Analysis of Reflectance spectra

Fig. 3.4 shows the surface images of DBRs I−VI by an optical microscopy in order to compare the macroscopic morphology of DBR samples with different quarter-wavelength thicknesses. In Fig. 3.4, no evidence of cracks was observed in all DBR samples. Nevertheless, the surface images of DBRs IV−VI show smoother macroscopic morphology than that of DBRs I−III. Specifically, the surface morphology becomes rougher with increasing total thickness in DBR layers, which may originate from the increased tensile strain. Since DBR I has large total thickness, the accumulation of tensile strain is more severe than DBR VI and may result in various types of defects when the accumulation of tensile strain is relaxed. Although the AlN/GaN interfaces are well defined in all DBR samples, as shown in Fig. 3.3, the interfaces of DBRs I and II show relatively rougher than that of DBRs V and VI. This situation is consistent with the observation from optical microscopy.

Fig. 3.5 shows the measured (solid line) and simulated (dashed line) reflectivity spectra of DBRs I−VI. In Fig. 3.5(a), experimental measurement shows that the peak reflectivity of DBR I at 440 nm is about 97.2% and the stopband width is 36.6 nm. To compare experimental and calculated reflectivity spectra, theoretical simulation based on transfer matrix theory was performed using the layer thicknesses listed in Table 3.1 for DBRs I−VI. The refractive index dispersion and the extinction coefficient of the GaN layer were taken from the measured data based on a bulk GaN grown on sapphire substrate. As for the parameters of the AlN layer, since the wavelength range considered here is far away from the bandgap of AlN, we only took the refractive index dispersion into account and ignored the extinction coefficient in our simulation. The corresponding parameters can be found in Refs. [67], [68]. The calculated reflectivity spectra of DBRs I−VI are also shown in Fig. 3.5. By comparing the measured and calculated results, the

characteristics of simulated reflectivity spectrum of DBR I including stopband width and the phase of the short- and long-wavelength oscillations are in good agreement with the measured spectrum, as shown in Fig. 3.5(a).

Fig. 3.4 Optical microscope images of (a) DBR I, (b) DBR II, (c) DBR III, (d) DBR IV, (e) DBR V, and (f) DBR VI.

The calculated peak reflectivity and stopband width are about 98.2% and 43.5 nm, respectively. These calculated values are larger than the measured results, which may come from the degradation of crystal quality in the samples and the structural imperfections such as the deviations from the designed layer thickness and interface

roughness between each epitaxial layer. Moreover, the mismatch between the measured and calculated reflectivity spectra in the short wavelength interference fringes is due to the absorption in the GaN layers because it is difficult to perfectly consider the scattering loss and absorption of the bilayers in our simulation. Additionally, the calculated reflectivity spectrum of DBR VI deviates obviously from the measured result, as shown in Fig. 3.5(f).

Fig. 3.5 Measured (solid) and simulated (dashed) reflectivity spectra of (a) DBR I, (b) DBR II, (c) DBR III, (d) DBR IV, (e) DBR V, and (f) DBR VI.

Since the stopband of DBR VI is centered at a shorter wavelength than tha GaN bandgap (~363 nm), the absorption from GaN layers will play a more important role in the case of DBR VI. Although the extinction coefficient of a bulk GaN was taken into account in our calculation, the effects of strain and defects in the GaN layers of DBRs will modify the original absorption in a bulk GaN. Similarly, the measured short wavelength interference fringes in Figs. 3.5(c)−(e) are not resolved as compared with the simulation results. Consequently, according to the difference between the measured and calculated reflectivity spectra the effect of GaN absorption in the AlN/GaN DBRs is larger than that in a bulk GaN layer. Furthermore, the measured and calculated maximum reflectivity values and stopband widths of the DBRs I−VI are summarized in Fig. 3.6. The GaN absorption significantly influences the reflectivity and stopband width when the designed DBR wavelength is shorter than about 380 nm.

360 380 400 420 440

Fig. 3.6 Measured and calculated maximum reflectivity values and stopband widths of the DBRs I−VI.

In order to further observe the difference of crystal quality between tha GaN layers in DBRs and bulk GaN layers, the RT PL spectra of DBR VI and a bulk GaN grown on sapphire were measured and plotted in Fig. 3.7. We deduced that the PL spectrum of

DBR VI mainly originates from the emission of GaN layers in DBR structures. Since the DBR samples were pumped by 325 nm laser from the top surface, the laser light will be fully absorbed by the GaN layers in DBRs before reaching the GaN buffer layer.

Therefore, the emission from GaN buffer layer could not be observed in the PL spectra.

340 350 360 370 380 390 400

0.0 0.2 0.4 0.6 0.8

1.0 DBR GaN

Bulk GaN

PL intensity (a.u.)

Wavelength (nm) RT

Fig. 3.7 RT PL spectra of DBR VI and a bulk GaN grown on sapphire substrate.

In Fig. 3.7, the emission peak from GaN layers in DBR VI is about 360.7 nm, which is obviously below the emission peak of bulk GaN layer (~363.3 nm). This difference could be induced by the condition of GaN layers grown on partially relaxed AlN layers. Under this circumstance, the GaN layer will suffer compressive strain and have larger bandgap energy than that of bulk GaN layer. Furthermore, by comparing the PL spectra of DBR VI and bulk GaN layer, it is notable that the PL spectrum of DBR VI is obviously broader than that of bulk GaN. The full-width at half-maximum (FWHM) values of the PL spectra measured on DBR VI and bulk GaN are 11.5 and 6.4 nm, respectively. The broader PL spectrum of DBR VI mainly originates from the effects of strain, defects, and dislocations, which will result in inhomogeneous strain distribution in DBR structures and induce different band edge emission energies [69].

As a consequence, the tail of the PL emission spectrum related to the GaN layers in DBR VI would be broader than that in bulk GaN.