# Stability of Single Electron Devices: Charge Offset Drift
## 3 Discussion  
The most salient feature of the experimental review presented above is that, while both metallic devices and all-silicon devices have TLSs in the amorphous insulators that contribute to the charge noise, only metallic devices show a large charge offset drift. This difference in the behavior of the TLSs in each material system would appear to be explained by the lack of interaction between TLSs in the Si/SiO\({}_{2}\) system, as evinced most directly by Figure 9. The TLSs in Si/SiO\({}_{2}\) devices are stable over time, gate voltage, and thermal cycling.  
Given the above influence of TLSs and the fact that the level of charge offset drift in metallic devices becomes more severe as the amount of amorphous insulating material increases (see Figure 5), it is natural to study the role of TLSs in these amorphous insulators. This field is known as glassy physics and is characterized by non-equilibrium relaxation. The relaxation is a consequence of structural relaxation due to tunneling in an array of TLSs. As an example, it is well-accepted that the long tail of heat released in calorimetry experiments on silica which show a \(1/t\) dependence [49] can be explained by this theory [50; 51; 52].  
The characteristics of a TLS can be seen in Figure 12. Here, the asymmetry of the well is characterized by \(\Delta\), \(V\) is the tunneling barrier, and \(d\) represents the well separation.  
The eigenstates of Figure 12 in the absence of tunneling are the position states \(|L\rangle\) and \(|R\rangle\). In the presence of tunneling the eigenstates are linear combinations of \(|L\rangle\) and \(|R\rangle\) with energies \(E_{\pm}=\pm\sqrt{\Delta^{2}+\Delta_{0}^{2}}\) where \(\Delta_{0}=\hbar\omega_{0}e^{-\lambda}\) is the tunnel coupling. These tunneling levels are coupled to electric fields [50], and we need only assume that some of these tunneling events are coupled electrostatically to the island of the SED and will contribute to charge offset drift to apply this model.  
The above theory was adapted to estimate an upper bound on time scale over which charge offset in a metallic SED changes [30]. The rate of change of charge offset drift was found to be \(\frac{dN}{dt}\approx~{}0.3\) h\({}^{-1}\) or about one event every 3 h. This is in general agreement with the data on metallicdevices and only applies to the transient relaxation phenomena in metallic devices. No theory of the equilibrium charge offset drift exists, and because glassy relaxation is a non-equilibrium theory, it cannot be directly applied to the equilibrium level of charge offset drift in metallic devices. However, the above agreement further validates an interpretation of charge offset drift in terms of interacting TLSs. Thus, it seems the high level of charge offset drift in metallic devices can be explained as a bath of interacting TLSs that are capable of inducing switching events in other TLSs. The crucial characteristic of the all silicon system would appear to be that the TLSs in SiO\({}_{2}\) do not interact with each other.  
It is clear that such TLSs exist in both AlO\({}_{x}\) and SiO\({}_{2}\) from the data above; however, some detailed aspects of the microscopic origin of the TLS and what atoms are tunneling are not clear. It has been suggested that the origin of the TLS and the associated structural rearrangement through tunneling is either stress produced in deposition or the presence of OH\({}^{-}\) ions [30] in metallic devices. In all-silicon devices, the origin of the TLSs may be caused by tetrahedra in the SiO\({}_{2}\) reorienting or charging and discharging.