Strong optical polarization in nonpolar $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N/AlN quantum wells

The optical polarization properties in nonpolar $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N/AlN quantum wells (QWs) are investigated over the full range of Al compositions. The $\mathit{k}·\mathit{p}$ calculation predicts that the lowest energy optical transition in $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N layers pseudomorphically grown on unstrained AlN is dipole allowed for the electric field vector parallel to the [0001] direction, and that the degree of polarization is hardly affected by the Al${}_x$Ga${}_{1-x}$N QW width regardless of the Al composition. Experimentally, Al${}_x$Ga${}_{1-x}$N/AlN QWs ($0\le x\le 0.81$) are homoepitaxially grown on AlN substrates. Photoluminescence spectroscopy reveals that the emissions of all QWs, including GaN/AlN QWs, are strongly polarized along the [0001] direction. This result agrees with the theoretical prediction.

Figure 1

Calculated A, B, and C valence-band energies in pseudomorphic $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N single layers on unstrained AlN as functions of Al composition. Relative energies with respect to the A valence band in AlN are drawn.

Figure 2

In-plane polarization degrees concerning A, B, and C band-related transitions in (a) pseudomorphic and (b) strain-relaxed $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N single layers on AlN.

Figure 3

(a) In-plane polarization degree of the A band-related transition in pseudomorphic $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N/AlN QWs on unstrained AlN. Assumed well widths are 1, 2, 5, and 10 nm. The inset indicates the in-plane polarization degree as a function of well width for GaN/AlN and Al${}_{0.25}$Ga${}_{0.75}$N/AlN QWs. Very small variation is confirmed. (b) Calculated effective hole masses along the $\left[1\overline{1}00\right]$ direction ($\perp$[0001]) for the A, B, and C bands in the unit of the electron mass ($m_0$). The strain within the $\left(1\overline{1}00\right)$ plane due to the lattice mismatch with the unstrained AlN underlying layer is taken into account.

Figure 4

Configuration of the crystal axes of the AlN substrate.

Figure 5

(a) PL spectra of nonpolar $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N/AlN QWs at 10 K. The well width of GaN QW is 0.5 nm, while those for the remaining QWs are 3.8 nm. (b) In-plane polarization PL spectra for select QWs.

Figure 6

In-plane polarization degree of nonpolar $\left(1\overline{1}00\right)$ Al${}_x$Ga${}_{1-x}$N/AlN QWs. Squares, circles, and crosses represent QWs with thicknesses of 0.5, 3.8, and 6.5 nm, respectively. Curves are the calculated polarization degrees for pseudomorphic and unstrained QWs.

Figure 7

Polarization degree and emission energy of GaN/AlN single QWs with various well widths.