Stochastic resonance behavior of single electrons in a quantum dot and its summing network is investigated theoretically. Dynamic behavior of the single electron in the system at finite temperature is analyzed using a master equation with a tunneling transition rate. The analytical model indicates that an input-output correlation has a peak as a function of temperature, which confirms the appearance of the stochastic resonance. The peak position and height depend on charging energy, tunnel resistance, and input signal frequency. It is also found that the correlation is enhanced by formation of a summing network integrating quantum dots in parallel. The present model quantitatively explains the stochastic resonance behaviors of the single electrons predicted by a circuit simulation (Oya, Asai, & Amemiya, 2007).
TopIntroduction
Single electron devices and their integrated circuits are expected to play important roles in future ultra-small and ultra-low-power nanoelectronics. However, there are several problems preventing their practical use. The most serious one is fluctuation, such as thermal and threshold voltage fluctuations. Decreasing the size for increasing operation temperature as well as increasing integration density, the device becomes very sensitive to various fluctuations. It is obvious that atomic-level imperfection of the structure is inevitable in large-scale integrated circuits (LSIs) integrating over million devices. This means that fluctuation of device characteristics is also inevitable. At this stage, a key issue in the single electron devices and circuits is to find a way to increase robustness against fluctuation rather than to remove or suppress it. Recently, it has been pointed out that stochastic resonance (SR) serves this purpose. It is a unique phenomenon in which response to a weak signal is enhanced by adding noise (Benzi, Sutera, & Vulpiani, 1981; Gammaitoni, Hänggi, Jung, & Marchesoni, 1998). It has been found to work in various biological systems (Douglass, Wilkens, Pantazelou, & Moss, 1993; Funke, K., Kerscher, N. J., & Wörgöter, 2007; Moss, Ward, & Sannita, 2004) and contribute to the robustness of the systems against fluctuation, even having molecular-level fine structures. The SR is also known to occur artificially in various electronic systems, such as Schmitt trigger circuits (Fauve & Heslot, 1983), pn-junction diodes (Jung & Wiesenfeld, 1997), Josephson junctions (Hibbs, Singsaas, Jacobs, Bulsara, Bekkedahl, & Moss, 1995), carbon nanotubes (Lee, Liu, Zhou, & Kosko, 2006), and nanowire field effect transistors (Kasai & Asai, 2008). Recently, Kagaya, Oya, Asai, & Amemiya (2005) and Oya, Asai, & Amemiya (2007) predicted the appearance of the SR in single electron systems and demonstrated by circuit simulation. A noteworthy indication is that the response becomes robust against temperature by forming a summing network and high correlation value is kept even when temperature far exceeds the charging energy. In addition, the system can work even with threshold variation under finite thermal fluctuation. These behaviors agree with “without tuning” nature of the stochastic resonance indicated by Collins, Chow, & Imhoff (1995). However, at present, the mechanism of the single electron SR as well as physical parameters controlling the phenomenon have not been understood yet. The purpose of this paper is to theoretically study the single electron SR in a quantum dot and its summing network. First, a system for the single electron SR is described and the behavior of the single electron is analyzed using a master equation with simple approximations. Then, the calculated results are presented and discussed. Comparison with simulation results reported by Oya, Asai, & Amemiya (2007) is also shown.