Nanoscale Tailoring of the Polarization Properties of Dilute-Nitride Semiconductors via H-Assisted Strain Engineering

In dilute-nitride semiconductors, the possibility to selectively passivate N atoms by spatially controlled hydrogen irradiation allows for tailoring the effective N concentration of the host—and, therefore, its electronic and structural properties—with a precision of a few nanometers. In the present work, this technique is applied to the realization of ordered arrays of ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wires oriented at different angles with respect to the crystallographic axes of the material. The creation of a strongly anisotropic strain field in the plane of the sample, due to the lattice expansion of the fully hydrogenated regions surrounding the ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x$ wires, is directly responsible for the peculiar polarization properties observed for the wire emission. Temperature-dependent polarization-resolved microphotoluminescence measurements, indeed, reveal a nontrivial dependence of the degree of linear polarization on the wire orientation, with maxima for wires parallel to the [110] and $[1\overline{1}0]$ directions and a pronounced minimum for wires oriented along the [100] axis. In addition, the polarization direction is found to be precisely perpendicular to the wire when the latter is oriented along high-symmetry crystal directions, whereas significant deviations from a perfect orthogonality are measured for all other wire orientations. These findings, which are well reproduced by a theoretical model based on finite-element calculations of the strain profile of our ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ heterostructures, demonstrate our ability to control the polarization properties of dilute-nitride micro- and nanostructures via H-assisted strain engineering. This additional degree of freedom may prove very useful in the design and optimization of innovative photonic structures relying on the integration of dilute-nitride-based light emitters with photonic crystal microcavities.

Figure 1

(a)–(c) Sketch of the process of spatially selective hydrogenation. Following the deposition of a H-opaque Ti mask (a), the sample is hydrogenated (b) at a temperature $T_H=300°\mathrm{C}$. Then, the Ti mask is removed (c), leaving a ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x$ wire embedded in a (GaAs-like) ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ barrier (the wire is oriented along the [100] axis in this sketch). The effective N concentration ($x_{\text{eff}}$, corresponding to the concentration of unpassivated N atoms) distributions displayed as a gray scale in (b) and (c) are the result of finite-element calculations based on the model of H diffusion introduced in Ref. [32] and correspond to hydrogenation times of 5000 and of 10 000 s, respectively ($T_H=300°\mathrm{C}$). The coordinate system established in (c) will be employed throughout the remainder of this work.

Figure 2

(a) Expanded view of the spatial distribution of the effective N concentration ($x_{\text{eff}}$) in the plane perpendicular to a ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wire [i.e., in the $yz$ plane; see, also, Fig. 1]. (b) $x_{\text{eff}}$ profiles along the horizontal lines displayed in (a), placed at four different points along the wire height (from bottom to top: light blue squares at 25 nm from the wire bottom; dark blue diamonds at 75 nm; red triangles at 125 nm; green circles at 175 nm). The N-induced photoluminescence (PL) redshift corresponding to each value of $x_{\text{eff}}$ is reported on the right-hand axis. (c) Nonpolarized micro-PL spectrum (temperature $T=10\mathrm{K}$; excitation power density approximately $100\mathrm{kW}/{\mathrm{cm}}^2$) of a single ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wire oriented at 45° (i.e., parallel to the [110] direction).

Figure 3

Spatial distribution (in the plane perpendicular to the wire) of the six components of the elastic strain tensor $ϵ$ in proximity of a ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wire oriented along the [110] crystallographic axis.

Figure 4

Top: False-color micro-PL images (acquired at a temperature $T=80\mathrm{K}$; the contribution of the substrate and of the hydrogenated barriers is filtered out with an 850-nm longpass filter) of the light emitted by arrays of ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wires oriented at 45° (black), 23° (red), 0° (blue), $-22°$ (green), and $-45°$ (yellow) with respect to the [100] axis of the underlying crystal. Center: Polar plots of the micro-PL intensity ($T=10\mathrm{K}$) of single ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wires of different orientations, acquired as a function of the angle $\mathit{\theta }$ between the polarization vector and the [100] crystallographic axis. The experimental data points are plotted as circles (having the same filling color as their corresponding micro-PL image; see above), while fitting curves based on Malus’s law are displayed as solid lines. The values of the degree (${\rho }_{\exp }$) and angle (${\alpha }_{\exp }$) of linear polarization obtained from the fits are also reported for each wire orientation. Bottom: Same as above but for $T=80\mathrm{K}$.

Figure 5

(a) Bar plots (bar width, 2 meV) of the computed energy dependence [at $T_c=80\mathrm{K}$; see Eqs. (5) and (6)] of the intensity of the low- (${\mathbf{I}}_1$, dark gray) and high-energy (${\mathbf{I}}_2$, light gray) transitions that make up the emission of a ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wire oriented at 23° with respect to the [100] crystallographic axis. For the plots shown in the upper (lower) part of the panel, the angle $\theta$ formed by the polarization vector and the [100] direction is set at ${\alpha }_{\mathrm{th}}=118°$ (${\alpha }_{\mathrm{th}}-90°=28°$); i.e., the angle for which the total computed intensity ${\mathbf{I}}_{\text{tot}}={\mathbf{I}}_1+{\mathbf{I}}_2$ is maximal (minimal). The plot relative to $\theta ={\alpha }_{\mathrm{th}}$ is vertically shifted for clarity. (b) Bar plots (bar width, 2 meV) of the computed energy dependence of ${\mathbf{I}}_{\text{tot}}$. The computed spectra corresponding to $\theta ={\alpha }_{\mathrm{th}}$ (118°, dark red) and $\theta ={\alpha }_{\mathrm{th}}-90°$ (28°, light red) are shown. (c) Polar plots of the computed dependence of ${\mathbf{I}}_1$ (dark gray triangles), ${\mathbf{I}}_2$ (light gray squares), and ${\mathbf{I}}_{\text{tot}}$ (dark red circles) on the angle $\theta$ between the polarization vector and the [100] crystallographic axis. In order to construct the curves reported in this panel, the computed intensities are integrated over the whole 40-meV energy interval displayed in panels (a) and (b).

Figure 6

(a)–(e) Average (see main text) PL spectra (temperature $T=80\mathrm{K}$) of the ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x/{\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x:\mathrm{H}$ wires oriented at 45° (a), 23° (b), 0° (c), $-22°$ (d), and $-45°$ (e) with respect to the [100] direction. For each orientation, the spectra relative to the polarization angles corresponding to the maximal (${\mathbf{I}}_{\max }$, red line) and minimal (${\mathbf{I}}_{\min }$, black line) PL intensity are shown, together with the average energy-dependent degree of linear polarization (${\overline{\rho }}_{\exp }$, gray line). (f)–(j) Bar plots (bar width, 2 meV) of the energy dependence of the wire emission calculated through Eq. (7) ($T_c=80\mathrm{K}$; see main text). As in the case of the experimental spectra, the maximum- (red bars) and minimum-intensity (black bars) spectra are shown for each wire orientation, together with the calculated values of the degree (${\rho }_{\mathrm{th}}$) and angle (${\alpha }_{\mathrm{th}}$) of linear polarization. The approximate 30-meV blueshift that can be observed between the experimental spectra and the computed ones is likely another effect of the saturation of the energy levels of the wire due to the high power density (approximately $100\mathrm{kW}/{\mathrm{cm}}^2$) employed in our micro-PL measurements (see main text). In this respect, it should be noted that the estimated dependence of the energy gap on the effective N concentration that is used in the computations $E_g(x_{\text{eff}})$ is, indeed, obtained from conventional macro-PL measurements, performed with a large excitation laser spot (approximately $200\mu \mathrm{m}$) and with a power density (approximately $30\mathrm{W}/{\mathrm{cm}}^2$) more than 3 orders of magnitude lower than the one used for the measurements summarized in (a)–(e).

Figure 7

(a) Dependence of the degree of linear polarization $\rho$ on the wire orientation. The experimental data (acquired at a temperature $T=10\mathrm{K}$) are shown as blue diamonds (the thin-dotted line is a guide to the eye), while the values of $\rho$ calculated at a carrier temperature of $T_c=10\mathrm{K}$ ($T_c=50\mathrm{K}$) are plotted as a solid blue (black) line. (b) Same as (a) for $T=80\mathrm{K}$. The experimental data are displayed as red circles, while the calculated values of $\rho$ ($T_c=80\mathrm{K}$) are shown as a solid black line. (c) Dependence of the angle of linear polarization $\alpha$ on the wire orientation. The experimental data acquired at $T=10\mathrm{K}$ ($T=80\mathrm{K}$) are shown as blue diamonds (red circles), whereas the calculated polarization angle is plotted as a solid black line. The dotted black line represents the angle perpendicular to the wire orientation and is provided as a reference.