Theory of the GaN crystal diode: Negative mass negative differential resistance

The classical description of the electric properties of the vacuum diode is modified to be applicable to the diode structure in a semiconductor crystal when scattering is negligible. The principal modification is the introduction of the effect of the conduction-band structure, and a simple model band structure is assumed. This introduces states with negative effective mass and the Bloch frequency into the problem. A small-signal analysis of the ideal case of ballistic transport in GaN describes conditions for the appearance of a negative differential resistance (NDR) associated with the negative effective mass and yields explicit expressions for the components of the impedance. We show that injection at a finite energy is necessary for NDR, which is present in the frequency range 0 to about 30 THz. An analysis incorporating space charge is also presented and the components of the impedance are calculated explicitly as a function of frequency.