Room-Temperature Polariton Lasing from GaN Nanowire Array Clad

Letter pubs.acs.org/NanoLett

Room-Temperature Polariton Lasing from GaN Nanowire Array Clad by Dielectric Microcavity Junseok Heo,† Shafat Jahangir, Bo Xiao, and Pallab Bhattacharya* Center for Photonics and Multiscale Nanomaterials, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109-2122, United States S Supporting Information *

ABSTRACT: Room-temperature polariton lasing from a GaN-dielectric microcavity is demonstrated with optical excitation. The device is fabricated with a GaN nanowire array clad by Si3N4/SiO2-distributed Bragg reflectors. The nanowire array is initially grown on silicon substrate by molecular beam epitaxy. A distinct nonlinearity in the lower polariton emission is observed at a threshold optical energy density of 625 nJ/cm2, accompanied by significant line width narrowing to 5 meV and a small blue shift of ∼1 meV. The measured polariton dispersion is characterized by a Rabi splitting of 40 meV and a cavity exciton detuning of −17 meV. The device described here is a demonstration of exciton−photon strong coupling phenomenon in an array of light emitters and paves the way for the realization of a room temperature electrically injected polariton laser.

KEYWORDS: Nanowires, exciton-polariton, microcavity, lasing

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strong coupling and polariton lasing from an array of GaN nanowires sandwiched by dielectric DBRs. The threshold for polariton lasing of the array is observed at ∼0.6 μJ/cm2. The nanowire−dielectric microcavity device is schematically shown in Figure 1a. The GaN nanowires sandwiched by the top and bottom dielectric DBRs serve as a microcavity. An undoped GaN nanowire sample shown in the inset is grown on (111) silicon substrate by molecular beam epitaxy (MBE). The nanowires are ∼600 nm long, 40−50 nm in diameter, and have a density of ∼1 × 1010 cm−2. It is important to note that the exciton Bohr radius of GaN, 2.8 nm,25 is much smaller than the nanowire diameter and hence there is no quantum confinement in the nanowires. This is confirmed by photoluminescence measurements on as-grown nanowire samples that show an emission peak wavelength coinciding with that of bulk GaN (see Supporting Information). As shown in the scanning electron microscope (SEM) image in the inset of Figure 1, the lengths of the nanowires are very uniform and their top ends are flat, which reduces surface roughness. After solvent cleaning of the nanowire sample, the top surface of the nanowires is planarized with spin-on-glass (SOG) and 12 pairs of Si3N4/ SiO2 DBR are deposited atop. The reflectivity of the DBR was measured to be ∼99% at the GaN luminescence center wavelength of 367 nm. The sample is then bonded onto an Aucoated Si wafer with the original Si substrate (on which the nanowires are grown) facing up and the latter is then selectively

oherent light emission described as polariton lasing exploits the strong coupling regime of emitter−photon interaction in a microcavity. The principle gain mechanism for such coherent emission is a phase coherent polariton−polariton scattering process, also known as bosonic final state stimulation. The separation of stimulation and emission results in coherent spontaneous emission without the requirement for population inversion and with a much smaller level of excitation than in a conventional photon laser.1 Polariton lasing by optical excitation has been demonstrated with both inorganic (InGaAs/GaAs, ZnO, CdTe) and organic (anthracene) semiconductors.1−11 In terms of high-temperature operation, the wide bandgap semiconductors with large exciton binding energy such as GaN (exciton binding energy Eb ∼ 30 meV) or ZnO (Eb ∼ 60 meV) are preferred and room-temperature polariton lasing has been demonstrated with these materials.5−8 Strong coupling effects and other polariton devices have also been studied and realized at room temperature in single ZnO and CdS nanowires without a dielectric microcavity.12−16 Recently, Das et al.7 have demonstrated ultralow threshold polariton lasing at room temperature in a single GaN nanowire embedded in a dielectric microcavity with an all-dielectric distributed Bragg reflector (DBR) mirror. Grown on Si substrate in the wurtzite crystalline structure, the nanowire ensembles are nearly free of extended defects and strain and have a large radiative efficiency.17−23 The surface recombination velocity of the nanowires is ∼103 cm/s,24 2 orders of magnitude smaller than that on the free surface of GaAs. Since the emission from a single nanowire is relatively weak, it is necessary to develop devices with much higher output power. To this end we demonstrate for the first time exciton−photon © 2013 American Chemical Society

Received: January 7, 2013 Revised: April 12, 2013 Published: May 1, 2013 2376

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addition to being confined in the z-direction, photons are also confined in the lateral directions, resulting in discrete photon in-plane wave vectors and 0D polariton modes.3 Because of the three-dimensional confinement of polaritons, the polariton− phonon scattering rate is expected to be even further enhanced. However, when multiple nanowires are very closely packed, as shown in Figure 1d, the light confined by each nanowire will be coupled to light confined by surrounding nanowires. As a result, the photon field spreads over the entire nanowire volume (as wave functions in a semiconductor superlattice) in the x−y directions. In the device investigated here, the nanowires in the microcavity are positioned in a SOG matrix between the top and bottom DBRs, similar to the schematic of Figure 1d. In order to characterize the cavity field distribution and photon localization in the nanowires of Figure 1d, threedimensional finite difference time domain (FDTD) simulation was performed. The active region was modeled as a hexagonal close packed nanowire array with individual nanowire diameter of 40 nm and average period of 45 nm and a periodic boundary condition was applied in the x−y direction. In order to prevent effects due to the possible formation of a photonic crystal, the nanowires were randomly positioned with a maximum offset of ∼7 nm from the periodic locations. The cavity quality factor was estimated to be ∼5000. However, the experimental value is envisaged to be significantly smaller due to the inherent nonplanar nature of the DBRs. Figure 2 depicts the calculated electric field distributions in the y−z, x−z, and x−y planes. The

Figure 1. (a) Schematic representation of the GaN nanowire array− dielectric microcavity. The inset shows the scanning electron microscope image of an as-grown nanowire sample grown on (111) silicon. The nanowires have an average diameter of 40−60 nm and a height of ∼600 nm. The aerial density and fill factor are ∼1 × 1010 cm−2 and 0.4, respectively; (b−d) schematic representations of nanowires embedded in a dielectric spin-on-glass cavity between DBRs: a single nanowire oriented parallel to the y-direction (b), single nanowire oriented parallel to the z-direction (c), and vertically aligned nanowire array (d).

removed by isotropic etching with XeF2. The exposed nanowires are planarized again with SOG and 10.5 pairs of Si3N4/SiO2 DBR are deposited. Low-temperature photoluminescence measurement with an identical nanowire sample yields a spectra with three free exciton transitions, XA,B,C corresponding to the wurtzite crystalline structure.7 Of these, the XA transition is the most dominant with the transition resonance at 3.38 eV. Single or multiple nanowires can be embedded in a dielectric microcavity in several ways, as shown in Figure 1. Because the excitons in the nanowires are in bulklike material, as mentioned earlier, the nature and degree of optical field confinement will determine the dimensionality of the polaritons. In the case illustrated in Figure 1b, where a single nanowire is embedded in a dielectric cavity between the dielectric DBRs,7,8 the optical field is well-confined in the nanowire along the x- and zdirections and a continuous in-plane wave vector along the ydirection creates one-dimensional (1D) polaritons for which momentum conservation in the x- and z-directions is relaxed and the polariton−phonon scattering rate is enhanced in comparison to the 2D polariton case. It may be remembered that the phonons are three-dimensional in nature. It may also be noted that a true Bose−Einstein condensate (BEC) is not observable in an infinitely long one-dimensional system since the energy density of states-ρ(E) does not vanish in the limit of E→0. However, an equiphase condensate in the ground state is made possible with the presence of a potential trap,26 or a defect, or in a nanowire of finite size.27,28 Figure 1c describes a single nanowire, similar to a micropillar, oriented parallel to the z-direction and bound by DBRs at either end. In this case, in

Figure 2. Calculated electric field intensity distribution of a nanowire array-dielectric microcavity device in the y−z (a), x−z (b), and x−y (c) planes. 2377

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cavity field in the x−z plane is well-confined in the nanowire region by the top and bottom DBRs and is mostly continuous over the nanowires, confirming that light is only confined in the z-direction and can freely travel in-plane. Hence, the nanowire cavity region can be regarded as a GaN−air 3D composite with a lower average refractive index, which has a continuous inplane wave vector as in a bulk cavity device.29 It may be noted, however, that a fraction of the cavity field is strongly localized between the nanowires in the y−z plane, since a y-polarized source was used in the simulation, and the electric field is therefore discontinuous along the y-direction. Such light localization in a subwavelength air gap results from the mutual enhancement of two evanescent fields in close proximity, as observed in slotted waveguides.30 To confirm a bulklike cavity behavior, the plane wave expansion (PWE) technique was employed to calculate cavity dispersion with respect to the inplane wave vector. A hexagonal close-packed nanowire array and a periodic boundary condition in the x−y direction were again assumed. The calculated cavity energy dispersion versus the in-plane wave vector k∥ shows a quadratic relation identical to that for a planar homogeneous cavity, Ecav = ℏc/nc(k2⊥ + k2∥)1/2, from which an effective cavity refractive index, nc = 1.84, is derived. The case of the nanowire array sandwiched between the DBRs is therefore similar to a 3D medium in which 3D excitons strongly couple with 2D photons. Because the polaritons are quasi confined in the z-direction, polariton− phonon scattering does not need to satisfy momentum conservation in this direction. For each value of k∥ (= (k2x + k2y )1/2, polaritons can emit phonons (which are 3D) into a continuum of kz states, as long as the phonons all have the same k∥-value as the polaritons. Angle-resolved photoluminescence (PL) measurements were made at room temperature to determine the microcavity polariton dispersion characteristics. The device was nonresonantly excited by a frequency tripled Ti:sapphire laser (λ = 267 nm) with a pulse duration of ∼150 fs and a spot size of ∼60 μm. The luminescence was collected by a fiber having a 200 μm core diameter mounted on extended rails of a goniometer centered on the sample. The output spectrum was analyzed with a high-resolution monochromator and detected with a photomultiplier tube using phase lock-in amplification. Figure 3a shows the output spectra recorded at various detection angles with the dotted line representing the free exciton A (FXA) transition measured in an as-grown nanowire sample. As the detection angle increases, a clear anticrossing of two peaks is observed around the exciton energy. The dominant peak which is observed at all detection angles and is seen to asymptotically approach the FXA transition energy at higher detection angles is identified as the lower polariton (LP) emission. In contrast, the peak above the FXA transition energy, which is observed only at higher detection angles, is confirmed to be the upper polariton (UP) emission. The LP and UP peak energies were analyzed by the exciton-photon coupled oscillator model considering only the FXA transition, due to weaker oscillator strengths of the B and C free exciton transitions. The Rabi splitting (ΩVRS) and cavity-to-exciton detuning (δ) derived from the analysis are 40 and −17 meV, respectively. The calculated LP and UP dispersions plotted as solid curves in Figure 3b show good agreement with the measured data. The calculated cavity dispersion discussed earlier with nc = 1.84 is used in the analysis and shown by the dotted curve in this figure. The relatively smaller value of Rabi splitting compared to that reported for a single nanowire device

Figure 3. (a) Photoluminescence spectra of GaN nanowire array− dielectric microcavity measured as a function of angle from 0 to 32° at 300 K at Einc = 500 nJ/cm2; (b) experimental polariton emission energy resonances obtained from the spectra of (a) as a function of angle and the polariton dispersion curves obtained from solutions to the coupled harmonic oscillator model.

(ΩVRS ∼ 48 meV)7 is attributed to the large fraction of cavity field residing in the air gaps between nanowires, assuming identical GaN material quality and oscillator strength of the FXA transition. To investigate nonlinear polariton emission from the k∥ ∼ 0 state, the device was photoexcited in the same manner as described above and the emission was collected in the normal direction. Figure 4a shows the integrated light output intensity plotted as a function of the incident optical energy density, Einc. The PL spectra at various incident energy densities are shown in the inset to this figure. The threshold of nonlinearity in the light output is clearly observed at an incident energy density of 625 nJ/cm2, which signals the onset of enhanced polariton− phonon and polariton−polariton scattering of LPs into the k∥ ∼ 0 state. The corresponding maximum LP density was estimated to be ∼3.5 × 1016 cm−3 (or a polariton sheet density of ∼2.1 × 1012 cm−2) using the relation N3D < Einc/(hνpump × L × ξ), assuming 100% of pump light absorption. Here hνpump is the energy of incident photons and is 4.64 eV, L is the length of the nanowire, 600 nm, and ξ is the fill factor of the nanowire array, which has a value of 0.4. It is worth noting that the estimated polariton density at threshold is 3 orders of magnitude smaller than the exciton Mott density of 3 × 1019 cm−331 and the observed nonlinearity is not a result of photon lasing due to population inversion in the weak coupling regime since the LP density is smaller than the transparency density in GaN.32 The nonlinearity of light output is accompanied by a significant line width narrowing of the emission from 22 to 5 meV and a blueshift of the LP emission peak of 1.13 meV (Figure 4b). The 2378

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In order to study the polariton emission distribution in kspace, we performed angle-resolved PL measurements below (Einc = 0.8Eth) and above (Einc = 6Eth) the threshold excitation energy. Figure 6 shows the time-integrated polariton emission

Figure 6. False color plots of momentum distribution of polaritons at incident photoexcitation energies of 0.5 and 3.75 μJ/cm2. The broad distribution of polariton emission below threshold in the in-plane momentum space changes to a highly localized one above threshold.

intensity in momentum space as false color plots. Below threshold, the LP emission has a broad distribution in all angles, whereas above threshold, the emission is localized in k space with Δk = 1.18 × 104 cm−1 (Δθ = 4°). It may also be noted that there is no obvious energy-relaxation bottleneck at all incident pump energies. This implies that various polariton scattering mechanisms such as polariton−phonon, polariton− electron, and polariton−polariton scattering efficiently thermalize the polaritons down to the k∥ ∼ 0 state. It is evident that the fast relaxation kinetics of the polaritons leads to the formation of a dynamic 2D polariton condensate which produces coherent light. In the device described here, similar to the case of a bulk microcavity, the excitons are in a 3D environment in each GaN nanowire. As shown in Figure 3, the in-plane photon wave function amplitude is nearly uniform across the whole plane of the microcavity, whereas the excitons, although not quantumconfined, are localized in each nanowire. Because of the large air-gap between the nanowires, the coupling between excitons in adjacent nanowires is weak and hence negligible. Therefore, when the 2D polariton density is sufficiently large (larger than the critical density for a finite-sized 2D quasi-condensate34), polaritons in each nanowire can condense to the k∥ ∼ 0 state and spontaneously emit coherent light and each nanowire is therefore an independent polariton laser. Since the variation in length of the nanowires leads to microscopic fluctuation of the cavity mode at different spatial regions of the nanowire array, the line width of the polariton emission spectrum is inhomogeneously broadened. A time-integrated measurement of the output polarization above threshold shows that the polariton emission is not linearly polarized (see Supporting Information). This is consistent with data reported for bulk GaN microcavity devices.27 In conclusion, we demonstrate strong coupling effects in a GaN nanowire array−dielectric microcavity at room temperature. The polariton dispersion in the system is characterized by a Rabi splitting of 40 meV and a cavity−exciton detuning of

Figure 4. (a) Integrated LP emission intensities measured as a function of incident pump energy at a zero detection angle. The nonlinear threshold is observed at Einc = 625 nJ/cm2. The inset shows PL spectra measured at and above threshold; (b) variation of LP emission line width and peak energy corresponding to the data in (a).

small blueshift occurs due to repulsive interactions between exciton-polaritons.33 As shown in Figure 4b, with further increase of the incident energy density (Einc > 7 μJ/cm2), the peak energy of emission approaches that of the cavity mode and the line width is broadened again, indicating the transition to the weak coupling regime. A second threshold, which we believe is due to photon lasing, is also observed at an excitation density ∼2 orders of magnitude higher than the polariton lasing threshold (shown in Figure 5).

Figure 5. Integrated photoluminescence intensity from the cavity mode as a function of excitation energy density showing the second threshold due to photon lasing at ∼4 × 104 nJ/cm2. The inset shows the two thresholds due to polariton and photon lasing. 2379

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−17 meV. With increase of optical excitation, a nonlinearity in the lower polariton emission intensity is observed accompanied by a significant reduction of the emission line width. The threshold of the nonlinear increase in emission occurs at an input excitation energy density of 625 nJ/cm2. These observations are attributed to enhanced polariton−phonon and polariton−polariton scattering and the formation of a degenerate polariton condensate at k∥ ∼ 0 in each nanowire of the array. The device demonstrated here can be a cornerstone for the realization of an electrically injected polariton laser operating at room temperature.

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ASSOCIATED CONTENT

S Supporting Information *

Additional figures, information, and reference. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

(J.H.) Department of Electrical and Computer Engineering, Ajou University, Suwon 443−749, South Korea. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Science Foundation under Grant ECS-1220715.

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