Results in Physics 20 (2021) 103732

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Results in Physics
journal homepage: www.elsevier.com/locate/rinp

Atomistic modeling of InGaN/GaN quantum dots-in-nanowire for graded

surface-emitting low-threshold, blue exciton laser
Mayada M. Taher a, *, Shahad Al-yousif b, Naser M. Ahmed c, *
a
Department of Laser and Optoelectronics Engineering, University of Technology, Baghdad, Iraq
b
Computer Engineering Techniques Department, Dijlah University College, Baghdad, Iraq
c
University Sians Malaysia (USM), School of Physics, 11800 Penang, Malaysia

A R T I C L E I N F O A B S T R A C T

Keywords: While the development of the quantum photonics field, including emitter–light coupling using photonic system,
Nonpolar InGaN laser device has given a lot of attention, it offers quantum control of light. However, the main challenge is coupling to
Graded interfacial engineering strongly photonic mode localization with nanosystem accuracy. This paper highlights the numerical simulations
Low-threshold
employed by atomically spin tight-binding model of realistically sized InGaN/GaN dots-in nanowire (NW) ar­
Blue coherent lasing oscillation
Exciton–photon coupling
chitectures. The effects of active region size/shapes, crystal growth directions, graded surface/interface prop­
Photonic nanofocusing erties, strain relaxation distributions, and polarization-induced potentials on the oscillator strengths of InGaN-
based lasers have been investigated. The 3D nanofocused photonic modes, which have been deterministically
coupled to multiple quantum dots (QDs) through graded surface/interface technique, have been demonstrated.
By using a thin graded layers of a site-controlled pyramidal QDs, the photonic nanofocusing on these QDs at the
nonpolar pyramid apex has been geometrically accomplished and successfully leads to stronger characteristics in
terms of exciton bandgap energy and polarized emission rate compared to its polar counterpart. For optimum
coupling, the nonpolar NW, with intrinsically lower built-in field, exhibits an enhancement of the QDs emission
rate as high as 0.98, which is 12% greater than that in a recently reported semipolar MQD structure. The
atomistic simulated emission rate for the core QDs buried in NW structure is then incorporated into a TCAD
simulator to obtain laser device characteristics. Here, the achievement of truncated pyramid–electrically injected
graded surface-emitting laser by nanofocusing the photonic modes formed in InGaN NW has been reported. The
nonpolar laser device operates at ~ 402 nm and exhibits a threshold current of ~ 391 A/cm2 , which is lower nine
order of magnitude lower compared to recently reported semipolar green laser diodes. Our model benchmarking
has been done against a reported experiment of polar InGaN disks in GaN NW. Significantly, this engineering
innovation proves the viability of InGaN nonpolar quantum dots-in-nanowire architecture as low threshold, high
polarized, coherent blue nanoscale lasing emitters, and opens future trends toward a next-generation of elec­
trically injected and interfacial grading-emitting nanolasers operating at high-frequency up to a GHz range.

Introduction spectra [1–8] due to the quantum confinement effect, which arises
from the relatively small number of atoms in the multiple quantum dots
One-dimensional nanowires (NWs) have been shown to be the active region in NWs. The strongly confinements of charge carriers
excellent building blocks for nanoscale optoelectronic devices due to (electrons, holes, excitons) that provided by QDs nanostructures offer
their hosting material or phasing combinations that are difficult to delta like density of states [9]that can facilitate population inversion, and
obtain in the bulk or in thin films. When multiple heterostructures hence significantly improve the quality of laser devices, such as better
including quantum dots can be obtained within nanowires, it is emitter, better temperature stability, and lower threshold would be
emphasized that some key advantages can be offered for higher optical expected from these quantum dots as compared to quantum wells. Be­
performance of the embedded quantum dots (QDs) within a nanowire sides that, the bandgap energy levels of multiple dots in the device’s
structure. Their novel electronic and optical characteristics are strongly active region can be engineered/tuned in order to involve tuning the
dependent on size, shape, stoichiometry, and polarization-sensitive absorption/emission [4], which may be used for different purposes, such

* Corresponding authors.
E-mail addresses: mayadataher25@gmail.com (M.M. Taher), shahad.alyousif@duc.edu.iq (S. Al-yousif), nas_tiji@yahoo.com (N.M. Ahmed).

https://doi.org/10.1016/j.rinp.2020.103732
Received 12 October 2020; Received in revised form 28 November 2020; Accepted 14 December 2020
Available online 18 December 2020
2211-3797/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
M.M. Taher et al. Results in Physics 20 (2021) 103732

as quantum key distribution (QKD) [10–14], optical quantum based III-Nitride, a broad spectrum range (from the ultraviolet range
computing [15], quantum information storage, and easy-coupling to to the visible spectral range) can be covered while this cannot be ach­
cavity modes for QD-based lasers. Furthermore, these ideal nano­ ieved by the other QDs-based conventional III–V semiconductor devices.
particles, which is the most exciting semiconductor nanostructures, Especially, they have been given considerable attention for the realiza­
highlight a cumulative attention in the nano-theranostics platforms’ tion of blue-emitting semiconductor laser (with the relatively short
development for quantum medical applications, such as simultaneous wavelength (400 – 480) nm and high energy) due to their prominently
sensing, biomedical imaging, and quantum therapy [16]. applications (e.g. laser projection display, lasing data recording, and
Moreover, such nanowire growth directions are very important for lasing bio-imaging [32,33]). Generally, the optical transition energies of
the effective III–V semiconductor materials. Due to their distinctive the semiconductor materials formed inside the photonic NW structures
geometrical structure, the sidewalls of polar (0001) crystal orientation are found to play a dynamic role for quantum lasing mechanism and to
nanowires can be considered as a nonpolar (101‾0) template for mul­ enhance emission characteristics, mainly in the low-dimensional quan­
tiple dots or disks growth for a core − shell device. However, the pre­ tum systems. Additionally, applying the external electric or magnetic
vious studies of polar InGaN MQDs, due to their lattice mismatch strain fields can result in finely tuned the emission energy of the QDs [34,35].
across the interface in nanowire laser structure that made from group III- Furthermore, the electronic energy states that confined in the reduced
nitrides and their ternary alloys, revealed that carrier-confined systems quantum nanoparticles can be coherently controlled [36].
of heterostructures have been slow [17,18]. Long-range cracks (defects) However, due to the very small nanoscale size of the quantum dots/
have been caused due to a significant strain along c-axis oriented. In disks, the regular design of quantum dots in nanostructures suffer from
addition, the polar multiple-dot-in nanowire showed a low degree of limited optical properties (e.g. high sensitivity to Auger recombination
optical linear polarization, which tilts the electronic energy band of and strong dephasing from the environment of the solid-state). These
these dots and then separates electrons and holes wave-functions, quantum dots poorly interact with the photon field, leading to somewhat
resulting in a wavelength-shift and a low radiative recombination rate low radiative emission rates [37,38] .Therefore, it is necessary to
[19,20] due to the so-called the quantum confined Stark effect (QCSE). overcome all these limitations. During the previous decade, there have
Accordingly, it shows low-value and broadening of the emission energy been extensive studies to ride of these issues by having strong Purcell
of lasing characteristics [21–23] and poor device performance [24–28]. effect (e.g. achieving spectral and spatial overlap between a quantum
As well, different anisotropies, which have been exhibited in most dot and the photonic modes), resulting in strong coupling of a quantum
conventional polar system, could result in random polarization axes, dot to intense photonic modes [39]. Since, a quantum dot in the archi­
leading to a highly undesirable polarization-based protocols’ imple­ tecture has the uncertainty of its size and position, thus it remains to a
mentation for several quantum applications [13]. The polarization- certain extent challenge and requires some techniques of control
induced piezoelectric field leads to distortion of the energy bands, dis­ [38,39]. Recently, nanofocusing of photonic surface has been developed
tribution the carriers at the interfaces, and reduction of the radiative using various tapered structures, such as a tapered waveguide [40],
recombination efficiency, thus leading to high threshold lasing current which is the best design for ultimate focusing of light.
density. These can be considered as the main problems with polar QDs In the work reported here, we intend to study the structural, elec­
ensembles [14]. trical, and optical properties of Inx Gax− 1 N nanowires by employing the
However, these issues along with that of fixed interfacial or surface atomically 10-band sp3s*-spin tight-binding (TB) approach. A special
polarization charges can be overcome by growing the NWs on alterna­ attention have been paid to achieve strong coupling between nano­
tive crystal planar of nonpolar (101‾0) m-axis and a-axis oriented di­ focused photonic modes and multiple quantum dots in nanowires by
rections, which result in more augmentation of the bandgap energy that well-designing grading surface/interface acting as pyramidal nano­
can be achieved by using greater 3-D quantum confinement whereby templates. The focusing of the photonic modes can highly be found near
enforcing stronger wave-function overlap and strain relaxation due to the quantum dots, which are formed on the truncated pyramid apex
the surface area enhancement, Higher reduction of the piezoelectric (top). The goal is exactly control the spectral and spatial matching be­
fields while allowing stronger pronounced localization effects that tween these modes and the emitting quantum dots and significantly
should lead to drastically more improvement in the device performance, functionalize the ultimate focusing of coherent light emitters. Signifi­
such as larger radiative efficiency, lower threshold current, and higher cant endeavors are being pursued to: (1) investigate the effects of active
modulation-speed in lasers, than the convolutional planar[29]. region size/shapes, crystal growth directions (including both polar c-
Recently, one of the most essential forefront fields in physics is and nonpolar m-planes), grading surface/interface properties, strain
controlling and optimizing the physical properties of optoelectronic relaxation distributions, and polarization-induced potentials have been
devices, definitely semiconductor nanostructures. The quantum dot accounted via the valence-force-field (VFF) model and the Poisson
structural adjustment is important that has the greatest approaches for solver within the simulator; (2) compare the oscillator strength and the
the desired electrical and optical device properties that can be allowable photonic coupling of polar (0001) and nonpolar (101‾0) nanostructures
by controlling the carrier overflow, and hence the device performance ; (3) explore the possibility of engineering the very fine QDs emitting-
[26]. Therefore, the structure-based QDs would be the good choice for layers through various grading techniques for emission enhancement
optoelectronic/photonic devices (e.g. light emitters, solar cells, laser and coherently control; (4) examine the structural perfection (for opti­
diodes). Obtaining the quantum dots of different sizes and shapes are mum coupling) of the graded active QD layers in nanowires to mainly
allowed via the new technology of fabricating nanoparticles to have the have a near-unity radiative efficiency (e.g. achieve an ideality for ulti­
special and interesting shapes, such as quadrangle, cone-like and mate laser focusing). This is required sophisticated physics geared to­
pyramid-like, which are of current interest in nanoscience [30]. ward electronic structure calculations and engineering geared towards
Moreover, the effects of the quantum confinement, shape/size, and transport simulations; and (5) significantly, incorporate the improve­
surface/interface of the active region nanostructures are significantly ment polarized emission rate into a TCAD simulator to obtain laser de­
different in mechanics, optics, electrics, and magnetics, as compared to vice characteristics, specifically gain spectra, threshold current, and
the bulk devices. if the size of laser structures goes down to nanoscale, emission wavelengths. Then, the results have been analyzed and
the proportion of the device surface/interface, which are related to the compared to the recent reported experiments.
carriers’ dynamic processes (e.g. generation and recombination)
involved from the converted energy between photons and electrons in Simulation model
nanostructured laser devices, would sharply increase. For this reason,
the device performance would be affected by the surface/interface Fig. 1 shows a briefly atomistic simulation strategy employed in this
properties [31]. Typically owing to the QDs nanoscale light emitting- work. Regarding the simulation modeling, the electronic and optical

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M.M. Taher et al. Results in Physics 20 (2021) 103732

⇀strained ⇀relaxed
Fig. 1. Multi-million atom simulation modules. In this work, r : strained positions of atoms, r : atom coordinates after relaxation, ̂ε : six (diagonal and off-
diagonal) strain tensors, W/O:simulation considering no strain relaxation, STRAIN: simulation with strain relaxation, PZ: polarization potential, ψ : eigen functions,
and ξ: eigen energies. Incorporating with Atlas SILVACO, optical problem has been solved for LASER.

characteristics have been calculated and analyzed from single-particle GaN buffers surrounding the multiple quantum dots for accommodating
eigenstate via using multi-million atom simulations (that is known as the impact of long-range strain and piezoelectric potentials in the elec­
the NEMO 3-D software toolkit) based on a variety of empirical tight- tronic structures and the optical transition calculations. As final point,
binding (TB) model (s, sp3s*, sp3d5s * ), which includes the in­ the determined quantum dot optical transition is incorporated into the
teractions of spin–spin and the external electromagnetic fields effects Silvaco TCAD device simulator [49] to obtain the laser device charac­
[41–44]. The formed strategy of the simulations depends on construct­ teristics, such as gain spectra, threshold current, and emission
ing the device geometry, calculating the atomistic strain, obtaining the wavelengths.
polarization field, calculating the electronic structure, and computing
the transition rate [29]. The calculation of several physical properties, Results and discussion
such as optical matrix elements and coulomb and exchange matrix ele­
ments, have been employed in the package software. Furthermore, the Model structures
eigenvalues of the single-particle energy and the wave-functions of the
particle (eigenvectors) have been obtained based on the complex Her­ Fig. 2(a) shows the atomistic view of the InGaN active dot layers
mitian Hamiltonian matrix. The total size of Hermitian matrix is a embedded in GaN nanowire architectures, as founded from NEMO 3-D
product of both orbital bases for a single atom and the total number of toolset. The boundaries of the very fine structures of the active-layers
atoms in designated 3-D device geometry. Here in this work, a 10-band have been engineered as graded interfaces inside the nanowires acting
sp3s*-spin tight-binding has been represented for calculating the elec­ as pyramids located in the middle of the structures, hence then they
tronic structures and the transition rates of quantum dots. Besides that, would experience the impact of shape symmetry and the tapering
some geometry constructor extensions/augmentations have been done structure. The semiconductor quantum dots formed as pyramids have
for the m-axis wurtzite nanostructure by appropriate lattice vectors, been grown on both hexagonal-base polar (0001) and square-base
rotational matrices, sp3-hybridized passivation schemes, and connec­ nonpolar (101‾0) growth directions. As in Refs. [38,50,51], the gener­
tivity matrices [45]. The information about an atom and its neighbor, ation of strongly focused photonic modes at the apex can be done by
including their bonding details, contributes in constructing the con­ designing multiple quantum dots (MQDs) at the pyramid apex in the 3D
nectivity matrix using the VESTA toolkit [46]. The atomistic valence- tapered nanowire structures. Each of the two simulated nanowire laser
force field (VFF) and strain-dependent Keating potentials have been structures consists of n-GaN (25 nm thick, doping density of 8
employed in the Nanoelectronic Modeling toolset in order to compute x1018 cm− 3 ) buffer layer, five undoped multiple In0.08Ga0.92N quantum
the strain relaxation [47]. When the total elastic energy of the optical dots (the core active region), undoped Al0.3Ga0.7N electron blocking
device is diminishing, this results in obtaining the relaxed atomic posi­ layer (EBL), and p-GaN (27.5 nm thick, doping density of 3 x1019 cm− 3 )
tions. The incorporations of strain and piezoelectric impacts are capping layer). The thickness of each InGaN quantum dot is 1 nm, while
involved in the large domain of atomistic strain. Related to the relaxa­ the thickness of the incorporated Al0.3Ga0.7N electron blocking layer is
tion calculation, the atomistic parameters of the strain are taken from 3.5 nm to ensure a strong interaction between quantum dots (QDs) and
Ref. [22]. Their validations are done via Poisson-ratio calculations. the nanofocused photonic modes. The thickness of a GaN quantum
Solving the equation of Poisson on the wurtzite lattice is used for the barrier is 1 nm. As in Ref. [29], the simulated nanowire has height of 86
polarization-induced piezoelectric field in simulating quantum dots. The nm, while its length is 14 nm. After many content examinations, the
incorporation of piezoelectric field is worked as an external potential in optimum Indium composition factor in InGaN has been reduced to be
such simulation. Both linear and nonlinear piezoelectric potentials are 8% for riding the difficulty of controlling the active layers [52]. The
calculated and included in the Hamiltonian [48]. For the nonpolar height (or diameter) of quantum dots sited at the apex (top) of truncated
crystal orientation, only the contribution of 1st-order piezoelectricity pyramid is 3 nm, while the base diameter is 11 nm. However ranged
has been significantly considered. The closed boundary conditions are from thin to thick pyramidal QDs nanowire, the truncation height of the
used for the electronic structure calculation, while the dangling bonds at quantum dots has been fluctuated from 3 nm to 9 nm responding to the
the surface atoms are passivated. Moreover, the polarization-dependent interfacial (confinement) grading to more examine the sharpness effect
optical transition rate is computed. Also, the momentum matrix is on the two laser structures.
calculated from the overlap of the wave-functions. It has been empha­ In this paper, our model of nanowire laser structures are based on the
sized here that all of the numerical simulations are performed over large results of C. Li et al. [2], who recently reported lasing from the

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M.M. Taher et al. Results in Physics 20 (2021) 103732

Fig. 2. (a) Atomistic view of pyramidal-QDs m-plane NW structure. (b) Z-polarization-induced potential for m-plane (red) and c-plane (green) structures. (For
interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

fabricated core − shell nanowire laser device with the five period symmetrical elevation. In nanostructure along m-axis direction, the net-
InGaN/GaN active region at room temperature in Sandia National La­ potential distributions reveals a great degree of control over the polar­
boratories, United States. The domain of the atomistic simulation con­ ization properties resulting in diminishing the carrier over barrier-flow
tains approximately 10 million atoms, while the electronic domain is and Auger recombination process [53]. Thus, it is leading to higher in­
relatively small. The electrical and optical properties, such as emission jection efficiency. This technique could be a useful tool for device
energies and polarization properties, have been investigated and engineering.
compared for InGaN/GaN quantum dots grown on both c- and m-axes in For fully incorporating the long-range impacts of strain and piezo­
nanowire architectures. Consequently, the realization of the geometrical electric fields, the large domains of an atomistic relaxation have been
and the spectral matchings have been examined between the photonic computationally used by solving the Poisson equation on the wurtzite
fields and the multiple quantum dots (MQDs) for the nonpolar laser lattice. In the framework of elasticity theory, the strain components have
device. However, the thermal properties of the devices have been been determined to estimate the atomistic strain states (including both
neglected here. diagonal (εxx , εyy , εzz ) and off-diagonal (εxy , εxz , εyz ) strain tensors) of
To study the effect of the photonic modes at the graded interface on nonpolar and polar structures as shown in Fig. 3. Less in-plane lattice
the polarized emission rate of the pyramidal active QDs and because the matching has been simultaneously obtained along the nonpolar plane,
piezoelectric fields are relative to the emission rate, the profile of the resulting in anisotropic in-plane strain, while this scenario is markedly
polarization-induced piezoelectric fields has been calculated for the different from the case of polar plane for which perfect (100%) lattice
active layers located at the apex of the pyramid m-axis and c-axis matching has been accomplished for an Indium composition near to 8%.
structures as shown in Fig. 2(b). The potential profiles have been Also, the quantum dots nanowires are subjected to inhomogeneous
introduced a dependence on the local atomic environment. As expected, strain. Particularly, in m-axis orientated structure, the atomistic strain
within InGaN active layers, m-plane structure exhibits a much smaller states are much weaker compared to its conventional counterpart.
(peak ~ 14 mV) potential as compared to its value (~24 mV) along the Considering εxx and εyy are compressive and εzz is tensile within the
polar one. The other layers of the structures exhibit zero polarization active quantum dots. The hydrostatic (εxx + εyy + εzz ) and biaxial (εxx +
potentials. The grading interface style with spatial (height) accuracy of εyy − 2εzz ) stain components are compressive in the InGaN active layers,
3 nm in the apex of pyramid NWs is considered here to reduce the impact while they are tensile in the GaN substrate and cap layer and also within
of piezoelectric on the carrier recombination process due to their the AlGaN layer. In the two structures, the strain anisotropy breaks the

Fig. 3. Atomistic strain profiles of InGaN/GaN based pyramidal QDs along the vertical (z) direction. The components of strain are shown which influence induces
polarization for polar (left) and nonpolar (right) NW structures.

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M.M. Taher et al. Results in Physics 20 (2021) 103732

equivalence of εxx and εyy components and controls the excited states by separation layer between the quantum dots layers. The observation of
breaking their degeneracy. The fact of breaking the QD shape-symmetry such hybridized states can be done either for closely quantum dots,
originated from the atomic nature of the underlying crystal are due to: (1) which are separated by very small distance (as reported here, or by
the atomistic interface between the active dot layer material (InGaN) and applying an external electric field [56]. In both c- and m-axes, the for­
the barrier material (GaN) creates the interfacial potential, which is mation of LUMO and HOMO (LUMO is molecular orbital level of mini­
fundamentally anisotropic; (2) the atomistic relaxations, due to the mum conduction band, which is principally constructed from the s-state
atomic size difference between Gallium (Ga) atom and Indium (In) of Gallium (Ga) atom and HOMO is molecular orbital level of maximum
atom, leads to propagate the interfacial potential further into the QDs valence band, which is principally constructed from the p-state of
material. This can results in amplifying the magnitude of the asymmetry; Nitride (N) atom) orbitals are clearly in the lowest (first) dot-in-NWs.
(3) the long-ranged strain-induced piezoelectric field develops in the Furthermore, the appearance of the localized/discrete carrier states, due
QDs material is anisotropic as explained in Ref. [54], . Moreover, to the inhomogeneous strain present in embedded quantum dots, is the
because of thin NWs (small dot height), the non-degeneracy and the main reason behind the limiting physical dimension of the wave-
optical anisotropy have been significantly diminished. Noticeably, the function in the NW structures.
small energy level-splitting in the excited states is due to the shape- Thanks to the QDs on pyramid apex correlated to the 3D grading
asymmetry and is a much studied issue in quantum applications by quantum confinement, the exciton wave-functions (in the x-z pro­
controlling the de-coherence time of electron-spin [55]. jections) center at the apex of the pyramid in the c-plane and m-plane
Next, the atomistic interfacial potential originated from different structures as shown in Fig. 4. Importantly, the lesser internal fields
facets in QDs in both polar and nonpolar nanostructures is also affecting observed for nonpolar (101‾0) direction, due to off-diagonal strain
the calculation of the electronic structures that has been done using a components that are non-vanishing to zero, indicates stronger localiza­
direct-diagonalization approach to the single particle in the potential tion of the conduction band and valence band, implying more powerful
representation. The quantization impacts of strain relaxation and piezo­ coupling, than its convolutional polar (0001) direction. This is in
electric fields lead to describe the wave-functions and their overlaps. agreement with the observation made in Ref. [29]. In addition, due to
These complex wave-functions can be described by a smaller supercell the small dot-spacer size of about 1 nm, the active layers in NWs expe­
because of the strongly focused modes and highly quantum confine­ rience: (1) mechanical dot-dot interaction through the strain field; (2)
ments of the states inside the QDs. quantum mechanical dot-dot interaction through the wave-function
It is attention-grabbing to note that the carrier wave-functions are overlaps. The higher wave-function overlap integral, involving stron­
originating form hybridized molecular states due to 1 nm GaN- ger radiative transition and weaker Auger recombination and attributing

Fig. 4. Atomic wave-functions of pyramidal QDs for (a) polar and (b) nonpolar NW structures.

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M.M. Taher et al. Results in Physics 20 (2021) 103732

to the presence of both atomistic strain relaxation and atomistic grading The variation of the bandgap energy spectrum has been displayed as a
confinements of the active QDs layers [57], is revealed due to the very function of QDs size, as shown in Fig. 6(a) and Fig. 6(b) for m-pane and c-
much focusing of the photonic modes in the m-axis structure than the c- plane, respectively. In this Figure, the effect of a strong photonic
axis structure. nanofocusing dependency on the truncated pyramid shape has been
Fig. 5 illustrates a polar plot of oscillator strength (radiative transi­ presented. For compressive strains in the InGaN active layers, the
tion rate between conduction band and valence band) of nanopyramid bandgap energy is blue-shifted compared to that of unstrained InGaN
structures. Clearly, the polar and nonpolar structures reveal good layers. When strain field is included in the calculations, the m-axis
enhancement in the oscillator strength. However, this emission bandgap energy have been obtained to increase by as much as 0.2 eV at
enhancement is much greater in the nonpolar m-plane pyramid structure 300 K, while the c-axis energy increased about 0.17 eV. However, when
compared to that in polar c-plane structure that comes from the larger piezoelectric field (PZ) is added, there is almost no change in the en­
photonic modes focusing at the pyramid apex and stronger localization ergies. The percentage changes in the bandgap energies for c- and m-
of the wave-functions for the nonpolar structure than its counterpart axes are 13% and 17.3%, respectively, due to net strain, while they are
structure. With a highly precision, the degree of polarization along zero% for both planes, due to piezoelectric field.
nonpolar nanowire of about 0.98 is larger than its value in the polar The dependence of the energies of the exciton state on the in-plane
counterpart of about 0.6, for smallest QDs-height. In wurtzite crystal, strains, the graded interface, and the QDs height of InGaN pyramid
when the crystal-field and spin–orbit interactions contribute in sepa­ structures is displayed in Fig. 6(c) and Fig. 6(d). It is found that the
rating the valence bands into the band with heavy hole, the band with energy spectrum is a bit higher in the c-axis device than in the m-axis
light hole, and the band with crystal-field split [58], the m-axis QDs film counterpart. Mainly, The InGaN QDs synthesized along nonpolar crystal
acts as a tunable light polarization and reports a highly-polarized attracted a great attention due to its better trend that has been observed
emission presenting a further enhanced optical properties as compared for strained and polarized InGaN, which increases the bandgap as the
to its conventional c-axis templet. It is worthwhile to mention that quantum dot size decreases, than those QDs along the polar crystal. This
modeling of our nonpolar m-plane pyramid QDs in-nanowire structure could most probably be assigned to the pyramid shape fluctuations
shows a remarkably higher stability and directionality of the polarized (from wide to sharp), leading then to have stronger confinements and
emitted light [51], with respect to its conventional polar c-plane pyra­ higher localizations in QDs along m-axis than c-axis. In forthcoming,
mid QDs structure, by a more favorable coupling. another investigation of tuning energy spectrum could possibly be per­
formed with different substrate and cap layers to show the dependence
of QDs states and the magnitude of energy level-splitting on the layers’
Graded-Interfacial engineering
size, due to the atomistic strain, and thus to check QDs coupling to the
photonic nanofocused modes in the structure.
To further optimize the performance of InGaN/GaN NW lasers,
Furthermore, the very small QDs height embedded within thin NW
multiple QDs within the NWs have been grown with varying QDs height
crystal leads to atomically relax the strain, which in turn can also alter
for studying the carriers’ dynamic processes. In this section, four
the polarization of the emitted light. As a result, more enhancement of
different samples with different grading surfaces/interfaces have been
emission strengths can be provided due to the effective lateral strained
investigated. Each sample has QDs-emitting layers that have been
and relaxed nanostructures that energetically act to reduce the piezo­
engineered as graded layers to form a truncated pyramid shape for
electric field in the quantum dots region, and hence mitigate the
quantum confinement improvement. This elegant technique provides a
quantum confined Stark effect (QCSE). Therefore, a further study on the
greatly focused photonic modes at the pyramid apex and thus it is
polarization properties in the photon emission of InGaN nanowires has
considered as a key factor in enhancing the device performance of the
been investigated for different interfacial grading (including various
QD-lasers. Significant endeavors are being pursued to find the atomic
QDs height located at the apex (top) of the pyramid structures). The
structural perfection (optimum QDs-size) by examining the pyramid
degree of polarization referrers to the emission intensity, which corre­
shapes.
sponds to the electric field along the polarization angles. Fig. 7(a) shows
In our grading technique, the QDs core height dependence of device
the polarized exciton emission as a function of the polarization angle.
properties is correlated mainly to the atomistic strain distributions,
Since the radiative emission rate varies dramatically with the sharpness
which play the important role in mixing the states with a different
of a nonpolar pyramid QDs, the great sensitivity of the photonic nano­
symmetry in InGaN core–shell NWs, hence tuning the energy bandgap.
focusing on the approximately taper shape has been reflected. For m-
plane, when the truncated pyramid with a height ranged from 9 nm to 3
nm, the enhancement of the emission has been around 50%, which goes
along with our numerically computed enhancement rate of the polarized
exciton emission of about 0.98. Clearly, it can be seen that the emission
is strongly polarized in the growth plane for the studied m-plane nano­
wire structure with a small QDs height of about 3 nm. Due to the
interfacial grading, the polarized laser light have been emitted by the
further confined m-plane pyramid in-nanowire and strong QDs coupling
with the nanofocused photonic modes. Since the strongest emission rate
corresponds to the smallest size (height) of the QDs on the apex of the
pyramid nanowire laser, an increasing the wave-function overlap and
oscillator strength of the 3D-confined exciton (electron–hole pair) are
happened at the apex.
The interpret of a highly polarized emission with a degree of linear
polarization of the investigated nonpolar dots-in-nanowire laser device
can be the mixing of the valence-band in the wurtzite III-nitrides that
induced by in-plane anisotropy due to an atomistic internal strain and a
quantum dots shape [50,59–61]. Each of these Refs. [38,50,61], and
[51] reported a smaller polarization degree of about 0.93, 0.92, 0.9, and
Fig. 5. Polarization angle dependent exciton emission for polar and nonpolar 0.86 respectively, compared to that in our nonpolar laser device. Fig. 7
pyramid QDs nanostructures. (b) displays the transitions (the polarized exciton emissions of the

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M.M. Taher et al. Results in Physics 20 (2021) 103732

Fig. 6. Comparison of the exciton energy bandgap and change in bandgap of pyramid QDs between polar and nonpolar nanostructures.

Fig. 7. The influence of the sharpness (i.e. ranged from 9 to 3 nm) of the truncated pyramid structure on the calculated polarized exciton emission enhancement. (a)
A polar plot of a peak polarized exciton emission as a function of the polarization angle in the nonpolar (m-plane) pyramid QDs-in-NW lasing structure, in the
presence of photonic nanofocusing. The strongly polarization degree is ~ 0.98 for 3 nm. (b) An average polarized exciton emission as a function of the quantum dots
(QDs) height to show the mono-exponential decay projected on the x-y plane, in both polar (c-plane) and nonpolar (m-plane) pyramid QDs-in-NW structures.

quantum dots) as a function of quantum dots height to show the mono- direction of the oscillator strength for lasing characteristics attributing
exponential decay. The dynamic of polar (c-plane) QDs structure is to that the photonic modes are greatly focused in close to the multiple
much faster. Significantly, the reduction of the oscillator strength of the quantum dots formed on the pyramid apex grown along m-plane. In
polarized emission in a polar nanowire is due to the magnitude of in- addition, the localized carriers (excitons) engendered in m-plane
plane anisotropy, which is corresponding to degenerate in-plane polar­ pyramid-shaped QDs NW structure make it possible to extract reason­
ized exciton states [50,62]. ably an efficient and a coherent light emission from the InGaN-based
Benefits from tuning a grading interface of the QDs-emitting layers, laser device. Furthermore, the selective value of 8% In (Indium)
the polarization profile of emission in a nonpolar pyramid have a prove composition is found to be a good choice for having a strong oscillator
that the grading interface fashion with lateral spatial (height) accuracy value.
of 3 nm is evidently standing out, in terms of both the magnitude and

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M.M. Taher et al. Results in Physics 20 (2021) 103732

Laser characterization smaller as compared to the slope above threshold. The threshold current
is evaluated from the L-I characteristic under different injection cur­
Based on the above analyses, the importance of the tapered geometry rents. A calculated lasing threshold of 391A/cm2 has been obtained via
is appreciated. The crystallographic nonpolar-based a thin pyramid NW fitting light power after changing slope with the linear function. From
of 3 nm QDs spatial height proves its perfection in the structural opti­ here the slope of the linear part of the L-I plot is analyzed. The slope
mization. Generally, the nanowire structure along m-axis shows the efficiency indicates the percentage of the injected current that has been
better qualitative results than another simulated structure, due to: (1) a converted to the output light being emitted from the quantum dots
high quantum confinement and a deterministic photonic coupling, nanowire laser; this is done by comparing the slope of the calculated L-I
which are provided by the grading control technique correlated to plots above threshold current with the slope of the L-I curve of the
nanoscale quantum dots shape and size; (2) a weak polarization field perfect efficient device. Nonpolar nanowire laser structure shows a high
value of 14 mV within InGaN active layer. The other layers of the efficiency because the photons in thin laser cavity tend to be emitted for
structures exhibit zero polarization potentials. For m-axis structure, the a shorter period of time. The analysis shows that the nonpolar cavity
polarization potential profile has atomically been introduced; (3) a long- length laser has an excellent response to lasing. Apart from the lower
ranged strain (including relaxation) that gives an improvement in the threshold current that nonpolar m-plane cavity exhibits, it has high slope
current spreading and a reduction in the carrier leakage; (4) a strong efficiency indicating that for small increase in the injection current it
exciton localization; (5) a high polarized degree; (6) a defect-free ­ exhibits rapid increase in the output light emission. In other words, it
nanowire architecture; (7) a high stability and a less strain-effect has a high conversion rate of input electrical power to output light
because of their crystal symmetry, which is elevated in the system; (8) power. The electrical injected current dependence of the light power
a weak carrier over barrier-flow and Auger recombination process There­ follows a linear trend indicating a ground-state exciton transition [50].
fore, InGaN/GaN pyramidal QDs in NW grown along the nonpolar With the purpose of the performance evaluation of the nonpolar
crystal plane is the selected one to examine its lasing performance. InGaN/GaN pyramidal QDs nanowire laser, the lasing threshold and the
Our model has a material system, which is an In0.08Ga0.92N, while an modal gain of the nanowire laser device have been calculated. A
Al0.3Ga0.7N is an electron blocking layer. The reflectivity on the facets of threshold current density and a sharp turn-on voltage of the nonpolar
the coherent cavity is considered here as RF = 90 and RR = 100. To nanowire laser device are ~ 391 A/cm2 and ~3.2 V, respectively. It is
characterize the electrical properties of the simulated laser device (Fig. 8 worth to note that these values are significantly lower than their coun­
(a)), the total power of the emission has been represented as a function terparts in the semipolar InGaN-based nano-disks laser structure, where
of the injected current densities (the L-I characteristic) curve from a the simpolar device has threshold of about ~400 A/cm2 and a turn-on
nonpolar nanowire laser as shown in Fig. 8(b). The nanowire laser de­ voltage of about ~3.3 V [51]. The main cause of the lower threshold
vice is characterized under continuous wave (CW) current biasing con­ value of the nonpolar InGaN/GaN quantum dots nanowire is a lower
dition at room temperature. The emitted light of 0.58μ W, which is transparency carrier density and higher differential gain [2] compared
extracted from the surface of the quantum dots in nanocrystal, is lower to semipolar InGaN quantum disks nanostructure. This observed
than the recently reported experiment of the core–shell semipolar improvement in the laser threshold indeed demonstrates the effective­
(0113) InGaN multiple disks nanostructure laser by Y.-H. Ra et al. (15 ness of pyramidal quantum dots as tool for exploring the limits of laser
μW), who design a device of a semipolar InGaN nano-disks crystal with a performance in the strongly interfacial confined regime and highly
height, a diameter, and a thickness of approximately 600 nm, 230 nm, nanofocusing photonic modes.
and 564 nm, respectively [51]. The output power of the multiple As compared to other nano-disk devices, the embedded quantum dot
quantum dots nanowire laser well below and well above the threshold (QD) within a nanowire (NW) structure give emphasis to the innovative
are linear functions of the injection current with two different slopes. electrical and optical characteristics due to: (1) a smaller quantum dot
When the multiple quantum dots nanowire laser is injected below size and it’s more unique shape; (2) a smaller number of atoms in QD
threshold, the dominant mechanism over other processes is the spon­ active region in a NW; (3) a stronger quantum confinement of charge
taneous emission because the modal gain is insufficient, which results in carriers including electrons, holes, and excitons; (4) offering a delta like
a lower radiative efficiency. Since, only a small amount of the sponta­ density of states; (5) facilitating a higher population inversion; hence it
neous emission has been coupled to the lasing mode, the coefficient of shows (6) a better laser emitter; (7) a better temperature stability; and
the spontaneous emission is much lower than one [2]. As a result, the (8) a lower lasing threshold.
slope of the calculated L − I characteristic curve below threshold is much In our model QDs laser nanowire, shortening the cavity length has

Fig. 8. (a) Schematic diagram of the simulated nonpolar (truncated) pyramid QDs-in NW laser device. (b) The total power emitted as a function of injected current
density (L-I characteristic) of nonpolar (m-plane) pyramid QDs NW laser device.

8
M.M. Taher et al. Results in Physics 20 (2021) 103732

three advantages over the nano-disk devices: (1) minimizing the

threshold current density; (2) enhancing a wall-plug efficiency for the
power budget (i.e. mW-μW level); (3) improving the high speed per­
formance for modulation. Besides that, our laser structure takes benefit
of the nonpolar effect in the active region for more reducing the polar­
ization field in InGaN wurtzite structure than a nano-disk device leading
to the best quality performance of our laser device.
The gain spectrum and the modal gain curves of the nanowire lasers
have been computed using SILVACO ATLAS simulator and analyzed
using the Helmholtz method for m-plane nanowire architecture.
Although a shorter length of the nanocavity and reduced volume of the
active region, considerably lower lasing threshold due to high gain has
been computed. Commonly, the gain spectrum of the nanowire laser is
also expressed as a function of the injected current densities (Fig. 9(a)).
On the other hand, when the nanowire is electrically injected above
lasing threshold, the stimulated emission process dominates over other
processes. Near the threshold value, the clamped carrier density, due to
the fast stimulated emission process leading to consuming excess car­
Fig. 10. Room-temperature luminous flux spectrum of nonpolar (m-plane)
riers during the recombination of the stimulated emission leads to
pyramid QDs NW laser.
quickly modal gain clamping and approaching to the total loss after
passing the lasing threshold value [2]. In this figure a presentative of the
originating from the topmost part of InGaN active region at a room
clamping modal gain that is consistent with the calculated L − I char­
temperature, covers the blue spectrum. However, the other parts of the
acteristic curve indicates lasing from the nonpolar nanowire laser. No
quantum dots absorb the light leading to an increase of the threshold
observation of blue-shifted wavelength of the peak gain has been
current density This figure displays an evidence for narrow, intense
founded with increasing electrically injected current. Notice, there is no
emission line, which is attributed to the fingerprint of the existence of
increase of the gain at long wavelength (~410 nm), but a high modal
InGaN quantum dots. From polarization analysis above, this powerful
gain was observed for short wavelength (Fig. 9(b)). In this figure, the
distinct quantum dots-like luminous flux line exhibits a highly linear
higher value of the modal gain is approximately 80,500 1/cm and
polarization degree. The spectral flux density is known as the photonic
centered at emission wavelength of the quantum dots ~402 nm, while
quantity of radiation energy transferring through a surface, per unit
the gain at ~ 410 nm is close to zero. When a lower required injected
surface area and per unit wavelength.
current density implies a higher gain quality, a nanowire structure that
The small QDs truncation height with the assistant of grading surface
has a higher gain quality corresponds to a lower lasing threshold as
of the nanowire laser strongly support the well-confined modes,
shown in the plot [2].
resulting in observation of the bright emission. These QDs grading
confinement regions, which is capturing excitons, work in preventing
Model validation
these carriers from diffusing towards the center of non-radiative surface
recombination. Since nonpolar plane exhibits a small polarization field
Fig. 10 illustrates the flux spectral density for obtaining further in­
in InGaN, the reduction of the spatial separation of the electron-hole (e-
formation about the radiative recombination behavior of our modeling
h) pairs and inhibition of the formation of the excitons can be less,
of m-plane truncated pyramid QDs in-nanowire laser structure, in the
implying a lasing mechanism to preferentially allow one or more
presence of photonic modes. When the nanowire has been injected
different wavelengths’ emission by the active region to grow stronger in
above threshold, a sharp lasing peak at ~402 nm wavelength (with a
intensity as compared to the convolutional structure. As suggested in
narrow linewidth of 1 nm) has been calculated to again be a confirma­
Ref. [50] more than one QD-like peak in the form of luminous emission
tion that the peak gain of the emitted light is meeting at this wavelength.
center in the InGaN active dots region. The polarization analyses suc­
The observations of the sharp line and the broad band are found because
cessfully provide an evidence for the achievement of a grading surface-
of exciton radiative recombination in the InGaN QDs at nonpolar pyr­
emitting laser. Additionally, the simulated exciton emission rate allows
amid apex and in the nanowire at the pyramid facet, respectively.
giving an estimate of the exciton recombination time (~1 ns), which is
During the stimulated recombination step, the exciton emission that is

Fig. 9. (a) Modal gain (red) and output power (blue) plotted as a function of the injected current density. While the modal gain clamps at the lasing threshold
indicated by the (L − I) characteristic curve, it is indicating the onset of lasing. (b) The gain spectra of the nonpolar InGaN/GaN pyramid QDs core − shell NW laser.
(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

9
M.M. Taher et al. Results in Physics 20 (2021) 103732

vital for high-speed operation [50] of photonic devices. This value is applications in future.
similar to the exciton lifetime measured in Ref. [50]. This is implying
that our model validation has been proved. While classic nonpolar CRediT authorship contribution statement
InGaN/GaN MQD nanowire structures have previously shown promise
for semiconductor lasers [29] and LEDs [45], this high radiative emis­ Mayada M. Taher: Design, Methodology, Analysis, Software,
sion rate indicates that these nonpolar pyramidal QDs nanowire archi­ Conceptualization, Data curation. Shahad Al-yousif: Visualization,
tecture are appropriate for the realization of lasing emission operating at Formal analysis. Naser M. Ahmed: Visualization, Formal analysis.
high-frequencies.
Declaration of Competing Interest
Conclusion
The authors declare that they have no known competing financial
A promising solution as a new generation of graded surface-emitting
interests or personal relationships that could have appeared to influence
laser diode using realistically-sized InGaN/GaN quantum dots-in-
the work reported in this paper.
nanowire device has been demonstrated under electrical injection at
room temperature. The presence of having a clearly low-threshold,
Acknowledgments
sharply narrow linewidth, fully distinct emission, and highly polarized
light definitely provides an evidence for achieving the ultimate focusing
The authors acknowledge the Department of Electrical and Com­
of a coherent lasing oscillation. The pyramidal QDs nanowires have been
puter Engineering, Southern Illinois University Carbondale, 1230
designed using the grading surface/interface confinement techniques,
Lincoln Drive, Carbondale, IL, 62901, USA and Department of Laser and
which is elegantly allowing a precise control of the emitting quantum
Optoelectronics Engineering, University of Technology, Baghdad, Iraq
dot that is essentially required to functionalize the coherently photonic
for providing the support and facilities. They thank Arizona State Uni­
emitters. Three dimensional tapered waveguides can be served by the
versity, USA for accessing to their computing system.
pyramid QDs in-nanowire structures for photonic nanofocusing at the
apexes of these pyramids. A 10-band (sp3s * -spin) atomistic tight-
binding combined with a VFF-3D Poisson model has been used to References
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