Phonons in Short-Period GaN/AlN Superlattices: Group-Theoretical Analysis, Ab initio Calculations, and Raman Spectra

Abstract

We report the results of experimental and theoretical studies of phonon modes in GaN/AlN superlattices (SLs) with a period of several atomic layers, grown by submonolayer digital plasma-assisted molecular-beam epitaxy, which have a great potential for use in quantum and stress engineering. Using detailed group-theoretical analysis, the genesis of the SL vibrational modes from the modes of bulk AlN and GaN crystals is established. Ab initio calculations in the framework of the density functional theory, aimed at studying the phonon states, are performed for SLs with both equal and unequal layer thicknesses. The frequencies of the vibrational modes are calculated, and atomic displacement patterns are obtained. Raman spectra are calculated and compared with the experimental ones. The results of the ab initio calculations are in good agreement with the experimental Raman spectra and the results of the group-theoretical analysis. As a result of comprehensive studies, the correlations between the parameters of acoustic and optical phonons and the structure of SLs are obtained. This opens up new possibilities for the analysis of the structural characteristics of short-period GaN/AlN SLs using Raman spectroscopy. The results obtained can be used to optimize the growth technologies aimed to form structurally perfect short-period GaN/AlN SLs.

The Effect of Interface Diffusion on Raman Spectra of Wurtzite Short-Period GaN/AlN Superlattices

“…Namely, the band at ~730 cm −1 , which corresponds to the A 1 (LO) phonon mode localized in GaN layers, dominates with approximately the same intensity for both m = 4 and m = 6. Besides, there are two lines for m = 4 and three lines for m = 6 in the spectral range B 1 – A 1 (LO) AlN , which agrees with the results presented in [ 35 ] for (GaN) m /(AlN) m SLs with sharp interfaces.…”

“…This is consistent with the large dispersion range of A 1 (LO) and B 1 (high) phonons of bulk AlN. By the number of such lines, one can estimate the thickness of the corresponding layers [35]. On the contrary, the dispersion of A 1 (LO) and B 1 (high) phonons in bulk GaN is nearly flat along the Г-A direction.…”

“…As a next step, using migration-enhanced epitaxy at a substrate temperature of 780 °C, a nucleation layer with the thickness of 65 nm was formed on these substrates, and then, using metal-modulated epitaxy at the same temperature, the buffer layers with a thickness of about 300 nm were grown as described in detail in [ 34 ]. The SLs with the total thickness of about 500 nm were grown at relatively low growth temperatures of 690–700 °C at metal-enriched conditions with the F III /F N2* flux ratio above 1, followed by periodic annealing of the excess metallic (Ga) phase in accordance with the approach described in [ 35 ]. Low growth temperatures were chosen to kinetically suppress Ga segregation, which usually manifests itself at the upper interface of GaN/AlN quantum wells of any thickness if they are grown at higher temperatures, which is associated with a significant difference in the binding energies of Ga and Al atoms with nitrogen [ 36 ].…”

“…Figure 2 shows the results of ab initio simulation of Raman spectrum of the (GaN) 6 /(AlN) 6 SL in the spectral region of A 1 (LO) modes. The calculations were performed under the assumption of sharp interfaces between the SL layers; a detailed description of such calculations is given in [ 35 ]. The same figure shows the experimental Raman spectra for two (GaN) 6 /(AlN) 6 SLs grown by PA MBE and MOVPE.…”

“…As noted above, in (GaN) m /(AlN) n SLs with sharp interfaces, the A 1 (LO) modes are standing waves confined in separate layers of the SL. It was shown in [ 35 ] that only half of them will give noticeable spectral peaks (this is determined by the parity of the harmonic). The most intense peak will correspond to a harmonic with a wavelength equal to half the thickness of the corresponding layer.…”