In one aspect, a transistor comprises a metal emitter, a first semiconductor barrier, a metal base, a second semiconductor barrier, and a metal collector. The first semiconductor barrier separates the metal emitter and the metal base and has an average thickness based on a first mean free path of a charge carrier in the first semiconductor barrier emitted from the metal emitter. The second semiconductor barrier separates the metal base from the metal collector and has an average thickness based on a second mean free path of the charge carrier in the second semiconductor barrier injected from the metal base. The metal base comprises two or more metal layers and has an average thickness based on a multi-layer mean free path of the charge carrier.
