Interface effects in the Raman scattering of InNÕAlN superlattices E. F. Bezerra, E. B. Barros, J. R. Gonc¸alves, V. N. Freire, J. Mendes Filho, and V. Lemos* Departamento de Fı ´sica, Universidade Federal do Ceara´, Centro de Cieˆncias, Caixa Postal 6030, Campus do Pici, 60455 – 900 Fortaleza, Ceara´, Brazil ~Received 11 April 2002; published 24 October 2002! Calculations of the Raman spectra of zinc blende InN/AlN superlattices were carried out assuming the existence of interface regions with thickness d varying from zero to three monolayers. The optical branches were greatly affected by interfacing, while the acoustic branches remained practically unchanged. Frequency shifts up to 80 cm 21 were observed for some of the optical frequencies when d 53. The higher frequency peaks were observed to shift downward with increasing the interface thickness. Many peaks appearing at the low frequency side shift toward the center position of the spectrum. As a consequence, pairs of the Raman modes become quasidegenerate giving rise to highly prominent structures in the spectrum for d 52 and 3. Effects of localization of atomic displacements at the interface regions are shown. DOI: 10.1103/PhysRevB.66.153314 PACS number~s!: 68.90.1g, 63.20.Dj, 63.20.Pw I. INTRODUCTION The great interest of group III nitride semiconductors quantum well ~QW! structures in the fabrication of optoelec- tronic devices is currently known. 1,2 The optical and electri- cal processes in GaN, AlN, and InN based QW and superlat- tice ~SL! structures are remarkably influenced by the existence of interfaces. In GaAs/AlAs QW’s, surface segre- gation leads to the generation of an atomic-scale disorder in the first overgrowth monolayers. 3,4 Several studies in GaAs/ AlAs SL’s suggest the need to consider interface effects in describing the optical phonon spectrum. 5,6 In addition to sur- face segregation the mismatch between the atomic radii of cations and anions is much larger in the nitrides. This aspect is of interest due to the increased disorder to result in wider interfaces. Actually, a typical interface width of 1 nm ~2 nm! was measured for the GaN/InGaN ~InGaN/AlGaN! interface. 7 For GaN/Al x Ga 1 2x N SL’s, Raman measurements indicate interface thickness to be of the order of 2 nm. 8 Those values are much larger than the interface thicknesses found for the arsenide based SL’s. Lattice dynamics calcula- tions result in bulk phonon frequencies to be of use in the simulation of the Raman scattering. 9,10 Previous results show that interfacing effects are responsible for considerable gain in intensity of Raman modes in zinc blende GaN/AlN and GaN/InN SL’s. 11,12 Even though the acoustic branch of bulk AlN overlap with the optical branch of InN, their optical dispersion curves do not overlap. 10,13 Therefore, it is inter- esting to analyze the interface dependence of optical phonons in the InN/AlN SL’s. Here, we calculate the phonon dispersion, ato- mic displacements and the Raman spectra of (InN) 8 2d /(InN 0.5 AlN 0.5 ) d /(AlN) 8 2d /(InN 0.5 AlN 0.5 ) d SL’s, with d 51,2,3. Most of the optical phonons were found to be confined in the abrupt SL probably as a consequence of non- overlapping optical branches of bulk constituents. Strong lo- calization of modes in the InN/AlN interfaced SL’s results as a consequence of interfacing. The insertion of an interface and also accidental degeneracies of modes resulted in the Raman spectrum for d 53 to show a middle frequency peak with intensity comparable with those limiting the optical range. II. RESULTS AND DISCUSSION The present work employs a modified linear chain model with each atom representing a plane of atoms in the actual SL. Therefore, the associated phonons propagating along the @001# axis can be described through a one-dimensional set of equations of motion. 14,15 They can be solved in the harmonic approximation and the eigenvalues and eigenvectors are ob- tained by diagonalization of the dynamical matrix. The force constants were obtained considering interaction to nearest and next-nearest neighbors, only. Alloyed interfaces were considered to have one-mode-type behavior, based on previ- ous demonstrations of this behavior for LO modes in other nitride alloys studied either experimentally, 16–20 or theoretically. 10,21,22 The bond-polarizability model, 14,15 which provides a good description of optical modes, was used to calculate the Raman spectra of the SL’s. Symmetry arguments show that only the LO modes should contribute in the Raman backscattering geometry along @001# of a perfect superlattice constructed with zinc blende–type components. 15 The polarizability constants were assumed to have fixed values throughout the SL. The bulk InN and AlN mode frequencies and the force constants are listed in Table I. The frequencies were chosen as experimental values, when possible, or theoretical values in the lack of the former. Therefore, the AlN zone-center LO frequency was taken as 902 cm 21 from experimental data of Harima et al. 16 and the InN LO( G ) frequency was taken as the value measured by using Raman scattering. 23 The acoustic LA( X ) and LO( X ) frequencies from the AlN dispersion relations reported by Karch et al. 24 Notice that those values are almost coincident TABLE I. Bulk AlN and InN mode frequencies as used in the model to derive the force constants k, q 1 , and q 2 . The frequency values are in units of cm 21 . LO ~G! LO ~X! LA ~X! k (Nm 21 ) q 1 (Nm 21 ) q 2 (Nm 21 ) AlN 902 a 723 b 594 b 222.8 30.0 2.7 InN 588 c 567 d 231 d 128.2 26.9 2.8 a From Ref. 16 c From Ref. 23 b From Ref. 24 d From Ref. 25 PHYSICAL REVIEW B 66, 153314 ~2002! 0163-1829/2002/66~15!/153314~4!/$20.00 ©2002 The American Physical Society 66 153314-1