1. Introduction

Nanometer-scale band potential fluctuations in ternary nitride semiconductor quantum wells (QWs) play an important role in the performance of GaN-based light emitting devices. The potential fluctuations induce carrier localization affecting the spectral linewidth and the recombination rate [1–3]. Several effects have been singled out as responsible for the band potential variations. These include alloy composition and well width fluctuations, and a local relaxation of strain. Often the influence of these effects on the recombination is treated indiscriminately. However, band potential fluctuations of different origins might have a different effect on recombination. For instance, alloy composition fluctuations would induce symmetric conduction and valence band potential variations, and the related nm-scale electric fields should not contribute to electron and hole spatial separation. On the other hand, nonplanarity of QW interfaces would induce an in-plane electric field that might separate electrons and holes and aid their localization at different sites. Such an effect has been suggested to be responsible for unexpectedly long radiative lifetimes in semipolar InGaN QWs with a high In content [3].

Apart from the recombination times, the band potential fluctuations affect the emission linewidth. While broadening due to the QW width fluctuations could possibly be reduced by increased sharpness of QW interfaces via optimization of growth, random alloy fluctuations can hardly be avoided. Thus, distinguishing between localization effects caused by the alloy composition and the well width fluctuations is important in order to understand the intrinsic limits of the emission linewidth and the rate of the radiative recombination.

In this work, we investigate the influence of alloy composition and QW width fluctuations on the carrier localization and recombination by studying photoluminescence (PL) of semipolar $(20\overline{2}1)$ plane InGaN QWs of different well widths. Since the localization depth increases with the alloy composition [4], we explore QWs with a high In content emitting in the green spectral region. To assess the band potential variations, we have used scanning near-field optical microscopy (SNOM) with a 100 nm spatial resolution. Even though this resolution is not sufficient to resolve individual band potential minima that, according to the calculations, are expected to occur on a few nm scale [2], the spectral linewidth of the near-field PL is less affected by the spatial averaging compared to the standard far-field luminescence. Our SNOM setup allows simultaneous mapping of the time-integrated and time-resolved PL as well as the surface morphology [5], allowing to trace correlations between PL parameters and surface morphology features, which might have an influence on the QW width.

2. Experimental details

Near-field PL measurements were carried out at 300 K with a SNOM apparatus exciting and collecting PL through an Al-coated UV fiber probe with a 100 nm aperture diameter. Carriers were photoexcited by 200 fs pulses with a 380 nm central wavelength from a frequency doubled Ti:sapphire laser operating at an 80 MHz pulse repetition rate. Near-field PL spectra were measured in a time-integrated mode with a spectrometer and a liquid nitrogen cooled CCD detector. Part of the PL signal was split, passed through band pass filters blocking radiation outside the PL peak, and directed into a photomultiplier tube connected to a time-correlated single photon counter (TCSPC). The temporal response of the TCSPC system was ~ 50 ps. During scans, the probe was moved between measurement points in 100 nm steps. A PL spectrum and a transient were measured at each point. A typical scan area was 10 × 10 μm². Median wavelength and full width at half maximum (FWHM) of the spectra, as well as transient amplitudes and decay times were used to build PL parameter maps. Sample morphology was measured using a feedback signal from a quartz tuning fork used to maintain a constant probe-sample distance. To evaluate radiative and nonradiative recombination times, the near-field measurements were complemented by standard time-resolved PL measurements in the 4 − 300 K temperature region using a spectrometer-streak camera system.

The studied QW structures were grown by metal organic chemical vapor deposition (MOCVD) on low (∼ 5 × 10⁶ cm⁻²) dislocation density bulk $(20\overline{2}1)$ plane GaN substrates, provided by Mitsubishi Chemical Corporation. The structures consisted of a 1 μm thick undoped GaN template layer, a 2, 4 or 6 nm strained single In_0.33Ga_0.67N QW, and a 10 nm GaN cap layer. The In content in the QWs was evaluated by X-ray analysis of calibration samples. One should note that spectral SNOM results should not depend on the growth technique (e.g. MOCVD or molecular beam epitaxy). On the other hand, nonradiative lifetimes, determined by the density of point defects, might be affected by the growth method and conditions.

3. Results and discussion

Figure 1 presents typical time-integrated near-field PL spectra and spectrally-integrated PL transients for the studied QWs. The spectra with a full width at half maximum (FWHM) of 170–180 meV are similar to previously reported far-field spectra for high In content $(20\overline{2}1)$ InGaN QWs [4, 6, 7]. The PL linewidths are primarily determined by the inhomogeneous broadening (the room temperature homogeneous broadening in GaN is 18 meV [8]). The quantum confined Stark effect is most pronounced for the 2 nm QW; for the wide wells, the emission wavelength is primarily determined by the alloy composition, as shown by band gap calculations performed self-consistently solving Schrödinger and Poisson equations using the SiLENSe software package from STR Group, Inc. [9] (see Table 1). The PL decay is nearly single-exponential with decay times increasing with the QW width. PL decay times measured at room temperature in the far-field are similar to the average near-field PL decay times. As will be discussed below, the 300 K radiative lifetimes are much longer than the PL decay times; thus, the latter are mainly determined by the nonradiative recombination. In InGaN QWs grown on GaN substrates with a low dislocation density, the main nonradiative recombination centers are point defects that are not particularly active at low temperatures [3, 10, 11].

 

Fig. 1 Normalized near-field PL spectra (a) and transients (b) for 2, 4 and 6 nm QWs.

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Table 1. Statistical parameters of the near-field PL scans for the studied samples.

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Figures 2 and 3 present spatial variations of the surface morphology, the median PL wavelength, the FWHM, and the PL decay time for the samples with 2 and 6 nm QWs, respectively. The 4 nm QW maps (not shown) display similar features. The surface morphology is smooth with root mean square values of ~ 0.7 nm. Surface striations, seen in the map, are characteristic for $(20\overline{2}1)$ plane GaN [12, 13]. PL decay time maps, especially for the 2 nm QW, have small variations, which indicates a uniform distribution of point defects.

 

Fig. 2 Maps of the surface topography (a), the median wavelength (b), the FWHM (c) and the PL decay time (d) for the 2 nm QW.

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Fig. 3 Maps of the surface topography (a), the median wavelength (b), the FWHM (c) and the PL decay time (d) for the 6 nm QW.

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In spite of the large In content, PL median wavelength and linewidth variations over the scanned areas are small. This indicates that the alloy composition and the well width, averaged over the probe aperture area, are homogeneous. Islands with a uniform median wavelength and the FWHM that is considerably larger than the homogeneous broadening indicate the presence of a dual, μm-and nm-scale localization [14]. The average PL parameter values and standard deviations σ are gathered in Table 1. The table also presents the narrowest near-field PL linewidths observed in the scans. As one can notice, the difference between the FWHM values for 2, 4 and 6 nm QWs is small.

Even though the correlation between the morphology and the optical maps for the whole scan is negligible with the Pearson product moment coefficient r < 0.1, a visual inspection of the maps suggests that some features in the median wavelength and the FWHM maps can be related to the morphology variations. One could expect that the surface striations, originating from the substrate, could induce variations of the QW width [12, 13]. However, the small median wavelength and FWHM variations for different facets of the striations do not support this assumption.

As mentioned, the spectral broadening may have different origins. Here we do not consider the strain relaxation at defects because it would lead to a large peak wavelength shift [15], not observed in the experiments. To distinguish between the remaining mechanisms of the well width and the alloy composition fluctuations, we compare our experimental data with calculated QW ground state transition variations for 2 monolayer (0.6 nm) well width fluctuations, typical for InGaN QWs [16].

For the narrow 2 nm In_0.33Ga_0.67N QW, the quantum confinement effect is strong, and ±0.3 nm well width fluctuations would induce a large transition energy variation of 105 meV (20 nm). For the 4 nm QW, the variation is much smaller, 27 meV (6 nm), while for the 6 nm QW the transition energy is barely sensitive to the 2 monolayer well width fluctuations with the variation of 8 meV (2 nm). Thus, if the well width fuctuations were the main cause of the linewidth broadening, one would expect narrower PL peaks for wider wells. However, the experimental PL linewidths have an opposite tendency, i.e. with increased QW width they increase. This discrepancy explicitly shows that the QW width fluctuations, at least for QWs with a moderate to high In content, cannot explain the inhomogeneous broadening observed in the experiment. The broadening has to be attributed to the variations of the alloy composition instead. Because light electrons spread over several potential minima reducing the effective localization potential [2], the emission linewidth should be mainly assigned to the spatial variations of the valence band.

However, the QW width fluctuations have a large impact on the recombination times. Maps of the radiative lifetimes for different QWs are plotted in Fig. 4 (a), (c) and (e). They were calculated following a procedure described in Ref. 5. In brief, the spatial variation of the radiative lifetime τ_r was considered to be proportional to the variation of the inverse PL transient amplitude I_PL, τ_r ∝ 1/I_PL. To get τ_r values at each point of a map, the average near-field radiative lifetime was assumed to be equal to the far-field radiative lifetime ${\tau }_r^{ff}$ determined from the streak camera measurements. The value of ${\tau }_r^{ff}$ at 300 K was estimated from the 4 K PL decay time and the temperature change of the transient amplitudes, ${\tau }_r^{ff}(300\mathrm{K})={\tau }_{PL}^{ff}(4\mathrm{K})I_{PL}^{ff}(4\mathrm{K})/I_{PL}^{ff}(300\mathrm{K})$. It was assumed that immediately after the pulse the recombination is purely radiative. The assumption of the prevailing radiative recombination in these low dislocation density QW structures is justified by small PL transient variations at low temperatures, also observed in polar, nonpolar and semipolar InGaN QWs [3, 17, 18]. Still, one should be aware that the result might be affected by the carrier trapping to deep centers that might take place at low temperature. We believe, though, that this effect at 4 K is minor compared to the radiative recombination. Of course, low temperature SNOM measurements would allow mapping the radiative lifetimes in a more direct way; however, our system is limited to the room temperature operation requiring to use the procedure described above. The average lifetime values and the standard deviations are listed in Table 1.

 

Fig. 4 SNOM maps of the radiative lifetimes for 2 (a), 4 (c) and 6 nm (e) QWs and nonradiative lifetimes for 2 (b), 4 (d) and 6 nm (f) QWs.

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The most striking result related to the radiative lifetimes is the large difference between the 2 nm and the wider QWs. The short radiative lifetime of 1.1 ns, observed for the 2 nm QW, is similar to the far-field value of a narrow m-plane QW [18]. The near-field map shows that the largest values in the scanned region do not exceed 1.18 ns. However, doubling the QW width to 4 nm increases the radiative lifetime by nearly a factor of five (the average value is 5.1 ns). For the 6 nm QW, the average radiative lifetime further increases up to ~8 ns.

Trying to understand this large difference in the radiative lifetimes, one should first examine the effect of the transverse electric field on the electron and hole wave function overlap, because the lifetime is inversely proportional to the squared overlap. In polar InGaN QWs, due to the strong field caused by the difference of piezoelectric and spontaneous polarizations of the well and the barrier layers, dependence of the overlap on the well width is strong [19]. In $(20\overline{2}1)$ QWs, the transverse field is smaller by an order of magnitude (~0.1 vs. ~1 MV/cm) [7], (and) the dependence of the overlap on the well width is much weaker. According to the SiLENSe calculations, the squared wave function overlap changes from 0.83 to 0.50 as the QW width is increased from 2 to 4 nm. This modest decrease cannot explain the fivefold increase of the radiative lifetime, observed in the experiments.

Previously, the long radiative lifetime in $(20\overline{2}1)$ InGaN QWs with a high In content has been attributed to a separate localization of electrons and holes [3]. It has been suggested that carrier separation is caused by an in-plane component of electric field induced by a zigzag shape of semipolar QW interfaces [13]. Apart from the semipolar QWs, this effect has been demonstrated by modelling c-plane QWs with well width fluctuations [1]. Thus, the long radiative lifetimes in our 4 and 6 nm QWs are likely to have the same origin. The in-plane electric field, however, does not depend on the QW width. In the zigzag interface model, the field depends only on the interface geometry and the alloy composition.

An effect that might explain the large radiative lifetime difference between 2 and 4 nm QWs is the well width dependence of the carrier mobility. The initial carrier trapping into localization sites occurs within a few ps after the photoexcitation [20, 21], and it is during that time that the in-plane field would cause the electron and hole separation. For the same value of the electric field and the time for trapping into localized states for the different wells, the carrier separation distance would be proportional to the mobility s ∝ μ. An electron mobility dependence on the well width for $(20\overline{2}1)$ plane InGaN QWs has not been reported; however, for polar AlGaN/GaN QWs a clear mobility decrease for narrow QWs has been observed and assigned to an increased interface roughness scattering [22]. Tight binding model calculations [2] performed for 2 nm m-plane InGaN QWs show that an electron wave function distributes over the whole QW thickness and even penetrates into the barriers. Thus, in our 2 nm QW the electron mobility should be affected by scattering at both QW interfaces. For wider QWs, the transverse electric field would shift the electron distribution toward one of the interfaces, reducing the interface scattering. Consequently, one would expect a substantial difference in the interface scattering for the 2 and 4 nm QWs. Likely, the reduced electron mobility is sufficient to prevent the spatial separation of the excited electrons and holes prior to their localization.

For wider QWs, the interface scattering is no longer dependent on the QW width [22]. The increase of the radiative lifetime for the 6 nm QW compared to the 4 nm can possibly be explained by an interplay between the in-plane and transverse separations of electrons and holes. A ratio of the radiative lifetimes for these QWs is 1.5, which can be compared to calculated ratio of the inverse squared wave function overlaps of 2.5. The latter value, however, is obtained for ideal wells with no in-plane localization. The carrier localization in the bulk of the wells would effectively reduce the influence of the transverse electric field, diminishing the difference of the radiative lifetimes in the wider QWs.

In spite of the large difference of the radiative lifetimes for different QWs, the relative spatial lifetime variations are similar for all samples. Ratios of the standard deviations to the average values are about 0.02 to 0.03. This spatial uniformity of the radiative lifetimes shows that for a particular QW the spatial electron and hole separation is quite uniform. Of course, one should bear in mind that the SNOM values are averaged over the probe aperture area of ~ 0.01 μm², and the smallest interface faceting scale is just a few nm [13]. Still, our results show that large scale (> 100 nm) well width variations do not seem to have a substantial additional effect on the carrier separation and the radiative lifetime.

The QW width has a profound effect on the nonradiative recombination times as well (Fig. 4 (b), (d) and (f). With an increased QW width, the average nonradiative lifetime increases from 0.2 to 2.9 ns. This effect could be related to the electron and hole separation as well. The nonradiative recombination of a spatially separated electron and hole through a point defect is longer than for carriers localized at the same site [23, 24]. The nonradiative recombination in the 2 nm QW could be further affected by an increased recombination at interface defects and defects in the GaN barriers, resulting in the large difference of the nonradiative recombination times for the 2 nm QW compared to the wider wells.

Maps of the nonradiative lifetimes are quite uniform as well. The standard deviations divided by the average values are 0.027, 0.032 and 0.048 for the 2, 4 and 6 nm QWs, respectively. This indicates that the nonradiative recombination primarily takes place through point defects because recombination through dislocations would be accompanied by much stronger variations in in the nonradiative lifetime maps [25].

For the 6 nm QW, a clear correlation between the radiative and nonradiative lifetimes with r = 0.8 is observed. For the narrower QWs, the correlation is much weaker (r = 0.2). The strong correlation in the QW, in which the separate carrier localization is most pronounced, supports the assumption that the carrier separation effect influences both the radiative and the nonradiative recombination times.

4. Conclusion

In summary, near-field PL measurements with 100 nm spatial resolution have been carried out on $(20\overline{2}1)$ plane InGaN QWs with different well widths in order to investigate the impact of the QW interface fluctuations on the spectral linewidth and the recombination times. Our experiments suggest that QW width fluctuations, compared to variations of the InGaN alloy composition, play a negligible role in defining the PL peak linewidth. However, the well width variation strongly affects the recombination times. It is proposed that in-plane electric fields caused by the interface roughness contribute to the electron and hole localization at different sites and increase the radiative and nonradiative lifetimes in the 4 and 6 nm QWs. For the narrow 2 nm QW, this effect was not observed, presumably because of a strong interface scattering.