Diffusion Analysis of Charge Carriers in InGaN/GaN Heterostructures by Microphotoluminescence

Lateral ambipolar diffusion in an InGaN/GaN single quantum well (SQW) structure grown on bulk GaN is studied by microphotoluminescence (μPL) investigations. The analysis is done via pinhole scans, that is, by decoupling the excitation area from the detection area and scanning the latter one. Knowing the size of the excited region, conclusions about the carrier transport in the in‐plane layer of the QW can be drawn. In this study, a diffusion length L d up to 12 μm is observed at room temperature. Furthermore, the energy of the spectral peak is analyzed as a function of distance, showing a pronounced blueshift at the excitation center. An increase in distance to the injection region is accompanied by a redshift. The indication of peak energy is used to relate the drop of PL intensity with increasing radius to actual diffusion of charge carriers. In addition, temperature‐dependent studies of the diffusion behavior are done, covering the range between 10 K and room temperature. No significant change of diffusion length can be seen with temperature, indicating that temperature dependencies of carrier lifetime and of mobility compensate each other.


Introduction
Transport and recombination dynamics of charge carriers determine the light-emitting diode (LED) efficiency. Recombination is explained in terms of Shockley-Read-Hall (SRH) bulk and surface non-radiative recombination, radiative recombination, and Auger recombination. [1][2][3] Surface recombination becomes important for optimizing μLEDs. [4] Transport dynamics of carriers on the chip level are described by the ambipolar drift diffusion model. [5,6] Remaining issues are carrier overflow [7] and lateral current crowding. [8,9] Vertical transport between different multiquantum wells (MQWs) is enhanced by thermionic and tunnel transport. [10] Here, we are interested in the lateral transport within the QWs, precisely in the ambipolar lateral carrier diffusion. Earlier experiments have shown a diffusion coefficient in the range between 0.01 and 3 cm 2 s À1 . [5,6,[11][12][13][14][15][16] In the work of Solowan et al., the carrier mobility was investigated as a function of temperature. [15] The study showed a freeze out of the carrier movement at T < 110 K and a localization of charge carriers at 10 K. In a more recent work by A. David, a carrier density-dependent diffusion was shown. [16] The ABC model describes longer carrier lifetimes at low carrier density, resulting in wider diffusion at low charge carrier densities.
In MQW structures, the vertical and lateral transport in the active region is difficult to separate. This motivated us to reproduce the experiment by A. David. In our study the single QW (SQW) was grown on bulk GaN to improve the spatial homogeneity of the emission wavelength and carrier lifetime. For the experiment, a modified microphotoluminescence (μPL) setup with spatially independent excitation and detection spots is used. We reproduce the intensity dependency of the diffusion length, as already observed by A. David, and additionally measure the local wavelength shift as a measure for the carrier density as a function of distance to the excitation spot. Furthermore, we measure the diffusion length as a function of temperature in the 10-294 K range. Our results show no significant change in diffusion range, indicating that temperature dependence of carrier lifetime and diffusion constant are cancelling out.
As comment of caution, we note that the measured PL spot size is interpreted as resulting from carrier diffusion, only. While the sample geometry should rule out secondary absorption by a reflected fraction of the exciting laser beam, reabsorption of the emitted photons cannot be ruled out. This radiative transfer can contribute to the observed spot size. While reabsorption was estimated to be weak in ref. [16], we suggest to reevaluate the observation in a model including the optical field and reabsorption. The spatially resolved shift of the peak emission shown here may help to evaluate a more complete model and further the understanding of lateral carrier transport.

DOI: 10.1002/pssb.202200565
Lateral ambipolar diffusion in an InGaN/GaN single quantum well (SQW) structure grown on bulk GaN is studied by microphotoluminescence (μPL) investigations. The analysis is done via pinhole scans, that is, by decoupling the excitation area from the detection area and scanning the latter one. Knowing the size of the excited region, conclusions about the carrier transport in the in-plane layer of the QW can be drawn. In this study, a diffusion length L d up to 12 μm is observed at room temperature. Furthermore, the energy of the spectral peak is analyzed as a function of distance, showing a pronounced blueshift at the excitation center. An increase in distance to the injection region is accompanied by a redshift. The indication of peak energy is used to relate the drop of PL intensity with increasing radius to actual diffusion of charge carriers. In addition, temperature-dependent studies of the diffusion behavior are done, covering the range between 10 K and room temperature. No significant change of diffusion length can be seen with temperature, indicating that temperature dependencies of carrier lifetime and of mobility compensate each other.

Spatial Distribution of Intensity
In Figure 1, a comparison of the laser spot (Figure 1 (left)) and the PL spot (Figure 1 (right)) is shown. For the determination of the laser beam radius, a smaller area was scanned (5 Â 5 μm 2 ) with a step width of about 0.1 μm (Δx ¼ Δy). For every other measurement, a larger scan area (36 Â 36 μm 2 ) was investigated using a step width of 1 μm (Δx ¼ Δy). The excitation beam radius (half width at half maximum) is about 0.25 μm. The radius at which the intensity drops to 10% (r 10 % ) for the laser is about 0.51 μm. This leads to an area (A ¼ πr 2 ) of about 0.82 μm 2 where 90% of the laser intensity can be found. On the logarithmic scale, the long-range behavior of the diffusion is revealed, showing a significantly wider spatial PL distribution compared to the actual excitation area. In the absence of diffusion, a smaller spot than the excitation area is expected for confocal microscopy. [12] This is obviously not the case in our experiment, which speaks for diffusion on a large scale. The PL intensity drops down to 1% at about 9 μm, whereas the laser signal is already extinct. Here the value for r 10 % is about 3.85 μm, resulting in an area where 90% of the PL signal is distributed of about 46.57 μm 2 .

Spatial Distribution of Peak Emission Energy
The same pinhole scan shown in Figure 1 is now presented again in Figure 2 on the left side, but in this case the peak emission energy is plotted. The energy is evaluated by the first moment of the spectrum. At the center, that is, where the charge carriers are optically injected, the emission energy shows a pronounced blueshift with an energy value of about 2.78 eV. With increasing distance to the center, for example, moving along the x-axis as indicated with the different colored stars in the image, the signal shifts increasingly to lower energies, converging to a value of about 2.68 eV at larger radii. The distinct blueshift at the injection region is attributed to the screening of the quantumconfined Stark effect (QCSE), that is, the screening of the internal electric fields in the QW and the band filling of higher energy states. [17,18] At the center, we find the highest charge carrier density; thus, the screening effect is dominant at this position. Charge carriers that are injected can either be localized or delocalized. In the latter case, carriers will move laterally in the QW and recombine nonradiatively or radiatively at a certain position. Only a minor part of the injected carriers diffuse away from the excitation center; hence, the density of carriers is smaller with increasing radii, for example, the charge carrier density at the black star is higher than that at the blue star. With the decreasing amount of carriers present, the effects responsible for the blueshift (screening of QCSE and band filling) are reduced, corresponding to an observable redshift. Now, this information about the actual peak emission energy allows us to distinguish between carrier diffusion and photon bouncing. Photons, which are directly generated at the center, can be guided by the in-plane layers followed by an outcoupling at a patterned sapphire structure (PSS) and at defects (photon bouncing). The photons could also be reabsorbed by charge carriers localized in the QW, where finally another radiative or nonradiative emission can take place (photon recycling).
From similar diffusion experiments with MQW samples on PSS, we observe a decay of scattered light with an extraction coefficient smaller than 10 3 cm À1 ¼ ð10 μmÞ À1 . In the present SQW sample on bulk GaN, scattering from the GaN-sapphire interface is absent. Scattering from defects (photon bouncing) is therefore estimated to cause a small and slowly decaying background at the energy of the peak emission in the center.
Reabsorption can be estimated from the absorption coefficient in the QW, for which we assume an upper limit of 50 000 cm À1 and overlap of the photon wave function and QW. Because there is no waveguide for the SQW on bulk GaN sample, the latter will be orders of magnitude smaller than the confinement factor for the waveguide of a laser diode, Γ % 0.01. Consequently, we assume the absorption length due to reabsorption to be much smaller than 500 cm À1 ¼ ð20 μmÞ À1 . Therefore, photon recycling www.advancedsciencenews.com www.pss-b.com is expected to cause a small and slowly decaying background at the redshifted energy far from the excitation spot. Photon recycling was discussed in detail and simulated for an InGaN SQW on bulk GaN substrate in ref. [16] with the conclusion that it has little impact on the observation of diffusion. Because of the high numerical aperture of 0.75 and the 300 μm-thick GaN substrate with rough backside, light from the exciting laser reflected from the backside is distributed over an area much larger than the observed diffusion, and its intensity is at least five orders of magnitude smaller. Because of this and as there are no other interfaces with a larger refractive index contrast inside the sample, we neglect the excitation by the reflected beam. Details on the excitation geometry are shown in the experimental section ( Figure 7).
In Figure 2 (right), the spectra at different spatial positions are shown. At the center, the spectral peak position is about 2.78 eV, which is also indicated by the red dashed line. The peak emission energy shifts to smaller energy values when moving away from the center in 1 μm step. The data is taken from the pinhole scan shown in Figure 2 on the left side.

Photoluminescence Cross-Sections
A quantitative analysis of diffusion is given by looking at the radial decay of the PL spots (see Figure 3). In this case the excitation power was varied from 6 μW up to 443 μW using a gradual Figure 3. Cross-section curves of the PL spots at different investigated excitation powers. The red line represents the laser data. The continuous and dashed lines indicate the experiment and simulation, respectively. Note the logarithmic scale. The simulation is done for a) A ¼ 4 Â 10 6 s À1 , B ¼ 3 Â 10 À12 cm 3 s À1 , C ¼ 1 Â 10 À31 cm 6 s À1 , and D ¼ 6 cm 2 s À1 and for b) A ¼ 1 Â 10 7 s À1 , B ¼ 3 Â 10 À12 cm 3 s À1 ,C ¼ 1 Â 10 À31 cm 6 s À1 , and D ¼ 12 cm 2 s À1 . www.advancedsciencenews.com www.pss-b.com filter wheel. The laser power was set to 30 mW and only the filter wheel was adjusted to achieve the desired excitation density on the sample. For determining the radial dependency of the PL, the center of the excitation is defined first. After that, the spectra for each pixel in the pinhole map are collected together with the radius, that is, the distance between the excitation and the pixel. Finally, every collected spectra is integrated from 408 to 518 nm. For all points with identical distance the resulting moments were averaged. For each value only one radius is plotted, that is, the density of points along the r-axis increases with r. First, it can be directly observed that the PL spot is obviously much larger than the excitation area for all measured power densities. The PL signal drops about one order of magnitude (note the logarithmic scale) per 5 and 3 μm radius for the lowest and highest excitation, respectively. Consequently, a clear tendency of the diffusion can be observed, where the diffusion length decreases going from low to higher excitation densities, that is, injected charge carrier densities. A theoretical model assuming a constant carrier lifetime τ (R ¼ n=τ) would lead to a constant slope in the diffusion curves. In our simulation (dashed lines in Figure 3), we include a carrier dependency of the lifetime τðnÞ; details will be described in the next section (Section 2.3). For now, the experimental trend is followed by the theory, proving that diffusion shows a dependency of charge carrier density. Also, the experimental data can be fairly well fit by the simulation.

Energy Cross-Section Curves
Additional information about the radial distribution of the charge carriers can be concluded looking at the decay of the peak emission energy with the radius (Figure 4). All curves show the same behavior for every excitation power: A pronounced blueshift at the center (r ¼ 0), followed by a rapid decay with increasing distance to the center and finally a slow decay beyond a certain radius (r > 4 μm). At respective large radii, the energy is expected to drop to the same energy level. However, this is not observed in the experiment. At lowest excitation level, we observe a shift of the peak energy for the whole observed region. This may be due to a global rise of background carrier density by the reflected and scattered excitation beam and by reabsorption or by a light-induced bias across the p-n junction. No external bias voltage was applied during the measurements, that is, the sample was not contacted. Because of the transparent conductive oxide (TCO) on the top surface, the bias change is global.
The pronounced blueshift at the center is, as previously explained, attributed to the screening of the QCSE and band filling. For all the excitations used within the experiment, a saturation of the blueshift is not accomplished, that is, the QW is still tilted even at the highest injection density. Furthermore, the slope of all experimental curves varies, for example, the slowest and fastest decay can be observed for the darkish blue and yellow line, which correspond to the lowest and highest injected charge carrier density, respectively. The smallest excitation density coincides with the longest carrier lifetime (A ∝ 1 τ ), whereas the highest excitation power corresponds to the shortest lifetime (Cn 2 ∝ 1 τ ). Therefore, the experimental data agrees to the observations of the radial intensity profile: the diffusion length is the longest at the smallest excitation power, that is, the longest carrier lifetime (L d ∝ ffiffi ffi τ p ).

Theoretical Model to Describe Diffusion
For the simulation of diffusion, a simple rate equation model is used where n, G, R, and D describe the charge carrier density, generation and recombination of charge carriers, and diffusion coefficient, respectively. The generation of charge carriers is given by the excitation source as a function of the radius r, which is a Gaussian beam I 0 and w 0 describe a normalization factor and the 1=e radius. The best fit of the laser profile is obtained for w 0 ¼ 311 nm. Describing the recombination RðnÞ in Equation (1) is done using the ABC model The B and C parameters are divided by the thickness of the QW d QW and d 2 QW , respectively, where we use 2.5 nm as the effective thickness of the QW. This is not the actual InGaN layer thickness, as the QCSE and interface roughness have an impact on the relation between the 3d and 2d carrier density. [19] Equation (1) is then written in polar coordinates, and the r-dependency is being solved until a stationary solution is reached for every excitation power used in the experiment with the numerical solver NDSolve of Mathematica in a 1d system using the Dirichlet condition for a radius of 50 μm with the initial condition of zero charge carrier density at t ¼ 0. [20] For plotting the PL, the term Bn 2 is finally computed. In Figure 3 the results of the simulation (dashed lines) are shown for charge carrier densities after a large time (t ¼ 10 μs). For fitting the experimental data, the A and D parameters are used, while the B ¼ 3 Â 10 À12 cm 3 s À1 and www.advancedsciencenews.com www.pss-b.com C ¼ 1 Â 10 À31 cm 6 s À1 parameters are taken from another study, where the ABC parameters for different SQW structures grown on sapphire are investigated. [21] Note that the analyzed structure in this study is grown on bulk GaN. For fitting the experimental data, different example evaluations using A and D values from previous publications are being compared to the data by eye. Two simulations of the diffusion behavior are shown together with the experimental data, one for D ¼ 6 cm 2 s À1 and A ¼ 4 Â 10 6 s À1 and one for D ¼ 12 cm 2 s À1 and A ¼ 1 Â 10 7 s À1 . The smaller value of D ¼ 6 cm 2 s À1 corresponds to a value used in ref. [16]. The larger value D ¼ 12 cm 2 s À1 better fits the experimentally observed narrower spread of the curves at larger radii. However, for a wide range of reasonable values of ABC parameters and diffusion constant D, a discrepancy between simulation and experiment at small radii remains. We assume that reabsorption and drift have to be included in the model to describe the behavior at smaller distances. Consequently, the values taken from a fit of the model to the data should be considered with caution. However, they do reflect the trend of an increased carrier diffusion with reduced carrier density as a consequence of the increasing carrier lifetime.

Carrier Lifetimes and Rates
In Figure 5, the carrier lifetimes and rates are plotted as a function of the distance. At low excitation ( Figure 5 left), the effective carrier lifetime τ eff is mainly dominated by the SRH recombination path, since the Auger lifetime is much higher in that excitation regime and the radiative lifetime τ rad shows smaller values than the SRH lifetimes for radii smaller 2 μm. However, the situation is different for the highest excitation ( Figure 5 right), where the Auger and radiative lifetimes are much shorter, while the SRH lifetime remains unchanged. In this case, the effective carrier lifetime is first dominated by the Auger recombination up to 2 μm, then the radiative recombination takes over up to a radius of about 14 μm, and finally the effective lifetime is governed by SRH recombination. Overall, carriers have a much shorter lifetime at higher charge carrier densities, because the radiative and nonradiative Auger recombination paths are more likely than the SRH recombination. With less lifetime, but the same mobility, carriers are not able to move as large distances as they can with higher lifetimes in the case of a smaller excitation density.
To estimate the carrier recombination rates in Figure 5, the integral Z r 0 2πr 0 R½nðr 0 Þdr 0 (4) for each recombination rate and radius r is calculated with the zeroth moment, where the upper integration boundary is iterated in 1/2 μm steps (starting with 1/2 μm) until a value of 20 μm is achieved. Each computed value is then plotted for the different recombination rates. The diffusion flux is described by Fick's law [22] F ¼ ÀD∇n For a comparison between the carrier recombination rates and the diffusion rate, the diffusion flux is multiplied by 2πr. The rates plotted in Figure 5 correspond to the carriers recombining per nanosecond within a circle of radius r for the respective recombination path and to the diffusion current of carriers per nanosecond out of the disc with the respective radius.
At the lowest excitation ( Figure 5 left), the effective carrier rate follows for smaller radii radiative recombination rate. At the cross-section of the radiative and SRH recombination rate (r ¼ 3 μm), the effective rate is governed mainly by the latter one. Additionally, a large diffusivity can be seen, where the diffusion rate is larger than the effective recombination rate for a radius up to 12 μm. Adding the effective recombination rate curve with the diffusion rate curve leads to a constant line, where the value equals the generation term from Equation (1). A much smaller impact of the diffusivity can be seen in the case of higher excitation density (Figure 5 right). Just for a small radius (2 μm), the diffusion rate is higher than the effective recombination rate. After that, however, the diffusion rate rapidly decreases to smaller values with increasing radius, whereas the effective recombination rate is much higher, that is, carriers tend to recombine at radii larger than 2 μm. This can be underlined by looking at the different recombination rates, the effect of SRH recombination is much smaller, leading to an effective recombination rate, which is governed by the radiative and Auger rates. The influence of the Auger rate can be observed Figure 5. Calculated carrier lifetimes and rates as a function of distance. Shown are the excitation densities 6 μW (left) and 443 μW (right). The continuous and dashed lines correspond to the carrier rates and lifetimes, respectively. The black, red, blue, and green curves indicate the effective, SRH, radiative, and Auger recombination. The purple line (only valid for rates) represents the diffusion term ÀD∇n. Note that the carrier lifetimes are plotted on a logarithmic scale, whereas the carrier rates are plotted linearly.
www.advancedsciencenews.com www.pss-b.com dominantly for radii smaller 2 μm. After that, the radiative rate takes over. Adding the diffusion rate and the effective rate leads to a constant line, but with a small peak at small distances (r < 2 μm).

Influence of Temperature
The diffusion length is given by We showed in Section 2.2 that the diffusion length is a function of the charge carrier density, because at least the carrier lifetime depends on the actual amount of injected carriers. At low charge carrier densities, where the largest carrier lifetime (τ ¼ 1=A ¼ 250 ns) can be found, the resulting diffusion length is the highest with 12 μm (using Equation (6) and the values for A ¼ 4 Â 10 6 s À1 and D ¼ 6 cm 2 s À1 ). In our theoretical model we do not consider a possible dependency of the diffusion coefficient on charge carrier density. Because diffusion constant and carrier lifetime in Equation (6) depend on temperature, [15,[23][24][25] diffusion length should also depend on temperature. In the work by Solowan et al. the diffusion coefficient was investigated for MQW and showed an increase with temperature, which supports the image of localization and antilocalization of charge carriers (S-shape). [15,26] In temperature-dependent studies of the diffusion coefficient in bulk GaN [27,28] and bulk InN, [29] the diffusion coefficient showed an opposite behavior, that is, increasing with declining temperature. In the case of a QW structure, strong In fluctuations are responsible for localization of charge carriers, whereas such fluctuations are absent in bulk material. Therefore, a comparison with the QW study by Solowan et al. is more appropriate, that is, assuming an increase of the diffusion coefficient with temperature. Additionally, we assume the carrier lifetime to decrease with increasing temperature due to thermal activation of defects, although different studies showed an opposite trend. [23,25] The dependencies of the effective carrier lifetime on temperature in these studies are small, changing with a factor of about 2. In another study by Nippert et al., the temperature change of the ABC parameter was investigated. [24] The SRH parameter increased with temperature due to thermal activation of defects. The radiative and Auger recombination rates showed a synchronous dependency of the temperature, both increasing when temperature increases. An increase of the C parameter can be modeled, including phonon-assisted processes. [30] The synchronous behavior of the B and C parameter was also investigated in earlier publications, but with an opposite trend, that is, decreasing with temperature. [31,32] In Nippert et al., the increasing B parameter with temperature is attributed to neighboring In atoms that may provide an effective carrier localization. In general the B parameter is expected to decrease with temperature (B ∝ T À1 QW or B ∝ T À3=2 bulk).
In our experiment we varied the temperature range from 10 K up to 294 K in 20 K steps and studied the diffusion with the help of pinhole scans for three several excitation densities. The results are shown in Figure 6. The integrated PL intensity (spectra are collected in a small area around the maximum intensity signal) decreases by a factor of about 0.7 comparing the lowest and highest temperature used in the experiment, representing the high internal quantum efficiency of the sample. For the cross-section curves, a different approach than that in Section 2.2 was done. In this case, we assumed a symmetric PL distribution and instead of doing a circle-like pinhole scan, a stripe shape was measured, that is, a small dimension in y-axis (6.8 μm) and a larger in x direction (41 μm). The step widths are Δy ¼ 0.40 and Δx ¼ 0.42 μm. The cross-section is then computed by searching the maximum of the intensity and taking all data going along the x-axis. For every temperature and excitation power, the PL signal drops down to a 1% intensity compared to the signal at the center (r ¼ 0) at about a radius of r ¼ 5 μm. For radii larger than 5 μm, only the photon-bouncing background is measured. Surprisingly, the diffusion length is independent of temperature within measurement accuracy. This appears to be counterintuitive at first, but can be plausible, since the diffusion coefficient increases with temperature, whereas the carrier lifetime decreases. Assuming a weak dependency on temperature of these two parameters, they might partially compensate each other, resulting in a constant diffusion length L d ðTÞ ¼ const. However, this possible interpretation has to be taken with caution, as the contribution of drift and reabsorption to lateral carrier redistribution are unknown and have to be considered in a full description. Furthermore, we want to point out that the dependency of the excitation density was not observed for the temperature-dependent experiment ( Figure 6) in contrast to the room-temperature measurement (Figure 3).

Discussion and Conclusion
In conclusion, the diffusivity of charge carriers is studied by scanning the image of a luminescent area around a small excitation spot. We observe a diffusion length up to 12 μm at room temperature. A simple rate equation model, including the carrier transport dynamics, is used to simulate and approve the experimental data. The spectral resolution gives additional information about the spatial distribution of the charge carrier density, thus allowing to distinguish carrier diffusion from photon bouncing.
Furthermore, the diffusion behavior is studied as a function of temperature, which is varied from 10 K up to room temperature. The experiment shows no significant dependency of the diameter of the area of the QW from which PL originates. Interpreted in terms of carrier diffusion, this would indicate a temperatureindependent diffusion length down to 10 K. An increasing diffusion coefficient and decreasing carrier lifetime with temperature may partially compensate each other, leading to a weak Figure 7. Schematic diagram of a) the experimental setup, b) the sample structure and the excitation beam that is focused on the active layer, and c) the excitation cone and detection cone. In (a) the continuous black lines indicate the collected luminescence when the alignment is confocal. If the pinhole is moved along the y-axis, the spatial detection of the luminescence on the sample is indicated with the red dashed lines.
www.advancedsciencenews.com www.pss-b.com temperature dependency of the diffusion length. However, the influence of drift and reabsorption to lateral carrier transport should be included in a rigorous model of transport and interpretation of the surprising experimental results.

Experimental Section
Pinhole Scan: For the analysis of the diffusion behavior, a blue InGaN SQW (3 nm-thick QW, composition [In] = 15%) test structure grown by metal-organic chemical vapor deposition on a 300 μm-thick bulk GaN substrate was investigated. The peak emission wavelength was about 450 nm and a μPL setup was used for the analysis of the carrier transport dynamics. The sample was mounted onto a copper heatsink and placed beneath the microscope objective, which had a magnification of 63Â and a numerical aperture of 0.75. The InGaN SQW was close (% 100 nm) to the optically smooth top surface, covered by a TCO. The backside surface was rough and metal coated. The experimental setup and the optical geometry of excitation and detection are shown in Figure 7.
The excitation laser with a wavelength of 375 nm was guided through a two-lens beam expander, that was used to magnify the Gaussian beam by an order of three. Thus, the numerical aperture of the objective was fully used, leading to a diffraction-limited spot size. The excitation source was quasiresonant, that is, only the QW layer was excited. A charge-coupled device (CCD) can be used for orientation along the in-plane layer of the QW and to verify the focus of the excitation beam. The PL of the sample was collected through the same objective and by a single-mode fiber with a core diameter of 10 μm. In our experiment, the fiber acted simultaneously as the pinhole. The collected light was guided to a 55 cm focal length spectrometer equipped with a back-illuminated CCD detector.
For the temperature-dependent measurements of Figure 6, the sample was mounted into a continuous-flow cryostat cooled by liquid helium. The temperature range was from 4 K up to 400 K; however, in this study, only temperatures from 10 K up to 294 K were investigated.
Finally, to identify the diffusion in the active layer, an x-y stepper motor moved the pinhole in the image plane. Consequently, the detection area was decoupled from the excitation area. A typical confocal μPL setup describes the alignment of the excitation area with the detection area. However in our experiments, the region of injected carriers was steady while the pinhole, that is, the detection, scanned the area around the excitation zone; we called such a procedure a pinhole scan. If the actual excitation area was known, conclusions about the diffusion range could be directly drawn from such a measurement.