The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values.

The effects of imperfections on the electrical performance of four-gate field-effect transistors (G4-FETs) have been studied. Variations in the oxide trap distribution and in the metallurgical boundary of the junction gates impact the low-frequency noise and the static (dc) performance of the G4-FET. By modeling, iterative characterization of published experimental data, and extensive simulations, it is shown that these effects originate from trap distributions in the gate oxides and in the depleted regions of the semiconductor channel. The proposed models are based on established models, such as the unified flicker noise model, with modifications and improvements that extend to trap distributions with gradients, variable frequency slope α of 1/f^α noise spectra, and are applicable for gate stacks with high-k dielectrics, such as HfO₂ and HfSiON. The characterization procedures allowed for identifying optimum profiles of the metallurgical boundary of junction gates, which simultaneously improve the dc and noise performances of the G4-FET, such as subthreshold swing and low noise. The results indicate the importance of the precise control of depletion and conduction in the channels of multiple-gate FETs.