Purcell enhanced electroluminescence of a unipolar light emitting quantum device at 10 micron

Technical Summary: Purcell Enhanced Electroluminescence of a Unipolar Light Emitting Quantum Device at $\lambda = 10$ $\mu$m

Problem Statement
Efficient radiation generation in the mid- and far-infrared (4–20 $\mu$m) has historically relied on lasers and coherent nonlinear optical phenomena. Standard light-emitting diodes (LEDs), which dominate the visible spectrum, are inefficient in this wavelength range. This inefficiency arises because the spontaneous emission rate ($\tau_{sp}$) scales with the cube of the photon energy ($\propto (\hbar\omega)^3$). Consequently, in the mid-infrared, the spontaneous emission lifetime increases by orders of magnitude, rendering the radiative channel vastly slower than non-radiative energy relaxation processes. As a result, conventional unipolar emitters (such as quantum cascade structures) operating in a standard mesa configuration exhibit extremely low efficiency, as non-radiative processes dominate over spontaneous emission.

Methodology
To overcome these limitations, the authors engineered a unipolar light-emitting device based on an array of patch-antenna nano-emitters, forming an active metamaterial. The device consists of an InGaAs/AlInAs heterostructure (designed for $\sim$9 $\mu$m operation) sandwiched between two metallic plates, creating double-metal microcavities.

• Structure: The active region is embedded in an array of microcavities with lateral size $s \approx 1.4$ $\mu$m, thickness $H = 0.75$ $\mu$m, and periodicity $p = 7$ $\mu$m. The top and bottom metal layers serve as both optical resonators and electrical contacts.
• Fabrication: The process involves wafer bonding, substrate removal, and the deposition of dielectric and metal layers to define the patch antennas via electron-beam lithography and dry etching.
• Characterization: Devices were characterized using Fourier Transform Infrared (FTIR) reflectivity, electroluminescence (EL) spectroscopy, and far-field radiation profiling using a Mercury Cadmium Telluride (MCT) detector at 78 K. The study compared the metamaterial device against a standard mesa-geometry device (without the cavity effect) to isolate the impact of the photonic environment.

Key Contributions and Results
The study demonstrates that reshaping the photonic environment via the Purcell effect can significantly enhance spontaneous emission in the mid-infrared, enabling efficient electroluminescent devices.

1. Beam Collimation and Directionality:
   The patch antenna array acts as a super-mode resonator coupled via surface plasmons. This configuration produces a naturally collimated beam with extremely low divergence. Far-field measurements of a $20 \times 20$ array revealed angular divergences of $\theta_{div,x} = 0.67^\circ$ and $\theta_{div,y} = 0.77^\circ$. This is a significant improvement over edge-emitting devices and surpasses the record values for THz QCLs based on similar metamaterials (typically $\sim 2^\circ$), eliminating the need for external collimation optics.

2. Power Enhancement and Quantum Efficiency:
   By embedding the emitter in the patch antenna metamaterial, the collected power was increased by two orders of magnitude compared to the mesa device. At 80 mA, the patch-cavity device emitted 2.9 $\mu$W, whereas the mesa device emitted only 0.03 $\mu$W. The emission quantum efficiency ($\eta_{QE}$) was measured at $2.25 \times 10^{-4}$, a value significantly higher than typical spontaneous emission sources in the infrared.

3. Spectral Filtering and Purcell Enhancement:
   The microcavity acts as a spectral filter, narrowing the electroluminescence linewidth by a factor of 2 compared to the mesa device. The quality factor of the EL spectrum ($Q_{EL} = 18$) exceeded that of the bare cavity ($Q_{cav} = 14$), indicating the cavity also functions as a resonator for modal gain.
   The authors quantified the emission rate enhancement using the Purcell factor ($F_P$). Calculations yielded a Purcell coefficient of $F_P = 7$. This enhancement is attributed to the coupling of the microscopic intersubband dipoles to the single cavity mode, which modifies the spontaneous emission rate.

4. Theoretical Modeling:
   The experimental data were successfully modeled using adapted quantum cascade laser rate equations that incorporate the Purcell factor for both spontaneous and stimulated emission. The model, solved in the sub-threshold regime, accurately reproduced the light-current characteristics. It identified a laser threshold current density of $\sim 25$ kA/cm$^2$. The authors note that this high threshold is currently limited by optical losses (10 times higher than ridge lasers), with approximately 80% of these losses being radiative (intended for efficient out-coupling).

Significance
The paper claims to demonstrate that it is possible to conceive efficient optoelectronic light-emitting devices operating close to thermodynamic equilibrium in the mid-infrared, similar to visible-range LEDs, by engineering the photonic environment. The work illustrates that the Purcell effect can be harnessed to overcome the fundamental inefficiency of spontaneous emission at long wavelengths.

The significance lies in the ability to generate a collimated, high-power beam from a spontaneous emission source without relying on stimulated emission (lasing) or external optics. The authors suggest that while the current configuration is limited by radiative losses inherent to the efficient out-coupling design, future improvements could be achieved by engineering higher-order cavity modes to increase the quality factor and lower the lasing threshold, potentially enabling true lasing action in these metamaterial structures.