# Stability of Single Electron Devices: Charge Offset Drift
## 2 Experimental Observations of Charge Offset Drift  
Figure 1a shows a circuit diagram representation of an SED. The tunnel barriers define an isolated island whose charge can only be changed by an integer number of electrons. As shown in the figure, the SED is a three terminal device where the gate electrode primarily controls the electrostatic potential of the island. Figure 1b shows an SEM image of one type of SED fabricated in silicon. The device consists of an etched and oxidized silicon nanowire with three finger gates wrapping around the device. These gates are used to form electrostatic tunnel barriers while an upper gate covering the wire from source to drain provides carriers (not shown). Dots are formed between the finger gates. The center finger gate can act as a barrier (to form two dots) or as a plunger gate when one dot is formed. Because the island is small, its total capacitance to the other electrodes is small. This implies a measurable electrostatic energy barrier for adding an additional electron to the island, \(E_{C}=e^{2}/C_{\Sigma}\). \(E_{C}\) is known as the charging energy and produces a ladder of chemical potential levels on the island separated by \(E_{C}\). Transport is only allowed when one or more of the dot levels falls within the source-drain bias window, \(eV_{D}\). At low source-drain bias only one charging level may fit in the bias window and one measures current resonances, between which the number of electrons on the island is fixed. This is shown schematically in Figure 1c. The capacitance between the island and the plunger gate determines the spacing in voltage between the peaks. As the source-drain bias is increased, one reaches a point where more than one charging level is in the source-drain bias window and transport is no longer blockaded. This occurs when \(V_{D}\) passes the top or bottom of the diamonds shown in Figure 1d. Therefore, the height of the diamonds allows measurement of the charging energy. At high bias, rather than measuring current resonances with zero current between them, the current oscillates sinusoidally without reaching zero current as shown in Figure 1c. The period of the oscillations is again defined by the gate capacitance, \(C_{P}\). The current oscillates, increasing as a new level enters the bias window and decreasing as a level leaves the bias window. Since the plunger gate capacitance is determined by the geometry, the period of oscillations as a function of \(V_{P}\) are as well. Thus, the period of oscillations is a consequence of the geometry of the device and can be simulated accurately through electrostatic solver tools such as Fastcap [28]. Therefore, two identically fabricated devices should have very nearly the same period in the single electron curve. While the period of the single electron curve should be very similar in different, but identically fabricated devices, the phase of the curve is not. Since the single electron oscillations are a function of gate voltage the phase corresponds to a voltage offset between successively measured curves. The difference in phase has its origin in the contribution from the local charge environment [29]. This is known as the charge offset, \(Q_{0}\equiv\frac{\mathrm{phase}}{\Delta V_{P}}e\). Devices fabricated simultaneously will exhibit different values of \(Q_{0}\) because the local charge environment is randomly determined by the different processing steps such as gate oxidation, etching, dopant distribution, anneals, etc. However, so long as the local charge environment remains stable, the voltage on the plunger gate can be used to compensate for this difference and each device can be brought into phase. If instead, the local charge environment changes with time, then the phase of the device will fluctuate randomly in time and such phase synchronization becomes essentially impossible. In this case, the device exhibits charge offset drift, \(\Delta Q_{0}\). In principle, the fluctuations in the local charge environment may occur at any frequency.