Resonant-tunneling diodes (RTDs) with auxiliary quantum wells (e.g., emitter prewell, subwell, and collector postwell) are studied using a Wigner transport equation (WTE) discretized by a thirdorder upwind differential scheme. A flat-band potential profile is used for the WTE simulation. Our calculations revealed functions of the auxiliary wells as follows: The prewell increases the current density (J) and the peak voltage (V (p) ) while decreasing the peak-to-valley current ratio (PVCR), and the postwell decreases J while increasing the PVCR. The subwell affects J and PVCR, but its main effect is to decrease V (p) . When multiple auxiliary wells are used, each auxiliary well contributes independently to the transport without producing side effects.