Limits of validity of the 1-dimensional approach in space-charge-wave and Gunn-effect theories

The dispersion relation for space-charge waves propagating in a thick (but finite) Gunn diode is derived. One of the solutions of this dispersion relation is found to be strongly coupled to the dielectric outside the semiconductor, and to exhibit a field amplitude which oscillates as it decays away from the semiconductor surface. The penetration depth of the field for this wave sets a lower limit to the semiconductor thickness, below which the usual 1-dimensional theory becomes questionable.