Excitons in GaN

The shift of the A line in the epilayers has been connected with the variation of the lattice parameters of GaN [1,11,12], The shift of this line was also measured in samples subjected to hydrostatic pressure (see Datareview A3.1). Combination of all these data permits one to obtain the whole series of excitonic deformation potentials [6,16], Two sets of data are available which are consistent with each other and are given in TABLE 1. The discrepancies between them are linked to the differences in the values of the stiflhess coefficients of GaN used by the authors. Gil and Alemu [6] in their work subsequent to the work of Shan et al [16] used data not available when Shan et al calculated their values. The notations are the same and are linked to the relationship with the quasi cubic model of Pikus and Bir [17], Deformation potentials as and a6 have been obtained by Alemu et al [8] who studied the anisotropy of the optical response in the growth plane of GaN epilayers orthorhombically distorted by growth on A-plane sapphire. For a detailed presentation of the theoretical values of deformation potentials of GaN we refer the reader to Suzuki and Uenoyama [20] who took the old values of the stiflhess coefficients of GaN [21]. 

TABLE 1 The most complete experimental series of deformation potentials in GaN. 

TABLE 2 Summary of free exciton binding energies in GaN. PLE, PL, PR, R, TPS mean photoluminescence excitation spectroscopy, photoluminescence, photoreflectance, reflectance and two-photon spectroscopy respectively. 

FIGURE 4 1.7 K reflectance spectra for GaN epilayers grown on various C-plane AI2O3 and 6H-SiC substrates. The strains are those measured from the radius of curvature at 293 K and corrected to 1.7 K. The data are taken from Skromme [1], who can also fit the evolution of the oscillator strengths with strain using his zero strain value for the A]s exciton line and a crystal field splitting parameter of 3.7 1.4 meV. 

D SELECTION RULES AND EXCITON COUPLING TO THE ELECTROMAGNETIC FIELD 

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In thick ( 300 pm) crystals of GaN electronic excitons of shallow dopants have been observed in far infrared absorption at 215 cm 1 [44], Interpreted as the ls-2p transition of a residual shallow donor, its binding energy was calculated to be (35.5 0.5) meV. Further modes at 149 and 242 cm 1 have been observed in mixed phase GaN/GaAs in Raman scattering and have been associated with electronic excitations of shallow donors in cubic and sphalerite GaN, respectively [45] see also [46], Far infared absorption at 23.2 cm 1 in magnetic fields has been used to determine the effective electron mass in GaN, m = 0.20 0.005 m, (corrected for polaron effects) in cyclotron resonance [47]. 

FIGURE 5 The emission from the n = 1 state of the A-exciton in a free-standing 300 pm GaN epilayer in perpendicular (a) and parallel (b) polarisations allows us to determine the LT splitting and the energy of the forbidden triplet exciton [39], In the perpendicular polarisation this peak is found at 3.47904 eV while in parallel polarisation 3.47892 eV is measured. The energy difference of 120 100 peV between the peaks is ascribed to the splitting of these states caused by the exchange interaction. 

Even though reflectance spectroscopy has provided valuable information about strain and excitons in thick GaN epitaxial layers, very little information has been obtained for GalnN/GaN quantum wells by means of reflectance studies. 

Temperature-dependent PL and low-temperature reflection spectra were recorded to determine exciton transition energies in GaN layers. In Fig. 2 the... 

GaN exciton energies for the samples studied and their theoretical dependencies on the strain values in GaN [7] are shown in Fig. 3. From these data we determine that the samples A and B have tensile strains in the GaN layer of about 6.6 kbar and 1.7 kbar, respectively. 

Figure 3. Excitonic recombination energies vs layer stress in GaN [7] and transition energies of the samples A and B.

To model the exciton-phonon coupling, it is necessary to make an assumption concerning the confined electronic wavefunctions in the nonpolar QDs considered here. The Bohr radius in GaN is 2.8 nm so that the potential well along the growth direction is smaller than the Bohr radius and is therefore strongly confining. On the other hand, the typical lateral extent of the QDs is much larger than the Bohr radius so that the carriers are laterally weakly confined. The wavefunction can thus be assumed to be quasi-two dimensional and formally described as under ... 

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