In this paper, a functional InGaP/GaAs/InGaAs step-compositional-emitter heterojunction bipolar transistor (SCEBT) is demonstrated. The excellent transistor performance, including a high current gain and a low collector-emitter offset voltage, is achieved under normal operation mode. In particular, an interesting three-state S-shaped negative-differential-resistance (NDR) switch is observed under inverted operation mode at room temperature because of the reduction of base barrier height and discontinuous confinement effects for electrons in a InGaP/GaAs heterojunction and InGaAs quantum well, respectively. The three-terminal base-controlled NDR characteristics and multiple-valued logic applications are also investigated. Consequently, the transistor action and switching characteristics of the studied SCEBT are promising for signal amplifier and logic circuit applications.