# Stability of Single Electron Devices: Charge Offset Drift
## 2 Experimental Observations of Charge Offset Drift
Usually, the literature focuses on what is called the \"long-term charge offset drift\" which occurs at frequencies \(<\)1 Hz because the amplitude of the fluctuations is so large. This lack of synchronization, and concomitant difficulty in integration, drives our interest in studying \(\Delta Q_{0}\). Measurements of charge offset drift are not difficult to make, though care must be taken to make sure that the measurement circuit and wiring are such that they do not artificially inflate the level of charge offset drift recorded. There are two typical measurement setups for quantifying the level of charge offset drift in a particular device [30]. In the first method, a set of Coulomb blockade oscillations are repeatedly measured with a time delay between each measurement. Each curve is then fit to a sinusoidal function of the form  
\[I_{D}(V_{P})=A_{0}+A\sin[2\pi(V_{P}/\Delta V_{P}+Q_{0}(t)/e)]+BV_{P}. \tag{1}\]  
In the above, \(A_{0}\) corresponds to a current offset, while \(A\) corresponds to the size of the oscillations, and \(\Delta V_{P}\) is the period of the oscillations as previously discussed. \(B\) may be used to account for any slope in the sinusoidal curve. The phase, \(Q_{0}(t)\) in the fit is extracted and represents the charge offset drift. This is the most common measurement method. The second method is to measure the change in plunger gate voltage necessary to keep the current constant on a device (i.e., to keep a constant operating point in Figure 1). Regardless of the method used, the data are usually presented such that the voltage variation in the phase of the curves is normalized by the period of  
Figure 1: **(a)** electrical diagram representation of a single electron device (SED); **(b)** scanning electron micrograph (SEM) of a silicon SED. The micrograph shows an etched and oxidized silicon nanowire with three wraparound finger gates made of doped polySi used to create barriers and form dots. An upper gate (not shown) provides the carriers and stretches from source to drain of the device; **(c)** coulomb blockade oscillations as a function of the plunger gate voltage depicted at high and low bias, \(V_{D}\). The phase is indicated and leads to our definition of \(Q_{0}=\frac{\mathrm{phase}}{\Delta V_{P}}e\); and **(d)** schematic of Coulomb diamonds (current measured as a function of plunger gate voltage and drain bias). The hatched areas exhibit non-zero source-drain current while the central diamonds show no current because the electrostatics fixes the number of electrons on the dot. The height of the diamonds gives the charging energy and the period in \(V_{P}\) gives the capacitance between gate P and the dot. the oscillation so that \(\Delta Q_{0}\) ranges from 0 to \(1e\). These two methods can detect a \(\Delta Q_{0}\geq 0.01e\) and \(\Delta Q_{0}\geq 0.001e\), respectively. As has already been mentioned, charge offset drift precludes device integration. Conventional Complementary Metal Oxide Semiconductor (CMOS) logic devices are built in state-of-the-art cleanrooms so that the devices operate as uniformly as possible. If the threshold voltage of a metal-oxide-semiconductor field-effect transistor (MOSFET) varies significantly from one device to another, the devices cannot be integrated together. This is because a threshold voltage variation can result in a particular device's on-state occurring outside the range of voltages available to switch it. The same effect can occur in SEDs through temporal variation of the turn-on characteristics of a device. If, as alluded to above, a current standard is to be built out of parallelized SEDs, then each device must be made to operate identically to reduce the tunneling errors that limit the accuracy of the device. If a standard is built from 100 devices each tuned so that the phase of their curves are synchronized with a desired error rate of \(10^{-4}\), then each device must be stable for at least \(10^{6}\) s or 12 days.