We report the coupling and interaction between shallow donors and microcavities in bulk GaN at THz frequencies. At 4K, the shallow donors lead to an absorption at 23.5 meV (5.7 THz) under optical pumping above the bandgap of GaN. The microcavities are based on metamaterials and are designed to resonate around 5.7 THz. At 4 K, the matter-cavity interaction is clearly demonstrated on differential transmission of the sample. The cavity resonance shifts when the absorption occurs. Our model and simulations are in good agreement with the experimental data.
© 2014 Optical Society of America
The realization of efficient terahertz (THz) radiation sources is one of the important objectives of modern applied physics, and has been subject to lots of effort . Nevertheless, achievement of room temperature emitters in this frequency range is still challenging. Systems generating THz light via frequency mixing are bulky and suffer from low efficiency and low duty cycle . THz quantum cascade lasers (QCL) offer a good alternative with a quantum efficiency of about 1% but cryogenic temperatures are still needed to operate these devices [3, 4]. An interesting approach is to combine these two systems which is mixing two mid-infrared QCL structure inside the same laser cavity ship that result in a room temperature THz source but still with a low output power [5, 6]. Recently, it has been proposed by Kavokin et al. that THz stimulated emission could be obtained in exciton-polariton lasers system . Under resonant optical pumping in the upper polariton branch, THz emission could be achieved at a frequency corresponding to the splitting of the cavity polariton modes. The optical transition between the upper and lower polariton branches is allowed if this transition is hybridized with a dipole which can be an intersubband transition, an intra-exciton transition or an impurity transition. From their calculations, a THz source with a quantum efficiency of 1% can be obtained under a reasonable pumping intensity, using a THz cavity with a cavity factor of about 20. To this aim, GaN material is a good candidate since room-temperature polariton lasing has already been demonstrated .
In this letter, we report the study of weak interaction between metamaterials as THz microcavities and shallow donors in bulk GaN. Metamaterials have been intensively study in the THz range . Used as resonant microcavities, they can amplify incoming THz pulses . Recently, the coupling between a metamaterial array and intrinsic dipole in the substrate medium was demonstrated and a Rabi-splitting was observed [11–14]. A single resonant microcavity has also been used in association with a THz quantum cascade gain medium and lasing was obtained at 1.5THz . In the THz domain, spectroscopy of GaN was studied to extract optical refractive index , impurities energy  and phonon mode. Intersubband transitions were studied in GaN/AlGaN heterostructures .
2. Sample fabrication
The sample used in this work consists of a 2.5 µm thick GaN semiconductor layer grown in an Aixtron 3x2” CCS metal-organic vapor phase epitaxy reactor on a 2 inch c-sapphire substrate. The sample was grown at a rate of 1.8 µm/h while the substrate temperature was held at 1050°C. The sample was not intentionnaly doped which lead to a residual n-doping of 5 × 1016cm−3.
To analyze the quality of the GaN epi-layer, photoluminescence (PL) was performed using a continuous wave (cw) HeCd laser emitting at λ = 325 nm with 1 mW output power focused in a spot of 100 × 100µm2. The PL spectrum was measured with the sample at 10 K in a closed cycle helium cryostat, using a 0.55 m focal length Jobin Yvon spectrometer with a CCD camera, offering a spectral resolution of 0.25 μeV. Reflectivity measurement was also performed on the same position of the sample. Results are displayed in Fig. 1. The PL spectrum shows several peaks: the peak at 3.485 eV is attributed to the luminescence of the donor bound exciton D0X while the higher energy peaks (3.492eV, 3.501eV, 3.512eV) are attributed to the XA(n = 1), XB(n = 1) and XA(n = 2) free excitons, respectively. These PL peak values are confirmed by the reflectivity measurement. All the measurements are in good agreement with literature [19, 20]. The full width at half maximum (FWHM) of the donor bound exciton D0X is only 3 meV, which attests a good quality of the GaN epi-layer. The PL spectrum is representative of the whole sample.
On the sample, we performed photoinduced absorption in the THz spectral range. With this experiment, small variation of transmission ΔT can be measured when carriers are generated by optical pumping. If the variation of transmission ΔT is normalized by itself and the reflexion is neglected, ΔT/T is equal to the absorption. We used an Argon laser emitting in cw, single line at λ = 363 nm or λ = 351 nm (below or above the bandgap of GaN at 4 K) with an output power of 200 mW focused in a spot of 1 mm2. THz illumination was provided by a blackbody globar focused in a spot of 1 mm2 as well. The transmitted light through the sample was analyzed in a vacuum Fourier transform infrared (FTIR) spectrometer (Bruker Vertex) at normal incidence without polarizer under optical pumping. For sensitive detection of the transmitted THz light, a Germanium based bolometer cooled at 4K was used. The modulated absorption signal was optimized by overlapping carefully the UV and THz beams. Measurements are shown in Fig. 2 for different sample temperatures. All the curves are normalized by the transmission of the sample at the respective temperature without optical pumping. In this graph, we can see an absorption peak at 23.5 meV (5.7 THz) under an optical pumping of 200 mW at λ = 351 nm. The amplitude of the absorption at 4K was about 5% at this optical power (not shown). Considering the strength of this absorption peak respect to the optical pump power, we attribute it by shallow donors absorption in bulk GaN (s-p transition) . These shallow donors are ionized at 4K and get populated under optical pumping above the bandgap of GaN. When the pumping wavelength is tuned below the bandgap (λ = 363nm), no absorption peaks are observed. The evolution of the modulated absorption respect to the optical power was linear which suggest that not all the impurities were neutralized in the spot area. At 4K, the FWHM is only 3 meV and gets broader up to 6 meV when the sample temperature increases to 125 K. At higher temperature, the absorption vanishes. The 3 meV linewidth is comparable to the luminescence linewidth of the donor bound excitons shown in Fig. 1 and the literature .Nevertheless, according to their measurements , we have to optically pump our sample over the bandgap to neutralized the impurity in order to see the absorption in the THz. This difference respect to the literature  is not fully understood. In the same graph, we can observe an absorption tail at low energy which is attributed to the free carrier absorption generated by the optical pumping.
On the top of the sample, we have deposited an array of split ring resonators. The deposition was done using standard photolithography (deep UV lamp at λ = 220 nm), metal evaporation (3 nm of Ti plus 60 nm of Au) and lift off [see Fig. 3(a)]. These split-ring resonators can be modeled as an RLC circuit where the length of the metallic ring is the inductor and its finite conductivity the resistor. The two vertical metallic fingers placed in the middle are assimilated to a capacitor where the medium between the two electrodes is shared between the GaN substrate and the air. We have fabricated a set of micro-resonators with different geometrical parameter to cover a broad spectral range in the THz in order to match the resonance frequency of the shallow donors absorption of our sample. The geometrical parameters of the different micro-cavities are listed in the Table 1. For all these cavities, the distance between the two metallic fingers d was kept constant while the length L and the width W of the ring were reduced progressively in order to sweep the resonance frequency of the cavity at higher energy.
The design of the cavity was done using the commercial software COMSOL Multiphysics® that solve the Maxwel’s equations in three dimensions and thus gives the Eigen frequency modes of the system. Figure 3(a) shows a scanning electron microscope (SEM) picture of the microcavity LC7 with the respective simulation results [Fig. 3(b) and 3(d)]. In the simulation graph, we can see that the vertical component of the electric field (Ey) is concentrated in the gap between the two central fingers, which act as a capacitor. The magnetic field (not shown) is instead maximal around the rings, giving rise to two parallel inductances. Using a static dielectric constant of ε = 9.5 for GaN at THz frequency , simulations shows for the cavity LC7 a resonance at ~5.7 THz and a quality factor of about 25 including ohmic losses. The conductivity of the gold was set at 4.5 × 107 Ω−1m−1.
Using THz Fourier transform spectroscopy, we measured the resonance frequency of our resonators that are deposited on the GaN epi-layer while not being optically pumped (see Fig. 4). As expected, the resonance frequency shifts from 11.8 meV(2.9 THz) to 22.6 meV(5.5 THz) as a function of the geometrical parameters of the LC resonators. When the length L and the width W of the rings (modeled as an inductance) decreases, the resonance frequency increases. The quality factor of these different cavities varies from 4 to 5.5 which is lower than the values obtained from simulation and explained by the inhomogeneity of the resonators in the array. Comparing with the simulation, the position of the resonance frequency is overestimated by 3.5%. The measured quality factor at the resonance frequency does not show significant temperature dependence down to 10 K.
Using the cavity LC7 (the highest in energy), we are able to match the resonance of the cavity to the shallow donors transition energy. In Fig. 5, the transmission of the sample at a temperature of 4K is plotted, both with and without optical pumping at λ = 351 nm. We can notice that the transmission spectrum is slightly modified by the optical pumping. To improve clarity, the transmission spectrum obtained under optical pumping is normalized by the transmission while not being optically pumped giving a differential transmission curve that is displayed in Fig. 6. This differential transmission curve differs from the one in standard matter-cavity coupling demonstration [12–14]. Indeed, the splitting of the resonances (Rabi-splitting) is usually directly measured from the transmission of the sample. In our case, the interaction matter-cavity is too small to be able to observe the splitting of the resonances. We have to display the differential curve to show the coupling and therefore the interaction between the cavities based on metamaterials and the shallow donors absorption line in GaN. This curve clearly demonstrates that due to the presence of the dipole in the GaN substrate, the cavity resonance is shifting. As expected, this effect does not appear when the optical pumping is tuned below the band gap of GaN (at λ = 363 nm) or at T = 300 K despite carriers are photo-induced in the conduction band.
To interpret our results, we used a simplified model that computes the complex impedance of an RLC circuit as a function of the frequency.21]. The capacitance C is modeled as two infinite metallic plates: C = ε0.εr × Area/distance and f is the frequency. One would think that these two last model to compute L and C are over simplified to adjust the resonance frequency of our micro-cavity but actually, a tuning of about 20% of the geometrical parameters like the length of the inductor and the area of the capacitor plate are enough to fit perfectly our data (L = 19pH and C = 4.4 × 10−2 fF). The optical absorption due to the shallow donors can be described via the optical susceptibility . To reach the 5% absorption measured, we set an arbitrary dipole length z = 1nm and a number of electron N = 1017cm−3. Then, since the dielectric constant is a function of the susceptibility, , we can implement the frequency dependent susceptibility into the capacitance of the complex impedance formula [Eq. (1)] and we can qualitatively model the full transmission of our system: metamaterial + shallow donors absorption. The resonators behave as a shunt impedance in a transmission line, located at the interface between air (Z = 377 Ω) and GaN .
By calculating the scattering matrix elements of the resulting transmission line circuit, the total transmission can be modeled. The evolution of the transmission model of our resonator without and with the implementation shallow donors absorption is illustrated in the Fig. 7(a) and 7(b) respectively. The difference between these two panels 7(a) and 7(b) is very weak like in our measurement data. To model our differential curve, we have to normalize the modeling result in the panel 7(b) by the one in the panel 7(a). Results are display in Fig. 7(c). By doing a cross plot at an inductor length corresponding of the resonance of the cavity LC7, we obtain our simulated curve superimposed to our measured data Fig. 7(d). We can see that our simulation gives a qualitative good agreement with our experimental data. However, to match our data, we had to decrease the coupling between the resonator and the medium by reducing the strength of the absorption by a factor 6. Otherwise, our simplified model predicts already a strong coupling regime between the 2 resonances (Rabi-splitting). The discrepancy between our model and the measured data can be explained by the fact that the 3D overlap integral between the electric field of the cavity and the optically pumped area is not taken into account and therefore, our model overestimates the coupling efficiency.
To conclude, we have demonstrated the existence of a coupling between metamaterial resonator and the s-p transition from shallow donors in bulk GaN at 5.7 THz. The coupling is observed in a differential curve that is well reproduced by our model. This work is a step towards realizing THz emitters from exciton-polariton lasers . Although the measured quality factor (Q ~5) is smaller than the one computed (Q ~25), we believe that for a single resonator the Q is higher than 20, which would be enough according to the proposal of Kavokin et al. . A key advantage of this proposed cavity is that the very small active volume that needs to be pumped, corresponding to the gap between the two electrodes of the LC resonator (2 × 2um2), matches very well the size of the cavity of a GaN polariton laser .
This work was supported by the Swiss National Science Foundation under the NCCR project Quantum Photonics program. The authors would like to thank Denis Martin for the growth of the sample and Christopher Bonzon for his help in the simulations.
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