Plasmon modes of a superlattice — Classical vs quantum limits

The collective plasmon excitations of a superlattice are investigated in both the classical and quantum limits. Using a model that is applicable to superlattices whose constituent layers are either semiconductor- semiconductor, semiconductor-metal, or metal-metal, we show that the surface plasmon interface modes of each layer (slab) couple via the long range Coulomb interaction into two bands of plasmons with dispersion along the superlattice axis. Results for plasmon dispersion are presented for the classical limit (de Broglie wavelength less than the layer width) where the response is treated via a solution of Maxwell's equations using the bulk 3-D dielectric constant to describe each intervening layer. These results are compared to the plasmon dispersion in the quantum regime where the wave-vector frequency dependent dielectric constant of the superlattice is calculated taking into account quantization effects (subband structure). The relationship between the modes in both limits is derived.