~ t Pergamon Solid State Communications, Vol. 91, No. 3, pp. 251-254, 1994 Elsevier Science Ltd Printed in Great Britain 0038-1098/94 $7.00 + .00 0038-1098(94)E0251-6 PLASMONS IN DOPED SEMICONDUCTOR SUPERLATTICE WITH CHARGE DEPLETION AND A CAPPING LAYER E.L. Albuquerque Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970-Natal, RN-Brazil (Received 15 November 1993; in revised form 14 March 1994 by A.A. Maradudin) We present a theoretical analysis for the collective plasmon-polariton modes of a doped superlattice consisting of two-dimensional electron gas and two-dimensional hole gas layers separated by media of alternating thickness and dielectric constant. Our theory takes into account the effects due to a capping layer, as well as charge depletion near the superlattice surface. We use a theoretical model based on linear response function together with a transfer matrix approach to determine the plasmons dispersion relation and Green functions. Numerical applications are made to semiconductor superlattices, with interesting features for the plasmon surface modes. WITH the development in recent years of modulation- doped semiconductor superlattices, many investiga- tions have been turned out to determine the collective excitations of periodic arrays of two-dimensional electron (hole) gas layers. Theories for the spectra of bulk and surface plasmon in these structures have been given, using various different models, by a number of authors [1-9]. On the experimental side, the Raman scattering measurements of Olego et al. [10] have provided confirmation of the theoretical predictions for the plasmon dispersion relation, with subsequent Raman scattering experiments for quan- tized plasmon modes of finite superlattices [11, 12]. More sophisticated structure, taking into account charge depletion in the electron gas layer nearest to the surface as well as the presence of a capping layer at the surface, has been recently reported [13], and these effects have been proved to give strong influence on the surface plasmon-polariton properties. It is the aim of this letter to present theoretical considerations about surface plasmon-polariton modes in doped semiconductor superlattice made up of two-dimensional electron (2DEG) and hole (2DHG) gas, respectively, separated by dielectric media. Our investigation takes also into account the effects of charge depletion and the presence of a capping layer. Our purpose is two-fold: First, we want to extend the work of Constantinou and Cottam [13], by considering a more complete structure, as well as our previous work [14], by including surface effects. Second, we would like to explore the existence of novel aspects in the surface plasmon-polariton spectra. Figure 1 shows our superlattiee model, where there is a 2DEG at z = c, L + c, 2L + c, etc., with L=a+b, a and b being the thickness of the dielectric media A and B that fills the space between the charge layers. Also, a 2DHG is found at z = c + a, L + c + a, 2L + c + a, etc. We denote the carrier concentration in each layer by n and p, except near the surface, where it has a different value ns and Ps. There is also a capping layer of dielectric medium C and thickness c on the superlattice surface. The medium outside the superlattice, at z < 0, is supposed to be filled with vacuum. The dielectric function in each medium may be frequency dependent, having the form ej eooj[1 2 2 = - ], (1) where O3pj is the plasma's frequency and ~oojis the back- ground dielectric constant of medium j = a, b, or c. Assuming a p-polarization for the electromagnetic mode, the solutions of Maxwell's equations inside each media can be written as Exj = AI# exp(-ajz) + A2# exp(ajz), (2) Hyy = - iwe°eJ [AIy exp(-ajz) + A21 exp(ajz)], (3) ~j 251