Thickness dependence of the superconducting critical temperature in heavily doped Si:B epilayers

We report on the superconducting properties of a series of heavily doped Si:B epilayers grown by gas immersion laser doping with boron content (n _B) ranging from ∼3×1020 cm^-3 to ∼6×1021cm^-3 and thickness (d) varying between ∼20 nm and ∼210 nm. We show that superconductivity is only observed for n _B values exceeding a threshold value (n_c,S) which scales as n_c,S 1/d. The critical temperature (T_c) then rapidly increases with n_B, largely exceeding the theoretical values which can be estimated by introducing the electron-phonon coupling constant (λ_e-ph) deduced from ab initio calculations into the McMillan equation. Surprisingly T_c(n_B,d) is fully determined by the boron dose (n_B×d) and can be well approximated by a simple T_c(n_B,d)≈T_c,0[1-A/(n_B.d)] law, with T_c,0∼750 mK and A∼8(±1)×1015 cm ^-2.