## 3 Results and Discussion
### PIN-Diodes Based on InAlN/GaN DHS with 15, 18, 21% In  
Opposite to the In\({}_{\rm x}\)Ga\({}_{1-\rm x}\)N/GaN DHS with shallow well/high barrier, in case of the In\({}_{\rm x}\)Al\({}_{1-\rm x}\)N/GaN DHS with deep well/shallow barrier, no Franz-Keldysh oscillations were observed. The \(E_{a}\), \(E_{b}\), and \(E_{c}\) transition energies of the GaN barrier showed instead a remarkable dependence on the applied modulation voltage in the range of 2-6 V AC, as depicted in Figure 8a. An ER spectrum with good resolved transitions between the three-split valence band and the conduction band of In\({}_{\rm x}\)Al\({}_{1-\rm x}\)N was recorded only in case of the PIN-diode based on the In\({}_{0.21}\)Al\({}_{0.79}\)N/GaN DHS with the maximum of the investigated indium fractions of 21% In; the respective transition energies of \(E_{a}\) = 3.695 eV,  
Figure 7: ER spectrum of PIN-diode based on In\({}_{0.055}\)Ga\({}_{0.945}\)N/GaN double heterostructure quantum-well with thickness interferences at energies below the band gap energy of In\({}_{0.055}\)Ga\({}_{0.945}\)N.  
3.723 eV, and \(E_{c}\) = 3.748 eV can be evidenced in Figure 8b. An approximated value of the polarization field in the quantum well and the barrier interface can be deduced directly from the measured \(E_{a}\) energy as \(E_{pol}^{W}=E_{a}/d_{QW}\) = 3.695 V/4 nm = 9.24 MV/cm and \(E_{pol}^{B}=E_{a}/d_{u}\) = 3.695 V/23 nm = 1.61 MV/cm, respectively. The mean value of \(E_{pol}\) = 5.42 \(\pm\) 1.63 MV/cm obtained by ER is in excellent agreement with the value determined by CVM as \(E_{pol}\) = 5.1 \(\pm\) 0.8 MV/cm [45]. Line-shape analysis of the ER spectra would exceed the objectives of the present work.  
Results of Comparative Studies of Polarization Fields by Electroreflectance (ER) Spectroscopy and Capacitance-Voltage Measurements (CVM)  
The values of the polarization fields \(E_{pol}\) of the In\({}_{0.055}\)Ga\({}_{0.945}\)N and the In\({}_{0.15}\)Al\({}_{0.85}\)N, In\({}_{0.18}\)Al\({}_{0.82}\)N, In\({}_{0.21}\)Al\({}_{0.79}\)N DHS determined by ER in this work are compared, in Figure 9, with the values determined by CVM in [44; 45; 46] and with theoretically predicted values [19; 26; 38]. The analytical approach indicates moderate polarization fields of In\({}_{0.055}\)Ga\({}_{0.945}\)N (\(-\)1.2 \(\pm\) 0.4 MV/cm) and high polarization fields of In\({}_{0.15}\)Al\({}_{0.85}\)N (5.9 \(\pm\) 0.8 MV/cm), In\({}_{0.18}\)Al\({}_{0.82}\)N (5.4 \(\pm\) 0.9 MV/cm), and In\({}_{0.21}\)Al\({}_{0.79}\)N (5.1 \(\pm\) 0.8 MV/cm) determined by CVM. The (total) polarization field of In\({}_{0.055}\)Ga\({}_{0.945}\)N (\(-\)2.3 \(\pm\) 0.3 MV/cm) determined by ER is in agreement, within the experimental and calculation errors, with the CVM result. The same holds for the polarization field of In\({}_{0.21}\)Al\({}_{0.79}\)N (5.4 \(\pm\) 1.6 MV/cm) extracted from the ER spectra. The field values predicted theoretically by [PERSON] et al. [19], [PERSON] et al. [26], and [PERSON] [38] are of the same order of magnitude. Nevertheless, they also foresee a field decrease with the increase of the In-content higher than experimentally measured, which could be indicative of an underestimation of the piezoelectric field contribution to the total polarization field. On the other hand, the experimental error is quite large, which is partially due to the particularly small InAlN and InGaN layer thickness of 10 nm maximal.  
Figure 8: ER spectra of PIN-diodes based on In\({}_{x}\)Al\({}_{1-x}\)N/GaN DHS: (**a**) selection of transition energies \(E_{a}\), \(E_{b}\), and \(E_{c}\) of the GaN barrier in In\({}_{0.15}\)Al\({}_{0.85}\)N/GaN DHS by variation of AC bias-voltage and (**b**) transition energies \(E_{a}\), \(E_{b}\), and \(E_{c}\) of InAlN in In\({}_{0.21}\)Al\({}_{0.79}\)N/GaN DHS.