The cause of the anomalously small electric field effect in thin films of Bi

Measurements of the electric field effect (EFE) in thin films of Bi exhibit an unexpectedly small effect. Even though the additional charge density is comparable with the intrinsic carrier concentration, the measured EFE is minute. We show that this can be attributed to the following facts: (1) The additional charge due to EFE is divided between the electron and hole bands correspondingly to the density-of-states (DOS). The Bi film is in the quantum-size regime, thus the carriers DOS depend linearly on the corresponding effective masses of DOS. (2) The nature of the scattering mechanism is such that the ratio of the carrier mobilities is almost equal to the inverse ratio of the corresponding effective masses. This near equality is the cause of the anomalous EFE in Bi films.