## 3 Results and Discussion
### PIN-Diodes Based on InGaN/GaN DHS with 5.5% In
edges, the \(E(k)\) relationship can be approximated by a quadratic equation, where m* is the associated effective mass [65; 66]:  
\[E(k)=\frac{\hbar^{2}k^{2}}{2m^{*}} \tag{7}\]  
A quantum well (QW) formed by two heterojunctions or three layers confines the free carriers in a two-dimensional (2D) system within the two well cladding barrier regions \(\varPhi_{b}\). The pinning of nodes at the boundaries of a well with infinite barrier height \(\varPhi_{b}\) and width \(d_{QW}\) leads to the quantization of \(n\) sub-bands; with respect to the band edges, each sub-band has bottom energy of:  
\[Z(\omega)=R_{S}+\frac{1/R_{P}-i\omega C}{1/R_{P}^{2}+\omega^{2}C^{2}} \tag{2}\]0  
Carriers reside on these sub-bands instead of the band edges of the initially continuous conduction band. The effective energy gap for interband transitions inside the quantum well becomes larger than the bulk \(E_{g}\). Studies on interband excitonic transitions in wurtzite single-crystal GaN films [67], InGaN alloys [68], InGaN/GaN [69; 70], and InGaAs/GaAs [71; 72; 73] single and multi-quantum well structures have already been reported, among them several using ER techniques [74; 75; 76; 77; 78; 79; 80; 81; 82; 83]. However, no reports on the polarization fields of InGaN/GaN double heterostructure quantum wells determined by electro-modulation (ER) in complement with capacitance-voltage (CVM) techniques have been available up to now. The ER spectra of the PIN-diodes based on the In\({}_{0.055}\)Ga\({}_{0.945}\)N double quantum well and the GaN reference structure are presented in Figure 4a,b, respectively. The three-split valence bands associated with the combined effect of crystal field \(\Delta_{cr}\) and spin-orbit \(\Delta_{so}\) splitting can clearly be seen, with the respective energies, \(E_{a}\), \(E_{b}\), and \(E_{c}\), assigned to the sub-bands of heavy holes (HH), light holes (LH), and split-off holes (SO). The transition energies of both the binary GaN and the ternary In\({}_{0.055}\)Ga\({}_{0.945}\)N compounds are in the energy range expected for x = 0 and x = 0.055 indium content [7]. \[Z(\omega)=R_{S}+\frac{1/R_{P}-i\omega C}{1/R_{P}^{2}+\omega^{2}C^{2}} \tag{2}\]1 **(left)** Crystal field and spin-orbit interaction in wurtzite GaN [33; 61; 62; 63; 64] leading to the sub-bands of heavy (HH), light (LH), and crystal-field split-off holes (CH); **(right)** valence band structure of wurtzite GaN with three-split valence bands reproduced from [64] with the permission of AIP Publishing (in the wurtzite structure, crystal-field splitting appears due to the structural anisotropy parallel and normal to the c-axis). Extensive research studies of the optical properties of bulk semiconductors and semiconductor microstructures under the application of modulation spectroscopy, in the past, are being renewed at present [84; 85; 86; 87; 88; 89; 90; 91; 92; 93]. Electromodulation is the most useful of various optical modulation methods since it yields, in general, the sharpest spectral features and is sensitive to surface (interface) electric fields. In the presence of relative stark internal fields, oscillations at energies above the band gap energy are ascribed to the Franz-Keldysh effect [94; 95; 96; 97; 98; 99]. Oscillations at energies 3.29-3.37 eV, in Figure 4b, are thus Franz-Keldysh oscillations (FKOs) of barrier regions of the InGaN/GaN DHS stimulated in the intermediate field regime. The main features of these spectra are the high-electric-field induced Franz-Keldysh oscillations above the \(E_{0}\) transition, the broadening of the excitonic \(E_{0}\) transition, and the clearly observed \(E_{0}+\Delta E_{0}\) In\({}_{0.055}\)Ga\({}_{0.945}\)N direct transition between the spin-orbit splitted valence band and the conduction band.