Electric field amplitudes, Es and Ep, and notations appearing in the transfer matrix method for anisotropic layered structures. Subscripts s (p) denote s (p) polarization. Superscripts + (−) denote right-going (left-going) plane waves. Thick arrows show the propagation direction of plane waves. Index-l values are associated with the multilayer surface (l = 1) and interfaces while the first subscript in the electric field symbols and the subscripts inrefractive indices, n, account for the layer count-number (0: medium of incidence, N + 1: substrate or exit medium). The electric vectors for s-polarization are represented by the ⊗ symbol, as being vertical to the plane of incidence.
Relation between the effective mass and the free carrier concentration used in the optical model.
The 6-layer model used to simulate the FTIR reflectance spectra of the InN/GaN/AlN/Al2O3 structures. A three layer model (red line) is used to account for the carrier concentration profile of the InN films.
(a) Best-fit simulations of the FTIR reflectance spectrum of heteroepitaxial InN with a nominal thickness of 500 nm, obtained considering a free carrier concentration profile consisting of a single layer (dashed line), two layers (dash-dot line), and three layers (short dashed line), respectively. The experimental spectrum is presented using a solid line. (b) The spectra of 4(a) plotted at wavenumbers above 950 cm−1.
(a) Experimental FTIR reflectance spectra of the GaN/AlN/Al2O3 template (solid line) where the InN films where grown. The growth of a 30 nm—thick InN layer leads (dashed line) to a significant change in the restrahlen band. (b) In the assumption of normal incidence, the reflectance-dip of the template related to the LO GaN vibration vanishes. (c) Comparison between simulations considering GaN isotropic (short dashed line) or anisotropic (dashed line). (d) Expanded view of the reflectance spectra of the samples in 5(a) at higher frequencies in the mid-infrared. Interference fringes due to multiple reflections in the GaN layer are apparent. The growth of a thicker InN layer (shifted short-dashed line) leads to a characteristic two –layer modulated interference fringe pattern.
Experimental (solid line) and best-fit calculated (dashed line) reflectance spectra of InN thin films grown on GaN/AlN/Al2O3. (a) 30-nm InN, (b) the 30-nm InN thin film of 6(a) at higher frequencies, (c) 70-nm InN, and (d) 100-nm InN.
(a) Reflectance of a 250-nm InN thin film grown on GaN/AlN/Al2O3. The increased reflectance exceeding the value of 0.5 in the low frequency limit, is attributed to the elevated sheet carrier density of 3.3 × 1014 cm−2. (b) Reflectance of a 500-nm InN thin film grown on GaN/AlN/Al2O3. The sheet carrier density is 6.8 × 1014 cm−2 explaining the high reflectance value of 0.7 observed in the low frequency limit. (c) Reflectance of a 2 -μm InN film grown on GaN/AlN/Al2O3. The free carrier excitations are dominant, screening almost completely the restrahlen band of the substrate. (d) Comparison between the experimental reflectance spectrum of the 2-μm InN film and the spectrum of the InN crystal calculated using the optical parameters of the 2-μm InN sample in 7(c) .
(a) The free carrier damping and plasma frequency in the intermediate layer of the triple-layer stack simulating the InN epitaxial layer versus the thickness of the InN epilayer. The thickness of 100 nm seems to be critical in establishing bulk-like values of free carrier damping and plasma frequency. (b) The values of free carrier concentration and mobility of the intermediate InN layer versus the InN epilayer thickness, extracted by the values of free carrier damping and plasma frequency of 8(a) .
Illustration of the sensitivity of the IR reflectance spectra of 500 nm InN by changing (a) the carrier concentration at the surface accumulation layer, (b) the carrier concentration at the interfacial accumulation layer, (c) the carrier concentration in the intermediate layer of the 3-layer model for InN, and (d) the damping constant in the intermediate layer of the 3-layer model for InN. Apart from the parameters varied, the best-fit values of the 500 nm InN thin film on GaN/AlN/Al2O3 were used in the calculations.
Comparison between the electrical and optical values of sheet carrier density in the InN epitaxial layer.
Electrically (squares) and optically (circles) determined values of sheet resistance in the InN epitaxial layer.
The optically determined values of layer thickness, electron volume concentration, and mobility of the three layers comprising heteroepitaxial InN.
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