This result shows that in this kind of systems, the presumption of a generalized Hartman effect is incorrect. Figure 3 The tunneling selleck chemicals time τ 6 as a function of reduced barrier separation and fixed barrier width. The tunneling time τ 6 as a function of reduced barrier separation

a/λ for fixed barrier width b, number of cells n=6 and electron energy E=0.15 eV with the corresponding de Broglie wavelength λ. The Hartman effect as a consequence of varying the number of cells was already discussed in [7]. In Figure 4 we show three qualitatively different examples on the behavior of the tunneling time as a function of n. In Figure 4a for energies in the gap (E=0.15 eV and E=0.2 eV), the compound screening assay saturation of the tunneling time exhibits

the well-known Hartman effect. In Figure 4b, the energy lies at the edge of a resonant region. The phase time τ n resonates for multiples of n=21. This behavior is clearly understood if we consider Equations 4 and 5. Equation 4 implies that the same resonance energy is found for different number of cells as long as the ratio ν/n is constant. This means that . From Equation 5, it is also evident the linear dependence of τ n on n. Figure 4 The tunneling time τ n as the number of cells n in a SL is varied. (a) Saturation of τ n for electron energies E=0.15 eV and E=0.2 eV in the gap. (b) The energy is close to a resonant band-edge. In this case, more resonances appear as n is increased with the energy fixed. No Hartman effect can be inferred find more from this figure. The Hartman effect and the electromagnetic waves Electromagnetic

waves have been used for discussions on the Hartman effect [9]. For a superlattice L(H/L) n made of alternating layers with refractive indices n L and n H , the phase time (PT) for each frequency component of a Gaussian wave packet through a SL of length n ℓ c −a is also obtained from Equation 2 with k L,H =ω n L,H /c and with [7] (8) (9) To see the effect of varying the size of the SL on the PT, one has to be sure that such variation will still keep the wavelength inside a photonic band gap. It was shown L-gulonolactone oxidase that by increasing the number of cells, for fixed thicknesses of layers and wavelength in a gap, the PT exhibits [7] the observed Hartman effect [2, 3]. However, this condition will not be possible by varying arbitrarily the thicknesses of the layers. The reason is that there is only a small range of thicknesses that one can use to keep the chosen wavelength to lie in a gap before going out of it and may even reach resonances, as shown in Figure 5 where the PT oscillates (with a band structure) and grows as a function of the reduced thicknesses a/λ and b/λ. This is analogous to the electron tunneling time shown in Figure 3. Figure 5 The phase times τ n as functions of the reduced thicknesses.