation of the 1s(A₁),1s(E),1s(T₂){→}np₀,np_± transitions in the Lyman spectrum of the neutral donors, where the p₀ and p_± 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(A₁){→}np₀, np_± transitions are observed at the lowest temperature, the 1s(E),1s(T₂){→}np₀,np_± transitions appear on thermally populating 1s(E) and 1s(T₂).In this manner we have recorded the 1s(E),1s(T₂){→}2p₀,2p_± 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(T₂) 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(T₂:Γ₅) resolving it into a doublet 1s(T₂:Γ₇) and a quadruplet 1s(T₂:Γ₈); 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(T₂:Γ₅) in Bi and yield a binding energy of 30.1 meV for 1s(E:Γ₈).