Chapter 4: Standard Tunneling Model
The disorder inherent in a glassy system strains interatomic connections. Whether the network is comprised of covalent, ionic, Van der Waals, or metallic bonds, it would not be surprising amongst that disorder to find a varying ease of fit for each component into its surroundings, and discover confinement potentials for each component ranging, from a quadratic harmonic oscillator that localizes the component around a single configuration, to one with a little extra space, flattening the bottom of the potential to something more like a square well that allows the component to exist within a broader range of configurations, to one with minima separated by a higher potential, hence showing a strong preference for distinct configurations [Fig. 4.1(a)]. The energy levels for such wells are shown in Fig. 4.1(b). The energy-level spacing for the harmonic oscillator is something like an atomic bond energy [O(eV)]; that’s much too large to be relevant at cryo-temperatures. That for a flat-bottomed potential is defined by the scale of confinement and the mass of the particle (a Si atom confined to a 1 nm box has its first energy step ≈2 × 10−5 eV ≈ 0.2K), increasing slowly at higher levels). Neither of those possibilities can naturally produce energy-level spacings close enough to be relevant at cryo-temperatures but with the next higher energy level sufficiently far to be frozen out…
