Breaking the Intersubband Selection Rules for Absorption with $\mathrm{Zn}\mathrm{O}$ Quantum Wells: Light Polarization Sensitivity under Normal Incidence

Intersubband (ISB) absorption in quantum wells (QW) at normal incidence is forbidden by the selection rules for light polarization. To be useful under this convenient geometry, QW structures require postgrowth texturing of the surfaces. Here, we demonstrate polarization-sensitive ISB absorption of light at normal incidence using as-grown, nonpolar m-plane $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ multiple QWs without any postprocessing. This breakage of the selection rules is possible due to the formation of a self-assembled V-groove grating QW profile in the direction perpendicular to the c axis, which lies in the growth plane. A geometrical model is developed that predicts the dependence of the ISB absorption strength with the angle of incidence and the QW V-groove angle and is verified by high-resolution transmission electron microscope analysis. As a result of the in-plane anisotropy of the QW grating geometry, a strong light polarization sensitivity is demonstrated under normal incidence, with a predicted polarization sensitivity contrast above 80:1 for a ±5° cone of angles.

Figure 1

(a) Cross-sectional HRTEM image of sample B. (b) Schematic describing the proposed mechanism by which polarization-sensitive, normal-incidence ISB absorption is allowed in m-plane $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ QWs. $\varphi$ is the angle between the QW interface and the growth plane.

Figure 2

(a) Schematic of the samples shown in this work. The table summarizes the relevant parameters. The electron concentration n is extracted from reflectance spectroscopy as described in the text. (b) Schematic describing the experimental setup for transmittance experiments. The plane of incidence of the light is the plane of the page. The angle of incidence of the light on the sample ${\theta }_{\mathrm{ext}}$ can be changed by rotating the sample around an axis perpendicular to the plane of the incidence. Both the polarization of the light and the c axis of the crystal can be independently set perpendicular to or included in the plane of incidence. (c) Calculated potential profile of sample B at room temperature. All the samples presented here show calculated profiles similar to this one. The image includes the Fermi energy for all three samples (dashed red lines).

Figure 3

Ratio of $\mathbf{E}\parallel c$ to $\mathbf{E}\mathrm{\perp }c$ transmittance spectra at normal incidence (a), and ratio of s-to-p polarization transmittance spectra at a 50° angle of incidence (b), for the three samples. The dotted lines in (b) indicate the calculated MSP resonance wave number.

Figure 4

Schematics describing the geometrical model. See details in text. (a) Illustration of the splitting of the problem into two halves. (b) Definition of the symbols and the effective angle of incidence. (c) Definition of the cross-sectional area as seen by the incoming light for $\varphi =0$ and $\varphi \ne 0$ on the left-hand side of the structure. (d) Same as (c) for the right-hand side.

Figure 5

(a) Illustration of the determination of the ISB transition integrated area. (b) The data points indicate the experimental ISB transition integrated area, as measured under p polarization of the incoming light, as a function of the external angle of incidence when c is perpendicular to the plane of incidence, so $\mathbf{E}\mathrm{\perp }c$ for all angles (blue), and when c is parallel to the plane of incidence, so $\mathbf{E}\parallel c$ when ${\theta }_{\mathrm{ext}}=0^{\circ }$ (brown). The lines indicate the calculated ISB transition intensity from the model, adjusting A so the calculation for $\varphi =0$ matches the results when c is parallel to the plane of incidence.

Figure 6

(a) Calculated polarization contrast at normal incidence as a function of the V-groove angle $\varphi$ for light with a $\pm 5^{\circ }$ cone of angles. The value for $\varphi ={14}^{\circ }$ is indicated with a dotted line. (b) Experimental ISB transition intensity at normal incidence as a function of the polarization with respect to the c axis (blue dots). The orange line is the equivalent calculation from the model.