Transmission and escape in finite superlattices with Gaussian modulation

Abstract

We study the transmission and escape energies dependent as a function of the electron energy in superlattices where the barriers height is modulated by a Gaussian function and they are compared with those produced by regular superlattices where all the barriers have the same height. We use for the calculations the effective mass approximation using the transfer matrix formalism. For Gaussian systems with 7 and 9 barriers, the transmission coefficient has passbands with almost perfect transmission. The escape energies $E=E_r+i\Gamma$ are situated near these transparency bands but they do not coincide with them and they can be far from the passbands. $E_r$ is the electron energy and $\Gamma$ describe the width of the states. For these systems the escape states are very wide. In the case of regular systems there are transmission bands which present only resonance peaks with unit value. The escape states are narrow and coincide with these resonances much better than in the case of Gaussian superlattices but the coincidence is not perfect. For 3 barriers where the height of the lateral barriers is reduced gradually, the resonances transform to transparency bands and the width of the escape energies increases. Although there is no coincidence, we associate the increase of width of the escape energies with the formation of transparency bands.