On Circuit Theories for Single-Electron Tunneling Devices

In this paper, various approaches to modeling tunneling and Coulomb blockade in circuits that include metallic single-electron tunneling devices are reviewed, and tested for their usefulness for designing nanoelectronic circuits. The approaches differ in the way they incorporate the quantization of charge into a circuit theory. First, the quantum phenomena important for single-electron tunneling devices are presented. Second, two energy-based theories are discussed, together often called orthodox theory of single electronics. The focus is on the transition from a device description to a circuit theory. In the orthodox theory the quantization of charge leads to the quantization of the continuous spectrum of energy states associated with the capacitance of small metal islands. In the third section, the on direct-tunneling-based impulse circuit model is discussed that translates the quantization of charge into the quantization of current and of time during a tunnel event. The conclusion is that the orthodox theory of single electronics poses severe problems when used as a circuit theory; the impulse circuit model provides a better starting point.