# Stability of Single Electron Devices: Charge Offset Drift
## 2 Experimental Observations of Charge Offset Drift
### Metal-Based Devices
This indicates that the device is dominated by a single or few TLS. The power spectral density does not always follow \(1/f^{2}\) at higher frequencies, however. In devices where the charge offset drift wanders continuously (without reproducible discrete jumps), the devices show a \(1/f\) dependence in the 1-100 Hz frequency range as shown in Figure 5. This is indicative of a large number of TLSscontributing to the charge noise in the device as a \(1/f\) spectrum results from the addition of a large number of \(1/f^{2}\) spectra with different knee frequencies. This distinction separates devices into those dominated by a few defects or a single defect (\(1/f^{2}\)), and those dominated by many (\(1/f\)). The devices in reference [41] also show the transient relaxation present in Figure 3. The inset of Figure 5 shows that the characteristic frequency of the charge offset drift follows a \(1/t\) dependence, where \(t\) is the experimental run time. The \(1/t\) time dependence results in a long-tail evolution, which is characteristic of glassy relaxation, a non-equilibrium relaxation process. At frequencies above about 0.1 Hz, a \(1/f\) dependence is observed which does not change as a function of the experimental run time (not shown), indicating it is an equilibrium process. Figure 3: (**a**) typical charge offset drift of metal (Al/AlO\({}_{x}\)/Al) devices. A large amount of drift is observed. Unlabeled vertical dashed lines correspond to either liquid helium transfers or accidental losses of data; (**b**) a zoomed in set of the data in (**a**) between days 19 and 22 showing the two distinct values of charge offset drifts in the device at this time. The data were recorded at 20 mK unless indicated in the figure with fine print above dashed lines. Reproduced with permission from reference [30], Copyright 2008, American Institute of Physics. Thus far, we have established that (i) the charge offset drift in metal devices is large; (ii) that the noise spectrum in some devices shows that nearby two-level systems (TLSs) participate; (iii) that charge offset drift events occur on the tens of minutes to hours time scale; and iv) that the drift at low frequencies can be a \"long-tail\" non-equilibrium process. Table 1, organized by device type, summarizes these results and the results for other types of devices discussed below. We can now discuss some attempts to mitigate \(\Delta Q_{0}\) by establishing some empirical correlations between the level of \(\Delta Q_{0}\) and some fabrication parameters or measurement protocols. Figure 5 shows the power spectral density for two different devices. The device plotted in red had extra oxide deposited on it to encapsulate the device while the blue device did not. This was done to investigate if the noise was  
Figure 4: (**a**) current fluctuations as a function of time and gate voltage in an Al/AlO\({}_{x}\)/Al device. The data are made up of steps or collections of steps from a single dominant defect. The frequency of steps increases with gate voltage while the amplitude and duty cycle remain the same; (**b**) power spectral density of the noise in (**a**) at selected gate voltages. The data show a Lorentzian, flat at low frequencies and \(1/f^{2}\) at high frequencies, dependence with different knee frequencies. Data were obtained at a temperature of about 15 mK. Inset shows the characteristic time extracted from the Lorentzian fits showing a roughly exponential dependence on gate voltage. Reproduced with permission from reference [40], Copyright 1997, American Physical Society. Figure 5: Power spectral density of charge offset drift fluctuations for two metallic devices. The device which was encapsulated with oxide shows larger \(S_{Q}\) at low frequency while the high frequency noise is similar. The **blue** curve also follows a \(1/f\) dependence at low frequencies indicating it is dominated by equilibrium noise. The inset shows the knee frequency as a function of the experimental run time. Data were obtained at a temperature of 25 mK.