Quantifying the local influence of terminal voltages within an electron device

For an N-terminal device, we can define N dimensionless functions of position by differentiating the electrostatic potential with respect to each of the terminal voltages. At any point in the device these functions sum to unity. They provide a natural generalization of the Shockley-Ramo theorem relating the motion of charges within the device to the terminal currents, and also tell us how the electric field lines originating from an extra charge placed into the device are partitioned among the different terminals. They provide a microscopic indicator of amplification: values of these functions can be negative or greater than unity only in active devices. An examination of some textbook device examples demonstrates how the information encoded in these functions may be interpreted, and shows how the effects that they quantify have been repeatedly invoked in an intuitive fashion in past device analyses. We also illustrate the application of these functions to a current problem: understanding the current-control characteristics of short-channel FinFET devices.