Two-level systems in evaporated amorphous silicon

In e-beam evaporated amorphous silicon (a-Si), the densities of two-level systems (TLS), n₀ and P¯, determined from specific heat C and internal friction Q^{- 1} measurements, respectively, have been shown to vary by over three orders of magnitude. Here we show that n₀ and P¯ are proportional to each other with a constant of proportionality that is consistent with the measurement time dependence proposed by Black and Halperin and does not require the introduction of additional anomalous TLS. However, n₀ and P¯ depend strongly on the atomic density of the film (n_Si) which depends on both film thickness and growth temperature suggesting that the a-Si structure is heterogeneous with nanovoids or other lower density regions forming in a dense amorphous network. A review of literature data shows that this atomic density dependence is not unique to a-Si. These findings suggest that TLS are not intrinsic to an amorphous network but require a heterogeneous structure to form.