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 (nB) 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 nB values exceeding a threshold value (nc,S ) which scales as nc,S ∝ 1/d. The critical temperature (Tc) then rapidly increases with nB, largely exceeding the theoretical values which can be estimated by introducing the electron-phonon coupling constant (λe-ph) deduced from ab initio calculations into the McMillan equation. Surprisingly Tc(nB,d) is fully determined by the boron dose (nB × d) and can be well approximated by a simple Tc(nB,d) ≈ Tc,0[1 − A/(nB.d)] law, with Tc,0 ∼ 750 mK and A ∼ 8(±1) × 1015 cm−2.