The electronic density decay lengths of freestanding Pb films are investigated by first-principles calculations.The results show that,like surface energy and work function,the electronic density decay lengthλexhibits pronounced oscillatory behavior as a function of film thickness and this is expected to have an impact on surface chemical reactivity.For freestanding Pb(111)films,λoscillates following a bilayer pattern interrupted by crossovers,and the separation between two neighbor crossovers is 9 monolayers.For the films on Si(111)substrates,the oscillations of the decay lengths are similar to those of freestanding films except for an extra phase shift.
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