A master equation model of multi-island single-electron transistors based on stability diagram

Multi-island single-electron transistor (SET) has attracted much attention for not only its ultra low power and small size but also its ability to work at room temperature. All of the reported master equation model of multi-island SET have a working voltage limitation which is not suit to simulate the hybrid circuits with CMOS. An improved master equation model for multi-island SET is proposed in this paper, which is based on the orthodox theory of single-electron tunneling. With the stability diagram, the states of the electrons occupied in the coulomb islands are chosen under certain bias voltage. The master equation model of double-island SET is also analyzed as a special instance of multi-island SET, which shows voltage-limitation-free advantages for the current calculation. This model is accuracy and fast, verified with Monte Carlo simulation. The model could adapt itself complexity according to the operating voltage. The splitting of the crest in the coulomb oscillation has been analyzed by means of the stability diagram.