Reversed polarized emission in highly strained $a$-plane GaN/AlN multiple quantum wells

The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been performed to determine the three components of the strain tensor in the active region. Moreover, the experimental results have been compared with the strain values computed by means of a model based on the elastic continuum theory. A high anisotropic compressive in-plane strain has been found, namely, $-0.6\mathrm{\%}$ and $-2.8\mathrm{\%}$ along the in-plane directions $\left[1\overline{1}00\right]$ and [0001], respectively, for the thickest quantum well. The oscillator strength of the lowest optical transition has been calculated within the framework of a multiband envelope function model for various quantum well widths and strain values. The influence of confinement and strain on the degree of polarization is discussed and compared with experiment considering various sets of material parameters.

Figure 1

Schematic showing the orientation of the coordinates $x$, $y$, and $z$ with respect to the crystallographic directions of the multiple QW samples.

Figure 2

(Color online) (a) Low-temperature PL spectra of the four multiple QWs with width $\left(d\right)$ varying from 2 to 16 nm. Full lines correspond to $E\perp c$ and dashed lines to $E\parallel c$. The inset shows the peak energy as a function of QW width (dots) together with the theoretical results obtained by using the parameters of Set 1 (full line). The dashed line results from redshifting the theoretical calculations by 100 meV. (b) DOP vs QW width. Dots correspond to the experimental values. Triangles show the result of calculations using the parameters of Set 1 while squares correspond to Set 2. Lines are guide to the eyes.

Figure 3

Low-resolution TEM image of the 16 nm QW sample along [0001] zone axis showing the morphology of the multiple QWs.

Figure 4

(Color online) HRTEM images taken along the [0001] zone axis and corresponding map of $a_x$ obtained from GPA analysis: [(a) and (b)] 2 nm QW and [(c) and (d)] 16 nm QW.

Figure 5

(Color online) Raman shift of ${\text{E}}_{2\text{h}}$ (squares), ${\text{E}}_1\left(\text{TO}\right)$ (triangles), and ${\text{A}}_1\left(\text{TO}\right)$ (dots) phonon modes of GaN as a function of QW width. The lines are guide to the eyes.

Figure 6

(Color online) Comparison between experimental (full symbols for XRD/TEM, empty for Raman) and theoretical (lines) values of strain as a function of QW width. Squares show the expansion along the growth direction $x$ while triangles and dots correspond to the in-plane compression along $y$ and $z$, respectively.

Figure 7

(Color online) [(a) and (c)] Oscillator strengths $f_y$ and [(b) and (d)] $f_z$ mapped as a function of in-plane strain. The figures correspond to bulk GaN (top) and to the 2 nm QW (bottom). Parameters of Set 1 were used. Contour lines are plotted at intervals of 0.2.

Figure 8

(Color online) Calculated ${\left(\text{DOP}\right)}_{\text{th}}$ mapped as a function of in-plane strain for a 16 nm GaN/AlN $a$-plane QW obtained by using the parameters of (a) Set 1 and (b) Set 2. The full line marks ${\left(\text{DOP}\right)}_{\text{th}}=0$. The open circles correspond to the values of strain obtained by TEM for the 2 nm (lower point) and the 16 nm QWs (upper point).