Optical effects based on intersub-band-transitions in quantum wells

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Abstract

Unipolar devices based on intersub-band-transition have been developed in the last decade [Appl. Phys. Lett. 65 (1994) 2901]. However, this technique will not be directed applicable for the longer wavelengths corresponding to Tetrahertz frequencies. In this work we analyze a THz device based on the intersub-band-transitions of an asymmetric double quantum well. We first study the intersub-band optical absorption in superlattice made of asymmetric double quantum wells tailored as a three level system. By applying an external electric field we obtain the Wannier–Stark ladder and can tune the transition energies between the sub-bands to reach the THz absorption between the two excited sub-bands. Although the dipole moments are big, the relative THz absorption to the other frequencies is small. However, reported lifetimes for this system encourage the possibility of getting population inversion, which is the main condition to design a laser. With this goal, it is presented a detailed study of the geometric design of the asymmetric double quantum well by performing an accurate calculation of the energies and wave functions, the dipole moments and the electron–LO-phonon interaction form factors, which are important ingredients of the scattering rates results. Furthermore, we analyze the role of electron–LO-phonon scattering in THz devices.

Introduction

Semiconductor nanostructures have attracted interest for many years due to their applications in microelectronics devices [1], [2]. The carrier–phonon interaction governs the transport and optical properties in semiconductors. One of the important issues in the study of electron tunneling in nanostructures is the scattering through the electron–phonon interaction. The effect of electron–phonon interaction on tunneling has been theoretically treated by several investigators [3], [4], [5]. It has been shown that the boundary conditions uniquely determine the transmission and reflected plane waves. On the other hand, it is known that intrawell–intersub-band-transitions yield a large radiative dipole moment and a lesser sensitivity to interface roughness, to properly design THz lasers. Recently it has been reported that measurements of narrow line-width THz intersub-band emission result from interwell–intersub-band-transitions from a three level system [6], [7]. Moreover, the second level can be emptied by fast LO-phonon scattering. A novel tailoring of a three level system is presented, in which the interwell transition with the features of intrawell transition is proposed. It is an asymmetric double quantum well (a-DQW) in which we have already estimated the charge buildup time by calculating the probability of finding the electron in each one of the two wells [8] and study the polaronic effect in its charge dynamics [9]. In this paper, an a-DQW superlattice is analyzed as a possible THz device and a systematic study of the role of geometry on the dipole moments and scattering rates is presented. The paper is organized as follows. In Section 2, the calculated absorption spectra are shown for an a-DQW superlattice, which is designed to behave as the active region of a THz laser based on the resonant tunneling that can be tuned with an external electric field. Section 3 is devoted to the study of the optimal geometric design of the basic device. Starting with a comparison of the results for the infinite confined system and the one with finite confinement, the most accurate eigen-energies values and wavefunctions are presented. Then the corresponding dipole moments are analyzed and also the form factor for electron–LO-phonon interaction is examined before the electron–LO-phonon scattering rates are obtained. Summary and conclusions are presented in Section 4.

Section snippets

The three level double quantum well as active region of a laser

In the region of THz radiation, between high-frequency electronics and mm-wave photonics, the electronic techniques rapidly roll off as these super high frequencies are reached, as semiconductor electron relaxation rates are approached and also photonics techniques fail at these low frequencies, partly because relative line-widths, which are narrow in the optical part of the spectrum become huge down in the THz. Solid state systems also bear many resonances in these region which render most

Optimization procedure

As a first step to choose the optimal geometric design of the three level device, we compare the infinite confined a-DQW with and the finite confined a-DQW. For the infinite confined well, the eigen-energies are higher than in the finite walls device as expected (Fig. 3). When varying the wells ratio: dl/dr (narrow well width to wide well width) the condition of only three solutions for both designs is obtained within the range 0.4–0.6. For the finite well, there are solutions up wells ratio

Summary and conclusions

An a-DQW designed as a three level resonant tunneling system working in the THz region of the electromagnetic spectrum is chosen to study the role of geometry on the optical properties of heterostructures by calculating very accurately the eigen-energies, eigen-functions, dipole moments, electron–LO-phonon from factors and scattering rates. The optical absorption of an a-DQW superlattice, designed to work in the THz region and in the presence of an electric field is studied and it is found that

Acknowledgements

This work was partially supported by Instituto Colombiano para el Fomento de las Ciencias y la Tecnologı́a Francisco José de Caldas-COLCIENCIAS, Grant 1204-05-11405 and Fundación para la Promoción de la Ciencia y la Tecnologı́a del Banco de la República, Grant 200302.

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