The characteristic potential method of noise calculation in multi-terminal homogeneous semiconductor resistors

Based on the characteristic potentials previously developed for multi-terminal diffusive mesoscopic conductors by Sukhorukov and Loss, the formulas are presented of both the short-circuit noise currents including thermal noise and excess noise (1/f noise and generation-recombination noise) currents and the open-circuit noise voltages of macroscopic multi-terminal homogeneous semiconductor resistors with arbitrary geometry under dc bias. The formulas are of neat volume integral form and they give the information about how much contribution a certain region of a device makes to the terminal noise currents or voltages. A comparison between the characteristic potential method and the impedance field method developed by Shockley and co-workers is presented. A direct experimental verification of the derived formulas has been provided by measuring thermal and 1/f noise of three-terminal homogeneous polycrystalline silicon resistors and carbon resistors.