The wide band gap semiconductor, GaN, and its heterojunction systems with AlGaN, has been intensively investigated during the past decade and has shown to be a very useful material for developing light emitting diodes, laser diodes, and high-power and high-temperature electronic devices 12. It features a parabolic lowest conduction band with a band gap energy of approximately 3.4 eV. The separation between the conduction band and the nearest satellite valley is approximately 1.4 eV. Due to the properties of its constituents, it is also characterized by high-energy optical phonons (ħω_LO ≈ 92 meV).

Carrier localization in III-nitride materials caused by compositional fluctuations in ternary alloys leads to tailing of the energy bands that is observed in both absorption and photoluminescence (PL) spectra. Furthermore, it has been claimed that this localization gives rise to the high quantum efficiency commonly found in III-nitrides by preventing the carriers from reaching the dislocation level (which acts as many non-radiative recombination centers) 34. These localizations are caused by alloy fluctuations in ternary semiconductors such as AlGaN 56 and InGaN 78 and in multi-quantum well structures such as AlGaN/GaN 9 and InGaN/GaN 10. In binary systems such as GaN nanorods, clear identification of exciton localization with an appropriate analysis has rarely been reported. Exciton localization features have, however, been identified on basal stacking faults (BSFs) in a-plane epitaxial laterally overgrown GaN both experimentally 11 and in numerical calculations 12.

In this paper, we report on exciton localization within binary semiconductor GaN nanorods that are grown directly on Si(111) substrates. Time-integrated micro-photoluminescence and time-resolved photoluminescence (TRPL) experiments were carried out in order to study the optical properties of the GaN nanorods. The Huang-Rhys (H-R) parameters were calculated from the phonon replica intensities in order to understand exciton localization due to potential fluctuations.

The temperature dependence of the PL emission from the nanorods, measured at temperatures from 4.2 to 75 K, is presented in Figure 2a. Figure 2b shows a zoomed-in section of the spectra in which a strong excitonic emission, originating from both donor-bound excitons (I₂ transition or D⁰X) and free excitons (FX) at energies of 3.468 and 3.476 eV, respectively, is observed. These peaks dominate the spectra at higher temperatures (note the log scale). The FX emission appears as a high-energy shoulder on the I₂ peak, and we observe that it becomes red-shifted as the temperature increases, in line with the band gap energy dependence on temperature. At temperatures above 75 K, the I₂ emission was deionized contributing to the FX emission. In contrast, the I₂ emission energy appears to be temperature independent, which supports the assertion that it originates from a localized source. To the best of our knowledge, this localization effect has not previously been observed in GaN epilayers, and indeed, we only observe the effect in samples such as the one investigated here, which exhibits the coalescence of many nanorods.

In addition to these two peaks, there is a broad emission (full width at half maximum (FWHM), approximately 30 meV) at 3.417 eV, which has been labeled I₁⁰. This has been attributed to both extended structural defects located at the bottom of the nanorods 17 and the recombination of excitons bound to the BSFs. The BSFs are produced during the initial phase of the growth and propagate perpendicularly to the c-axis from the substrate toward the surface of the sample 1819. Indeed, densely merged GaN nanorods on the surface (as shown in Figure 1) may result in the formation of the localized defects.

A series of satellite peaks at the low energy side of the aforementioned transitions, which is assigned to phonon replicas of the I₁⁰ emission, are also observed. The energy separation of each adjacent peak is approximately 92 meV, in good agreement with the longitudinal optical (LO) phonon energy in GaN. We denote the intensity of the nth phonon replica for I₁⁰ as I₁ⁿ (n = 0, 1, 2, etc), where n = 0 corresponds to the main emission line (non-replica). The intensity ratio of adjacent phonon replicas can be expressed as

I n + 1 I n     =     S n n + 1   , n = 0 ,     1 ,     2 ,   3...

where S, the H-R parameter, is defined as

S     =     ∑ q | V ( q ) | 2 E L O

Here, E_LO is the LO phonon energy and V(q) is the matrix element for the interaction between the exciton and the phonon, with wave vector q. The H-R parameter is therefore a quantitative measure of the exciton-phonon coupling strength 2021 and, by extension, a measure of the degree of localization (localized excitons have a stronger interaction with phonons as their wavefunctions contain large q components 22).

The inset of the Figure 3 shows the extracted H-R parameters for the I₁ transition as a function of temperature (T). The value of S₁ at T = 4.2 K for the I₁ is measured to be 0.29. It is a well-documented phenomenon that the value of S₀ is always smaller than the H-R parameter measured between higher order satellite peaks 21 due to the fact that whilst all recombining excitons contribute to the zero order peak, only those that are deeply confined contribute meaningfully to the higher order satellites. The ratio of S₁/S₀, or the extent to which S₀ is reduced by this effect, can therefore be used as a measure of the proportion of carriers that are localized 521. Value of S₁/S₀ much in excess of unity represents a situation with few localized carriers. Figure 3 shows the temperature dependence of the ratio S₁/S₀ for the I₁ transition. The value of S₁/S₀ initially decreases with increasing temperature (4.2 to 30 K) before rapidly increasing for temperatures above 30 K. Similar behavior has been observed previously in InGaN QWs 23 and Al_xGa_{1 - x}N alloys 5 and is explained by exciton localization: Carriers that are strongly localized to deeper states at low temperature interact with the phonons but become delocalized by thermal energy with increasing temperature. The rise of S₁/S₀ for temperatures over 40 K roughly corresponds to, and is indeed caused by, the onset of a fall in S₀ while S₁ continues to rise. The continuing increase of S₁ (and S₀ for T < 50 K) with temperature is due to an increased population of phonons. The fall in S₀ (T > 50 K) is most likely due to the delocalization of excitons at I₁⁰, causing a reduction in the intensity at I₁¹ (and indeed I₁²). The emission intensity of I₁⁰, however, is due to emission from all recombining excitons, so the thermal delocalization will have a less immediate effect on I₁⁰resulting in a decrease of S₀ and hence the increase of the ratio S₁/S₀.

In order to further understand the carrier recombination dynamics of the excitons in GaN nanorods, we performed TRPL measurements on the sample at a range of photon energies. Two representative TRPL decay traces, taken at 10 K, along with the instrument response function (IRF), are presented in Figure 4. The shoulders in the IRF traces are due to electron reflections. This is a common problem in time-correlated photon counting system when relatively short time decays are involved. Software has been used to take into account this response function in the fitting procedure. The FWHM of the IRF is approximately 40 ps and was de-convoluted from the measured decays with commercial decay analysis software (PicoQuant Fluofit, PicoQuant GmbH, Berlin Germany). The mono-exponential lifetimes of the emission at 3.417 and 3.468 eV are calculated to be approximately 68.1 ps and approximately 92.2 ps, respectively. The decay rate is fast due to surface recombination on the nanorods, which is enhanced by the large surface to volume ratio exhibited by the columns. This is consistent with the results by Schlager et al 24. The surface recombination lifetime, τ_s, which is strongly dependent on the surface recombination velocity, v_s, can be approximated to d/4v_s for the case of a hexagonal column of diameter d 2425. We estimated the surface recombination velocity to be 27 × 10³ cm.s^-1, which is a little larger, but comparable, than that calculated by Schlager et al, owing to the faster decays observed in our case. It should be noted, however, that in the literature, there is little consistency in the lifetimes quoted for the donor-bound and acceptor-bound excitons. In fact, in GaN, the lifetimes range widely from a few tens to a few hundreds of picoseconds 262728293031.

In summary, we have investigated the exciton localization in bulk-like GaN nanorods by micro- and time-resolved photoluminescence measurements. In the temperature-dependent photoluminescence measurements, several phonon replicas at the lower energy side of the exciton bound to the BSFs (I₁⁰) are observed. By analyzing the H-R parameter as a function of temperature deduced from the phonon replica intensities, we found that the excitons are strongly localized in the lower energy tails. For the I₁ transition, the value of S₁/S₀ slightly decreases when the temperature increases from 4.2 to 30 K and then rapidly increases with further temperature increase, up to a value of 75 K. The PL decay times for the emissions at 3.468 and 3.417 eV were measured to be 92.2 and 68.1 ps, respectively. These fast decays are due to surface recombination, which is enhanced due to the large surface to volume ratio of the columns. It is finally concluded that exciton localizations in III-nitride materials can be observed not only in ternary alloys but also in binary semiconductors.

The authors declare that they have no competing interests.

YP carried out sample growth, performed PL measurements and drafted the manuscript. MH participated in PL measurements. YS participated in the structural analysis of the sample. IY participated in the growth of the sample. HI performed the data analysis and drafted the manuscript. RT participated in PL measurements and in the design of the study. All authors read and approved the final manuscript.