Derivation of Hooge-Like Dependence on the Number of Charge Carriers for Number-Fluctuation Noise in Bulk Semiconductors

Flicker noise is a phenomenon present in almost any physical system, and which has recently proven to be relevant also in quantum technologies, in particular from the point of view of its action as a source of decoherence. The origin of flicker noise is usually explained as a consequence either of the effect of fluctuations in the mobility of the charge carriers, or of fluctuations in the number of such carriers. In addition, the flicker noise power spectral density is often assumed to be inversely proportional to the number of carriers in the device, as in the well-known Hooge formula, in the case of mobility fluctuations and to the square of the carrier number in the case of number fluctuations. Here, instead, we show that for the case of a bulk semiconductor the flicker noise power spectral density resulting from carrier number fluctuations can indeed, under specific conditions, be inversely proportional to the number of carriers.