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Influence of the structural inhomogeneity on the luminescent properties of nitride multiple quantum wells grown by MOCVD

We investigated GaN/InGaN multiple quantum wells grown by MOCVD for LED application in the blue and green regions. The sample considered was characterized by a significant number of defects on the interfaces between the layers. We examined the heterostructure by means of cathodoluminescence. Due to the composition and the layer's thickness fluctuations on a small and a large scale, we observed peak splitting and broadening. In order to justify our assumption, we compared the experimental results with our theoretical calculations. The theoretical model used is based on the T-matrix formalism.


Introduction
The III-nitride layered heterostructures have acquired widespread applications as building blocks in manufacturing of devices for optical communication, high-electron-mobility transistors, ultra-violet lasers and resonant-tunneling-based structures for THz applications [1][2][3]. Along with the attractive characteristics [4], they also possess very specific ones, such as well pronounced piezoelectric and spontaneous polarizations along the low-symmetry axis. These features should always be taken into account when considering thin III-nitride layers, especially in superlattices and multiple quantum wells. The optical properties of such structures are greatly affected by the presence of macroscopic polarization in the layers. Another important factor that influences the optical properties is the interface roughness, which is manifested as wells with fluctuations [5][6][7].
In this study, we examined by means of cathodoluminescence an InGaN/GaN multiple quantum well (MQW) grown by MOCVD on a GaN substrate. All measurements were conducted at room temperature. Further, we compared the experimental results with our theoretical calculations based on the model briefly described in [8]. Our main goal was to demonstrate that, despite the idealizations and the simplifications we have made, our calculations are in a satisfactory agreement with the experimental results. We conducted our calculations in the framework of the effective-mass approximation and the T-matrix formalism. To ensure the accuracy desired, the Airy function formalism was used to solve the one-dimensional Schrödinger's equation for the MQW potential.

Theoretical framework and calculation details
The multi-layered structure examined was composed of three layers of In x Ga 1-x N (forming the potential wells) alternating with three layers of GaN (forming the potential barriers), grown on a GaN substrate. In order to calculate the levels of the electrons and the holes and, therefore, the optical transition energy, we examined the one-dimensional potential of the MQW. Due to the spontaneous and piezoelectric polarization in the layers, the profiles of the wells and the barriers assume a trapezoidal shape. The magnitudes of the corresponding electric fields were calculated to be [9]: in the wells and barriers regions, respectively. Here w,b P represents the total polarization in a layer, L , its thickness, w,b ε , the relative permittivity of the materials, and 0 ε , the permittivity of vacuum.
Having determined the potential across the MQW, we found the electron and hole states in the wells (using the effective-mass approximation) and, thereupon, the interband transition energies. In order to perform the calculations, one needs a set of material parameters, which are systematized in table 1. All the parameters of GaN and InN were extracted from [10] The parameters of In x Ga 1-x N were calculated following [9] by setting 0.2 x = : The transition E1 HH1 → as calculated to have an energy of 2.81 eV, which corresponds to a wavelength of 441nm . In order to estimate the influence of the structural inhomogeneity of the In 0.2 Ga 0.8 N layers (the wells), we performed the same calculations for MQW structures with different   , and kept all other parameters the same throughout the calculations.

Results and discussion
The luminescent spectrum shown in figure 2 was obtained from the sample considered above. Two distinct peaks are clearly observed. The leftmost peak on figure 2(a)  for the quantum wells with a nominal width ( w 40 nm L = ). For the quantum wells whose width is increased by 2 ML, the transition energy is calculated to be  The splitting observed in the luminescent spectrum is most likely due to fluctuations in the InGaN well width, which inevitably occur during the growth process. This assumption is supported by the fact that the difference of 110 meV between the peaks (in the measured spectrum) is very close to the difference of 90 meV between . In our theoretical results, we observed a certain tendency toward the lower transition energies, which is most likely due to a composition ratio that differs from the nominal during the growth process, or to the chosen set of band parameters. For example, a higher value of the InGaN bandgap energy would have resulted in higher transition energies. Apart from this, our calculations are in a good agreement with the experimental results.

Conclusions
We examined both theoretically and experimentally the transition energies in InGaN/GaN MQW grown by MOCVD. We calculated the optical transition energy taking account of the well-width fluctuations. The splitting of the peak that corresponds to the E1 HH1 → transition was explained by the well-width fluctuations. The luminescence spectrum observed supported our theoretical results, although the latter showed a certain shift toward the lower energies. This might be corrected in further calculations by choosing another set of parameters or by changing the composition ratio.