2.1 Experimental set-up

Two undoped hexagonal GaN films were prepared by organo-metallic vapor phase epitaxy Reference Leroux, Beaumont, Grandjean, Gibart, Massies and Faurie[6] Reference Leroux, Beaumont, Grandjean, Golivet, Gibart, Massies, Leymarie, Vasson and Vasson[7] Reference Grandjean, Massies and Leroux[23] on (0001) sapphire substrates with the c-axis parallel to the growth axis. The samples I and II are 17 micrometers and 7 micrometers thick respectively. In our PL and PLE experiments, excitation is provided by a cw Xe 450W short arc lamp, whose wavelength is selected by a f=32cm double monochromator. The photoluminescence signal is analyzed through a f=1m double monochromator by a Hamamatsu R212 photomultiplier, followed by standard lock-in technics. A reference signal is simultaneously stored which allows a correction of the PLE signal. The energy resolution of our system is 2 meV, for an excitation intensity of several mW.cm⁻². The temperature can be varied from 4K to 300K.

2.2 Low temperature luminescence and luminescence excitation spectra

The PL spectrum of sample I at low temperature (T = 2K) is shown in Figure 1a, the excitation energy is 4 eV. In the following, we will present experimental results on sample I only, as results on sample II are very similar. Several emission bands are observed. The very broad band peaking around 2.3 eV is the yellow band Reference Dingle, Sell, Stokowski and Ilegems[4] Reference Ogino and Aoki[5]. We detect at 3267 meV the donor-acceptor pairs (D⁰−A⁰) recombination involving the usual residual donors and acceptors of GaN Reference Strite and Morkoç[2]. Two phonon replica can be seen at 3175 meV and 3083 meV (the energy of the LO phonon is hω_LO=92meV Reference Cingolani, Ferrara, Lugara and Scamarcio[24]). The whole spectrum is dominated by band edge transitions involving the band and free fundamental A exciton Reference Pankove, Berkeyheiser, Maruska and Wittke[3] Reference Dingle, Sell, Stokowski and Ilegems[4] Reference Leroux, Beaumont, Grandjean, Gibart, Massies and Faurie[6] Reference Leroux, Beaumont, Grandjean, Golivet, Gibart, Massies, Leymarie, Vasson and Vasson[7]. Figure 1b shows the details of the PL spectrum in the energy range 3.4-3.5 eV. Two peaks are observed at 3457 meV and 3474 meV, and a shoulder is seen at 3482 meV. An increase of the temperature leads to an efficient quenching of the two lower energy peaks and a great increase of the shoulder, which becomes the only observed peak at T>100K. Due to temperature induced detrapping of excitons from impurities, only free excitons are observable at high temperature. So we interpret the peak at 3457 meV as an acceptor bound exciton I₁, the peak at 3474 meV as a donor bound exciton I₂, and the shoulder at 3482 meV as the fundamental intrinsic A exciton (this will be confirmed by PLE spectra). A phonon replica of I₂ can be seen at 3380 meV Reference Strite and Morkoç[2] Reference Dingle, Sell, Stokowski and Ilegems[4] Reference Leroux, Beaumont, Grandjean, Gibart, Massies and Faurie[6] Reference Leroux, Beaumont, Grandjean, Golivet, Gibart, Massies, Leymarie, Vasson and Vasson[7].

Figure 1a. Photoluminescence spectrum at low temperature (T=2K), the excitation energy is E_exc = 4 eV.

Figure 1b. Close-up on this photoluminescence spectrum in the range 3.4 - 3.5 eV.

At low temperature, the ratio of the I₂ peak intensity to the yellow band peak intensity or the D⁰−A⁰ emission intensity is about 10³. Band edge excitonic emission is thus much stronger than impurity related emissions, indicating the good quality of our samples.

Figure 2 shows the PLE spectra at 30K, with different detection energies: I₂, D⁰−A⁰, and the yellow band. The A exciton at 3479 meV and an excited excitonic transition at 3498 meV (see below for its interpretation) are very well observed in the PLE spectrum detected at I₂. On the contrary, A exciton appears very weakly in the PLE spectra when we detect at D⁰−A⁰ and at the yellow band. This suggests that the A exciton absorption preferentially promotes the I₂ luminescence. At high energies (far above 3.5 eV), in the electron-hole pairs states, we still get signal when we detect energy at the D⁰−A⁰ line or the yellow band. However, we measure very weak luminescence when the detection energy is set to the I₂ line (see figure 2). We may deduce that e-h pairs are preferentially involved in the relaxation towards the D⁰−A⁰ line and the yellow band.

Figure 2. PL spectrum (dashed line) and PLE spectra (solid lines) detected on I₂: E_det = I₂ = 3.457 eV, on D⁰−A⁰: E_det = D⁰−A⁰ = 3.26 eV, on the yellow band: E_det = yellow band = 2.3 eV. The temperature is T=30K. Spectra have been scaled and shifted for the sake of clarity.

2.3 Luminescence and luminescence excitation spectra versus temperature

The PL spectra for 30 and 150K are reported in figure 3. As temperature increases, the A exciton PL line intensity decreases for the benefit of the D⁰−A⁰ line and the yellow band. The yellow band luminescence intensity turns out to be the strongest at high temperatures. Figure 4 exhibits the PLE spectra of the yellow band versus temperature: the A exciton line becomes increasingly intense as temperature increases. We conclude that the relaxation from the A exciton towards the D⁰−A⁰ transition and the yellow band, which appears to be very difficult at low temperature (see figure 2), is made easier by temperature.

Figure 3. Photoluminescence spectrum at 30 (solid line) and 150K (dashed line). The excitation energy is 4 eV.

Figure 4. Photoluminescence excitation spectra detected at the energy of the yellow band (2.37eV) for 30,100 and 190K. Spectra have been scaled and shifted for the sake of clarity.

We first interpret the excited line we detect at 3498 meV (30K). Following former PLE measurements Reference Ogino and Aoki[5] Reference Monemar[10], we may assume this is the C exciton line. However, many experimental results based on reflectivity (REF) and strain determination Reference Gil, Briot and Aulombard[12] Reference Shikanai, Azuhata, Sota, Chichibu, Kuramata, Horino and Nakamura[13] Reference Volm, Oettinger, Streibl, Kovalev, Ben-Chorin, Diener, Meyer, Majewski, Eckey, Hoffman, Amano, Akasaki, Hiramatsu and Detchprohm[15], have been obtained. These REF-based results suggest this line could also be the excited A(2s) (as it is, most of the authors reinterpret Monemar's C line Reference Monemar[10] as being the A(2s)).

Let us first assume this excited transition (3498 meV at 30K) is the A(2s) line. As the A line lies at 3479 meV at the same temperature, we would end up with an A binding energy of 25.3 meV. This would be in agreement with other experimental results which yield the A exciton binding energy between 20 meV Reference Smith, Chen, Lin, Jiang, Asif Khan, Sun, Chen and Yang[25] Reference Chen, Smith, Lin, Jiang, Wei, Asif Khan and Sun[26] Reference Reynolds, Look, Kim, Aktas, Botchkarev, Salvador, Morkoc and Talwar[27] and 28meV Reference Chichibu, Azuhata, Sota and Nakamura[18].

Figure 5 exhibits the energy positions of the fundamental exciton A and of the first excited excitonic transition for temperatures from 30K to 250K as measured by our PLE experiments (detection is set to the yellow band). We see the A excitonic transition energy decreasing from 3479 meV to 3436 meV, while the first excited excitonic transition energy decreases from 3498 meV to 3472meV, as T is tuned from 30K to 210K. This implies that the energy difference A(2s,T) − A(T) ranges from 19 to 36 meV within this temperature variation. That is, the Rydberg energy would change with temperature. This could only be explained by a thermally induced modification of the reduced masses, this modification being actually caused by thermally induced strains. Shikanai et al Reference Shikanai, Azuhata, Sota, Chichibu, Kuramata, Horino and Nakamura[13] have shown that the reduced effective masses, and thus the binding energy of the A exciton does not depend on strains: therefore, A(2s,T) − A(T) cannot vary with temperature. We conclude that the excited feature we observe must be attributed to the C exciton line.

Figure 5. Energy positions of the observed peaks in our PLE spectra detected at the D⁰A⁰ line and at the yellow band, versus temperature.

We still have to explain why the energy difference A - C changes with temperature. The temperature dependence of the excitonic energies in a bulk Reference Teisseyre, Perlin, Suski, Grzegory, Porowski, Jun, Pietraszko and Moustakas[14] Reference Tsay, Gong, Mitra and Vetelino[28] comes from electron-phonon interactions Reference Tsay, Gong, Mitra and Vetelino[28] and thermal expansion effect, which accounts for the effect of the change of lattice constants on the energy gap. Measurements and calculations of A and C energy positions versus temperature in a GaN bulk are not yet available to our knowledge. However, looking at results on other würtzite materials like Zn0, CdS or CdSe bulks Reference Sobolev, Donetskikh and Zagainov[29], we see that the evolutions of A - C energy versus temperature are practically parallel and we may expect the same tendency for GaN bulks. We thus need another feature to explain the A - C variation with temperature. In our case of a GaN layer grown onto a Sapphire substrate, we must also take into account the different thermal expansion coefficients of these two materials, which will induce additional strains in the GaN layer. Taking a rough evaluation of the thermal expansion coefficients of GaN: α_GaN = 5.6.10⁻⁶ K⁻¹, and of Sapphire: α_Sapph=7.5.10⁻⁶K⁻¹ Reference Buyanova, Bergman, Monemar, Amano and Akasaki[9], we find that varying the temperature from 2K to 250K induces a strain of the order of magnitude of 0.05% in the GaN layer. Shikanai et al Reference Shikanai, Azuhata, Sota, Chichibu, Kuramata, Horino and Nakamura[13] have studied by reflectivity several samples with various strains. If we look at their A-C energy positions versus strain, we see that a variation of 0.05% will cause A-C to change by about 15 meV. This is in reasonable agreement with our results since in our case the shift from 30 to 210K (inducing a strain evaluated to 0.05%) causes A-C to vary by 17meV. We would like to emphasize that this is only an evaluation: to explain quantitatively the different temperature evolutions of A and C excitons, we need to know the strain tensor, the deformations potentials, the thermal dilatation coefficients (and mostly their dependence on temperature), but these data are not available in literature yet.

Following Monemar's idea, we may interpret the small dip in figure 4 (30K) at 3508 meV as the beginning of the band to band absorption. This would yield a binding energy of 29 meV for the A exciton. This value may be debated as PLE experiments are not a straightforward way to determine the Rydberg energy: a fit of the absorption coefficient (including the electron-hole correlation effects) and of the relaxation mechanism would be necessary.