Radiative Recombination Rates in GaN, InN, AIN and their Solid Solutions
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INTRODUCTION Nowadays, the nitride semiconductors such as GaN, AIN and InN attract a considerable attention due to their outstanding physical, chemical and mechanical properties and also because of the recent progress in the technology that allowed to produce high quality nitride films with help of MOVPE and MBE (for a recent review, see Ref. [1]). The attractive
properties of the nitrides include high heat conductivity, hardness, chemical stability and high luminescence intensity. These wide gap semiconductors are very promising materials for LEDs and semiconductor lasers in wide spectral interval from ultra-violet to green and even orange [2] because their solid solutions may have the energy gap varying from 2 eV in InN to 6.2eV in AIN. Important characteristics of materials used in luminescence devices are the rates of different electron-hole recombination processes. However, there is no information at the moment
about the intensities of these processes in the nitrides. In this work, we concentrate on the calculation of the radiative recombination rate in GaN, InN, AIN and their binary alloys GaAl-_,N and InAll_,N on the base of the experimental absorption data that is present in the literature [3-7], the calculated electron energy band dispersion laws [8-11] and the
temperature dependence of the band gaps in the pure materials [12,13]. ENERGY SPECTRA OF THE NITRIDE SEMICONDUCTORS We consider more common and popular hexagonal phase of the nitrides. All of them belong to the crystal class C6,. Their conductivity bands are non-degenerate, and their 69 Mat. Res. Soc. Symp. Proc. Vol. 423 0 1996 Materials Research Society
electron states originate from atomic s-functions. In the P point of Brilluine zone they transform according to 1-, the unite representation of C6,. The valence band is complicated and consists of two branches. One of them transforms according to P1i whereas the other is degenerate and form the two-dimensional representation 1P. If spin-orbit interaction is taken into account, P6 farther splits into two bands, Pr and P7 [14]. However, the latter splitting manifest itself only along k, and k,, but it equals zero in the very P point and along k,, z being the direction of the hexagonal axis c which usually coincides with the normal to the film. We will neglect this splitting and consider P6 as a degenerate band. According to the results of Ref. [6,8-10,15,16], the order of levels in the valence band of the nitrides is different: in GaN and InN, P6 branch lies above P1 , whereas in AIN it lies below Li. The symmetry of the electron wave functions in different bands and band branches leads to the following selection rules for the radiative transitions: * For the transition from r' to P', only z- component of the transition matrix element differs from zero, and correspondingly, the emitted photon is polarized along z axis. * On the contrary, for the transition from PFto Pr, z-component of the transition matrix element equals zero, and the emitted photon polarization is perpendicular to z axis. RADIA
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