# Electroluminescence and current-voltage measurements of single (In,Ga)N/GaN
nanowire light-emitting diodes in the nanowire ensemble

D van Treeck1, J Ledig2,3, G Scholz2, J Lähnemann1, M Musolino1, A Tahraoui1,
O Brandt1, A Waag2, H Riechert1 and L Geelhaar1 1 Paul-Drude-Institut für
Festkörperelektronik, Hausvogteiplatz 5–7, D-10117 Berlin, Germany  2 Institut
für Halbleitertechnik, TU Braunschweig, Hans-Sommer-Str. 66, 38106
Braunschweig, Germany  3 Physikalisch-Technische Bundesanstalt, Bundesallee
100, 38116 Braunschweig, Germany<EMAIL_ADDRESS>
###### Abstract

We present the combined analysis of the electroluminescence (EL) as well as
the current-voltage (I–V) behavior of single, freestanding (In,Ga)N/GaN
nanowire (NW) light-emitting diodes (LEDs) in an unprocessed, self-assembled
ensemble grown by molecular beam epitaxy. The data were acquired in a scanning
electron microscope equipped with a micromanipulator and a luminescence
detection system. Single NW spectra consist of emission lines originating from
different quantum wells, and the width of the spectra increases with
decreasing peak emission energy. The corresponding I–V characteristics are
described well by the modified Shockley equation. The key advantage of this
measurement approach is the possibility to correlate the EL intensity of a
single NW LED with the actual current density in this NW. This way, the
external quantum efficiency (EQE) can be investigated as a function of the
current in a single NW LED. The comparison of the EQE characteristic of single
NWs and the ensemble device allows a quite accurate determination of the
actual number of emitting NWs in the working ensemble LED and the respective
current densities in its individual NWs. This information is decisive for a
meaningful and comprehensive characterization of a NW ensemble device,
rendering the measurement approach employed here a very powerful analysis
tool.

##  1 Introduction

Group-III nitride nanowire (NW) ensembles have been employed for a wide range
of applications, especially optoelectronic devices [1]. Considering the
analysis of these devices, most studies focus mainly on the characterization
of the NW ensemble properties. However, the properties of single NWs in the
ensemble may differ considerably from the mean value measured for the
ensemble. For instance, in the particular case of light-emitting diodes (LEDs)
based on self-assembled NW ensembles, the emission wavelengths of single NWs
were found to vary substantially from wire to wire [2, 3, 4, 5]. Hence, in
order to better understand the final behavior of NW ensemble devices, a
careful analysis of the individual properties of the single NWs in the
ensemble is mandatory.

In order to characterize NW ensemble LEDs in depth, a combined analysis of the
emission and transport behavior of single NWs under electrical carrier
injection is needed. One way to do such a combined analysis is to remove the
nanowires from the ensemble, disperse them on a substrate and contact them
using lithographic methods. However, the contact properties between the NW and
the substrate, which might influence the overall performance of the single NWs
in the working ensemble, can not be studied by investigating dispersed NWs. To
overcome the disadvantages of the dispersion approach, single NWs can be
directly contacted with a probe tip installed in a scanning electron
microscope (SEM). For instance, using this technique, Lee et al. studied the
current-voltage (I-V) characteristics of single GaN based NW LEDs in the
ensemble, however, they were not able to measure the respective
electroluminescence (EL) signal [6]. Yet another approach was implemented by
Bavencove et al. and Musolino et al [4, 7]. They did not contact single
(In,Ga)N/GaN NWs with a probe tip, but detected diffraction-limited EL spots
in the working ensemble device using a confocal microscope. However, with this
approach they could not measure the currents in the investigated NWs.

Here, we present simultaneous measurements of the I–V behavior as well as the
EL of single, freestanding nanowire LEDs in a self-assembled NW ensemble. To
this end, as-grown NWs are contacted without any further processing with a
probe tip installed in a SEM, which is equipped with a parabolic mirror in
order to collect light emitted from the sample and couple it into a
spectrograph. This method was already applied to investigate local electro-
optical properties of much larger µ-LEDs and is now applied to nanostructures
[8, 9, 10, 11]. Investigating in detail the spectral shape of the EL of single
NWs, we find that different emission lines occur in the single NW spectra and
that their width increases linearly with the peak emission wavelength.
Furthermore, analyzing the I–V data of various NWs, we determine the series
resistances as well as the threshold voltages of the single NWs. Finally, we
analyze the dependence of the external quantum efficiency (EQE) on the current
in single NW LEDs. By comparing the trends for single and ensemble
measurements, we estimate the number of active NWs in the ensemble LED. This
information allows us to determine fairly accurately the current density in
the NWs in the working ensemble LED, which is an important parameter for
device analysis.

##  2 Experimental details

The NW LED structures investigated in this work were grown by means of self-
assembly processes with molecular beam epitaxy (MBE) on an n-doped Si(111)
substrate. They consist of an intrinsic multiple quantum well structure grown
on a Si doped n-GaN base of about 600 nm length. The active region is composed
of four (In,Ga)N insertions with an In content of (20$\pm$10)% and a thickness
of (3$\pm$1) nm. The insertions are separated by GaN barriers of 8 nm
thickness, where a 13 nm wide, Mg-doped Al0.15Ga0.85N electron blocking layer
follows the last insertion. On top of the active region a GaN:Mg cap of about
120 nm length forms the p-type region. This results in NWs with a mean length
of about 800 nm and a mean diameter of around 100 nm. Figure 1 (a) shows a
micrograph of the as-grown NW ensemble acquired in a Hitachi S-4800 field-
emission SEM.

Figure 1: (a) Cross sectional micrograph of the investigated self-assembled
GaN NW LEDs on Si acquired in the field-emission SEM. (b) Bird’s eye view
micrograph of a probe tip contacting single NWs taken in the thermionic
emission SEM with a magnification at the edge of the resolution. (c) Sketch of
a tungsten probe tip contacting a NW LED.

The NW ensemble LED we use as a reference for the EL and I–V characterizations
in this study was processed from the same sample. The NW ensemble was
planarized by spin coating using a solution of hydrogen silsesquioxane (HSQ).
Subsequently, the upper 70 nm of the p-type segments of the NWs were uncovered
by dry etching with CHF3 and a 120-nm-thick indium tin oxide (ITO) layer was
sputtered onto the NW tips. Finally, Ti/Au bonding pads and an Al/Au n-type
contact were deposited on the top contacts and on the back side of the Si
substrate, respectively. A more detailed description of the growth and
processing procedure as well as the EL and I–V characteristics of the NW
ensemble LED can be found in Ref. [12].

The EL and I–V measurements on single NW LEDs were carried out in a Zeiss
DSM962 SEM system with an Everhart-Thornley SE detector. The resolution of the
SEM system was optimized by means of reducing the probe energy and thus the
scattering volume inside the NWs. However, in contrast to a field-emission
SEM, the resolution is limited by the energy spread of the thermionic electron
source resulting in chromatic aberrations. In order to contact nanostructures,
the SEM system is equipped with a Kleindiek MM3A-EM micromanipulator which
provides a metal tip of a nominal tip radius of 100 nm [tungsten tip from GGB
Industries Inc., visible in Figure 1 (b)]. The probe tip as well as the sample
holder are connected to a Keithley SMU 2635 source meter to apply and record
the respective currents or voltages while the electron probe of the SEM is
blanked. In an Oxford Instruments MonoCL2 the parabolic mirror above the
sample holder collects light emitted from the sample and guides it out of the
SEM chamber, through a monochromator to an Andor iDus 420 BV CCD camera. A
slit width of 500 µm was chosen which corresponds, with respect to the grating
ruling density of 150 lines per mm, to a resolution of about 7 nm in the EL
spectra. The obtained EL spectra were corrected taking into account the
spectral responsivity of the system. An automatized measurement environment of
this setup enabled a fast sequence of spectral and electrical operation points
of contacted single NW LEDs in the ensemble while stepwise sweeping electrical
injection. The EL and I–V measurements of all measurement positions shown in
the manuscript (except position E) were acquired by sweeping the current with
steps of 5 nA. Only for measurement position E, we sweeped the voltage instead
of the current with steps of 200 mV.

For this study, the EL and I–V measurements were performed at room temperature
for various measurement positions on the sample, where one position
corresponds to a single or a few contacted NW LEDs below the tungsten probe.
Using the SEM live mode, the piezo element-driven probe tip was approached
very slowly to the NWs. The distance between probe tip and NW tips could be
well estimated by comparing the shadow of the tungsten probe on the sample
surface in the SEM live image with its actual position. When the shadow and
the probe tip came together, the probe slightly changed its moving direction,
thus indicating the contact to the sample [see Figure 1 (b)]. The probe tip
was then slowly lifted while applying voltage to monitor the electrical
contact between NW and tip. With this procedure, it was possible to minimize
the pressure while contacting the NWs. The spring force which is applied to
the NWs in vertical direction once the probe is moved downwards, mainly
results from the bending of the tungsten wire and can be estimated to be in
the range of several tens of nN. Figure 1 (c) shows a sketch of a single
contacted NW LED.

##  3 Results and discussion

Figure 2: The colored spectra (normalized) represent the EL measured with the
probe tip at four different positions on the unprocessed NW ensemble for a
driving current of 100 nA. The black spectrum is the EL of the processed
ensemble LED [12].

Figure 2 shows a representative collection of EL spectra obtained for four
different measurement positions on the as-grown sample and the EL spectrum of
the NW ensemble device processed from another piece of the same wafer.
Comparing the spectra of the four measurement points, they show very different
emission characteristics in terms of the number of emission bands, their
emission energy and relative intensity. For instance, spectrum C has one
defined emission band with a broader tail towards lower energies, whereas for
the other spectra at least two emission bands are visible. The emission bands
can be found at various emission energies in a range from 1.77 eV up to 2.53
eV. The relative intensities differ from emission band to emission band and do
not show a specific pattern. Nevertheless, the emission bands at lower
energies are usually broader than the ones at higher photon energies. In
general, it was not possible to draw a reasonable comparison between the
absolute intensities of the different measurements, since the shadowing of the
probe tip and the different measurement position with respect to the
collection mirror is expected to have a strong influence. Moreover, it should
be noted that whenever the tungsten tip was in contact with the sample and a
current (voltage) was applied, an EL signal could be detected. This is
consistent with the conclusions of a previous investigation on similar samples
that most of the NWs are well contacted to the substrate [5].

The comparison of the single NW measurements to the spectrum of the NW
ensemble LED clearly suggests that the specific shape of the EL characteristic
of the ensemble results from the superposition of the contributions of single
NW LEDs with a substantial spread in emission properties. This finding is in
agreement with the results of CL and EL studies on single NWs with a similar
structure [3, 4, 7]. A more detailed discussion of the ensemble luminescence
of the same NW ensemble can be found elsewhere [12].

The resolution limit of the SEM and the restricted angle between sample and
probe tip in combination with the high NW number density (5$\times$109 cm-2)
of the investigated NW ensemble did not allow an identification of the number
of contacted NWs during the various measurements by SEM. Hence, it is very
likely that for the spectra A, B, and D in Figure 2 more than one NW is
contacted. A larger number of contacted NWs would result in a larger number of
emission bands in the EL spectrum. Indeed, there are indications that the
emission bands in the individual spectra of Figure 2 originate from different
single NWs. For measurements where the probe tip is slightly moved sideways
across the tips of the emerging NWs, one emission band after the other
vanishes in the live-monitored EL spectrum and/or eventually new bands appear
at different emission energies. In the supporting information we discuss in
detail an example that shows the disappearance of an EL band due to a movement
of the probe tip and the respective change in the I–V characteristics. Within
a set of more than 20 measurement positions, spectrum C is representative for
those spectra where only one major, slightly asymmetric emission band was
visible. A similar band profile of the EL spectra of single NWs has already
been reported in the literature [4, 7]. Hence, we assume that spectrum C shows
the luminescence of a single nanowire LED.

Figure 3: (a) EL spectra of NW C for currents in the range 10 – 400 nA. The
inset shows the corresponding current-voltage characteristic. (b) The
different line profiles in the spectra for driving currents of 20, 40, 60, and
400 nA (data plotted as gray lines) were fitted by Lorentzian curves. The
cumulative fit curves are displayed as purple dashed lines. (c) The graph
shows the peak energy extracted from the fits of the different line profiles
in (a) for driving currents from 20 – 400 nA. For clarity the x-axis with the
driving current is plotted vertically. Moreover, the lines connecting the
different data points for each emission line are a guide to the eye.

In order to better understand the emission behavior of single NWs, we now
investigate the evolution of EL spectrum C with increasing driving current
from 10 to 400 nA, as illustrated in Figure 3 (a). The first clear EL signal
is obtained for a driving current of about 20 nA. Assuming that at point C, we
contact a single NW LED with a diameter of 100 nm (mean value for the
ensemble), the current range from 10 to 400 nA would correspond to current
densities in the single NW of about 130 A/cm2 to 5 kA/cm2, although it should
be noted that it is not clear whether the current density is homogeneous
across the NW. The respective I–V characteristic (inset) shows a clear diode
behavior and hence indicates a stable contact between probe tip and NW. With
increasing current two distinct emission lines around 2.24 and 2.34 eV can
clearly be distinguished in the spectra and for currents higher than 100 nA,
an additional shoulder becomes visible at about 2.43 eV. Figure 3 (b) shows
that the EL spectra for the whole current range can be very well described by
fitting the different emission lines with Lorentzian functions. The analysis
demonstrates that for a driving current of 20 nA the emission line at lower
energy (line 1) dominates, until the high energy line (line 2) takes over at
about 40 nA. The shoulder that appears for currents higher than 100 nA can be
well modeled by a third emission line (line 3), whose intensity increases with
increasing current. Analyzing the evolution of the peak energies of the
emission lines 1, 2 and 3 for driving currents from 20 to 400 nA as shown in
Figure 3 (c), we find that all emission lines experience a distinct blue-shift
with increasing current. For clarity the x-axis with the driving current is
plotted vertically in Figure 3 (c).

The appearance of two main emission lines and their peculiar evolution with
increasing current densities as shown for spectrum C is similar to what we
recently observed analyzing single NW spots in top-view EL maps of a
comparable processed NW ensemble LED [7]. By modeling strain, electric field,
and charge carrier density inside the active region of a single NW LED, it was
found that the different emission lines in the spectra and their observed
evolution with increasing injection current result from different emission
energies and intensities of the four (In,Ga)N insertions. The low energy line
was attributed to the EL of the first insertion (QW 1) next to the n-type base
of the NW, whereas the high energy line was linked to the superposition of the
EL of the other three insertions. The variations in emission properties of
single QWs were explained by different spontaneous and piezoelectric
polarization fields within the different insertions, mainly caused by ionized
donors and acceptors in the adjacent doped segments and by the non-uniform
strain distribution along the active region, respectively.

Also in the case of NW C in Figure 3, the comparatively strong shift of
emission line 1 for currents up to 100 nA suggests the presence of strong
polarization fields within the contributing QW(s). Furthermore, the
fluctuations of the peak energies of line 2 for the current regime up to 100
nA may be explained by the fact that line 2 is a superposition of the
emissions of several QWs with slightly different emission characteristics, as
discussed above. Note that for the low current regime, the contribution of
emission line 3, which is only well identifiable for currents higher than 200
nA, might be hidden in line 2. We note that the similarity between the line
analysis in Ref. [7] and the data presented here corroborates our assumption
that spectrum C corresponds to a single contacted NW.

Figure 4: (a) Normalized EL spectra at various measurement points, including
NW C for a driving current of 100 nA ($\approx$ 1.3 kA/cm2). (b) FWHM of the
EL spectra of single NW LEDs as a function of their peak emission energy.

The previous analysis illustrates that contacting single NW LEDs in the
ensemble is a powerful investigation tool to better understand the emission
behavior of these structures under electrical carrier injection. In Figure 4,
we now analyze and compare the emission properties of a set of different
measurements on single NW LEDs. Figure 4 (a) shows a comparison of the EL
spectra of four different measurement points for a driving current of 100 nA.
The collection includes measurements of three single NW LEDs C, E and G
emitting at different energies. The latter two were selected since they showed
a similar emission behavior with increasing current as the previously analyzed
NW C. The fourth measurement point F exhibits a rather broad spectrum, so it
can be assumed that at least two NWs are contacted by the probe tip. This
point was chosen for comparison, and we will get back to it later. Comparing
the width of the single NW spectra C, E and G, one finds that it increases
with decreasing emission energy. Figure 4 (b) shows the full width at half
maximum (FWHM) of ten EL spectra that could be attributed to different single
NWs, including the values of C, E and G for a driving current of 100 nA. The
width follows a linear decrease from about 380 to 130 meV. Such a trend may be
explained by a higher local fluctuation of the material composition and a more
inhomogeneous strain distribution within the insertions due to an increase in
In content [13, 14]. Also for (In,Ga)N based core-shell NW structures grown by
metalorganic chemical vapor deposition it was found that the FWHM increases
with decreasing emission energy [13].

Figure 5: (a) I–V characteristic of points C, E, F, and G. The dashed line
shows an example for a linear fit to the I–V curve of NW C for the current
range from 60 – 100 nA from which the series resistance $R_{\mathrm{tot}}$ and
the threshold voltage $V_{\mathrm{th}}$ are derived. The inset depicts the I–V
behavior of the ensemble. (b) Semi-log plot of the I–V curve (blue dots) of NW
E and the respective fit (orange line) of the data, obtained by using Eq.1.

In order to better understand the charge carrier transport in single NW LEDs,
in Figure 5 (a) we analyze the I–V curves for the NWs C, E, and G, as well as
for the bundle of NWs F for currents in the range 0 – 100 nA. The I–V
characteristic of the NW ensemble LED is displayed for comparison in the
inset. All curves exhibit a clear diode behavior and for currents higher than
about 60 nA, the I–V curves show a linear behavior. In this region, the curves
differ in slope and thus in series resistance. The series resistances
$R_{\mathrm{tot}}$ of C, E, F and G, evaluated from a linear fit of the I–V
curves for the range 60 – 100 nA are shown in Table 1.

LED(s) |  |  $R_{\mathrm{tot}}$ ($\Omega$) |  |  $V_{\mathrm{th}}$ (V)
---|---|---|---|---
C |  | 58 $\times$ 106 |  | 7.0
E |  | 43 $\times$ 106 |  | 7.3
F |  | 22 $\times$ 106 |  | 3.5
G |  | 34 $\times$ 106 |  | 7.8
ensemble |  | 30 |  | 3.3
Table 1: . Series resistance $R_{\mathrm{tot}}$ and threshold voltage
$V_{\mathrm{th}}$ of the single NWs C, E, and G, as well as of the bundle of
NWs F and the NW ensemble.

In general, the main contributions which cause the high values of
$R_{\mathrm{tot}}$ are the resistance of the n-GaN/n-Si interface
$R_{\mathrm{GaN/Si}}$, the contact resistance $R_{\mathrm{c}}$ between p-GaN
and the tungsten probe and the resistance of the NW LED $R_{\mathrm{NW}}$
itself. The contributions of the n-Si substrate and the measurement setup were
determined to be in the range of a few Ohms and therefore can be neglected for
our considerations. Unfortunately, it was not possible to separate the single
contributions of $R_{\mathrm{GaN/Si}}$, $R_{\mathrm{c}}$ and $R_{\mathrm{NW}}$
in our measurements. For comparison, we estimate the resistance of a single NW
in the working NW ensemble LED by
$R_{\mathrm{tot}}^{\mathrm{est.}}=A\,d_{\mathrm{on}}R_{\mathrm{S}}$ with the
device area $A$, the series resistance $R_{\mathrm{S}}$ and the number density
of emitting NWs $d_{\mathrm{on}}$. With values of 0.19 mm2, 30 $\Omega$ and
about 3 $\times$ 108 cm-2 for the ensemble (see Ref. [12]), respectively, one
obtains a value of 17 M$\Omega$, which is comparable to the values obtained
for the single NW measurements (Table 1). Later in this report, we present an
independent estimate of $d_{\mathrm{on}}$ that is higher by a factor of two,
which results in an even better agreement between single NW and ensemble
$R_{\mathrm{tot}}$. Nevertheless, a value of $R_{\mathrm{c}}$ of several
M$\Omega$ in the case of single unprocessed NW LEDs contacted by a probe tip
cannot be excluded. The comparatively small $R_{\mathrm{tot}}$ of point F can
be explained by the fact that for this measurement point most certainly two
NWs are contacted, resulting in half the series resistance as for the single
NW measurements C, E, and G.

Another parameter that can be extracted from the I–V behavior is the threshold
voltage $V_{\mathrm{th}}$, which is defined as the zero-crossing of the linear
fit function of the respective I–V curves. As an example, the dashed line
shows the linear fit for NW C. The threshold voltages for the different
measurements are shown in Table 1. These values are in agreement with the
actual turn-on voltage for which the first EL signal was detected. The
comparatively high threshold voltages of single NW measurements in comparison
to the 3.3 V of a NW ensemble LED with a processed ITO top-contact most likely
result from a Schottky type contact at the p-GaN/tungsten interface.

To analyze the I–V behavior of a single NW in more detail, Figure 5 (b) shows
the I–V curve of NW E in semi-log scale. For positive voltages, the current
increases continuously with increasing voltage and can be well described by
the modified Shockley equation as it is commonly used in the literature [15,
6, 16, 17, 18],

${}I=I_{0}\left[\exp\left(\frac{e(V-IR_{S})}{n~{}k_{B}T}\right)-1\right]+\frac{V-IR_{S}}{R_{P}}.$
(1)

From the fit (orange line), values for the saturation current $I_{0}$ and the
ideality factor $n$, as well as the parallel resistance $R_{\mathrm{P}}$ and a
series resistance $R_{\mathrm{S}}$ of the contacted NW LED or NW LEDs could be
obtained, which are 80 pA, 50, 1.5 G$\Omega$ and 18 M$\Omega$, respectively.
For positive voltages ¡ 2 V, the I–V behavior is dominated by the parallel
leakage current defined by $R_{\mathrm{P}}$. The voltage regime 2 – 9 V is
mainly characterized by the diode term where the ideality factor $n$
determines the slope of the curve until $R_{\mathrm{S}}$ dominates the current
for voltages ¿ 9 V. With a value of 50, the ideality factor $n$ is far from
unity. Also other studies of single NW diodes based on GaN obtained ideality
factors of about 20 – 30 [6, 16, 18, 19, 20] or even 161 [21]. Regarding the
origin of these high ideality factors, it was found that in particular the
contact to the p-type GaN, in our case the tungsten/p-GaN interface, may be
responsible for ideality factors $\gg\,2$ [22, Zhu2009]. We emphasize that for
the NW ensemble LED with optimized ITO top contact to the p-GaN NW tips the
ideality factor is with 9.2 [12] much smaller than for the single NW
measurement presented here. Thus, we conclude that the high ideality factor
found here is caused by the contact between the tungsten tip and the p-GaN or,
much less likely, the absence of the dielectric covering the nanowire
sidewalls in the processed LED, but not related to processes inside the NWs
themselves. The large difference in the ideality factor points to limitations
of the single NW measurements for a detailed analysis of IV characteristics.

For negative voltages the I–V characteristic shows a rapidly increasing and
rather high reverse leakage current, which cannot be described by the modified
Shockley equation. At $-5$ V the reverse current is with 1.5 nA about one
fourth of the forward current at 5 V. For a more detailed discussion of the
reverse leakage current we refer the reader to our previous study [24] where
we present a comprehensive model that describes quantitatively the I–V
characteristic of nanowire LEDs under reverse bias.

In contrast to investigating EL maps of the NW ensemble LED, one major
advantage of our measurement approach is that one can correlate the EL
intensity of a single NW LED with the actual current flowing through this NW.
This allows a current-dependent analysis of the integrated EL intensity and
the relative EQE of single NW LEDs in the ensemble. The relative EQE is
defined by the quotient of the integrated EL and the respective driving
current [26]. The term ”relative” takes into account that the total emitted
intensity at the different measurement positions is unknown due to shadowing
effects of the probe tip and different angles between measurement positions
and collection mirror. Hence, no absolute values for the EQE could be
determined. Furthermore, for a given, externally imposed driving current, we
can assume that the influence of any high contact resistance between probe tip
and NW LED on the integrated EL and hence the relative EQE is negligible.

In Figure 6 the integrated EL and the relative EQE are shown for the same
collection of measurement points C, E, F, and G. The respective current
densities in the single NW LEDs C, E, and G for this range are given at the
top x-axis and were estimated using the extracted mean NW diameter of 100 nm.
These values are not valid for point F, since here more than one NW is
contacted resulting in lower current densities. The integrated EL was obtained
by integrating the single EL spectra for the different driving currents.
However, as explained above, one has to be careful with directly comparing the
absolute values of the integrated EL for the different measurement points.
Nevertheless, the current dependence of the integrated EL should be
meaningful. For most of the measurements a continuous linear increase of the
integrated EL with the driving current was observed over the whole measurement
range. A similar trend was also found for the ensemble LED, which is shown in
the inset of Figure 6 (a) [12].

Figure 6: (a) Integrated EL and (b) normalized relative EQE of the measurement
points C, E, F, and G as a function of current. The respective insets in the
graphs (a) and (b) show the integrated EL and relative EQE of the NW ensemble
LED.

The relative EQE of the different points plotted in Figure 6 (b) shows a
maximum for all the single NW measurements C, E, and G at a current value of
around 80 nA, which corresponds to a current density of about 1 kA/cm2. The
maximum of point F only appears for a current of about 300 nA. Once the
maximum relative EQE is reached, the EQE slightly decreases but remains at a
rather high level. In general, the majority of the measurements where single
NW LEDs were contacted, showed a relative EQE maximum for injection currents
between 60 and 100 nA. Interestingly, there seems to be a correlation between
the appearance of the relative EQE maximum and the presence of strong
piezoelectric fields within the QWs, as suggested by the pronounced spectral
blue shift of the EL lines for currents below 100 nA in Figure 3 (c). Strong
polarization fields cause a spatial separation of electrons and holes in the
QWs which in turn leads to a reduced radiative recombination rate and hence a
reduced relative EQE for small injection currents. Due to the lack of
temperature dependent measurements, it was not possible to draw any hard
conclusions about the origin of the slight decrease of the relative EQE once
the maximum was reached and its rather constant subsequent behavior for higher
current densities. The absence of a significant relative EQE drop for NW LEDs
for high current densities was also reported in several studies on NW ensemble
LEDs [25, 27].

The comparatively high current for which the relative EQE of point F peaks,
can be explained by taking into account that for this point more than one NW
is contacted. Hence, for the same driving current at point F, the mean current
density in the single contributing NWs is lower. As a consequence, for an
increasing number of contacted NWs, the maximum in the relative EQE only
appears for higher driving currents, since the current
$I^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{NW}}$ for which the saturation of
the relative EQE of the single NW LEDs sets in, is not yet reached.
Considering a NW ensemble LED, this means that the device current density
$J^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{device}}$ (driving current divided
by device area) for which the EQE of the device has its maximum, strongly
depends on the number density of emitting NWs $d_{\mathrm{on}}$ in the
ensemble and is given by the relation
$J^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{device}}=d_{\mathrm{on}}I^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{NW}}$.
Hence, the lower the number density of active single NW LEDs in the ensemble,
the lower is the device current density for the maximum relative EQE and vice
versa. It should be noted that this relation is only true if the NWs have
similar contact resistances, resulting in a homogeneous current spreading in
the ensemble device. The side-by-side comparison of ITO and Ni/Au top contacts
in Ref. [12] showed that with ITO a homogeneous p-type contact can be achieved
throughout the whole device. This was not the case for the Ni/Au top contact,
for which the contact resistance varied significantly across the sample.
Considering the EQE characteristics of a device, such a pronounced variation
leads to a rather high, strongly varying contact resistance resulting in very
different currents in the single NWs and hence a slow rise of the ensemble
EQE.

The relative EQE of the ensemble device with the ITO top contact fabricated
from the same sample investigated in this study is shown in the inset of
Figure 6 (b). The graph depicts that the relative EQE saturates for a device
current density $J^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{device}}$ of about
47 A/cm2. Taking the latter value and the value for
$I^{\mathrm{EQE_{\mathrm{max}}}}_{\mathrm{NW}}$ of 80 nA we obtain from our
measurements on single NW LEDs, one can estimate the actual number density of
emitting NWs $d_{\mathrm{on}}$ in the ensemble, which is 6 $\times$ 108 cm-2,
using the above mentioned relation. With a number density of about 5 $\times$
109 cm-2 for the as-grown ensemble, this corresponds to about 12% emitting NWs
in the processed NW ensemble which contribute to the total EL emission. This
is in agreement with the rough estimation obtained by analyzing the ensemble
LED [12], but the current procedure provides a more precise and reliable
value. The fairly low fraction of active NWs can be attributed to the complex
post-growth processing of NW LEDs, where, e. g., a homogeneous planarization
of the NW ensemble and homogeneous ITO top-contact to the p-GaN tips of the
NWs are crucial factors which strongly influence the number of emitting NWs
[12, 5]. Furthermore, the current densities in single NW LEDs in the working
NW ensemble device can be estimated to be in the range from 20 A/cm2 to 1
kA/cm2 for device current densities of 0.9 – 47 A/cm2. We emphasize that
without the single NW measurements introduced here, calculations of the actual
current density per active NW in an ensemble device are limited in accuracy
since it cannot be easily determined how many NWs actually participate in
charge conduction.

##  4 Summary and Conclusions

In this study, we employed a specially equipped SEM to contact as-grown single
(In,Ga)N/GaN NW LEDs with a probe tip and acquire simultaneously I–V
characteristics and EL. Even though the NW number density of our sample is so
high that direct imaging by the SEM does not reveal the number of contacted
NWs, a careful analysis of electrical and EL data allows to distinguish with
confidence between cases where single and multiple NWs are contacted. The
emission energy of individual NWs varies, and the ensemble EL spectrum can be
understood as a superposition of the individual spectra. The FWHM of the
individual spectra decreases with increasing emission energy, which is
consistent with previous reports [13] and can be explained by compositional
fluctuations as well as by inhomogeneous strain distribution within the
insertions being more pronounced for higher In contents [13, 14]. The
individual spectra consist of three emission lines whose intensity changes in
a characteristic way with current. This phenomenon is caused by the N polarity
of the NWs and the three-dimensional strain profile resulting from elastic
relaxation at the free sidewall surfaces, as previously shown in Ref. [7].

I–V curves acquired for single NW LEDs exhibit diode characteristics similar
to ensemble measurements. However, the threshold voltage and ideality factor
are significantly higher for the single NW experiments, likely because of a
high contact resistance between tungsten probe tip and p-GaN NW top. Taking
this effect into account, the two types of measurement are consistent. An
important result is that the single NW analysis confirms the high leakage
current under reverse bias found for the ensemble. This agreement implies that
the leakage behavior is inherent to the as-grown NW structure and is not
caused by deficiencies in processing.

The key advantage of our measurement approach is the possibility to correlate
the EL intensity of a single NW LED with the actual current density in this
NW. Qualitatively, EL intensity and relative EQE increase with current as seen
for the ensemble LED, and the latter trend exhibits a maximum followed by a
slight decrease. However, the decisive difference is that for the ensemble
measurement the fraction of NWs participating in charge transport and emitting
EL can only be roughly estimated, essentially because the NWs in the dense
ensemble cannot be optically resolved [12]. Furthermore, from the comparison
of different processing protocols it is known that it is very challenging to
obtain EL from a substantial fraction of NWs [5]. In contrast, for the single
NW measurements introduced here, the current density is known fairly well. By
comparing the currents at which the maximum in relative EQE occurs for single
NW and ensemble measurements, we could determine for the ensemble the fraction
of active NWs emitting EL and the current density in them. The value of only
12% active NWS we found, implies that there is still a large potential for the
optimization of processing, which would lead to significant improvements of
the overall performance of NW LEDs. More importantly, information about the
actual current density in the semiconductor heterostructure is crucial for a
meaningful assessment of NW ensemble devices, in particular in comparison with
planar devices. This information is equally decisive for the comparison of
device simulations as reported in Ref. [7] with experimental results for NW
LEDs. Therefore, the measurement technique employed here is a very powerful
analysis tool for the investigation of LEDs based on NW ensembles and provides
new opportunities for their detailed study.

We are grateful to C. Herrmann, H.-P. Schönherr, and C. Stemmler for the
maintenance of the MBE system, and A.-K. Bluhm for SE micrographs.
Furthermore, we are thankful to Alexander Kuznetsov for a critical reading of
the manuscript. Financial support by the European Commission (Project DEEPEN,
FP7-NMP-2013-SMALL-7, Grant Agreement no. 604416) is gratefully acknowledged.

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# Adding Interactivity to Education of
Complex Wireless Networks
Using Digital Game-Based Learning

Seungmo Kim, Senior Member, IEEE S. Kim is with the Department of Electrical
and Computer Engineering, Georgia Southern University in Statesboro, GA, USA.
The corresponding author is S. Kim who can be reached at
<EMAIL_ADDRESS>
###### Abstract

Can we make undergraduate engineering education easier and more fun? This
research aims to see if we can answer the ambitious question! The digital
game-based learning (DGBL) has been found to increase the efficacy of learning
when applied in engineering classes thanks to its ability to make students
feel easy and fun. However, the state-of-the-art DGBL schemes still observe
challenges in various aspects including cost, efficacy, readiness of
instructors and students, etc. Motivated from the challenges, this research
proposes to design a DGBL platform that features visualized and systematic
views. Specifically, we identify the blockchain applied to wireless
communications and networking systems as a key ecosystem that we capitalize
the benefit of the proposed platform.. As such, in this paper, we lay out a
comprehensive DGBL pedagogy that includes (i) creation of relevant assignment
activities and class materials in a relevant course and (ii) evaluation of the
pedagogical efficacy. In a long-term view, a successful delivery of this
research will increase the confidence of undergraduate engineering students on
the “in-concert” dynamics of various factors determining the performance of a
blockchain system built on a wireless network.

###### Index Terms:

DGBL, Interactivity, Visualization, Wireless Communications and Networking,
Electrical and Computer Engineering

##  I Introduction

This paper certifies request of presentation at the ‘Innovative in Practice’
track of the ‘Work in Progress (WIP)’ session.

###  I-A Motivation

There is a jumble of symbols, concepts, systems, and protocols that make
engineering and science sound very vague and incomprehensive. The question we
raise is: Can we provide effective access and understanding of these concepts
and introduce them into an undergraduate curriculum?

Digital game is one of the most efficient tools to motivate youngsters: they
feel easy, keen, confident, and fun in dealing with games, which makes them
enjoy thriving to go through challenges. Taking advantage of this, the digital
game-based learning (DGBL) is known to make learning more attractive,
motivating, and personalized from the learner’s viewpoint [1][2]. Some
difficulties in carrying out typical forms of inquiry-based learning in a
class have been pointed out [3]-[6]: to summarize, (i) the complexity in the
contexts and (ii) the students’ low engagement level. However, when delivered
in the form of a digital game-based activity, greater chances of being more
joyful and efficient have been found: specifically, (i) self-discovery and
construction of one’s own reality [7]-[11]; (ii) increase in students’ inquiry
experience [12][13]; (iii) engagement of students in applying knowledge to
real-world contexts [14]-[19]; and (iv) collaborative learning where two or
more learners interact and engage to learn together [20]-[22].

In further studies, it has been found that the level of students’ engagement
influences their inquiry learning effectiveness [3][23]-[25]. It motivates the
need for precise evaluation of students’ feedback on management of the
proposed gamified learning platform (as shall be described in Section VI).

We identify blockchain applied in wireless communications as the new content
to explore the effectiveness of DGBL in an undergraduate curriculum. The key
rationale is that this rapidly evolving field of technology offers great
opportunities for students to experience multidisciplinary topics involving
elements of mathematics, (i.e., abstract algebra and number theory),
cryptography, computer networks, etc. The necessity for systematic
comprehension of such an interplay among various, dissimilar areas makes a
compelling case in favor of infusing new learning materials and strategies to
enhance an undergraduate education program. In fact, the wireless technology
is experiencing a variety of completely new problem domains including spectrum
sharing [26] and vehicle-to-everything (V2X) networking [27][28]. Nonetheless,
at the blockchain consensus 2017, scholars have concluded that academics are
not keeping pace with blockchain change [29].

Given the significance of blockchain expertise in new undergraduates, strong
educational support is vital and current educational curricula should reflect
cutting-edge trends and needs in this sector. Specifically, students are
challenged more than ever to be creative to confront contemporary issues
related to blockchain. Hence, educational environments should cultivate
students that are equipped with a set of tools to formulate, solve, and
properly tackle multidisciplinary problems.

###  I-B Contributions

While playing on the proposed gamified platform, students are expected to
learn on such multifaceted interplay that is enabled by visualization of cause
and effect of different approaches and decisions that they make. For instance,
the connectivity is a critical factor determining the performance of a
network, which is not a straightforward concept to grasp when not visualized.
In the proposed platform, through visualization, students will be able to (i)
perceive which areas are better or less connected, (ii) route their own nodes
toward the directions that they remain in a maximum connectivity, and (iii) in
turn, maximize the data exchange performance through a round of the game. Such
pedagogical improvement led by this research will provide a model for similar
approaches in other challenging science, technology, engineering, and
mathematics (STEM) education domains.

##  II State-of-the-Art at Other Institutions and Their Limitations

###  II-A Current Undergraduate Programs and Limitations

Several institutions have deployed DGBL in their undergraduate curricula. We
discuss their contributions and limitations as follows.

Virginia Tech [30] has developed an online learning platform providing
visualization and gamification and published advantages on education of
wireless communications engineering [31]. Yet, the need for connecting 48
physical hardware nodes, the system requires significant amounts of time and
cost to maintain or host demonstrations or competitions. Moreover, it also
left pedagogical challenges including: inabilities to visualize and analyze
(i) mobility of nodes in a network and (ii) systematic perspectives as a
result of interplay among multiple mobile nodes and parameters determining a
network characteristic.

The Game Studio at American University [32] offers academic programs
(including baccalaureate and graduate) across interdisciplinary fields
including human-computer interaction, civic engagement, journalism, art,
education, and health. However, the published games’ contents are not suitable
for immediate adaptation to STEM education. Moreover, access to the actual
games are not available for general users, which limits the applicability.

The City University of New York (CUNY) Games Network [33] connects educators
to games and other forms of interactive and inquiry-based learning. However,
the games available on the network do not provide capabilities to understand
systematic interplay among multiple variables and factors, which is easily
encountered in a STEM-related problem solving.

The Embry-Riddle Aeronautical University [34] investigated efficacy of games
in understanding human behavior–i.e., personality, motivation, performance,
teamwork, etc. But, being dedicated to psychological disciplines only, their
pedagogical findings have little implication to improvement of a STEM
curriculum.

In Fall 2013, via the A-Games Project [35], the University of Michigan
surveyed 488 K-12 teachers nationwide about the efficacy of DGBL. From uses of
games to cover content mandated by state/national or local/district standards,
the majority of teachers were found to believe games were effective for
motivating students, helping students reinforce or master previously taught
content, providing useful information about student learning, and teaching
students new content.

###  II-B Common Challenges

Some scholarly work has also studied general challenges found from other DGBL
programs: (i) cost of games [35]; (ii) limited time to deploy the games and
analyze the efficacy [35]; (iii) lack of technology literacy by teachers and
students [35]; (iv) lack of place to find appropriate games [35]; (v)
performance evaluation methods still relying on standardized test scores [35];
(vi) necessity of additional resources (i.e., pedagogical and technical
supports) [36]; (vii) issues of access and the digital divide [36]; (viii)
necessity of periodic examination on whether students actually prefer this
approach to teaching [36]; and (iv) fear of distraction due to perception of a
game as leisure rather than academic drive [37][38].

##  III Problem Statements and Respective Action Plans

The goal of this research is to modify current undergraduate electrical and
computer engineering (ECE) education pedagogy to employ an innovative gamified
tool, which will make concepts related to blockchain more accessible to
undergraduates. While the DGBL has been found to be effective in education of
many engineering aspects, this research is particularly focused on enhancing
the efficacy of learning dynamic behaviors of complex wireless networks (e.g.,
V2X networks). The key rationale is the need for systematic understanding of
orchestration of various topics forming the basis of such a complex wireless
network: e.g., probability and statistics, optimization, communications
theory, networking theory, graph theory, cryptography, etc.

As a result of careful investigation about the currently available DGBL-
related literature and resources, this research specifies three problem
statements:

  * •

P1: No DGBL focuses on training a systematic view on complex behaviors of a
network

  * •

P2: No explicit finding exists on the efficacy of DGBL focusing on such
systematic understanding

  * •

P3: It is critical to monitor students’ perception on a new learning tool

In response to the problem statements, we design this research in such way to
undertake three action plans :

  * •

A1: Development of a gamified learning platform

  * •

A2: Incorporation into a number of undergraduate courses

  * •

A3: Evaluation of the efficacy of the proposed approach

As such, this research aims to transform a difficult-to-grasp field into an
easily accessible learning environment, which will contribute to a
breakthrough in ECE education.

Figure 1: Example of a character view Figure 2: Screenshot of an example map
with nodes distributed Figure 3: Screenshot of platform development Figure 4:
Example of block management process

##  IV Current Status

We report that the current status of this project is approximately 50% toward
the completion of A1. Technical details follow in this section.

####  IV-1 Player Character

As illustrated in Fig. 1, each user is able to choose a character. Each
character is assigned a certain role between a “full” node and a “half” node.
A full node has full capabilities including block generation, mining (i.e.,
validation), and connection to networks. A half node, on the other hand, has
all the capabilities but is not able to mine a block. Also, other capabilities
(i.e., block mining speed, mobility speed, indoor-outdoor penetration, jump,
etc) are differentiated among the characters.

While playing a game, a user sees a map to move its character, as shown in
Fig. 2. The user is able to switch the display into the “character view” as
shown in Fig. 1, to check the current status of (i) energy consumption and
(ii) connectivity. Note that energy consumption is monitored because it is one
of the key parameters measuring the efficiency of an entire blockchain system
[39], which will be explained in more depth in the Scenarios part of this
section.

####  IV-2 Map

The game will be designed as a role-playing game (RPG) [40], to focus on
visualizing the interplay among parameters of network connectivity. As shown
in Fig. 3, we have already (i) started developing a game environment and thus
(ii) is familiar with related tools to enhance the quality. A user is able to
switch to the blockchain status as shown in Fig. 4, which displays all the
activities of (i) block generation, (ii) attempt of validation, (iii) result
of validation, and (iv) addition to the chain.

####  IV-3 Connectivity

For modeling signals’ propagation, we adopt the standard models defined by the
3rd Generation Partnership Project (3GPP) [41], which determine the size of a
cell and types of obstacle (e.g., cars, buildings, etc). While the
geographical type can be selected by a user, as mentioned earlier in the
Platform part, other geographical settings will be randomized in every round
of the game–e.g., locations of roads, base stations, obstacles, etc. Also, the
network type will be differentiated depending on the game character that a
user has selected. For instance, character Alice can be connected to Wi-Fi,
3G, and 5G, while character Bob can be connected to Wi-Fi and Bluetooth.
Lastly, network coverage will also be varied. Not all the area is being
covered by the network coverages: some areas will be left to be uncovered, in
which no block can be exchanged [42][43]. Each user can make a strategy to
route to maximize the coverage, which will in turn maximize the performance of
a blockchain system.

####  IV-4 Scenarios

Each student’s character control the character on the roads in the map as
shown in Fig. 2. A block is generated every $N$ seconds at a random user (no
matter a full or a half node), and has to be “validated” to go through a PoW
and be added to the chain [44]. A block can only be validated by a full node
[45], and thus must be handed to another full node for validation [46]. The
time until a rendezvous with a full node varies according to various
parameters–e.g., connectivity, a character’s moving speed, location on the
road, number of obstacles, etc. The rationale is that it usually takes a
tradeoff between the blockchain’s pursuit of the distributed decision making
and the wireless’ complexity in dealing with the distributed networking
architecture [47].

##  V Pilot Plan

The outcome of this project will be incorporated into interactive assignments
and class materials and piloted in a course that the author is currently
teaching, in such a way to accomplish A2. We will develop two types of
activities based on the proposed gamified learning platform–namely,
interactive lab session and hands-on assignment. The following materials will
be developed and used commonly in both types of the assignment: lecture,
student report format, quiz, survey, and activity instruction manual.

The next step is to evaluate the efficacy of the proposed pedagogy, which will
accomplish A3. The impact of using the proposed interactive tool on student
learning will be assessed based on the criteria of student learning outcomes
(SLOs) for engineering by the Accreditation Board for Engineering and
Technology (ABET) [48]. The Computing Accreditation Commission (CAC) SLOs [49]
will be used as a secondary reference. Moreover, since the experiment will
collect data from human participants, all experimental protocols will be
reviewed and approved by both institutions’ Institutional Review Boards
(IRBs). The IRBs will confirm that the protocols are compliant with all state
and federal regulations involving human subjects testing, ensuring proper care
throughout the recruitment of subjects and collection of data.

##  VI Conclusions

This research aims to (i) build a DGBL platform, (ii) incorporate into an ECE
course, and (iii) evaluate the pedagogical efficacy. The project had been
motivated from three problem statements, which corresponded to three action
plans. As reported in this paper, we have made the progress through A1, while
A2 and A3 are left clearly planned. To elaborate our progress in A1, we have
built a DGBL framework that is similar to a RPG where multiple players can
explore different maps with different levels of wireless connectivity. By
doing so, students are expected to learn how the connectivity affects the
performance of a wireless network and a blockchain system overlaid on the
network. In conclusion, the success of this research will cultivate students
that are equipped with skillsets to deal with a wide variety of problems
raised in the rapidly evolving ecosystems of blockchain and wireless
communications.

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