1. Introduction

Facilitating electrical excitation of quantum well exciton-polaritons [1–5] was an important step towards real-world applications of exciton-polariton devices. Exciton-polariton systems can exhibit a nonlinear output of coherent emission in a condensate regime that does not rely on stimulated emission of photons but on stimulated scattering of hybrid light-matter particles. The possibility to excite exciton-polariton samples optically as well as electrically, to manipulate exciton-polaritons by external magnetic fields [6, 7] and to define arbitrary potentials lithographically [8–10] open up a pathway for exciting new applications. For instance, polariton condensate transistors that have already been demonstrated under optical excitation [11] may be combined to form compact all-optical or electro-optical logical circuits [12].

In order to improve the performance of electrically driven polariton samples, the strength of the light-matter interaction and the current injection into the cavity region need to be optimized simultaneously. By adding more quantum wells (QWs) in a sample the exciton-photon coupling strength is increased [13], but at the same time homogeneous current injection becomes more demanding. More elaborate current injection schemes than the simple p-i-n-diode like injection through doped top and bottom mirror will likely be necessary for electrically driven polariton samples with large Rabi splittings. For instance, selective injection of only some of the incorporated QWs via an intra-cavity contact has been proposed for GaN-based devices [14].

We propose an exciton-polariton light emitting diode (LED) with a reversely biased tunnel junction [15] incorporated in the intrinsic cavity of a p-i-n doped microcavity sample. The tunnel junction is placed between the top two of the three QW stacks. Interestingly, this concept, i.e. microcavities with multiple QW stacks and tunnel junctions, has been used to realize lasers with internal quantum efficiencies exceeding unity [16]. In our sample under an applied bias in forward direction electrons can tunnel from the valence band into the conduction band in the tunnel junction and are then transported to the topmost QWs where they form excitons with holes that are injected through the upper mirror. The excitons are then radiatively distributed to all QWs in the cavity region as the photons emitted by recombining excitons in the top QWs are reflected multiple times between top and bottom mirror and thus can be absorbed in all QWs. The timescale of this radiative distribution in a strongly coupled microcavity is determined by the Rabi splitting [17] and is of the order of 100 fs for a device with GaAs quantum wells which typically exhibits a Rabi splitting between 5 meV and 15 meV. We would like to point out that injecting electrons only from the mirror below the bottom QW stack and holes from the mirror above the top QW stack in a simple p-i-n-diode like scheme leads to low quantum efficiencies for this sample design. Holes are localized in the QWs closest to the p-doped layers, as has been shown in LEDs with multiple InGaN QWs [18], preventing efficient exciton formation.

2. Sample structure

2.1. Band structure calculation

Prior to sample growth band structure calculations were performed using a Poisson solver. The doping concentrations of the p- and n-doped part of the tunnel junction were varied for a fixed width of the tunnel junction of 20 nm in order to achieve an energetic overlap of conduction and valence band without external bias. This ensures that tunneling of carriers is possible even for a small forward bias applied to the LED. Figure 1(a) shows the calculated band structure of the cavity-region of a sample with three QW stacks and a tunnel junction without external bias. The exact position of the tunnel junction is illustrated in the plot of the nominal aluminum concentration of each layer, also shown in Fig. 1(a). For the calculation no tunneling currents were taken into account and all dopants were assumed to be ionized. Choosing experimentally achievable doping concentrations of 2 × 10¹⁹ cm⁻³ for the p- and n-doped parts of the tunnel junctions yields an energetic overlap of conduction and valence band in the tunnel junction. It is worth noting that even though AlAs is an indirect semiconductor the tunneling transition in the junction that is formed by a p-doped AlAs layer and an n-doped Al_0.2Ga_0.8As layer is a direct one because electrons can tunnel between the Γ-point of the valence band of AlAs and the Γ-point of the conduction band of AlGaAs.

 

Fig. 1 (a) Calculated band structure (left axis) and nominal aluminum concentration of each layer (right axis) of the studied sample without external bias in the region of the cavity. (b) Refractive index (black) and nominal concentration of silicon (red) and beryllium (green) dopants of the studied sample. The square of the calculated amplitude of the light field is plotted in blue in arbitrary units.

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2.2. Sample growth

The sample we studied was grown by molecular beam epitaxy on n-doped (001) GaAs substrate. The refractive index profile, nominal doping concentrations and calculated light field of the sample are shown in Fig. 1(b). A λ/2 wide intrinsic cavity layer is sandwiched between two distributed Bragg reflectors (DBRs) consisting of 10 (14) periods of λ/4 wide AlAs/Al_0.2Ga_0.8As layers in the upper (lower) mirror. Three stacks of 4 GaAs QWs are placed in the central antinodes of the electric field, i.e. in the center of the cavity and at the first AlAs/Al_0.2Ga_0.8As interface of both mirrors. The cavity region as well as the first pair of AlAs/Al_0.2Ga_0.8As layers is undoped, while the top (bottom) mirror is p-doped with beryllium (n-doped with silicon). The doping concentration in the DBRs was lowered towards the cavity to reduce optical absorption and δ-doped layers were introduced at every second interface to reduce the series resistance of the DBRs [1]. Polariton LEDs were then fabricated by etching 100 μm wide circular mesas into the wafer onto which, after planarization with benzocyclobutene, ring-shaped titan/gold contacts were evaporated. The n-contact is formed by a AuGe-NiAu alloy deposited on the backside of the wafer.

The tunnel junction is placed at the interface between the cavity and the upper mirror. It is formed by an AlAs layer which is doped with a Be concentration of 2 × 10¹⁹ cm⁻³ and an Al_0.2Ga_0.8As layer which is doped with Si. The tunnel junction is placed in a node of the light field, as seen in Fig. 1(b), to reduce absorption by the highly doped layers. In order to overcome the limitation of Si n-type doping to several 10¹⁸ cm⁻³ in AlGaAs [19], δ-doping is inserted after every nm of Si-doped Al_0.2Ga_0.8As [20]. Analysis of the doping profile by secondary ion mass spectroscopy shows that doping concentrations exceeding 1 × 10¹⁹ cm⁻³ are reached for Be and Si in the cavity of our sample.

3. Results and discussion

3.1. Room temperature electroluminescence

The electroluminescence (EL) measurements of the LEDs were first performed at room temperature. The momentum-energy distribution of the signal was analyzed by Fourier space spectroscopy [8]. Figures 2(a) and 2(b) show momentum resolved spectra of such an EL measurement at low and high injection current. Two distinct branches are visible which we attribute to emission from the upper and the lower polariton. The momentum-energy dispersion of both branches is clearly non-excitonic as the dispersion of a purely excitonic state appears flat in the selected momentum range due to the exciton’s high effective mass. For high injection currents, a redshift and broadening of both branches is observed due to device heating. The redshift of the polariton branches amounts to ca. 0.5 nm (1 meV). Assuming that the redshift of the polaritons is mostly caused by the redshift of the exciton of 0.45 meV/K around room temperature [21] allows us to estimate a heating of the sample for high injection currents of 2 K.

 

Fig. 2 (a) Normalized momentum resolved EL spectrum at low injection current (5 μA). Dashed lines are the fitted dispersions of the exciton (red), cavity photon (green) and the two polariton branches (white). (b) Normalized momentum resolved EL spectrum at high injection current (3.315 mA). Dashed lines are the fitted dispersions of (a) at low injection current to illustrate the redshift of about 0.5 nm (1 meV) due to device heating. (c) EL spectra at k_|| = 0 for injection currents between 2 μA and 3.3 mA. (d) Area of the peaks fitted to the spectra of (c) versus injection current for both polariton branches.

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No narrowing of the emission in momentum space or of the emission linewidth is observed at increased current, i.e. there is no sign of polariton lasing. Under optical excitation, polariton lasing has only been observed at temperatures up to 70 K when using GaAs quantum wells [22, 23]. Room temperature polariton lasing can be observed e.g. by using GaN QWs [24] because of their higher exciton binding energy [25], but electrical excitation of exciton-polaritons remains rather challenging in that material system. We note that room temperature polariton lasing might be achievable using GaAs QWs for samples with a very large Rabi splitting (>20 meV) [26] which highlights the potential for electrically excited exciton-polariton samples with a large number of QWs.

A coupled oscillator fit [27] of the dispersion of both branches seen in Fig. 2(a) yields a Rabi splitting of 6.5 meV and a detuning between exciton and cavity photon of −1.7 meV. The value of the Rabi splitting is comparable to the one we measured at room temperature in the reflectivity of a sample with identical layer design but without any extrinsic doping (not shown here). This confirms that indeed all 12 QWs strongly couple to the cavity mode in our current injection scheme. The Rabi splitting we measure is considerably larger than previously reported values of 4meV using InGaAs QWs [28] and of 4.5meV using GaAs QWs [29] for exciton-polariton LEDs operating at room temperature.

From the momentum resolved spectra the k_|| = 0 spectra are extracted, as seen in Fig. 2(c). Two broad but well resolved peaks are observed for all injection currents. The fitted area of the peaks is plotted against the injection current in Fig. 2(d). The input-output curves of the two polaritons run parallel over the whole range of applied injection currents. We observe a slight kink at 100 μA in the otherwise linear curves. This is probably a consequence of the sample geometry where 6 devices are driven in parallel. A slight drop in resistance of one or more of the mesas may result in a kink in the input-output curve as observed in Fig. 2(d). Please note that while we did investigate the other devices connected parallel to the diode discussed in this paper, we did not measure spectra differing greatly from the ones shown in Fig. 2.

3.2. Temperature dependent electroluminescence

Our sample is designed for measurements at room temperature but the devices can also be operated at lower temperatures. When the temperature is lowered beneath room temperature, the exciton is detuned from the cavity because the temperature dependence of the energy band gap of GaAs (causing the blueshift of the exciton) is bigger than that of the refractive indices (causing the blueshift of the cavity) [30]. Figure 3 shows EL-spectra at a constant bias of 5 V for temperatures ranging from 220 K to 300 K for the same LED as in Fig. 2 and fitted energies of the peaks. During this measurement, the injection current grows linearly from 0.787 mA at 220 K to 1.458 mA at 300 K because of the decreasing series resistance of the doped DBRs. At 220 K the detuning is 25 meV and the Hopfield coefficient [31] |X|² is 0.98, i.e. the upper polariton is 98% excitonic at 220 K. The emission intensity of the upper polariton is very low at low temperature as the polariton emission depends on the leakage of cavity photons through the mirrors and therefore on the photonic content of the polaritons. The upper polariton becomes brighter with increasing temperature because the detuning and correspondingly |X|² decrease. Between 290 K and 300 K we observe an anticrossing of the polariton branches and obtain a vacuum Rabi splitting of 6.7 meV. This value is in good agreement with the result of the fit to the momentum resolved EL spectra at room temperature seen in Fig. 2.

 

Fig. 3 EL spectra for different temperatures at k_|| = 0 (left axis). The spectra are normalized to 1 and shifted vertically for clarity. Open symbols are fitted positions of the lower (red circles) and upper polariton (black squares) versus temperature (right axis).

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3.3. Bias dependent photoluminescence

Additionally, we performed photoluminescence (PL) measurements with varying applied bias. The sample was excited nonresonantly at 630 nm with a continuous-wave diode laser while a bias between −0.8 V and +0.8 V was applied. The k_|| = 0 spectra of this measurement are presented in Fig. 4(a). With a forward bias of +0.8 V the two polariton peaks are observed at the same wavelengths as in the EL measurement of Fig. 2. With decreasing bias both polaritons exhibit an approximately equal redshift and the intensity of the lower polariton decreases relative to the upper polariton. At 0 V both polariton peaks are equally bright. When a reverse bias is applied, the redshift of the lower polariton becomes more pronounced than that of the upper polariton while its intensity decreases until the lower polariton peak disappears at around −0.6 V. The upper polariton exhibits no further shift and no change in emission intensity for reverse bias lower than −0.6 V. The fitted energies of the polaritons are plotted in Fig. 4(b). Comparing the energies at +0.6 V and at −0.6 V yields an overall redshift of around 4 meV (2 meV) for the lower (upper) polariton which is explained by the quantum confined Stark effect [30, 32]. The exciton exhibits a redshift in an electric field whereas the cavity is almost unaffected by an applied field. We therefore conclude that both branches observed in this measurement have a significant excitonic content. For voltages lower than −0.6 V only few excitons form because photoexcited carriers rapidly tunnel out of the QWs. Consequently, the system enters the weak coupling regime and the uncoupled cavity mode remains unaffected from the applied bias.

 

Fig. 4 (a) Room temperature PL spectra at varying bias at k_|| = 0. Dashed lines are guides to the eye. The spectra are normalized to 1 and shifted vertically for clarity. (b) Fitted peak energies of the PL spectra versus applied bias.

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4. Conclusion

In conclusion, we have demonstrated a polariton LED with a tunnel junction incorporated in the cavity in order to improve the injection of current into the spatially separated QW stacks. At room temperature, we observe emission from two branches with pronounced polaritonic dispersion. The two polariton branches are separated by a vacuum Rabi splitting of ca. 6.5 meV. The strong coupling of excitons and photons in our sample also explains the anticrossing of the two branches in a temperature dependent EL measurement as well as the redshift of 2 meV (4 meV) for the upper (lower) polariton branch in a bias dependent PL measurement. We anticipate that similiar current injection schemes can be adapted to facilitate low or even room temperature GaAs-based polariton lasers with pronounced Rabi splittings.