# Stability of Single Electron Devices: Charge Offset Drift
## 2 Experimental Observations of Charge Offset Drift
### Metal-Based Devices  
In general, metal-based devices suffer from the worst charge offset drift behavior. Here, we are referring to devices fabricated from Al/AlO\({}_{x}\)/Al, where the AlO\({}_{x}\) provides the tunnel barriers shown in Figure 1a. These devices are typically fabricated through a technique known as double-angle evaporation [36]. A pattern is generated in electron beam resist through electron beam lithography and Al is evaporated at an angle. This Al is oxidized in a controlled environment within the deposition chamber, and then the deposition angle is changed. With a carefully designed pattern and the right angles, an SED is formed with AlO\({}_{x}\) tunnel barriers. Of course, devices have been fabricated from other metallic materials [37; 38]. These devices can exhibit \"clean\" Coulomb diamonds without large jumps in the data characteristic of large charge offset drift while still exhibiting some low frequency time instability [39]. Unfortunately, we are unable to find rigorous measurements of charge offset drift, as outlined above, in metallic devices made from anything other than Al/AlO\({}_{x}\). Therefore, we focus on Al/AlO\({}_{x}\) devices in this section. A typical measurement of the charge offset drift for a metallic device is shown in Figure 3a [30]. As is plainly apparent from the data, the charge offset value wanders between 0 and 1\(e\) over the course of the measurement (and, in fact, probably wanders through several \(e\)). The time scale for the drift is on the order of minutes to hours. In addition, the data show periods of rapid evolution, some periods of relative stability, and sudden jumps. The evolution from a very rapidly changing charge offset value to one which subsequently changes more gradually or only with sudden steps, is known as \"transient relaxation\". We will discuss this relaxation in more detail below. Figure 3b shows data that appear in Figure 3a between days 19 and 22. These data mainly consist of two distinct levels of \(Q_{0}\) between 0.2 and 0.3. This indicates that the drift is driven by some switching behavior and will be discussed in more detail later. Finally, vertical dashed lines in the figure denote either mechanical disturbances or deliberate temperature excursions to investigate the temperature dependence, the effects of thermal cycling, or the effects of exposure to air. Mechanical changes such as refilling the dewar with liquid helium have no discernible effect. The same is true for temperature excursions up to 40 K. However, it is possible that thermally cycling the device up to room temperature and/or exposing it to air does change the qualitative nature of the charge offset drift measured. Figure 4a shows source-drain current measured as a function of time through a metal-based SET for different values of the plunger gate voltage [40]. As the voltage on the plunger gate, \(V_{A}\), is increased, the fluctuations in the current become more rapid, while the amplitude and duty cycle remain constant. Looking closely at the data, one can see that it consists of discrete jumps, some of which appear as a quick succession of small steps and others which appear as a single large step. This is qualitatively similar to the data in Figure 3b where only two levels are seen. If each jump has its origin in the switching event of a single TLS, we can interpret jumps of different size as being due to defects at different distances from the dot with smaller jumps being due to defects further away from the dot. It is instructive to examine not only the time dependence but also the frequency dependence of the current noise in these devices. Examination of the power spectral density, \(S(\omega)\), allows us to separate equilibrium charge noise from non-equilibrium noise. \(S(\omega)\) for the traces in Figure 4a is shown in Figure 4b along with a simulated set of data and Lorentzian fits. Consistent with the fits, the data show an approximately \(1/f^{2}\) dependence over some frequency range (different for each curve).