What special type of diode is capable of both amplification and oscillation?

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Tunnel diodes have a very heavily doped p-n junction, which makes the depletion region extremely thin. This allows quantum tunneling to occur even when the diode is forward biased, producing a region of negative differential resistance in the current–voltage curve. That negative resistance enables the device to act as both an amplifier and a microwave oscillator when biased with an appropriate load and circuit elements. Zener diodes rely on breakdown to regulate voltage and don’t provide gain or sustained oscillation. Point contact diodes were early detectors and mixers, not designed for amplification with a negative-resistance region. Junction diodes follow the normal diode I–V behavior and lack the negative resistance needed for amplification or oscillation.