Room temperature strong coupling effects from single ZnO nanowire microcavity

Strong coupling effects in a dielectric microcavity with a single ZnO nanowire embedded in it have been investigated at room temperature. A large Rabi splitting of ~100 meV is obtained from the polariton dispersion and a non-linearity in the polariton emission characteristics is observed at room temperature with a low threshold of 1.63 μJ/cm, which corresponds to a polariton density an order of magnitude smaller than that for the Mott transition. The momentum distribution of the lower polaritons shows evidence of dynamic condensation and the absence of a relaxation bottleneck. The polariton relaxation dynamics were investigated by timeresolved measurements, which showed a progressive decrease in the polariton relaxation time with increase in polariton density. ©2012 Optical Society of America OCIS codes: (140.3945) Microcavities; (140.3948) Microcavity devices. References and links 1. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. 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Lett. 97(14), 146402 (2006). 33. J. Kasprzak, D. D. Solnyshkov, R. André, S. Dang, and G. Malpuech, “Formation of an exciton polariton condensate: thermodynamic versus kinetic Regimes,” Phys. Rev. Lett. 101(14), 146404 (2008). The strong coupling regime of light-matter interaction in semiconductor microcavities has been of interest for the relative ease of fabrication of such microcavities and the ability to embed a variety of bulk or quantum confined emitters in them [1–5]. Strong coupling occurs when the emitter-cavity photon coupling rate is larger than the emitter and photon decay rates. The elementary excitations in strongly coupled exciton-photon systems are polaritons, characterized by an anti-crossing in their dispersion characteristics [4,5]. The energy separation between the lower and upper polariton branches (LPB and UPB) at the anticrossing is the normal mode cavity splitting, commonly termed the Rabi splitting [6,7]. Since the effective mass of exciton-polaritons is four orders of magnitude smaller than the electron mass, the effective temperature for Bose condensation is relatively large. In addition to studying the underlying physics of exciton-polaritons and Bose-Einstein condensation, strong coupling in microcavities enables the realization of polariton lasers in which coherent polariton states generate coherent light by spontaneous radiative recombination, without the requirement of population inversion as in a conventional photon laser. To observe strong coupling effects [8–16] at temperatures close to or equal to room temperature, materials which provide large coupling strength, and hence large exciton oscillator strength and binding energy, are desired. Therefore, attention has shifted from GaAs-based microcavities to GaN-based [13,14,16], and more recently to ZnO-based ones #163893 $15.00 USD Received 29 Feb 2012; revised 30 Apr 2012; accepted 5 May 2012; published 10 May 2012 (C) 2012 OSA 21 May 2012 / Vol. 20, No. 11 / OPTICS EXPRESS 11831 [17–22]. ZnO is a wide bandgap semiconductor with an exciton binding energy EB ~60 meV and a Bohr radius aB ~1.4 nm. The critical temperature for Bose condensation, TC is ~560K [23]. In comparison, EB is ~7-9 meV and TC is ~100K for GaAs quantum wells. The characteristics of exciton-polaritons and their strong coupling in bulk [17–19], microwire and nanowire [20,21] ZnO-based microcavities at room temperature and polariton lasing in a bulk ZnO 

The strong coupling regime of light-matter interaction in semiconductor microcavities has been of interest for the relative ease of fabrication of such microcavities and the ability to embed a variety of bulk or quantum confined emitters in them [1][2][3][4][5].Strong coupling occurs when the emitter-cavity photon coupling rate is larger than the emitter and photon decay rates.The elementary excitations in strongly coupled exciton-photon systems are polaritons, characterized by an anti-crossing in their dispersion characteristics [4,5].The energy separation between the lower and upper polariton branches (LPB and UPB) at the anticrossing is the normal mode cavity splitting, commonly termed the Rabi splitting [6,7].Since the effective mass of exciton-polaritons is four orders of magnitude smaller than the electron mass, the effective temperature for Bose condensation is relatively large.In addition to studying the underlying physics of exciton-polaritons and Bose-Einstein condensation, strong coupling in microcavities enables the realization of polariton lasers in which coherent polariton states generate coherent light by spontaneous radiative recombination, without the requirement of population inversion as in a conventional photon laser.
In the present study we have investigated strong coupling effects in a single nanowiredielectric microcavity at room temperature.The single ZnO nanowire is embedded in a dielectric and surrounded by distributed Bragg reflectors (DBRs) in the top and bottom.Thus the excitons strongly couple to normal cavity modes in this configuration and not to whispering gallery modes [21] or to cavity modes along the length [20], as in the case of a free-standing nanowire, which itself also serves as the resonant cavity.The embedded nanowire modifies the cavity field and reduces the mode volume, thereby increasing the coupling constant.The polariton dispersion characteristics at room temperature have been calculated and measured by angle resolved photoluminescence from which a Rabi splitting of 103 meV is obtained.Non-linear emission characteristics are observed at room temperature with a distinct threshold at a very low optical excitation density of 1.63 µJ/cm 2 , accompanied by linewidth narrowing.The measured population distribution in momentum space and the polariton relaxation and recombination times confirm the absence of a relaxation bottleneck and the attainment of quantum degeneracy at k || ~0.The aerial density is ~1x10 9 cm −2 ; (b) high resolution transmission electron microscope (HRTEM) image of a ZnO nanowire with the selective area diffraction (SAD) pattern in the inset.The image shows that the nanowire is free of extended defects or stacking faults.The SAD pattern confirms that the nanowires have the wurtzite crystalline structure and grow along the c-axis.
ZnO nanowires (NW) were grown on (111) silicon substrate by the pulsed laser deposition technique [24] The nanowires are typically 1-2µm long and 150-700nm in diameter based on scanning electron microscope (SEM) imaging.An SEM image of the nanowires is shown in Fig. 1(a).The nanowire density is estimated to be ~1 × 10 9 cm −2 .Figure 1(b) shows a high resolution transmission electron microscope (TEM) image of a single nanowire, which has good crystalline structure and no dislocations and stacking faults are observed.It is worth mentioning that the contrast present in this image is due to the relatively large diameter (D) of the nanowire, ~200-300 nm.A schematic representation of the mesa-shaped single nanowire-dielectric microcavity is shown in Fig. 2(a).The microcavity was fabricated by depositing the bottom DBR (15 pairs of alternating SiO 2 and Si 3 N 4 ) and 44 nm of the 3λ/2 SiO 2 cavity on a Si substrate by plasma enhanced chemical vapor deposition (PECVD).Next, nanowires are dispersed by drop-casting a low density mixture of iso-propyl alcohol and nanowires on the surface.The ZnO nanowire is 200 nm in diameter and hence it extends over 2 antinodes of the 3λ/2 cavity.To isolate a single nanowire, grid masks with alignment marks are prepared for the sample and a single nanowire is located by scanning electron microscopy with respect to the alignment marks.Because of the relatively large NW diameter, the surface was planarized by spinning and baking PMMA.Finally, the rest of the SiO 2 cavity and the top DBR are deposited and 10 µm mesas, centered around the single nanowires, are etched down to complete the microcavity.The mesas are atleast 1 mm apart and hence a 100 µm excitation spot only excites a single mesa.Finite difference time domain (FDTD) simulations were performed with the polarization of the excitation source set perpendicular to the c-axis of the nanowire because X A and X B transitions are more dominant over X C as discussed later.For simplicity, the ordinary refractive index of ZnO was only taken into account, instead of considering the anisotropy of ZnO.The calculated profile of the dominant cavity mode (shown in Fig. 2(b)) confirms that E x and H y field components are the dominant ones.The field along the zdirection is similar to that of a planar microcavity.In addition to the ZnO-dielectric index step, the top and bottom DBRs of the microcavity provide better confinement along the zdirection, so that the light is more strongly confined within the nanowire.The polarization field in the nanowire is small and assumed to be of the same order, ~0.1 MV/cm, as in comparable GaN nanowires.Both of these factors contribute to a large oscillator strength in the ZnO nanowire [14].The estimated quality factor is ~300, which corresponds to a cavity Q factor of a 10 µm long isolated nanowire without anyDBR.Thus the dielectric microcavity provides a relatively high Q for a very short length of the nanowire.It is worthwhile to mention that polariton lasing at 120K in a planar bulk ZnO based microcavity with similar Qfactor has been reported recently [22].The optical properties of the nanowires were first studied by photoluminescence (PL) measurements on a nanowire sample performed with excitation from a frequency-tripled mode locked Ti:Sapphire laser (pulse width 130 fs; repetition rate 80 MHz) at 267 nm.The wurtzite crystalline structure gives rise to three free exciton transitions, X A , X B and X C , of which the X A and X B excitons are polarized perpendicular to the c-axis whereas the X C exciton is strongly polarized parallel to the c-axis, as confirmed by interband momentummatrix calculations [25,26].The PL spectrum at 10K, shown in Fig. 3(a), is characterized by free (X A , X B ) and donor-bound exciton transitions and their LO-phonon replicas.The temperature dependence of the free exciton (FX A ) peak can be fitted well with the Manoogian and Wooley equation and is shown in Fig. 3(b).At 300K the FX A peak is observed at ~3.312 eV.The transmission characteristics of the nanowires were also measured at room temperature and are shown in Fig. 3(c).The energy position of the absorption edge measured from the transmission characteristics coincides with that of the PL peak, indicating negligible Stokes shift and a low density of defects in the nanowires.
The anti-crossing behavior of the resonant polariton modes were determined by both temperature dependent and angle resolved PL measurements.Excitation for these measurements is again provided by the frequency tripled Ti:sapphire laser focused to a spot size of 100 µm on the sample.Temperature-dependent PL spectra measured in the normal direction are shown in Fig. 4(a).The spectra are characterized by a strong lower polariton (LP) peak below the FX A transition energy while the resonant energies in the UPB are not observed at all, similar to previous observations with wide bandgap materials [17,19,27,28].The emission feature is also not from a Bragg mode which is observed at 3.139 eV in the 300K reflectivity spectrum (not shown here) measured in the normal direction.The LP peak energy is plotted in Fig. 4(b), together with the measured temperature-dependent FX A energies, E X , as described above, and cavity resonance E C .Data obtained from angle resolved PL measurements are shown in the color contour plot of Fig. 4(c).The orientation of the angle is orthogonal to the wire since the excitons are coupled to a 2D-cavity mode in adirection perpendicular to the wire.A clear signature of the LPB is again seen at all angles of the out coupled photons and the LPB energy asymptotically approaches the X A energy at high angles.This proves that the emission is not from a cavity mode.The experimental results have been analyzed with the exciton-photon coupled oscillator model, considering only the coupling of X A exciton and cavity mode, since the X B exciton exhibits a weak oscillator strength in PL spectra.The exciton linewidth used in the Hamiltonian is obtained from independent temperature dependent PL measurements from ZnO nanowires.The polariton dispersions calculated by the coupled oscillator model are shown by solid lines in Fig. 4(b) and by dotted lines in Fig. 4(c).The analysis yields a cavity-to-exciton detuning δ = + 1 ± 2 meV and Ω = 100 ± 3 meV.The large value of Ω is attributed to the excellent crystalline quality of the ZnO nanowires and a concentration of the cavity field within the single nanowire in the microcavity.A Rabi splitting ~100 meV creates a LP trap depth of ~50 meV even with a positive detuning.The squared modulus of the exciton and photon Hopfield coefficients derived from the analysis reveals that the LPB is mostly exciton-like with an exciton fraction of ~0.51 at k || = 0.These characteristics are very desirable for achieving condensation and quantum degeneracy of polaritons at room temperature in a microcavity with moderate Q, since with increase of exciton fraction the polariton relaxation times are reduced and the radiative lifetimes are enhanced [29].However, it is realized that a positive detuning is not optimal for achieving a low threshold density of excitation for the observed non-linearity described below [30].To investigate non-linearity and coherence properties of polariton emission from k || ~0 states, the microcavity was excited at an angle and the luminescence at zero detection angle was analyzed as a function of pump power.The integrated emission intensity is plotted in Fig. 5(a) as a function of the incident energy density (E exc ) and the corresponding LP density N 3D = E exc /(E pump D).Here D = 200 nm, E pump = 4.64 eV; it is assumed that 100% of the pump photons is absorbed and all injected hot electrons relax down to the ground state of the lower polariton branch without losses.The estimation gives an upper bound of the LP density 14 .A distinct non-linearity of the output power is observed at an incident energy density of 1.63 µJ/cm 2 , where the characteristics change from a sub-linear (with slope 0.7) to a more superlinear increase (with slope of 1.75), which corresponds to a threshold polariton density n th = 1.1 × 10 17 cm −3 .The latter is an order of magnitude smaller than the Mott density at which the transition from excitons to e-h plasma takes place in ZnO [31].The onset of non-linearity is accompanied by a significant decrease in the emission linewidth (shown in Fig. 5(b)) from 17 meV to ~3.7 meV at the non-linear threshold, which is well below the cavity photon linewidth of ~11 meV estimated from FDTD simulations.It may be noted that we do not observe multimode emission with very small individual linewidths below and above thresholds.Such multimode emission has been attributed to photonic defects leading to localization [13,22] or simply to the different transverse modes in the nanowire 14 .It is possible that such modes are present, but are not detected due to lack of resolution and thermal broadening and the measured linewidth of 3.7 meV is an aggregate of several peaks.For larger excitation intensity, the linewidth increases again.This behavior is commonly observed and is believed to be due to decoherence induced by polariton-polariton interactions.The onset of nonlinearity in the LP emission is also accompanied by a very small blueshift (<1 meV) in the emission peak energy with increasing excitation intensity.A small blueshift is desirable and confirms that the coherent emission is from the ground state and not from the cavity mode which is at a higher energy by ~50 meV.
To learn more about polariton relaxation and dynamic condensation in k-space as a function of excitation, we have performed two different measurements.In the first we have determined polariton occupancy as a function of k || .To determine occupancy we convert the time-integrated intensity of the angle-resolved LP emission into the number density of LPs by , where T LP is the effective polariton temperature, N 0 = N LP (k || = 0), and the LP ground state energy is used as the zero energy reference.Far below threshold (0.36P th ), neither distribution fits the data well; just below threshold (0.82P th ), the data can be fitted with the MB distribution using T LP = 323K; and above threshold, a good fit to the data is obtained with a BE distribution, using T LP = 380 and 415K, for P = 1.3P th and 1.8P th , respectively.These values of T LP , significantly larger than 300K, indicate that the polariton condensate at k || ~0 is not in equilibrium with the lattice, but only in self-equilibrium [33].Such a dynamic condensation process is sufficient to reach quantum degeneracy, but is not adequate for achieving an equilibrium Bose condensate at k || ~0 [32,33].In the second experiment we have performed time-resolved PL (TRPL) measurements with a streak camera to determine the LP relaxation time.The system has an overall temporal resolution of ~5 ps.The transient data for excitation powers below, equal to, and above threshold power are depicted in Fig. 6(b).The rise time, which principally reflects the filling of the exciton reservoir, in all instances is limited by the system resolution.On the other hand, with increase in excitation power the decay times decrease rapidly due to enhanced polariton relaxation from the exciton reservoir to the k || ~0 states.

Fig. 1 .
Fig. 1.(a) Scanning electron microscope (SEM) image of ZnO nanowires grown on n-type Si substrate.The wires have an average diameter of ~200-300 nm and a height of ~1.5 -2.0 µm.The aerial density is ~1x10 9 cm −2 ; (b) high resolution transmission electron microscope (HRTEM) image of a ZnO nanowire with the selective area diffraction (SAD) pattern in the inset.The image shows that the nanowire is free of extended defects or stacking faults.The SAD pattern confirms that the nanowires have the wurtzite crystalline structure and grow along the c-axis.

Fig. 2 .
Fig. 2. (a) schematic of the nanowire-microcavity device with the SEM image of a single nanowire placed on the partial cavity; (b) The calculated electric field intensity distribution of the fundamental x-polarized resonance mode around the nanowire of length 1 µm and diameter 300 nm, embedded in a dielectric cavity.The figure shows the cross-sectional profile of the electrical field intensity in the x-z plane.The boundary of the nanowire in the x-z plane is indicated.Also shown alongside is the refractive index profile of the structure.

Fig. 3 .
Fig. 3. (a) Low temperature photoluminescence spectrum from nanowire ensemble measured perpendicular to the c-axis of the nanowire showing peaks corresponding to free (XA,XB) and donor bound excitons and their phonon replica; (b)temperature dependence of the exciton resonance and its phonon replica; (c) photoluminescence and transmission characteristics measured from an ensemble of ZnO nanowires.

Fig. 4 .
Fig. 4. (a) Photoluminescence spectra from the ZnO nanowire-microcavity structure for different values of temperature at zero emission angle.Relative tuning of the exciton resonance X through the cavity mode C is achieved by exploiting different energy shifts of the two modes with temperature; (b) extracted peak energies of polariton emission, shown in a, as a function of temperature.The solid lines are obtained from a solution to the coupled harmonic oscillator model; (c) color contour plot of the angle-resolved dispersion characteristics.The dashed lines representing LP and UP energies are obtained from solving the coupled harmonic oscillator model.

Fig. 5 .
Fig. 5. (a) Integrated photoluminescence intensity measured normal to the device as a function of excitation.The non-linear threshold is at an incident excitation density Eexc = 1.63 µJ/cm 2 which corresponds to a LP density of 1.1x10 17 cm −2 .Inset: PL spectra measured below, at, and above threshold.The spectra reveal progressive linewidth narrowing along with the non-linear increase in the peak intensity; (b) variation of the emission linewidth and peak energy corresponding to a.

Fig. 6 .
Fig. 6.(a) Occupancy of LPB as a function of pump power obtained from angle-resolved photoluminescence measured below, at, and above threshold.The solid lines are theoretical fits based on MB or BE distributions (see text); (b) Time resolved photoluminescence measured normal to the sample (from k|| = 0) below, at, and above threshold with a streak camera having an overall resolution of 5 ps.taking into account the k || -dependent density of states and the LP radiative lifetime weighted by the relative Hopfield coefficients [32].In Fig. 6(a), the LP number density per k-state is plotted as a function of the energy difference with Ε(k || = 0) for different excitation levels.The plots are analyzed by using the Maxwell-Boltzmann (MB) distribution, N MB (k) = N 0 exp(-E/k B T LP ) or the Bose-Einstein distribution: N BE(k) = 1/[exp(E/k B T LP )(1 + N 0 −1 ) -1], where T LP is the effective polariton temperature, N 0 = N LP (k || = 0), and the LP ground state energy is used as the zero energy reference.Far below threshold (0.36P th ), neither distribution fits the data well; just below threshold (0.82P th ), the data can be fitted with the MB distribution using T LP = 323K; and above threshold, a good fit to the data is obtained with a BE distribution, using T LP = 380 and 415K, for P = 1.3P th and 1.8P th , respectively.These values of T LP , significantly larger than 300K, indicate that the polariton condensate at k || ~0 is not in equilibrium with the lattice, but only in self-equilibrium[33].Such a dynamic condensation process is sufficient to reach quantum degeneracy, but is not adequate for achieving an equilibrium Bose condensate at k || ~0[32,33].In the second experiment we have performed time-resolved PL (TRPL) measurements with a streak camera to determine the LP relaxation time.The system has an overall temporal resolution of ~5 ps.The transient data for excitation powers below, equal to, and above threshold power are depicted in Fig.6(b).The rise time, which principally reflects the filling of the exciton reservoir, in all instances is limited by the system resolution.On the other hand, with increase in excitation power the decay times decrease rapidly due to enhanced polariton relaxation from the exciton reservoir to the k || ~0 states.