Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

AIP/123-QED

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
Shunra Yoshida1 , Yusuke Fujii1 , Giovanni Alfieri2 , Ruggero Micheletto1*1
1. Yokohama City University, 22-2 Seto, Kanazawa-ku, 236-0027,
Japan
2. Hitachi Energy, Fabrikstrasse 3, 5600 Lenzburg, Switzerland(*Electronic mail: ruggero@yokohama-cu.ac.jp)(Dated: 6 April 2023)

The blinking phenomenon in InGaN single quantum wells is a phenomenon where localized photoluminescence changes over time. Understanding its physics is important for the
manufacture of more efficient light emission diodes. We present a study using two InGaN
single quantum well samples, emitting at 460 nm and 510 nm wavelength, respectively. We
confirmed that the luminescence intensity fluctuates in localized blinking regions and we
found that these optical variations are not random, but are instead correlated in pairs, witheither positive or negative coefficient, to a distant reference blinking point. Measurements
were performed to obtain standard deviation and cross correlation maps. Invoking thequantum confined Stark effect we realized a simple phenomenological model that shows
how charge carriers are exchanged among pairs of adjacent opposite correlation regions.
As a result, it is suggested that the phenomenon is caused by fluctuations in the number ofthese exchanged carriers. Our model gives an explanation for the blinking phenomenon in
InGaN single quantum wells and it is important for a deeper understanding to InGaN-basedmaterials.

1Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
Understanding the fundamental properties and carrier dynamics of GaN and InGaN is essential
for the development of GaN-based light emitting diodes (LED) devices and other applications.
However, this is challenging due to the effects of a high defect density, the influence of large
strain-induced polarization (caused by lattice mismatch) and also the lack of a suitable theoreticalbackground1,2 . The optical blinking phenomenon (BP) affecting the local luminescence in InGaN
single quantum wells (QW) is one of these unknown phenomena that needs to be clarified.
The BP in InGaN QW was firstly observed by Micheletto et al.3 with photo luminescence (PL)measurements. The phenomenon is triggered by illumination with light at 365 nm exciting both
InGaN and GaN layer and occurs in a region of stronger optical emission compared to the average(intense luminous centers, ILCs). As most ILC’s show stable optical emission, presence of blinking regions indicates locally high In composition and variable accumulation of carriers4–7 . For
this reason, the relationship between blinking and spatial inhomogeneity of In composition was
discussed8 . Depending on the indium concentration the BP phenomenon changes. For example,
samples emitting 460 nm light optical blinking is observed, but less prominent and noticeable thanfor samples emitting green light such as those emitting at 510 nm and 540 nm3,4 .
Optical instabilities, such as blinking, are also reported in other materials like CdSe nanocrystals9
and GaAs quantum dots (QD)10 . Although these instabilities can be treated as an on/off flashingand explained with Auger ionization as in CdSe nanocrystals9 , this explanation cannot be applied
to our InGaN quantum well samples where the blinking has not a simple on/off behaviour11,12 . A
comparison study of our sample blinking and blinking due to quantum jump model has been donein previous studies3 .
Several theories exist that could explain BP. One of them is quantum confined Stark effect(QCSE)3,13,14 , where the electric field changes the overlap of the electron and hole wavefunctions
inside a quantum well. It is known that the piezoelectric field present in strained quantum wells
composed of GaN and InGaN causes QCSE15 . In addition, QCSE was also used to qualitatively
explain the optical memory effect in InGaN thin film16 . Since in this model the emission wavelength shortens with increasing intensity, it can explain the tiny shift in emission wavelength inBP, i.e. the wavelength becomes shorter when the intensity increases, and vice versa, due to theelectric field of carriers trapped in deep levels3,14 . These deep levels are possibly originating fromdefects at the InGaN/GaN interface17,18 . However, the QCSE model cannot explain other experimental results such as intensity distribution and dynamics for the BP3,19 . In another candidate
model, interference of thermal vibration of the crystal lattice is implied as the cause of instability
2Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
in InGaN single QW19 , but it can not sufficiently explain other experimental features of blinking.
In a recent study, it was found that the adsorption of gas at different pressures, such as oxygento the surface of the InGaN QW, increases the presence of ILCs and BP20 . A similar effect was
confirmed21 by PL observation of the samples immersed in liquids. It was suggested that blinking
could be caused by the interaction of surface molecules with impurities present within the QW.
Based on such recent results and in order to obtain a more detailed insight between the BP and therole of defects. In this study, we report on the spatial time-correlation between blinking points in
InGaN single QW and give a qualitative explanation of the BP based on our PL results.
In this study, the InGaN single QW samples are stacked over a 4 µm undoped GaN layer, a
3 nm Inx GaN(1−x) active layer, a 5 nm undoped GaN capping layer and they were grown alongthe (0001) direction by metal-organic vapor phase epitaxy (MOVPE) on sapphire. The emission
peaks of the samples depend on the In concentration x in the Indium layer. The peak can range
between 400 nm up to 540 nm or more5 . In this study we used two samples that emit at 460 nm
and 510 nm wavelength.
Samples were cleaned by one minute ultrasound sonic bath (US-2R, AS ONE, Japan) in distilled water before PL measurements. The measurements recorded with a CCD camera (HDRSR1, SONY) attached to a selective excitation fluorescence microscope (BX51WX, Olympus).
The optical emission from the surface was recorded at 30 frames per seconds and stored in a
730x730 pixels AVI format. Our recordings were of 30 s duration on an area of about 180x180µm.
The 30 seconds recording were excluding initial lamp induced transients. Ultraviolet Hg lamps
were used as excitation light (365 nm and 405 nm emission lines, the photoluminescence was detected through a color filter centered about 450 nm to cut away unwanted UV signal from the GaN
bulk layer). Since the main purpose of the investigation is to study the blinking points time correlation, we have chosen an arbitrary reference blinking point and for each pixel intensity time-series
we calculated the cross correlation to it. All our observations were made using the sole 365 nm
excitation light that excites both the InGaN layer and the GaN layer3 .
Firstly, using 30 seconds PL recordings, the standard deviation was calculated for all positionsand visualized as standard deviation (SD) maps to identify the location of the blinking point (thatis: if the PL is constant in a location, the standard deviation should be zero, if instead it fluctuates
there will be a positive SD). Then, in each sample, one blinking point is selected as the reference
point to obtain the correlation coefficient with all other positions and visualized as correlation
coefficient (CC) maps.
3

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

FIG. 1. The photoluminescence of the two samples (left), standard deviation maps (middle) and correlation
maps (right). Top and bottom row correspond to 460 nm and 510 nm sample respectively. Each image isabout 180 µ m in size and comprises of 730 pixel in both directions. The standard deviation and correlation
maps are obtained elaborating the 900 points PL time-series associated for each CCD’s pixels. The correlation is in respect to an arbitrary blinking point chosen as reference, indicated by the solid circle in panel (b)and (e). The maps in (c) and (f) represent the correlation coefficient of all the other pixels time-series withthe reference one. The circled areas in (f) are regions where positive/negative correlation blinking domains
are present.

Figure 1 shows the results of the PL measurements, its correlation analysis. The standard
deviation (SD) and correlation coefficient (CC) maps were obtained from the PL measurements,using the 900 points time-series recorded for each pixels in the image. From that, we calculated
the SD of the optical intensity during the 30 s recording, and plotted a value for all positions
resulting in the images. In this way, we could visualize the location of the blinking points (weconsider a blinking point any region where the standard deviation is bigger than 7). Let’s compare
the photoluminescence maps on the left and the corresponding images in the center that represent
the fluctuations amplitude of those points during the 30s recording. Noticeably, all blinking points
correspond to bright emission regions (ILCs), but not all ILCs do blink. Moreover, the blinking
locations seen in the central image, are smaller in area than the corresponding ILCs visible in thephotoluminescence maps on the left. Comparing the left and right images, we note that some4Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
blinking domains are actually not so intense in luminescence as others. On the central panels, foreach sample, one blinking point is selected as the reference to obtain the cross correlation (CC)with all positions. The CC coefficient is then visualized as color map, red for positive correlation
and blue for negative on the right. As the figure shows (Fig. 1(a)), the 460 nm sample has large
areas of stable luminescence and small SD (Fig. 1(b)).
Figure 1 shows these PL measurement results in panels (a) and (d), SD maps in (b) and (e),and the CC maps in (c) and (f). It can be qualitatively understood from the PL maps that there
are many bright and isolated emission centers in the 510 nm sample. The SD maps show thatthe 460 nm sample has many areas with small SD and shows comparatively stable luminescence,
while the 510 nm sample has many intense blinking points. Intriguingly, the CC maps show that
the PL fluctuations are not completely random, but a residual correlation to far away regions ispresent. The 460 nm sample, which exhibits stable luminescence, shows that the entire sample
has relatively uniform correlation in respect to a reference point circled in panel (b). The 510 nm
CC map instead shows a complex structure with positive and negative correlations relative to thecircled point in (e). In addition, blinking points with positive or negative correlation coefficients
exist in pairs adjacent to each other. This results are congruent with previous studies21 where
samples immersed in liquids cause intense BP and show similar maps. While we found that theemission intensity changes over a broad region that has positive correlation in the 460 nm sample,
we observed a spatially distant correlation in the 510 nm sample. This observation can be assumed
to be important to understand the root causes of the blinking phenomenon.
The histogram in Fig. 2 shows the distribution of the correlation values of the whole image
and it appears as a Gaussian distribution. To verify this relationship, a normal distribution withthe same mean and standard deviation as the experimental one is plotted in Fig. 2 (red solid line).
The similarity with a perfect Gaussian distribution indicates that there is almost an equal numberof blinking points with opposite correlation.
Figure 3, shows PL curves of three pairs adjacent blinking points that fluctuate with opposite
correlation relatively to a distance reference blinking point, the smaller circle in figure 1(e). Panel(a) shows the three pairs of curves with positive (magenta) and negative (cyan) correlation. We
call them "pairs" for the simple reason that they are located at a close distance to each other. The
experimental points are fitted with a fifth order polynomial curve as a guide for the eyes. These
results indicate that when one of the point is increasing in intensity, the other one in the pair isdecreasing. By averaging the intensities for each of those in Fig. 3(a), the curves in Fig. 3(b) are
5

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

FIG. 2. Histogram for the correlation coefficients map of the 510 nm emission sample in figure 1(f). The
mean and standard deviation of the distribution are reported in the inset. A red line represents the normal
distribution with same mean and standard deviation of the observation.

(a)

(b)

(c)

FIG. 3. (a)Intensity changes of three pairs of blinking points in the 510 nm sample of figure1(d). Magenta
and cyan lines correspond to positive and negative coefficients in the correlation map respectively, also thegray dashed and dot-dashed lines are 5th order polynomial fitting of them, indicated as I f (t) in the equationsin the text. The top panel represent the PL intensity profile of the pair regions in the position represented
with the solid circle, the middle panel the dashed circle and the bottom panel the dotted circle. In the circles
two distinct small areas with high positive (magenta) and negative (cyan) correlation are noticeable. (b)The
mean of two near blinking points intensity chosen as in panel (a). In (c) is shown histograms of the averaged
intensities in panel (b).

obtained. Notably, the averages are almost constant in time, suggesting that carrier recombination
has a common source for each pair. Panel (c) shows the histogram of the intensities of panels (b)and all of the distributions seem to have a symmetric Normal distributed shape.
6

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

FIG. 4. An example of quasi-telegraphic (binarized) intensity blinking in our 510nm emission sample. The
upper panel shows the intensity profile of one point of and the lower panel its histogram that shows two
distinct peaks, characterizing the telegraphic behaviour. These points were very rare to find and are notindicated in Fig. 1.

Previous studies have reported paired blinking points3 which can be viewed as a two-state
PL emission behavior, that is the PL mainly falls on two distinct intensity levels. In our current
experiment, the general behaviour was not-telegraphics, that is those kind of blinking points werevery rare to find (we found only one that blinks in a fashion that could be considered as "binary")
and were neglected in the theoretical analysis. As an example we show one of these fluctuations
in figure 4 with its double peaked distribution.
To summarize the results obtained so far, the blinking phenomenon is often found on adjacent
blinking points whose intensity changes with positive or negative correlation. Their CC, withrespect to a distant reference blinking point, follows a normal distribution (Fig. 2). In addition,
the averaged intensities of adjacent pairs, that have opposite correlation, is an almost constantNormally distributed profile as in figure 3(b). This fact suggests that the carrier recombination at
the blinking points pairs are originated from a common nearby carrier source to that pair, with theintensity of one blinking area increasing, while that of the other is decreasing of about the sameamount.
Now, we attempt to formulate a rigorous mathematical description for the BP behavior. To
simplify the problem, we deal only with the intensity change of two blinking pairs. Based on
7

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
the results so far, two conditions need to be fulfilled: (a) the two blinking points have opposite
correlation and (b) averaging the intensities between the two points leaves only a constant offset
plus a Normally distributed residual.
Condition (b) can also be phrased as saying that if we take the average of the two functions,
we are left with pure noise. As a consequence, the function that describes the intensity changesof each blinking point can be expressed as the sum of three contributions: a main form term I f (t),a noise term I pn (t), Inn (t) and a constant offset term I p0 , In0 (the subscript p and n represent thepositive or negative correlation). Therefore, the intensity of a pair of blinking points is expressedas:I p (t) = I f (t) + I pn (t) + I p0 ,

(1a)

In (t) = −I f (t) + Inn (t) + In0 ,(1b)These theoretical functions are representing the experimental results of Fig. 3(a). If we then takethe average of Eq. (1a) and (1b), the result is expressed as:
I p (t) + In (t)2
I pn (t) + Inn (t) + I p0 + In0=
2= Imn (t) + Im0

Im (t)=(2)

Where (I pn (t) + Inn (t))/2 and (I p0 + In0 )/2 are replaced with Imn (t) and Im0 (t) respectively. Thisfunction describes the result of Fig. 3(b), where we see a constant level of noise for all the 30 s ofrecording.
Now, we consider the quantum confined Stark effect taking in account the two conditions (a)and (b) mentioned above. QCSE is observed when the internal electric field generated inside aquantum well affects the charge carrier wavefunctions, therefore affecting the recombination probability and finally the photoluminescence. The electric field due to the piezoelectric properties ofthe material is modulating the wavefunction properties. Restricting ourselves to the phenomenological aspect, we suppose that some carriers are trapped in deep levels near the QW or that are
emitted from the same traps. Thus we assume that the PL intensity is reduced if carriers are trappedand increases when instead released16,22 . Such trapping/emission of charge carriers is considered
to be stochastic and, based on the discrete nature of electric charge23 , the exchange of carriers at
deep levels follows a Poisson distribution. Since there is a great number of recombination events,
we can simplify this further by assuming that this Poisson distribution P can be approximated by
8

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
a normal distribution, as follows:
P(µ) ≈ N(µ, µ)(3a)P(λ ) ≈ N(λ , λ )(3b)Where the stochastic variable following Eq. (3a) represents the number of carriers migratingfrom the positive correlation region to the negative one, and (3b) represents the vice versa. Here,according to Poisson statistics, the two parameters in the brackets of the normal distribution N are
identical and represent the mean and the variance respectively. Now, if we consider the number ofcarriers in each trap as the the difference between Eq. (3a) and Eq. (3b). Taking in account that
we have two traps that have opposite correlation, using the properties of the normal distribution it
follows thatN(λ − µ, λ + µ) = N(ξ , λ + µ)(4a)N(µ − λ , µ + λ ) = N(−ξ , µ + λ )(4b)Where Eq. (4a) and Eq. (4b) are the distribution for the number of exchanged carriers in the trap
for the positive and negative correlation area. The parameter ξ represents λ − µ. If ξ is larger than0, the recombination rate (that is the PL intensity) in positively correlated regions increases andvice-versa (if ξ is smaller than 0, this relationship is reversed). Noticeably the variance results tobe λ + µ for both cases. For comparison with our experimental observations, finally, we examine
the distribution obtained by averaging Eq. (4a) and Eq. (4b). From the properties of the normal
distribution, the mean of the distributions in Eq. (4a) and Eq. (4b) is
N(0,

λ +µ
)
2

(5)

This means that the average number of exchanged carriers trapped in the positive and negative correlation area follows a normal distribution with mean 0 and variance (λ + µ)/2. This corresponds
to the experimental results of Fig. 3(c).
We now introduce the time dependence (t) symbol and summarize the correspondence between
the variables described previously and the distributions parameter of above:I f (t) ↔ ξ (t)(6a)

I pn (t), Inn (t) ↔ N(0, λ (t) + µ(t))(6b)

Imn (t) ↔ N(0,9λ (t) + µ(t)
)
2

(6c)

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

(a)

(b)

FIG. 5. (a) Residual signals obtained subtracting the PL intensities of Fig. 3(a) with the interpolation curves
I f (t). (b) The average of the two intensity curves in panel (a).

In this way I f (t) represents the amount of carriers exchanged, and it corresponds to ξ (t) for boththe positive to negative correlation areas. This rigorously shows how the intensity fluctuations
in each regions and the averaged intensity between them results to be normally distributed andassociated to the amount of exchanged carriers.
Using this formalism, the dotted curves in Fig. 3(a) are both represented by the same function
ξ (t) for each pair of blinking points. Subtracting it to the photoluminescence we obtain the I pn
and Inn . This is evident from the experimental data plotted in Fig. 5(a).
Now, in the same fashion, when we take the average intensities of the experiments in Fig. 5(a)and obtain Fig. 5(b). Our formalism predicts that the variance of this should be half that of thetwo PL intensities before the averaging (see Eq. (5)).

To confirm the above, we have chosen ten pairs of negative/positive correlation regions. These
are ten blinking areas chosen using from figure 1(f), each of them include pairs of blinking pointsof opposite correlation as in Fig. 3(a). We examined their variance, before and after averaging
the pairs, and plotted the SD value. The result is shown in Fig. 6. The box on the left panel,indicated symbolically on the horizontal axis with I pn , Inn , is the variance calculated over thetwenty individual positive or negative correlation regions. The other box on the right, symbolizedon the horizontal axis as Imn , represents instead the ten variance values obtained by averaging
each positive/negative pairs. We point out that the variance is obtained from 30 s recordings, these10Time-correlated Luminescence Blinking in InGaN Single Quantum Wells

(a)

(b)

FIG. 6. Box plots for the variance of intensities (left) and for their ratios (right). The red crosses indicate
averages. The labels on the horizontal represent the experimental data for the positive correlation and thenegative correlation areas (Ipn , Inn ), and the average of them Imn . The Ipn , Inn box comprises of 20 variancevalues, the box on the right (Imn ) comprises of 10 variance values, obtained after averaging the PL timeseries of the adjacent blinking pairs with positive and negative correlation. The fact that the averages ofthese two class of variances has a relation of about 2:1, panel (b), as predicted in Eq. 6c is not trivial.

intensity values should be completely independent from each other. On the contrary, we found that
their variances are related as Eq. (5). This shows that the variance of the intensity, centered aroundthe value 2, is about half the value before averaging. This is consistent with what is theoretically
predicted.
Two different ways of understanding BP, experimental formulation and model with statistics,
lead to equal result and support the validity of our hypothesis. Since this hypothesis is consistent
with the application of QCSE to explain the optical memory effect in InGaN thin films16 , this is
the first step toward providing a unified theoretical background for complex optical phenomena in
InGaN-based materials, as well as in InGaN single QW.
We thank Yokohama City University for the its support with the "Research Fund 2022" that helped
the realization of this research.
Experimental data are available upon reasonable request.
11

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
REFERENCES
1 S. Strite and H. Morkoç, “Gan, aln, and inn: A review,” Journal of Vacuum Science and Tech-

nology, B 10, 1237–1266 (1992).
2 F. Stefani, J. Hoogenboom,and E. Barkai, “Beyond quantum jumps: Blinking nanoscale lightemitters,” Phys. Today 62, 34–39 (2009).
3 R. Micheletto, M. Abiko, A. Kaneta, Y. Kawakami, Y. Narukawa,and T. Mukai, “Observationof optical instabilities in the photoluminescence of ingan single quantum well.” Applied Physics
Letters 88, 061118 (2006).
4 A. Kaneta, M. Funato,

and Y. Kawakami, “Nanoscopic recombination processes in ingan/gan

quantum wells emitting violet, blue, and green spectra,” Phys. Rev. B 78, 125317 (2008).
5 R. Micheletto, N. Yoshimatsu, A. Kaneta, Y. Kawakami,

and S. Fujita, “Indium concentration

on pl spatial in homogeneity in ingan single quantum well structures detected by an original low
cost near-field probes,” Applied Surface Science 229, 338–345 (2004).
6 Y. Narukawa and Y. Kawakami, “Role of self-formed ingan quantum dots for exciton localiza-tion in the purple laser diode...” Applied Physics Letters 70, 981 (1997).
7 S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, “Spontaneous emission of localized excitons

in ingan single and multiquantum well structures.” Applied Physics Letters 69, 4188 – 4190
(1996).
8 R. Micheletto, M. Allegrini, and Y. Kawakami, “Near-field evidence of local polarized emission

centers in ingan/gan materials,” Applied Physics Letter 95, 211904 (2009).
9 M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris,andL. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383,
802–804 (1996).
10 D. Bertram, M. Hanna,and A. Nozik, “Two color blinking of single strain-induced gaas quan-tum dots,” Applied Physics Letters 74, 2666–2668 (1999).
11 A. Efros and M. Rosen, “Random telegraph signal in the photoluminescence intensity of a single

quantum dot,” Physical Review Letters 78, 1110–1113 (1997).
12 R. Cook and H. Kimble, “Possibility of direct observation of quantum jumps,” Physical Review

Letters 54, 1023–1026 (1985).
13 M. Sugisaki, H.-W. Ren, S. V. Nair, K. Nishi,

and Y. Masumoto, “External-field effects on the

optical spectra of self-assembled inp quantum dots,” Phys. Rev. B 66, 235309 (2002).

12

Time-correlated Luminescence Blinking in InGaN Single Quantum Wells
14 Y. Kawakami, A. Kaneta, K. Omae, A. Shikanai, K. Okamoto, G. Marutsuki, Y. Narukawa,T. Mukai, and S. Fujita, “Recombination dynamics in low-dimensional nitride semiconductors,”
physica status solidi (b) 240, 337–343 (2003).
15 T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano,and I. Akasaki,“Quantum-confined stark effect due to piezoelectric fields in gainn strained quantum wells,”
Jpn. J. Appl. Phys. 36, L382 (1997).
16 B. B. Wang, J. J. Zhu, D. G. Zhao, D. S. Jiang, P. Chen, Z. S. Liu, J. Yang, W. Liu, F. Liang,

S. T. Liu, Y. Xing, L. Q. Zhang, and M. Li, “Deep levels induced optical memory effect in thiningan film,” AIP Advances 8, 085222 (2018).
17 J. Speck and S. Rosner, “The role of threading dislocations in the physical properties of gan andits alloys,” Physica B: Condensed Matter 273-274, 24–32 (1999).
18 A. Y. Polyakov and I.-H. Lee, “Deep traps in gan-based structures as affecting the performanceof gan devices,” Materials Science and Engineering: R: Reports 94, 1–56 (2015).
19 R. Micheletto, K. Oikawa, and C. Feldmeier, “Observation of lattice thermal waves interferenceby photoluminescence blinking of ingan quantum well devices,” Applied Physics Letters 103,
17109 (2013).
20 T. Tsutsumi, G. Alfieri, Y. Kawakami,

and R. Micheletto, “The relation between photolumi-

nescence properties and gas pressure with 0001 ingan single quantum well systems,” Applied
Surface Science 392, 256–259 (2017).
21 S. Yoshida, Y. Fujii, G. Alfieri, and R. Micheletto, Semicond. Sci. Technol. 37, 095009 (2022).
22 C. Feldmeier, M. Abiko, U. T. Schwarz, Y. Kawakami,

and R. Micheletto, “Transient memory

effect in the photoluminescence of ingan single quantum wells,” Opt. Express 17, 22855–22860(2009).
23 Y. Blanter and M. Büttiker, “Shot noise in mesoscopic conductors,” Physics Reports 336, 1–166(2000).

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