# Intersubband transitions in nitride heterostructures: theoretical aspects

First, theoretical study of ISB transitions in GaN/Al(Ga)N QWs was performed by Suzuki *et al.* [Suzu 97]. The authors have predicted the possibility of tuning the ISB transition energy to the telecommunication wavelengths and to achieve 1.55 pm for 1.3-1.5-nm-thick GaN QWs with barriers containing at least 80% Al. Electron scattering rates have been calculated [Suzu 98] showing that for a 1.5-nm-thick GaN/Alo.sGao^N QW the dominant mechanism for ISB relaxation is the interaction with longitudinal-optical phonons with a characteristic time of ^100 fs. The carrier thermalization to the subband minimum (intrasubband relaxation) is due to electron-phonon, electron-electron, and electron-impurity scattering, and is as fast as ^10 fs. The quantum confinement in GaN/Al(Ga)N heterostructures have been further simulated by different authors [Kish 02b, Kish 02a, Suzu 03, Iizu 02, Hosh 02]. Kishino *et al. *[Kish 02b, Kish 02a] have calculated the ISB energy *e _{12}* in a GaN/AlN QW as a function of its thickness using the effective-mass approximation. This study allowed evidence for a strong impact of the internal electric field on the transition energy in large QWs, and to calculate a lower limit for the ISB wavelength equal to 1.07 pm. Similar calculations by Iizuka

*et al.*[Iizu 02], taking the electric field in the well as a fitting parameter, allowed estimation of its value as 5-6 MV/cm. Hoshino

*et al.*[Hosh 02] showed that the ISB energy increases when increasing the internal field. Finally, Suzuki

*et al.*[Suzu 03] have performed self-consistent calculations by solving Schrodinger-Poisson equations accounting for the non-parabolicity of the conduction band of GaN.

In the following, we expose the theoretical framework used for the description of ISB transitions in nitride heterostructures.