Intersubband electroluminescent devices operating in the strong-coupling regime

We present a detailed study of the electroluminescence of intersubband devices operating in the light-matter strong-coupling regime. The devices have been characterized by performing angle-resolved spectroscopy that shows two distinct light intensity spots in the momentum-energy phase diagram. These two features of the electroluminescence spectra are associated with photons emitted from the lower polariton branch and from the weak coupling of the intersubband transition with an excited cavity mode. The same electroluminescent active region has been processed into devices with and without the optical microcavity to illustrate the difference between a device operating in the strong- and weak-coupling regime. The spectra are very well simulated as the product of the polariton optical density of states, and a function describing the energy window in which the polariton states are populated. The evolution of the spectra as a function of the voltage shows that the strong-coupling regime allows the observation of the electroluminescence at energies otherwise inaccessible.

Figure 1

(Color online) Band diagram of the quantum cascade structure at a voltage of 6 V obtained by solving coupled Schrödinger and Poisson equations. The bold curves represent (1) the fundamental and (2) excited state of the radiative transition, as well as the injector state (inj). The energy difference between the state 1 and the injector quasi-Fermi energy is indicated by $\Delta$. The injection and extraction minibands are schematized by triangles.

Figure 2

(Color online) Absorption coefficient of the device with the top mirror: (a) $1-R$ calculated as a function of the photon in-plane momentum and energy, without including the contribution of the intersubband transition. The horizontal dashed line indicates the energy used in the inset. (b) Calculated absorption spectrum, including the contribution of the intersubband transition. The simulation has been obtained by using $E_{21}=161\text{meV}$ and $N_1=6\times {10}^{11}{\text{cm}}^{-2}$. Inset: simulated absorption (in logarithmic scale) at $E_p=160\text{meV}$, plotted as a function of $k_{\parallel }$.

Figure 3

(Color online) Absorption coefficient of the device without the top mirror (air on top): (a) $1-R$ calculated as a function of the photon in-plane momentum and energy, without including the contribution of the intersubband transition. (b) Calculated absorption spectrum, including the contribution of the intersubband transition.

Figure 4

(Color online) Electroluminescence spectra at 4.5 V (14 mA, 50% duty cycle) and 77 K for a device with (left panel) and without (right panel) top metallic contact. The curves indicated by squares have been obtained at a low value of the internal angle while those indicated by circles have been obtained for an angle close to ${\theta }_{res}$. The values of the integrated optical power for the four spectra are the following: left panel: 200 pW $\left(71.8°\right)$, 87 pW $\left(57.9°\right)$; right panel: 68 pW $\left(71.8°\right)$, 120 pW $\left(56.6°\right)$. The inset is an optical microscope picture of the two mesa devices.

Figure 5

(Color online) Electroluminescence spectra (symbol) measured at different voltages from the polaritonic device at an angle of approximately $58°$. The continuous lines are the best fit of the experimental data, given by the sum of two Gaussian functions, shown by dashed lines.

Figure 6

(Color online) Electroluminescence as a function of the photon energy and in-plane momentum measured at 4.5 V (14 mA) and 77 K for the device (a) with and (b) without top metallic mirror.

Figure 7

(Color online) (a) Contour plot of the simulated electroluminescence at 4.5 V, obtained by using Eq. (4). The injector energy position with respect to the fundamental subband is 150.5 meV and its width 12 meV. (b) “Photonic injection” simulated as the product of the electroluminescence spectrum in Fig. 4, left panel, at $57.9°$ times the calculated absorption and the Fresnel coefficients.

Figure 8

(Color online) Contour plots of the electroluminescence spectra measured at different voltages. The values of the current for the voltages indicated in the figure are, respectively: 4 mA, 14 mA, 58 mA, 258 mA, 718 mA, and 2 A. The electroluminescence signal in the contour plots is normalized to one. The peak power is, respectively (from the lowest to the highest voltage): 2.6 pW, 14 pW, 73 pW, 340 pW, 720 pW, and 2.1 nW.

Figure 9

(Color online) Contour plots of the simulated electroluminescence spectra at different voltages. The parameters used for the simulations are presented in Table .

Figure 10

(Color online) (a) Simulated electroluminescence for the polaritonic device, obtained with $N_1=4\times {10}^{11}{\text{cm}}^{-2}$ (red dashed line) and $N_1=1\times {10}^{11}{\text{cm}}^{-2}$ (black continuous line). (b) Normalized electroluminescence signal at the energy of the intersubband transition as function of the in-plane photon momentum, measured at different voltages: 4 V (black line), 4.5 V (red line), 5 V (blue line), 6 V (green line), 7.75 V (pink line), and 13 V (light blue line).

Figure 11

(Color online) (a) Integrated EL measured as a function of the internal angle of light propagation at different voltages: 4 V (black squares), 4.5 V (red circles), 5 V (green triangle), 6 V (blue down triangle), 7.75 V (light blue diamond), and 13 V (pink left triangle). (b) Simulation of the integrated EL at the same voltages as the experiments.

Figure 12

(Color online) Electroluminescence spectra measured at 4.5 V at different energies: 161 meV (Blue triangles), 150 meV (red circles), and 140 meV (black squares). The spectra have been normalized at the weak-coupling peak, in order to evidence the polaritonic emission with respect to the weak-coupling one.