1. Introduction

The large dipole moment of intersubband transitions allows to reach the strong and ultrastrong coupling regime when coupled to a microcavity. Metallic cavities with subwavelength confinement of the mode such as LC [1] resonators and patch antennas have been successfully employed to demonstrate intersubband polaritons in the terahertz spectral range [2–5] after their first realization in the mid-IR frequency range [6–8]. Large Rabi frequencies of more than a quarter of the intersubband transition frequency have been observed in such structures [5, 9] and new physical effects like generation of non-classical light are predicted [10–14] in this ultrastrong coupling regime. Fast switching of polaritonic states is important for the observation of the described physical phenomena.

We use devices similar to the ones in [15] to demonstrate electrical gating of intersubband polaritons in the THz range. Electrical gating of intersubband polaritons in the mid infrared range has already been demonstrated [16]. In [15], the electron gas in the quantum wells was excited in plane and a Si₃N₄ layer was electrically insulating the metal ground plane. This is unsuitable for electrical gating due to its low dielectric constant. In the present realization, we use an epitaxially grown high-ε Al_0.45Ga_0.55As layer. By biasing the Schottky barrier at the metallic ground plane, tuning of the polariton states is achieved via charge density modulation. Note, that using a thinner Si₃N₄ layer instead of switching to Al_0.45Ga_0.55As would also allow improved gating. However, in real devices thinner Si₃N₄ layers are prohibited by large leakage currents.

2. Fabrication and modeling

The samples are realized with parabolic quantum wells sandwiched between a metallic ground plane and metallic cavities. A schematic is shown in Fig. 1(a). The sample surface is 1 × 1 mm large. It features a source and a drain contact on two opposing sides of the top surface and can be operated as a transistor with the Schottky barrier at the ground plane as a gate, allowing modulation of the electron density in the quantum wells. As the Rabi frequency scales with the square root of the carrier density [2], the polariton states can be tuned using this gate.

 

Fig. 1 (a) Sample schematic. Source and drain contacts on two opposing sides of the sample top surface allow electrical in-plane pumping. A 150 nm thick Al_0.45Ga_0.55As barrier separates the quantum wells from the gold ground plane and forms a Schottky barrier, allowing gate operation. (b) shows an electron micrograph of a part of the cavity array. (c) simulated electric field distribution at at a Schottky bias of −9 V for the present sample and a device with a nitride isolation layer. The step-like structure is a result of the discretization in the simulation. The inset shows the total carrier density integrated over all undepleted quantum wells as a function of the applied gate bias. The incomplete (47%) charge transfer into the well is taken into account. (d) depicts a current-voltage characteristic of the device. After an initial nonlinear region close to the origin, the dependence is linear as expected for the source-drain contact. The leakage current to the gate is significant in magnitude and nonsymmetric with respect to an exchange of source and gate contact.

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The sample consists of eight parabolic quantum wells grown by molecular beam epitaxy, similar to the samples used in [15]. Parabolic confinement is achieved by a digital GaAs/Al_0.15Ga_0.85As alloy. The wells are modulation doped and separated by 12 nm thick Al_0.30Ga_0.70As barriers. In each quantum well, the carrier density amounts to 2.9 × 10¹¹ cm⁻². For the present device with eight quantum wells, the sum is 2.3 × 10¹² cm⁻². With a 150 nm thick Al_0.45Ga_0.55As layer terminating the epitaxial growth, the cavity thickness is 950 nm. The epitaxial layer is Ti/Au metalized and wafer bonded to a hosting substrate. After removal of the original substrate, cavities are defined by optical lithography and lift-off technique. Ge/Au source and drain contacts are deposited and annealed on two opposing sides of the sample top surface allowing in-plane electrical pumping. The samples are mounted on copper heat sinks and wire bonded. The empty cavity frequency of the sample is estimated to be 2.9 THz as determined by reflection measurements in undoped but otherwise similar samples. An electron micrograph of a part of the sample is shown in Fig. 1(b).

The simulated electric field distribution in the sample along the growth direction with the ground plane on the left is shown in Fig. 1(c). The high dielectric constant of the Al_0.45Ga_0.55As isolation layer allows a stronger carrier depletion compared to the previously used Si₄N₃ layer. The total charge per area as a function of gate voltage is plotted in the inset. Note, that the dopant transfer into the parabolic quantum well is incomplete as 2.9 × 10¹¹ cm⁻² dopants are transferred into each quantum well, while the nominal doping is 6.2 × 10¹¹ cm⁻² (47% transfer efficiency). This is taken into account in the simulation. The simulation assumes a constant volume doping while the real sample is modulation doped between the parabolic quantum wells. Figure 1(d) shows the current-voltage characteristic of the source, drain and gate contacts. The leakage current to the gate is significant.

3. Characterisation

The devices are characterized in reflection measurements using a Fourier-transform infrared-spectrometer (FTIR) with a He-cooled bolometer detector. All measurements are performed at a heat sink temperature of 10 K. Reflection spectra are shown in Fig. 2(a) for different bias voltages applied to the gate relative to the source and drain contacts, which were kept on the same potential. The polariton splitting is scaling with the square root of the doping density [2] and therefore with applied bias. Extraction of the peak positions with a Lorentzian fit shows a polariton tuning of 140 GHz for the lower polariton and 120 GHz for the upper polariton. The voltage dependent polariton tuning is shown in Fig. 2(b). The maximum detuning at −9 V bias corresponds to a reduction of the electron density by 33 % via partial depletion of the quantum wells. A stark-shift of the intersubband transition can be excluded as a source of the polariton tuning, as such a shift would cause both polaritonic branches to shift in the same direction, which doesn’t agree with the experimental observation of a blueshift of the lower polariton and a redshift of the upper polariton. At high negative Voltages, the coupling strength between the cavity and intersubband resonance is decreased. Besides a tuning of the polariton frequency, this leads to a decoupling of the lineshapes into intersubband like and cavity like resonances.

 

Fig. 2 (a) Reflection spectra measured at a heat sink temperature of T=10 K. Lower (LP) and upper polariton (UP) resonances are labeled. They show a dependency of the polariton splitting on the gate Voltage. (b) Shows the polariton splitting as a function of the applied gate bias (dots) and a corresponding simulation (solid line).

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Intersubband polariton generation has been proposed as a route for efficient THz emitters, because the strong light-matter coupling in the device should naturally enhance the radiation properties [17]. The advantages of this enhanced coupling are partially negated by simultaneous excitation of dark states. In this work, as in [15], we have studied the emission properties of the polaritons using non-resonant excitation by an in-plane current. This heating of the electron gas doesn’t modify the coupling strength [4].

Electroluminescence spectra are measured in a home-built FTIR with a He-cooled bolometer detector and a lock-in amplifier. The lock-in phase was determined with a laser, ensuring the correct sign on the Fourier-transforms. The electron gas is excited in plane by a source-drain current at 50% duty cycle with a floating gate. An anticrossing curve taking into account the cavity, doping and intersubband parameters is shown in the inset in Fig. 3(a). The continous line shows a calculation and the two black dots correspond to the polariton resonances of the sample used for the present work. The source-drain current requires a bias of several volts between source and drain, so the voltage at the Schottky barrier is space dependent. That voltage drops from the source to the gate along the device and therefore along the gate electrode spanning the whole device. As a consequence, the potential at the gate is a function of space along a coordinate from source to drain. This is different from the previously described reflection measurements, where source and drain are kept at constant potential and the potential does only change along the growth direction. We show the real part of the Fourier-transform of the interferogram at two source-drain currents (−50 mA, +80 mA) in Fig. 3(a) and (b). The observed power is on the order of 70 pW for both bias conditions. For the negative current (a), we observe a differential signal for the upper and lower polariton resonance with large negative components while the signal for the positive bias condition (b) remains nondifferential. The asymmetry of the spectra with respect to the current direction is attributed to inhomogeneous gate leakage current across the sample.

 

Fig. 3 Electroluminescence spectra measured for source-drain currents of −50 mA (a) and +80 mA (b). Positive, as well as differential line shapes are observed in the same sample. The inset shows a calculated anticrossing curve in dependence of the empty cavity frequency following the model described in [3]. Intersubband transition line (ISB) and empty cavity line (Cavity) are also shown. The polariton resonances of the used sample are shown as black dots. (c) Reflection spectra in the biased and unbiased state. The polariton resonances can shift, depending on the bias condition, which causes differential peaks in luminescence measurements.

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The emission experiment using lock-in technique finds the difference in the emission between the biased and unbiased state. We therefore measure them individually in a new set of reflection measurements where we repeat the conditions of the emission experiments in terms of sample bias.

These reflection spectra with applied source-drain currents, which have a space dependent gate potential, are shown in Fig. 3(c). This separate set of reflection measurements is necessary, as the previous gated reflection spectra don’t have such a space-dependent gate potential. With negative (−50 mA) applied bias, a shift of the polariton peaks is observed in the reflection spectrum compared to the unbiased sample. The corresponding emission spectrum in Fig. 3(a) is differential as expected due to the differential nature of the lock-in measurement. Under positive bias (+80 mA), no appreciable polariton shift is observed in reflection compared to the unbiased sample. The corresponding emission spectrum is also not differential.

We can interpret the observed emission spectrum as the sum of two contributions:

Tuning of the polariton states with applied bias causes differential signal for both (emission and reflection) contributions. Note, that there is a direct measurement of the first component in a sample with a nitride isolation layer in [15] in an all cold environment. There, modulated reflection can be safely neglected.

4. Conclusion

In conclusion, we demonstrate a polaritonic device with a gate allowing control of the charge density. We use this effect to tune the polaritonic resonances over a range of 140 GHz. On one hand, the use of an Al_0.45Ga_0.55As isolation layer allows depletion of the quantum wells by application of an electric voltage. On the other hand, pumping the structure with an in-plane current for electroluminescence measurements requires a bias of several Volts. This bias also causes electron density modulations and therefore polariton tuning. The added sensitivity of charge density to gate bias is therefore at the same a disadvantage for emission experiments relying on in plane pumping of the electron gas, causing differential peaks in some cases.