Tungsten 'fuzz' growth re-examined: the dependence on ion fluence in non-erosive and erosive helium plasma

The thickness x, of tungsten fuzz layers are measured for non-varying helium (He) plasma exposure conditions spanning four orders of ion fluence Phi (10(24)-10(28)m(-2)) and flux Gamma (10(19)-10(23) m(-2) s(-1)), at 1000-1140 K under low energy He ion impact (50-80) eV. The data obtained are complemented by previously published data of similar growth conditions, and collectively analysed. The new analysis allows for the reconciliation of fast high flux growth with commonly observed slower growth at lower flux. It is demonstrated that the standing t(1/2) time dependence is a special case of a more general expression for determining the layer thickness, x(Phi) = (C(Phi - Phi(0)))(1/2), that depends on Phi, an incubation fluence Phi(0), and the growth constant C = 2.36(-0.56)(+1.54) x 10(-38) m(4) , which is temperature dependent. The incubation fluence, which must be exceeded before the observation on the onset of fuzz surface morphology is determined to be Phi(0) = 2.5(-1.0)(+1.5) x10(24) m(-2). In fuzz growth-erosion regimes, characterized by an erosion constant epsilon(fuzz), that is proportional to the sputter yield, an analytic solution for x(Phi) has been found, by solving the growth-erosion equilibria problem of prior work with the Lambert W function. Simple limit expressions follow from the solution for determining the equilibrium fluence and fuzz thickness; the predictions of such being in good agreement with previous fuzz growth-erosion equilibria results in the literature.