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 similar to 3 x 10(20) cm(-3) to similar to 6 x 10(21)cm(-3) and thickness (d) varying between similar to 20 nm and similar to 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) proportional to 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 (lambda(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) x d) and can be well approximated by a simple T-c(n(B),d) approximate to T(c, 0)inverted right perpendicular1 - A/(n(B).d)inverted left perpendicular law, with T-c,T-0 similar to 750 mK and A similar to 8(+/- 1) x 10(15) cm(-2).