Anisotropic absorption and emission of bulk $\left(1\overline{1}00\right)$ AlN

The intrinsic anisotropic optical properties of wurtzite AlN are investigated in absorption and emission. Full access to the anisotropy of the optical response of the hexagonal material is obtained by investigating the $\left(1\overline{1}00\right)$ plane of a high-quality bulk crystal allowing electric field $\mathbf{E}$ polarization perpendicular ($\mathbf{E}\perp \mathbf{c}$) and parallel ($\mathbf{E}\parallel \mathbf{c}$) to the optical axis $\mathbf{c}$. Spectroscopic ellipsometry yields the ordinary (${\varepsilon }_{\perp }$) and extraordinary (${\varepsilon }_{\parallel }$) dielectric functions (DFs) from $0.58$ up to 20 eV. The comparison of the experimental data with recently calculated DFs demonstrates that Coulomb interaction has a strong impact not only on the spectral dependence around the fundamental absorption edge but also on the high-energy features usually discussed in terms of van Hove singularities. The fits of the second-order derivatives of ${\varepsilon }_{\parallel }$ and ${\varepsilon }_{\perp }$ provide the transition energies for the main features in this range. The DFs close to the fundamental absorption edge, dominated by free excitons, exciton-phonon complexes, and the exciton continuum, are independently confirmed by reflectivity and synchrotron-based photoluminescence excitation studies. Values for the band gaps, the crystal field (${\Delta }_{\mathrm{cf}}=-221\pm 2$ meV), and spin-orbit splittings (${\Delta }_{\mathrm{so}}=13\pm 2$ meV) are obtained. Furthermore, we obtain accurate values for the static dielectric constants of ${\varepsilon }_{\mathrm{S}}\perp =7.65$ and ${\varepsilon }_{\mathrm{S}}\parallel =9.21$, entering, e.g., the calculations of exciton binding energies. Photoluminescence is used to investigate the emission properties of the same sample.

Figure 1

Experimental (a) real and (b) imaginary parts of the ordinary (E $\perp$ c, black) and extraordinary (E $\parallel$ c, red) dielectric functions of wurtzite AlN at room temperature in an energy range from $0.58$ to 20 eV. The labels are explained in the text; corresponding energy values are summarized in Table . (c) The imaginary parts of the ordinary (black) and extraordinary (red) dielectric functions of wurtzite GaN are shown in the same energy range for comparison, composed from Refs. 25 and 28.

Figure 2

Comparison of experimental (blue and red) and calculated (black) imaginary parts of the dielectric functions. The top graph shows the ordinary part, and the lower one shows the extraordinary part. Theoretical results are taken from (a) Ref. 22 and (b) Ref. 23.

Figure 3

Second derivative of the extraordinary dielectric function multiplied by the square of the photon energy (symbols), together with the according fits (solid lines) to evaluate transition energies with high accuracy.

Figure 4

Imaginary parts of (left) the extraordinary and (right) the ordinary dielectric functions as a function of temperature.

Figure 5

Comparison of experimental (blue and red) and modeled (black) imaginary parts of the dielectric function at $T=10$ K. The decomposition of the spectra allows us to assign free excitons including excited states ($\mathrm{FX}$), exciton-phonon complexes (EPC), and contributions due to the exciton continuum or band-to-band absorption. The sum of all contributions is also shown and is in good agreement with the experimental data.

Figure 6

Model fit of the imaginary parts of (top) ordinary and (bottom) extraordinary dielectric functions at room temperature. FX marks a free-exciton transition including excited states with the corresponding valence band symmetry given in brackets. EPC means exciton-phonon coupling, and exc. continuum labels the contributions into the exciton continuum.

Figure 7

(bottom) Selected photoluminescence spectra for different temperatures ($T=10$, 25, 44, 78, 98, 124, 150, 200, 230, $290$ K). The high-intensity part is cut, and the spectra are shifted for clarity. ${\Gamma }_1$ and ${\Gamma }_5$ label the radiative bands assigned to free excitons formed with holes from the ${\Gamma }_{7+}$ valence band and mark their symmetry, respectively. (top) Logarithmic plot of the spectrum at $T=10$ K. Two similarly intense donor bound excitons $D^{0}X$ dominate the spectrum. Bound- and free-exciton spectra for different polarization directions of the electric field are shown in red (E $\parallel$ c, stronger spectrum) and blue (E $\perp$ c, weaker spectrum), respectively.

Figure 8

Temperature-dependent positions of free excitons (symbols) and corresponding Pässler fits (solid and dashed lines). The Pässler parameters are given. In the left graph the green solid squares are resonance energy positions obtained by ellipsometry, and the open symbols are peak energies as read from PL spectra. In the right graph all experimental data points were taken from ellipsometry.

Figure 9

The bottom graph compares a photoluminescence excitation spectrum (red, top trace) with photoluminescence (green, bottom trace). The bound excitons of the PL spectrum are cut for clarity. The top graph shows shifted reflectivity spectra measured by synchrotron radiation under tilted incidence (blue, bottom trace) and by a deuterium lamp under nearly perpendicular incidence using unpolarized light (black, middle trace). Additionally, a calculated reflectivity spectrum for the same conditions is shown (red, top trace). All data are recorded at 10 K.