APPLIED PHYSICS LETTERS 103, 172109 (2013)

Observation of lattice thermal waves interference by photoluminescenceblinking of InGaN quantum well devices
R. Micheletto,a) K. Oikawa, and C. Feldmeier
Nanoscience and Technology, International Graduate School of Art and Sciences, Yokohama City University,
Seto, Kanazawa-ku, Yokohama 236-0027, Japan(Received 14 September 2012; accepted 23 September 2013; published online 24 October 2013)
The photoluminescence of III-V wide band-gap semiconductors InGaN is characterized by local
intensity fluctuations, known as “blinking points”, which despite decades of research are not yet
completely understood. In this study, we report the experimental data and a theoreticalinterpretation that suggests that they are caused by the interference of thermal vibrations of thequantum well lattice. With far-field optical tests we could observe the lower frequency tail of theseinterference waves and study their dynamics as they propagate up to distances of several tens of
C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4826088]
microns. V
The phenomenon called “photoluminescence (PL)blinking” has been observed in confined structures, forexample, in semiconductors nanocrystals.1 Because of thelocal nature of these systems, the theoretical treatment inliterature is zero-dimensional (considering time-energy dependence in one point). The blinking process appears to be
associated with the temporary quenching of photoluminescence due to highly efficient non-radiative recombination
processes, such as, for example, the Auger effect or othernon-radiative processes.2 Nevertheless, in InGaN devices theband structure is an infinitely wide quantum well (QW), so azero-dimensional description is insufficient and the understanding of the blinking phenomenon remains elusive.3–6
In this letter, we present experimental data and a wave
model interpretation that suggests that the discussed opticalfluctuations are a general phenomena caused by the interference of thermal vibrational waves that spread along thequantum well. We want to suggest that the spatial vibrationsin the lattice alter the overlap integral of matrix elements
responsible for photo-luminescence, modifying the recombination rate and promoting the PL blinking. This idea is difficult to grasp because thermally induced vibrations aresupposed to be incoherent and of very high frequency,
whereas PL blinking is observable as a slow phenomenon
that shows some sort of regularity.
However, in confined regions, atomic composition andmechanical properties are homogeneous, giving rise to THz
range vibrations with defined frequency and local coherence.
In the presence of dislocations or impurities, the mechanicalproperties of adjacent domains differ, and confined vibrational interferences are generated. These interferences, hereafter called beats, have a broad frequency distribution
centered around the frequency differential of the interacting
oscillations. The lower tail of this interference pattern iswhat is observable as photoluminescence blinking.
We were able to confirm the thermal nature of thephenomenon with low temperature investigations. Moreover,using a simple far field correlation methodology we coulda)Electronic mail: ruggero@yokohama-cu.ac.jp0003-6951/2013/103(17)/172109/4/$30.00

observe the propagation and spread of the PL beats along thequantum well area up to distances of tens of microns.
In a quantum well structured semiconductor as
InxGa(1x)N, the photoluminescence intensity is regulated by
the matrix element that mediate the electron-density andhole-density wave function in the vicinity of the well.7,8The spatial overlap of these two functions is proportional
to the recombination rate, and the latter results in an increaseor a reduction of photoluminescence. The difference ofinter-atomic distances (lattice mismatch) between the doped
and non-doped regions causes piezo-electric stresses that distort the energy bands. This results in diminished wave function overlap and lower recombination rates due to quantum
confined stark effect (QCSE).9,10
Here, the Wurtzite InGaN quantum well is treated as a
two-dimensional system subject to a stress along the direction xz; because of spontaneous thermal vibration,11 thisstress is subject to very small oscillations that alter theenergy band structure (see the sketch in Fig. 1).
The tension applied on the line of adjacent atoms is indicated by To, x is a direction in the plane of the quantum welland z is the crystal growth vertical axis. We are interested
only in displacements along the z axis, i.e., those that influence
the matrix elements relative to the recombination rate. We
derive the expression for the forces projected over the z axis
qdxZ€ ¼ To sinðaÞ  To sinðbÞ;(1)

where dx is a small displacement along the well, Z is the vertical displacement about the rest position, and q is a parameter proportional to the local linear mass density. Thisapproach leads to the general differential expression of awave oscillating along the crystal growth axis
d2 Zðx; tÞ To d 2 Zðx; tÞ / dZðx; tÞ c
 Zðx; tÞ:
¼

q dx2
dt2
q dt
q

(2)

For generality friction (u) and restoring (c) parameters
are also included. In this classical approximation, the influence of far away atoms is dumped by friction, hence the local
solution is a wave of the form sinðxt  kxÞ, where x is
related to To and q by Tqo  ðxk Þ.

103, 172109-1

C 2013 AIP Publishing LLC
VThis article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
163.212.32.61 On: Mon, 28 Oct 2013 03:16:55

172109-2

Micheletto, Oikawa, and FeldmeierAppl. Phys. Lett. 103, 172109 (2013)
TABLE I. Table of the predicted thermal behaviour of the lattice’s vibrational states at different temperatures according to Boltzmann statistic. The
higher and lower probability values nmx, nmn represent a band of 62% intemperature, d is the spread. This profile is compared with photoluminescence tests where the increase in intensity and the spread of luminosity athigher temperatures are confirmed. The elastic potential is calculated using
GaN Young modulus Y ¼ 350 GPa, for simplicity S ¼ 1 nm2 ; L0 ¼ 1 nm, thedisplacement from the rest position is set to x ¼ 0.01 nm.

FIG. 1. An exaggerated scheme in which the Wurtzite structure is stretchedalong the crystal growth direction Z and the corresponding energy density diagram. The mechanical stress along adjacent atoms is represented in two arbitrary points by the tension vector To shown in red. The points are tangent to thedeformation with angles a and b. The deformation modifies the overlap ofelectron-hole wave functions we ; wh and this results in observable photoluminescence variations. The x represents one of the spatial coordinates.

Elastic mechanical oscillations can interact quasicoherently in the confined scales; with the term quasi-coherent
we mean that the waves have phase relation in confined ranges,
but this relation is lost over longer distances.
Observed optical intensities are fluctuating of about
10%–20% around a mean value. Experiments on InxGa(1x)Ndevices show that the quantum well thickness dependence on
the intrinsic radiative lifetime is about 1 order of magnitude
per nanometer.12,13 Supposing that the PL fluctuations aresolely due to this phenomenon, then the greatest spatial displacement along the growth direction is in the range of 0.1
nm, a value compatible with the GaN crystal structure.
Since the phenomenon is driven by spontaneous forces,
wavelengths are in the order of 1000 cm–1 (about 10THz) as
shown in Raman studies and related literature.14–17 It may notseem possible that the observed slow optical oscillations are
induced by frequencies of such high value. Nevertheless, wehave to consider that vibrations are localized in a real,
non-ideal, crystal system with different Indium concentrations,dislocations, and impurities that alter the overall vibrationalmodes. In a classic interpretation, this implies that the frequency of oscillation x is in actual fact a spectrum of distributed values that depends on coordinates on the crystal plane.
The mechanical interference of different distributed frequencies
results in a wide band of lower frequencies beatings centredaround dx ¼ x1  x2 . In this, x1 and x2 are center frequencies of the vibration spectrum relative to two adjacent domains.
Since mass distribution changes are subtle, dx have extremely
small tails when compared with the original pulsation x.
Higher frequency oscillations are cut off by the sampling rate,that is in the order of 30 ms in our case. Previous Fourier measurements18 demonstrated blinking rates centred on low valuesof about 5 Hz in nano-scaled blinking domains.
If the observed optical intensity fluctuations are caused
by elastic oscillation due to thermal energy, we shouldobserve the characteristic Boltzmann temperature profile ofan elastic lattice in spontaneous vibration.19,20 To test this,we setup an experiment in which the blinking is observedand characterized in controlled temperature conditions.
First of all, we derive the appropriate Boltzmann distribution profile using InGaN elastic potential, then we plot its
temperature dependence and test it with our experimental
photo-luminescence data.

T (K)

nmn (a.u.)

nmx (a.u.)d (a.u.)

200
230
250
270
280
290

1.99
4.49
6.92
10.0
11.7
13.7

1.54
3.6
5.65
8.29
9.83
11.5

0.44
0.88
1.27
1.71
1.95
2.20

In a solid, we use as potential energy the expression
2
P:E: ¼  12 YS
Lo x , where Y is the Young modulus, S the surface involved in the oscillation, L0 its rest position, and x thedisplacement from it. Assuming n ¼ n0 eP:E:=kT , where n is
the probability density per unity of area, fixing a displacement one tenth of the maximum discussed above, x ¼ 0.01
nm, and using InGaN Young modulus of 350 GPa,21 we canderive the theoretical density dependence in the range oftemperatures used in cryostat experimental tests (Table I).
The theoretical behaviour shown in Table I was confirmedwith very straightforward tests. A fluorescence microscope(BX51WX, Olympus) was coupled with a vacuum cryostat
chamber (RC102-CFM, CIA, Inc.) to observe the blinking atdifferent temperatures ranging from 290 down to 200 K. At
lower temperatures not only the average luminosity slightly
reduces but also the variations become less prominent (lessblinking) accordingly to the thermal model. Figure 2 compare
raw intensity values for a blinking and not blinking point atroom temperature, Figure 3 shows data for a single point atseveral temperatures and in Figure 4 the corresponding luminosity distribution histograms are plotted. The predictedspread and reduced luminosity of the blinking are evident.
We were able to directly detect the horizontal propagation of these interference waves alongside the quantum well.
A CCD camera was mounted on an Olympus BX51-W1
microscope to record the photoluminescence on a wide areaof an InGaN crystal. The sample is exited with 365 nm light

FIG. 2. An example time intensity profile for a blinking point (upper) and a
not blinking one, at room temperature. Not blinking points do not show thermal dependence. The luminosity is integrated over an area of about
0.25 lm2, time resolution about 30 ms, about 10 seconds of data are shown.

This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
163.212.32.61 On: Mon, 28 Oct 2013 03:16:55

172109-3

Micheletto, Oikawa, and FeldmeierAppl. Phys. Lett. 103, 172109 (2013)

concentration of the QW cannot be measured directly16
but accordingly to the formula InxGa(1x)N, we estimatex  0:2. First, we chose a dominant blinking target point in
the recorded area, then we analysed the time-correlation of
every other pixel to this point that we call xo. The analysis
was done in a time span of 120 s. In Figure 5, we show thecorrelation coefficient map referred to a blinking point
located at xo ¼ (10,30). Correlation r is calculated as
r¼

FIG. 3. The behaviour of a single blinking point at the six different temperatures indicated. The blinking becomes less prominent at lower temperatures,with a trend compatible with the thermal vibration beating wave hypothesis.
The optical data are acquired from the same blinking point at an interval ofs ¼ 30 ms for a total of about 70 seconds. Variation of luminosity over 50% isobserved at higher temperatures, against less than 10% at lower values. Nonblinking regions of the sample do not show such a typical thermal dependence.
This is excluding that the behaviour is a generalized thermal noise phenomena.

covðxo ðtÞ  xi ðt þ lagÞÞ
;rðxo ðtÞÞ  rðxi ðt þ lagÞÞ

where xo and xi are the intensities at central target point oand generic point i, cov represents the covariance function,and r the standard deviation one. The map in panel (a) showsthat regions adjacent to the target have an optical dynamics
that is correlated to that point, whereas far away points havea more independent dynamics. This behaviour is expected,
however, at increased time lag values, we observe that thecorrelation diminishes in the vicinity of the target, andfrom a filtered Xenon light integrated in the microscope. The
sample was grown on a sapphire substrate (0002) of about
half a centimetre area composed by a 1.5 lm layer of
undoped GaN, over which a 3 nm thick single quantum well
(SQW) active layer of Indium doped GaN and a final 5 nm
capping layer of GaN is deposited. The precise Indium

FIG. 4. Using each temperature of the data in Fig. 3, five histograms areplotted. Increased intensity and the spread of luminosity at higher temperatures are confirmed in accordance with a vibrational Boltzmann statistic.

FIG. 5. The cross-correlation coefficient map to the point located in (10,30)
for two different time lags. The blinking behaviour of this single point iscorrelated with the rest of the map at different times (panel (a), simultaneously, panel (b) with a delay equal to 9 frames, about 270 ms). The correlation coefficient decreases in the source and increases and expands at greater
distance with time, suggesting that the beating wave is propagating.
Correlation values higher than 0.3 have the same colour for ease of identification, one pixel corresponds to about 1 lm.

This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
163.212.32.61 On: Mon, 28 Oct 2013 03:16:55

172109-4

Micheletto, Oikawa, and Feldmeier

regions relatively distant from the center of blinking appear
to increase in correlation (see area around xi ¼ (12,10) in Fig.
5, panel (b)). This behaviour reveals the expansion of mechanical beats located on the target and diffusing away fromit. The structure and granularity of the correlation coefficient
map indicates changing compositional and mechanical properties along the lattices.
We have developed a simple model and experimental
tests that suggest that optical instabilities in InGaN quantum
wells are caused by mechanical beats of thermal vibrationsof the quantum well lattice. Optical effects induced by thesebeats have been observed experimentally through monitoringwith CCD camera the photoluminescence and making a time
resolved correlation analysis. The thermal dependence of thephenomena is compared with a Boltzmann distribution of aharmonic oscillating lattice, resulting in good match andagreement with the original hypothesis.
We believe that the understanding of the thermal natureof the optical blinking in these devices is important not only
for the research of the fundamental phenomena involved in
the emission of InGaN materials, but it can also constitutethe basis for a new general methodology of analysis of
InGaN subtle local mechanical properties, revealing with avery simple and pure optical method, extremely small variation of doping concentration and possibly other fine compositional or structural anomalies of the crystal.
This study was supported by the Japanese grant
KAKEN (project number 24560014), we also want tothank AAA Translations UK for help in improving themanuscript.

Appl. Phys. Lett. 103, 172109 (2013)
1

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman,
T. D. Harris, and L. E. Brus, Nature 383, 802 (1996).
C. Brosseau, M. Perrin, C. Silva, and R. Leonelli, Phys. Rev. B 82, 085305(2010).
3
R. Micheletto, M. Allegrini, and Y. Kawakami, Appl. Phys. Lett. 95,
211904 (2009).
4
R. Micheletto, M. Abiko, A. Kaneta, Y. Kawakami, Y. Narukawa, and T.
Mukai, Appl. Phys. Lett. 88, 061118 (2006).
5
Y. Kawakami, A. Kaneta, K. Omae, A. Shikanai, K. Okamoto, G.
Marutsuki, Y. Narukawa, T. Mukai, and S. Fujita, Phys. Status Solidi B
240, 337 (2003).
6
F. Stefani, J. Hoogenboom, and E. Barkai, Phys. Today 62(2), 34 (2009).
7
S. Chuang and C. Chang, Phys. Rev. B 54, 2491 (1996).
8
S. Chuang and C. Chang, Appl. Phys. Lett. 68, 1657 (1996).
9J. H. Rice, J. W. Robinson, A. Jarjour, R. A. Taylor, R. A. Oliver, G.
Briggs, D. Andrew, M. J. Kappers, and C. J. Humphreys, Appl. Phys. Lett.
84, 4110 (2004).
10
A. Das, G. P. Dimitrakopulos, Y. Kotsar, A. Lotsari, Th. Kehagias, Ph.
Komninou, and E. Monroy, Appl. Phys. Lett. 98, 201911 (2011).
11
S. R. Jian, J. J. Shian-Ching, L. Yi-Shao, Y. Ping-Feng, Y. Chu-Shou, W.
Hua-Chiang, and T. Chien-Huang, Mater. Chem. Phys. 109, 360 (2008).
12
E. Berkowicz, D. Gershoni, G. Bahir, A. C. Abare, S. P. DenBaars, and L.
A. Coldren, Phys. Status Solidi B 216, 291 (1999).
13
J. Bai, T. Wang, and S. Sakai, J. Appl. Phys. 88, 4729 (2000).
14
E. Gotz, N. M. Johnson, D. P. Bour, M. D. McCluskey, and E. E. Haller,
Appl. Phys. Lett. 69, 3725 (1996).
15
T. Deguchi, D. Ichiryu, K. Toshikawa, K. Sekiguchi, T. Sota, R. Matsuo,
T. Azuhata, M. Yamaguchi, T. Yagi, S. Chichibu, and S. Nakamura,
J. Appl. Phys. 86, 1860 (1999).
16
R. Micheletto, N. Yoshimatsu, A. Kaneta, Y. Kawakami, and S. Fujita,Appl. Surf. Sci. 229, 338 (2004).
17
E. Kurimoto, M. Takahashi, H. Harima, H. Mouri, K. Furukawa, M.
Ishida, and M. Taneya, Phys. Status Solidi B 228, 103 (2001).
18
K. Oikawa, C. Feldmeier, U. T. Schwarz, Y. Kawakami, and R.
Micheletto, Opt. Mater. Express 1, 158 (2011).
19
P. Heino, J. Comput. Theor. Nanosci. 4, 896 (2007).
20
N. D. Mermin and N. W. Ashcroft, Solid State Physics, 1st ed. (HRWInternational, Philadelphia, PA, USA, 1988).
21
S.-R. Jian, T.-H. Fang, and D.-S. Chuu, Appl. Surf. Sci. 252, 3033 (2006).
2

This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
163.212.32.61 On: Mon, 28 Oct 2013 03:16:55