Infrared optical anisotropy of diluted magnetic ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}∕c$-sapphire epilayers grown with a GaN buffer layer by metalorganic chemical vapor deposition

Optical anisotropy of hexagonal ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ ($x$ from 0.0% to 1.5%) epitaxial films grown on $c$-plane sapphire substrates has been investigated using far- and mid-infrared $s$- and $p$-polarized reflectance spectra at oblique incidence (at 10°, 22°, and 32°, respectively). The experimental data at room temperature can be well reproduced simultaneously in the measured frequency region of $200–2000{\mathrm{cm}}^{-1}$ $(5–50\mu \mathrm{m})$, which was based on a four-phase layered system using a $4\times 4$ matrix method [M. Schubert, Phys. Rev. B 53, 4265 (1996)]. The lattice vibrations perpendicular and parallel to the optic $c$ axis ($E_1$ and $A_1$ modes) were expressed by Lorentz oscillator dielectric function model. There was a striking absorption dip at the $A_1$ phonon frequency in $p$-polarized reflectance spectra due to the optical anisotropy. These infrared-active phonon parameters were obtained with uniaxial dielectric tensor. It was found that the $A_1$ longitudinal-optical phonon frequency linearly increases with the Mn composition for the diluted magnetic semiconductor epilayers. The broadening values of the $A_1$ phonon changed from 3.6 $(\pm 1.3)$ to 9.0 $(\pm 1.6){\mathrm{cm}}^{-1}$, showing the high film crystal quality. Moreover, the ordinary and extraordinary dielectric functions ${\epsilon }_{\perp }$ and ${\epsilon }_{\Vert }$ of the epilayers were determined. It indicated that ${\epsilon }_{\Vert }$ was larger than ${\epsilon }_{\perp }$ for the ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ films in the reststrahlen region, which can be ascribed to slight structural degradation of the wurtzite lattice.

Figure 1

Calculated $p$-polarized infrared spectra $R_p$ corresponding to (a) Berreman effect and (b) optical anisotropy of the GaN film on sapphire at different angles of incidence. The solid, dashed, and dotted lines represent the data at the incident angles of 0°, 15°, and 30°, respectively. The insets show the $R_p$ reflectance at larger angles of incidence in the $E_1\left(\mathrm{LO}\right)$ and $A_1\left(\mathrm{LO}\right)$ phonon frequency regions, respectively.

Figure 2

Experimental infrared reflectance spectra (dotted lines) of the GaN film and sapphire, and their best-fit results (solid lines) at oblique incidence. Note that $s$-polarized spectra $R_s$ and $p$-polarized spectra $R_p$ are used for the GaN sample, whereas unpolarized spectra $R_u$ at near-normal incidence are used for the sapphire substrate. The straight dotted and dashed lines indicate the $E_1\left(\mathrm{LO}\right)$ and $A_1\left(\mathrm{LO}\right)$ phonon frequencies, respectively. The horizontal coordinate is the logarithmic unit to enlarge the reststrahlen region.

Figure 3

Experimental infrared reflectance spectra $R_p$ (dotted lines) of the ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ films on the GaN/sapphire and their best-fit results (solid lines) at an incident angle of 32°. The insets show an enlarged fitting region of the $A_1\left(\mathrm{LO}\right)$ phonon mode.

Figure 4

(a) High-frequency ${\epsilon }_{\infty }$, (b) static dielectric constants ${\epsilon }_0$, and (c) the $A_1\left(\mathrm{LO}\right)$ phonon frequencies of the ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ films derived from the Lorentz oscillator model. The solid lines are the linear fitting results to guide the eyes. The symbols “⊥” and “‖” represent the perpendicular $\left(E_1\right)$ and parallel $\left(A_1\right)$ to the optic $c$ axis, respectively. For comparison, the values “◀,” “▶,” and “★” for GaN in (c) are taken from Refs. 28, 29, 30, respectively.

Figure 5

The infrared anisotropic dielectric functions of the ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ epilayers. For clarity, the evolution of ${\epsilon }_{\perp ,\Vert }$ with the Mn composition $x=0.0$, 0.8%, and 1.5% are plotted. The inset is an enlargement of the $E_1$ (dotted lines) and $A_1$ (solid lines) phonon frequency regions for the energy loss functions $\mathrm{Im}(-1∕{\epsilon }_{\perp })$ and $\mathrm{Im}(-1∕{\epsilon }_{\Vert })$, respectively.