The vacuum Rabi splitting of exciton–polariton emission is observed in cathodoluminescence (CL) and photoluminescence spectra of an AlN epitaxial film. Atomic force microscopy and CL measurements show that the film has an atomically flat surface, high purity, and high crystal quality. By changing the temperature, anticrossing behavior between the upper and lower polariton branch can be obtained in low temperature with a Rabi splitting of 44 meV, in agreement with the calculation. This large energy splitting is caused by strong oscillator strength, intrinsically pure polarization in wurtzite AlN semiconductor, and high fraction of free exciton in the sample. These properties indicate that AlN can be a potential semiconductor for the further development of polariton physics and polariton–based novel devices.
In the past three decades, the exciton–polariton in semiconductors has attracted considerable attention in both practical and theoretical research because of its strong light–matter coupling, bosonic effects, and various interesting properties in terms of quantum optics and spin–optoelectronic. Currently, numerous experiments have focused on observing the coherence effects of exciton–polariton at low temperature, including phase transition, superfluidity, superradiance, and entanglement. With the assistance of microcavity structure and the rapid development of crystal growth technology, the emphasis of study on exciton–polariton coherence is on higher operating temperature or lower critical density for the Bose–Einstein condensation1,2 and spontaneous emission, parametric amplification, and spin–memory of polariton–based novel devices, among others3,4,5. Given its prefect crystal quality, GaAs– or CdTe–based structures first achieved exciton–polariton coherence at cryogenic temperature. However, the exciton–polariton in those semiconductors suffers from weak exciton oscillator strength, small exciton binding energy, and small longitudinal–transverse (L–T) splitting energy. Moreover, low phonon energy and phonon scattering rate at liquid helium temperature, for example in GaAs, may result in a lower branch bottleneck, i.e., a large depletion at the bottom region relative to high k states, which remarkably limits the emission from coherent condensate state6. Recently, numerous studies have focused on the wide bandgap semiconductors ZnO7,8 and GaN9 because of their large binding energies (60 meV for ZnO and 25 meV for GaN), which can survive at room temperature. The oscillator strengths of ZnO and GaN are approximately one order of magnitude larger than that of GaAs10.
In the AlN semiconductor, the binding energy of free exciton can reach up to 55 meV11, which is higher than that of GaN and close to that of ZnO. The 7.3 meV splitting energy between the longitudinal and transverse exciton mode of AlN is almost seven times larger than the splitting in GaN12. Having the largest direct bandgap (~6.2 eV) among available semiconductors, AlN is a potential semiconductor in deep–ultraviolet solid–state light source. In contrast to ZnO–based devices limited by p–type doping, AlN has already been fabricated into p–i–n homo–junction light–emitting diode (LED) with electroluminescence peak at 210 nm at room temperature13,14. Therefore, AlN can be considered as the future light source of quantum information processing because of its high channel capacity in communication. Recently, the epitaxy technique of AlN semiconductor has undergone major developments, leading to a dramatic improvement of crystal quality11,15. However, no direct evidence or striking spectral indication of exciton–polariton emission has been obtained in AlN, which can be attributed to the lack of high quality and high purity samples.
To explore the fundamental physics and potential applications of exciton–polariton in a new system, we are working on the preparation of AlN high quality and purity epitaxial films via metalorganic vapor phase epitaxy (MOVPE). Optical properties can be characterized through temperature–dependent cathodoluminescence (CL) and photoluminescence (PL) measurements, thereby allowing us to reveal more exciton behavior and interactions in AlN under different temperatures.
Under atomic force microscopy (AFM), the morphology of the AlN sample exhibits an atomically flat surface (RMS = 0.16 nm) with atomic steps (Figure 1), which reveal good quality with layer–by–layer growth. Figure 2(a) shows the CL spectrum of the AlN epilayer measured at 80 K. The spectrum is dominated by the line at 6.030 eV. Three additional distinct peaks with similar line shapes but weaker intensities are resolved at low energy side. To examine the origin of luminescence peaks, CL spectra were measured with temperature increasing. Energy separations between the main line at 6.030 eV to each emission peak are plotted in Figure 2(b). As the temperature increases, these peaks follow the dominated line with almost the same energy interval, thus revealing that the peaks have similar origins. Given that the energy interval 106 meV is approximately equated to the longitudinal optical (LO) phonon energy16, we assign three distinct peaks as the LO phonon–assisted emissions of the dominated line. Considering the energy position of 6.030 eV at 80 K and its visibility up to 265 K, the dominated line is identified as free A–exciton related transition, which agrees with Ref. 11. A shoulder at 6.080 eV, which is higher than the main line, is noted. Similarly, a small shoulder with similar energy interval can be observed on the right side of each LO replica. Thus, we consider that the small shoulders originated from the same physical mechanism as that of the LO phonon–assisted emission. Generally, luminescence peak with energy higher than that of the free A–exciton can be associated to the excited state (n = 2) or B– and C–exciton (crystal–field splitting). However, the energy spacing of 50 meV in our CL spectra is higher than the reported values between the ground state and the excited state (approximately 40 meV11,17,18,19) and lower than the predicted energy of the crystal–field splitting (more than 100 meV20). Compared with the measurements of other groups at the same temperature region11,15, no obvious luminescence peak related to bound–exciton recombination is visible in the CL spectra. Nevertheless, up to three–order LO phonon replicas are observed. These findings verify the high purity and crystal quality of the sample. Crystal with high purity and quality will result in high fraction of free exciton and coupling of free exciton and photon and then to form exciton–polariton. These quasi–particles typically have an anticrossing behavior in dispersion relation. To clarify the origin of this shoulder at 6.080 eV, we extend temperature to liquid helium.
Similar to the above CL studies, PL spectrum at 5.8 K is dominated by free A–exciton related emission at 6.023 eV, as shown in Figure 3. At its high–energy side, the shoulder we focus on can be distinguished well at 6.078 eV. The entire luminescence spectrum shifts as a function of temperature, except for the peak labeled “S” at 6.139 eV. This peak is assigned as an unintentional Raman scattering line from the copper sample stage because this line still existed when the sample was discarded. Unlike the typical temperature–dependent variation of bandedge emission, the energies of both the main line and its higher energy shoulder do not show monotonous shifting with temperature decreasing (see Figure 3). At high temperature region, the main line shifts toward higher energy, as expected. However, when the temperature drops to lower than 60 K, the redshift is observed. Considering the main line keeps a similar line shape with linewidth of around 20 meV, this redshift cannot be explained by an evolution from free exciton recombination toward neutral donor bound recombination. When temperature is below 100 K, the higher energy shoulder can be distinguished from the “S” peak. It keeps a redshift with temperature decreasing, but stays at the energy of 6.078 eV after 20 K. These special behaviors differ from the spectral shift of exciton with temperature.
In the case of several exciton states, the energy versus wavevector polariton dispersion can be described by the dielectric approximation as following equation21, where εb is the background dielectric constant, βi = ETi/Mi, ETi and Mi are the transverse exciton energy and the effective exciton mass respectively, γi is the exciton damping constant and Fi is the oscillator strength. Considering a large energy interval between A– and B–exciton and dipole–active states allowed for polarized light, here we only consider single excitonic resonance (A–exciton), i.e. i = 1. Given that ET follows the temperature dependence of bandgap and dielectric constant (or refractive index) also changes with temperature, the anticrossing characteristics of exciton–polariton can be exhibited by temperature variation4. The temperature dependence of bandgap can be described by the Varshni model of E(T) = E(0) − αT2/(β + T) with α = 1.8 meV/K and β = 1462 K, and the Bose–Einstein model of E(T) = E(0) − 2aB/[exp(ΦB/T) − 1] with aB = 471 meV/K and ΦB = 725 K for AlN semiconductor22. The dielectric constant, generally, varies linearly with temperature, and can be simply described by an empirical formula: ε(T) = ε(0)(1 + λT), where ε(0) is the dielectric constant at 0 K and λ(≡ ε(0)−1dε/dT) is the temperature coefficient. Typically λ is of the order of 10−4 per K23, so that the change of εb with temperature is much weaker than that of ET. Differed from in cavity structure, light emission in an AlN film cannot achieve a pure geometry (k⊥c) and polarization (). The oscillator strength Fi of 1.14 × 10−2 for AlN12 should be corrected with a factor sin224, in which the is the angle between a vector parallel to the c–axis and the wave vector k of photon (see Figure 4(a)). The damping factor γi is about 0.5ΔLT21, . By using the characteristic parameters above, the exciton–polariton dispersions of AlN at different temperatures are calculated. As shown in Figure 4(b), the entire dispersion curve shifts to high–energy region with temperature decreasing. The bottleneck region, from where light is usually emitted, is located around 45°. In our experiment, the collection angle θ is also fixed at 45°. The energy of polariton from corresponding k–state with temperature variation, thereby, can be calculated from this angle.
Figure 5(a) gives the energy variation of the main line in PL spectra from 5.8 K to 300 K. The calculated curve (solid line) reproduces the peak shifting very well over the entire temperature region, in particular, the redshift deviated from an exciton behavior (Varshni model) at lower temperature region. Furthermore, we calculated the curves for both LPBA and UPBA at lower temperature region, shown in Figure 5(b), which is also consistent with the experimental energy variations of the main line and its higher energy shoulder in PL and CL. The insert figure gives the calculated energy splitting between upper and lower branch as the function of temperature. The splitting energy reaches the minimum of 46.7 meV at 17 K, close to the value of 44 meV obtained from PL measurement at 20 K. This anticrossing behavior confirms a strong light–matter coupling regime, namely, an exciton–polariton formation in sample. On the basis of analysis above, we assign the dominated line at 6.023 eV as the lower polariton branch of A–exciton (LPBA) and the higher energy shoulder at 6.078 eV as the upper polariton branch (UPBA).
In semiconductor, the light propagating in crystal usually couples to the transverse mode of exciton and splits into upper and lower polariton. In a typical dispersion relation, the UPB begins at the longitudinal eigenenergy of exciton () for k = 0 and bends upward with increasing k, whereas the LPB starts from and k = 0 and adjusts to transverse eigenenergy of exciton () at high k states above the bottleneck region25. Around this bottleneck region, the splitting between UPB and LPB has a minimum value, which is proportional to the L–T splitting (). In AlN, ΔLT can reach up to 7.3 meV with the oscillator strength (F = 1.14 × 10−2). This value is much larger than that of GaAs and seven times larger than the splitting in GaN, revealing an intrinsically strong light-matter coupling strength in AlN semiconductor.
Furthermore, for wurtzite AlN, the valence band at the Γ point of the Brillouin zone is divided into three bands by spin–orbital and crystal–field splitting. Given a negative crystal–field splitting, the transition of A–exciton is Γ7 × Γ7, which can be decomposed into Γ1 + Γ2 + Γ5. Only the Γ1 and Γ5 symmetries are dipole allowed for the polarization of light parallel and perpendicular to the c axis, respectively26. However, for A–exciton in AlN, the oscillator is almost completely excited by light in and k⊥c (π–polarization). Related light emission is strongly polarized for (polarization ratio P = 0.995) and has a maximum light intensity perpendicular to the c–axis27. For GaN, P is estimated as 0.527. Similarly, in ZnO, the component of polarization emission is comparable with the E⊥c component7. Considering the high refractive index of AlN (n = 2.8 at 6.0 eV) and the atomically flat surface, significant amount of light will be confined in epitaxial film by total internal reflection. Therefore, the purely π–polarized light emission implies that majority of the confined light will couple with A–exciton, leading to a higher coupling efficiency than in GaN or ZnO. If the AlN semiconductor has microcavity structure, then the coupling strength will be expected to reach a significantly large value. Here we suggest a whispering gallery resonator7 different from the conventional planar microcavity in the AlN (0001) orientation because of the high refractive index and strong π–polarization emission of AlN semiconductor.
For the exciton–polariton condensation, the LO phonon–assisted process is an efficient way of accelerating the polariton relaxation and reducing the stimulation threshold in strongly coupled microcavities28. Due to the strong ionic nature and low symmetry of the wurtzite structure of group III–nitrides, the Frohlich interaction with LO phonon becomes the dominant interaction29,30 and AlN owns the largest LO phonon energy of 110 meV among III–nitrides. Therefore, only the LO phonon–assisted emission is observed in our spectra. Considering the exciton–like nature around or above the bottleneck region, polariton–LO phonon coupling can be expressed by the Huang–Rhys factor31. At all temperatures, the contribution of the pth LO phonon replica is related to zero phonon line, which is expressed by where p represents the number of LO phonon involved, n is the thermal average of the vibrational quantum number, is the LO phonon energy, Ip means the modified Bessel function with imaginary argument of order p, and S is the Huang–Rhys factor, which provides quantitative description of exciton–phonon coupling strength. By analyzing the CL and PL intensities of the pth replica, the obtained S factors of LPBA are lower than 0.08. The value of S indicates strong exciton–phonon interaction in AlN compared with in GaN (lower than 0.01)29, which provides efficient relaxation that bypasses the slow–acoustic–phonon thermalization process and suppresses the polariton bottleneck effect.
The abovementioned analysis denotes that the AlN semiconductor is a new candidate for the realization of polariton coherence at high temperature and even at room temperature. (1) By improving the crystal quality and purity of epitaxy films, the formation of exciton–polariton can be observed in AlN semiconductor. (2) Given their large binding energy (about 55 meV of free A–exciton), the exciton–polariton is stable at room temperature, which is the most important factor for high–temperature polariton coherence. (3) Strong oscillator strength and purely polarized light emission obtain a record Rabi splitting of 44 meV in the thin film, which is expected to be enlarged in microcavities. (4) With an energy of 110 meV, the LO phonon in AlN can rapidly cool down the polariton and can suppress the bottleneck effect in polariton relaxation. These properties found in the AlN semiconductor will help achieve high operation temperature and low critical excited density for exciton–polariton condensation.
The AlN film grown by MOVPE has been investigated in this work. AFM and optical measurement results show that the AlN film has high crystal quality and purity. At low temperature region, both the temperature–dependent luminescence spectra and the calculated result show an anticrossing behavior. We identified that this behavior originated from the formation of exciton–polariton because of intrinsically strong oscillator strength and purely polarized emission in AlN semiconductor. The LO–phonon–assisted transition is considered the strongest polariton–phonon interaction that plays the most important role in polariton relaxation. We demonstrated that the factors observed in the AlN semiconductor system are mostly adapted for the further improvement of polariton coherence, for the continuation of studies on polariton physics, and for the development of novel polariton devices, such as optical spin Hall effect32, branch entanglement33, quantum degeneracy34, polariton superfluid transition35, and ultrafast parametric amplifiers36.
The sample investigated was a c (0001)–orientated undoped AlN epitaxial film grown by low–pressure MOVPE (Thomas Swan 3 × 2 in. close–coupled shower head) on the c–face sapphire by using trimethylaluminum (TMAl) and ammonia (NH3) as precursors, and H2/N2 as the carrier gas. Low–temperature AlN buffer was first deposited in a V/III ratio of 2400 at 800°C, followed by high–temperature AlN layer at 1080°C with a V/III ratio of 400.
The morphology of the epilayer was investigated by AFM (SPA400, Seiko Instruments Inc.). CL spectra were obtained by using an electron gun (Orsay Physics “Eclipse” FEB Column), which was installed in an ultrahigh vacuum chamber (manufactured by RHK technology). Sample can be excited at various temperatures inside a cooling cryostat. The electron beam was operated at 15 kV with current density of 7 × 10−2 A·cm−2. The emitted light was dispersed by a 320 mm focal–length monochromator (Horiba Jobin Yvon iHR320) equipped with 1200 groves/mm gratings with a spectral resolution of 0.06 nm. A cooled photomultiplier tube was mounted to the monochromator. PL measurements were performed via mode–locked frequency quadrupled Ti–sapphire laser (177 nm) with power of 0.3 mW as an excitation source. The pulse width and repetition rate were 100 fs and 76 MHz, respectively. The incidence and collection angles of light on the sample were 90° and 45°, respectively.
We would like to thank Li Chen and Xiaolong Zhuo for their experimental assistance. This work was supported by National Key Basic Research Program of China (973 Program No. 2012CB619300, 2011CB925600) and National Natural Science Foundation of China (No. 61227009, No. 91321102).