# Data-driven Discovery for Robust Optimization of Semiconductor Nanowire
Lasers

Stephen A Church  [<EMAIL_ADDRESS>Francesco Vitale  [
Aswani Gopakumar  Nikita Gagrani  [  Yunyan Zhang  [  Nian Jiang  [  Hark Hoe
Tan  Chennupati Jagadish  [  Huiyun Liu  [  Hannah Joyce  [  Carsten Ronning
[  Patrick Parkinson<EMAIL_ADDRESS>[

###### Abstract

Active wavelength-scale optoelectronic components are widely used in photonic
integrated circuitry, however coherent sources of light – namely optical
lasers – remain the most challenging component to integrate. Semiconductor
nanowire lasers represent a flexible class of light source where each nanowire
is both gain material and cavity; however, strong coupling between these
properties and the performance leads to inhomogeneity across the population.
While this has been studied and optimized for individual material systems, no
architecture-wide insight is available. Here, nine nanowire laser material
systems are studied and compared using 55,516 nanowire lasers to provide
statistically robust insight into performance. These results demonstrate that,
while it may be important to optimise internal quantum efficiency for certain
materials, cavity effects are always critical. Our study provides a roadmap to
optimize the performance of nanowire lasers made from any material: this can
be achieved by ensuring a narrow spread of lengths and end-facet
reflectivities.

###### keywords:

high-throughput, nanowire lasers, interferometry, photoluminescence

UoM] Department of Physics and Astronomy and The Photon Science Institute, The
University of Manchester, M13 9PL, United Kingdom Jena] Institute for Solid
State Physics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743
Jena, Germany ANU] Department of Electronic Materials Engineering, Research
School of Physics, The Australian National University, Canberra, ACT, 2601
Australia Zhejiang] College of Integrated Circuits, Zhejiang University,
Hangzhou, Zhejiang 311200, China Cambridge] Department of Engineering,
University of Cambridge, CB2 1PZ, United Kingdom ANU] Department of Electronic
Materials Engineering, Research School of Physics, The Australian National
University, Canberra, ACT, 2601 Australia UCL] Department of Electronic and
Electrical Engineering, University College London, WC1E 7JE, United Kingdom
Cambridge] Department of Engineering, University of Cambridge, CB2 1PZ, United
Kingdom Jena] Institute for Solid State Physics, Friedrich Schiller University
Jena, Max-Wien-Platz 1, 07743 Jena, Germany UoM] Department of Physics and
Astronomy and The Photon Science Institute, The University of Manchester, M13
9PL, United Kingdom

The miniaturisation of opto-electronic devices is an area of rapid development
across multiple research fields 1, 2, 3. In its simplest form this involves
the development of devices at the centi- and millimeter-scale, enabling
previously bulky apparatus to become light-weight and portable, facilitating
accurate field-based testing, with applications including quality control 4
and medical screening 5. Further miniaturisation, to the micron-scale, has
yielded significant advancements in commercial technology. This includes
micro-LEDs 6, which form the foundation of ultra-efficient, high-resolution
and wide colour-gamut display technologies 7, enabling commercial virtual and
augmented reality headsets 3.

Nanoscale coherent light sources are widely sought after as biological
probes8, 9, sensors, in quantum applications 10, 11 and most often as active
components for photonic integrated circuitry12, 13, 2, 14 that integrate
micron-scale light sources, waveguides and detectors at high densities to
perform light-based computing processes 15. A wide range of architectures have
been proposed as solutions, spanning off-chip coupling, flip-chip integration
and hetero-epitaxial growth16, 17, 18. However, repeatable, high-density and
high-yield laser sources are rare. Of particular concern is the strong
coupling between material quality, cavity design and performance, which mean
that small variations in defect density, surface passivation, hetero-junction
parameters and geometry lead to significant effects for performance6, 20, 21.

Nanoscale lasers based on semiconductor nanowires (NWs) have long been
proposed as coherent light sources that are well suited to integration22, 23,
24, 25, 26; these provide diverse emission properties, such as wavelength,
pulse duration and modal structure, arising from the wide choice of material
system, while being united in their fundamental operating principle of the
nanowire forming a monolithic cavity and gain material. These NW lasers (NWLs)
typically have widths of 100’s nm and lengths up to 10’s $\mu$m. High
refractive indices result in strong optical confinement, and the narrow NW
widths often lead to a deterministic relationship between cavity, material and
performance properties that necessitate optimization of each parameter 27. The
variety of material systems has led to a divergence in this optimization and
development, and to-date high quality systems have been demonstrated in
chalcogenides28, 29, nitrides30, 31, perovskites32, 33, metal oxides34, 35 and
III-Vs36, 37, 4. This range of systems provides significant advantages for
selecting lasing wavelength, for high-speed operation39 or providing specific
non-linear properties40, however it has led to a fragmentation in
characterization methods 41 resulting in a lack of robust inter-class
comparison. This is exacerbated by the differences between growth mechanisms
(for instance, selective-area growth42 versus vapour-liquid-solid43) and the
inclusion of plasmonic39 or dielectric-enhanced34 emission.

Tight control of the device fabrication is therefore required to minimise
variation in performance and to maximise the useful yield. This is a crucial
step towards commercialisation of these miniature technologies, with yield
requirements as high as, for example, $99.9999\text{\,}\mathrm{\char
37\relax}$ in the microLED industry 44. Whilst an increasing number of reports
now provide statistically robust intra-type results45, 36, 27, 46, comparison
between nanowire types is rare, causing two significant roadblocks to further
nanowire laser development: the lack of a common measurement methodology27 to
produce comparable data, and the resultant impossibility of obtaining globally
meaningful insight from specific studies.

In this work, we use the principles of experimental data-led discovery 47 to
generate an experimental understanding of nanowire laser (NWL) performance.
This involves studying nine different NWL designs with nine independent
automated experiments36, including bright field optical imaging, fluence-
dependent photoluminescence, time-correlated single photon counting (TCSPC)
and interferometry, with 55,516 NWLs investigated in total. The approach
enables the best-in-class NWLs to be identified, a statistically rigorous
comparison of the performance of each NWL type and the identification of
global trends and important factors that are independent of the NWL design.

Figure 1: An example of the measurements taken from one individual InP NW,
with numbers in the titles indicating the total number of NWs each measurement
was performed for. (a) Power dependent photoluminescence spectra showing the
emergence of a single lasing mode above a threshold fluence. (b) The light-in-
light-out curve for this NWL. The insets show the bright field and lasing
emission images. (c) TCSPC PL decays measured below lasing threshold at low
fluence and high fluence. (d) Interferogram of the lasing emission, with a
Gaussian envelope, used to extract the coherence length.

A summary of the measurements performed on one individual InP nanowire are
displayed in Figure 1. Power-dependent photoluminescence measurements exhibit
a broad spontaneous emission peak at all pumping fluences, along with a
narrow-band emission peak, above a threshold fluence, that is attributed to
stimulated emission. The threshold is identified by analysing the light-in-
light-out (LILO) curves of the excitation fluence vs the intensity of the
emission, an example of which is shown in Figure 1(b). These curves are
produced and processed using an established algorithm 36. In short, the
emission intensity increases approximately linearly above lasing threshold,
and a straight line was fit to this data and extrapolated to $y=0$ in order to
estimate a lasing threshold fluence. Using this approach, the threshold for
this NW was determined to be $178\pm 3.\text{\,}\mathrm{\SIUnitSymbolMicro
J}\text{\,}{\mathrm{cm}}^{-2}$.

TCSPC decays measured below the lasing threshold for the example NW are shown
in Figure 1(c). For this NW, the 1/e decay time was $0.17\text{\,}\mathrm{ns}$
at low fluence, increasing to $0.30\text{\,}\mathrm{ns}$ at higher fluences.
We attribute this fast decay to non-radiative recombination at point defects
in the InP crystal structure. This is in agreement with earlier studies, where
InP NWs, and SAG grown NWs, have shown low surface recombination velocities
48.

Finally, a time-gated interferogram of the lasing emission above threshold was
measured, shown in Figure 1(d), using an approach detailed in ref 36. A
modulation envelope can clearly be observed in the data. The laser coherence
length of the radiation was defined as the full width at half maximum (FWHM)
of this envelope, which was found to be $0.28\text{\,}\mathrm{mm}$ for this
NW. This coherence length is several orders of magnitude longer than the NW
length ($6\text{\,}\mathrm{\SIUnitSymbolMicro m}$). This is typical behaviour
for the strong waveguides that are formed by NWLs 49, and is comparable to
previous measurements on alternative materials 36. Using this result, the end-
facet reflectivity was calculated to be using a previously detailed approach
50. This reflectivity is enhanced beyond the simple Fresnel reflection
coefficient for this material ($30\text{\,}\mathrm{\char 37\relax}$) 51, which
is indicative of a high quality cavity 49.

Table 1: The nine types of nanowires investigated in this study. Bright field
optical images are shown for an example NW of each type, along with lasing
emission images of the same NWs, demonstrating that the majority of the lasing
emission is from the end facets. Emission imaging for GaN and ZnO was not
possible due to a lack of sensitivity of the imaging camera to UV light. The
lowest threshold NW has been identified for each NW type, and the light-in-
light-out curves for each are shown, along with the threshold fluence. The
heterostructure image has been adapted from ref 50.

A large, multidimensional dataset was generated by performing the measurements
in Figure 1 for NWs of different architectures, which are summarized in Table
1. This includes “bulk” selective-area-grown InP 3, vapour-liquid-solid grown
surface-passivated GaAs 4, Zn-doped GaAs 1, core-shell quantum well (QW)
heterostructures AlGaAs/GaAs 5 and
GaAsP/GaAs, which has 2 growth batches - 1 and - 2 55, 50. Also included are
NWs which demonstrate excitonic emission at room temperature due to large
exciton binding energies: CdS 8, GaN 57, and ZnO 10, 59. Table 1 shows an
examplary bright field optical image for each type of NWL. For comparison,
images of the spatial emission profile above lasing threshold for the same
wires are also shown in Table 1. In this regime, the majority of the light
couples out of the end facets of the NW Fabry-Perot cavity. Each end facet
acts as an independent, coherent, point source of light and interference
fringes between these two sources are observed in the far field 4.

Using this dataset, it is trivial to identify the best-in-type lasers by
assessing the lasing thresholds. The LILO curves for these champion NWLs are
shown in Table 1. The lowest observed threshold was $35\pm
1.\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$ from a
ZnO NWL. This is consistent with measurements using similar excitation
conditions on NWs of comparable size and geometry 60. However, this is two
orders of magnitude higher than the lowest-reported thresholds in the
literature 61, highlighting the sensitivity of this measurement to the
experimental conditions and NW size.

The GaAsP/GaAs - 1 NWLs also perform favourably, with a lowest threshold of
$51\pm 1.\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$,
which is similar to the best in the literature for this material 55, 50.
However, the alternative growth batch GaAsP/GaAs - 2, has a champion threshold
which is more than five times higher - emphasising the impact that tuned
growth conditions can have on performance. Despite this, it is interesting to
note that the best-in-class thresholds are of a similar order of magnitude
($100\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$) for
most types. This implies that, for the best-performing NWLs, the functional
performance in the pulsed excitation regime may be limited by the same
effects, independent of the design and material used. This is possibly because
the excitation and lasing occurs on timescales faster than many material-
dependent carrier recombination processes 50.

Figure 2: Intra-type statistics. (a) The lasing threshold fluence (box plot)
with lasing yield (bar chart) for each NWL type. (b) The peak wavelength of
the fundamental lasing mode at threshold. The lasing spectra of selected NWLs
are also shown. (c) Cavity length for all NWs measured from bright field
imaging, accurate to $\approx$$0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$. (d)
The carrier recombination lifetime measured at low fluence, the coloured
background indicate dominated radiative (GaAsP/GaAs - 1) and non-radiative
decays (white background), and those which are resolution limited (green
background). (e) The end-facet reflectivity calculated from the coherence
length, the dashed lines are the calculated Fresnel reflection coefficients
for a planar surface, assuming the refractive index of InP, GaAs and CdS 51.
Reflectivity values were not obtained for GaN or ZnO NWLs due to a lack of
sensitivity to UV emission for this technique.

The data-led approach enables our study to extend from simple best-in-class
measurements (Figure 1), through providing robust intra-class measurements of
single NWL types (Table 1), to understanding global (inter-class) NWL
architecture effects. The lasing threshold fluence and the lasing yield (the
percentage of NWs with a lasing threshold below their damage threshold) are
displayed in Figure 2(a). The lowest median threshold is seen in ZnO, with
$65\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$.
Furthermore, the GaAsP/GaAs - 1 NWLs, despite having one of the lowest
threshold champion devices, demonstrate a large variation in the threshold,
such that the median is $163\text{\,}\mathrm{\SIUnitSymbolMicro
J}\text{\,}{\mathrm{cm}}^{-2}$, and close to that of the other NWLs. In
contrast, the lasing yield for GaAsP/GaAs - 1 NWLs is one of the highest
available ($86.5\text{\,}\mathrm{\char 37\relax}$), and is significantly
higher than the yield of ZnO NWLs ($31\text{\,}\mathrm{\char 37\relax}$).
Clearly the interplay between yield and threshold is not straightforward.
Reporting best-in-class values for NWLs is at best ambiguous, and at worst
misleading for inter-class comparison.

The largest median thresholds and threshold variation are seen in the
AlGaAs/GaAs and GaAsP/GaAs - 2 core/shell QW NWLs, which have thresholds
between 1000 and $2000\text{\,}\mathrm{\SIUnitSymbolMicro
J}\text{\,}{\mathrm{cm}}^{-2}$. These NWs also have the lowest yields, just 2
and $3\text{\,}\mathrm{\char 37\relax}$; this is likely because the lasing
thresholds are close to the damage threshold of the NWs. Careful NWL
heterostructure design is essential to ensure that the QWs overlap well with
the transverse lasing modes, and this must be maintained across a population
through growth optimisation.

The distribution of the lasing wavelength for each class is shown in Figure
2(b). These wavelengths depend upon both the laser gain spectrum and the
cavity 4. The wavelength variation in each class can be as high as
$100\text{\,}\mathrm{nm}$: as a result, the full NW population has continuous
wavelength coverage across the spectral window between 700 and
$880\text{\,}\mathrm{nm}$. While this variability presents the most
significant obstacle to scale-up, this does provides a means of effectively
tuning the wavelength by selecting a NWL with the desired properties62. To
demonstrate this coverage, the lasing spectra for 12 NWLs are shown in Figure
2(b); these NWLs have been chosen to change the lasing wavelength by
$20\text{\,}\mathrm{nm}$ across the 700 nm-880 nm range, although it is
possible to select NWLs based on wavelength with nm-level precision, due to
the size of the NW population. This type of data-driven screening is useful as
a way to target ideal devices for transfer printing into photonic integrated
circuits 46.

The distribution of NW lengths are shown in Figure 2(c). The lengths vary
between $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which is the resolution of
the optical imaging, and $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$. These
distributions offer a simple assessment of the uniformity of the growth
dynamics and the NWL transfer process 63. In this case, the InP NWs stand out
as being the most uniform, with an interquartile range (IQR) of
$9\text{\,}\mathrm{\char 37\relax}$; as the only selective-area grown
nanowires, this uniformity is a demonstration of the advantage of catalyst-
free growth for geometrical homogeneity. The GaAsP/GaAs - 1 length
distribution is also distinctive, as this has the largest median length of
$16.4\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which is more than
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ longer than the other
heterostructure NW types. This is a strong indication of the importance of the
NW length on the performance: Figure 2(a) shows that these NWs also have an
order of magnitude lower threshold than the other heterostructures, including
those of the same material, which is due to the larger volume of gain material
for longer NWs 6.

Figure 2(d) shows the distributions for the below-threshold photoluminescence
lifetime measured from TCSPC decays. This metric is intrinsic to each material
system, and is a combination of the radiative and non-radiative recombination
rates. The InP, GaAs, AlGaAs/GaAs, GaAsP/GaAs - 2, CdS, GaN and ZnO NWs all
exhibit lifetimes that are short when compared with radiative lifetimes of
comparable materials 64, 65, 66, 67, 68, 69, with median values between 100
and $640\text{\,}\mathrm{ps}$, and are therefore dominated by non-radiative
recombination effects. However, the impact of the surface is likely to be
reduced for these samples: this is evidenced by low surface recombination
velocities for InP NWs 48, the passivation of the surface for the GaAs,
AlGaAs/GaAs and GaAsP/GaAs NWs and comparable measurements for layers of CdS,
GaN and ZnO 70, 71, 72. Each class shows pumping fluence-dependent TCSPC
measurements similar to Figure 1(c), so we associate this lifetime with non-
radiative recombination of point defects in the NWs. The lifetime therefore
provides a proxy of the material quality: a higher defect density will shorten
the recombination lifetime. The Zn-doped GaAs NWs show the fastest mean
lifetime of $57\text{\,}\mathrm{ps}$, however this measurement is limited by
the time resolution, and is due to rapid recombination, with a previously
measured lifetime of 3-$6\text{\,}\mathrm{ps}$ 73, 1.

In contrast, GaAsP/GaAs - 1 NWLs show the longest median recombination
lifetime of $1\text{\,}\mathrm{ns}$. This NWL batch has been previously
studied 36, where it was established that the recombination efficiency is
around $39\text{\,}\mathrm{\char 37\relax}$, meaning that the rates of non-
radiative and radiative recombination are comparable. The median radiative
lifetime is therefore $2.5\text{\,}\mathrm{ns}$, and the median non-radiative
lifetime is $1.6\text{\,}\mathrm{ns}$. This suggests that the material quality
of this sample is improved, in particular in comparison to GaAsP/GaAs - 2,
such that the non-radiative recombination rate has been reduced by around an
order of magnitude.

The end-facet reflectivity was calculated from measurements of the coherence
length50 as shown in Figure 1(d), and the distributions are shown in Figure
2(e). The vast majority of NWs have reflectivities that are enhanced above the
Fresnel reflection factors for planar surfaces. This is consistent with
previous measurements of a single NW class 50, 36 and experimentally verifies
the theoretical predictions that have underpinned the use of the NW
architecture for two decades 49. The InP, GaAs, GaAsP/GaAs - 1 and CdS NWs
show low median reflectivities around 0.6 and IQRs up to 0.31. This large
degree of variation may be associated with differences in NW width - and thus
changes in the waveguiding properties 49: irregular morphology at the end
facets, either due to the NW transfer procedure 63, or from an abundance of
lattice defects in this region 74, may also play a role. The other NWs,
Zn:GaAs, AlGaAs/GaAs and GaAsP/GaAs - 2, have high median reflectivities
between 0.89 and 0.91 and IQRs up to 0.08. While statistically significant,
these findings are likely a result of selection bias in the measurements due
to the low yield of these NWLs. Due to the nature of the measurement,
reflectivities can only be determined for lasing NWs: thus, high material
quality NWLs can operate with poor cavities, while low material quality (poor
IQE) NWLs require a high quality cavity to show lasing below their damage
threshold.

Whilst analysing each parameter distribution in isolation can provide useful
information regarding inhomogeneity in each type of NW, a key benefit of the
holistic high-throughput approach is the ability to directly compare the
distributions of different parameters for the same NWLs and isolate
correlations to investigate physical phenomena. In particular, the parameters
that are most important in controlling the lasing threshold can be determined.
This is facilitated by the large population sizes in this study: for example,
if a correlative analysis is attempted in a small data study, with
approximately 100 NWs, an important correlation between two parameters will be
obscured by the significant variation in the other parameters, as suggested by
the boxplots in Figure 2.

To investigate the most important factors that influence the lasing threshold,
the datasets were normalised by subtracting the median and dividing by the
standard deviation of each distribution for each NW type. This data was then
grouped into 3 classes, as defined by Table 1: excitonic, “bulk” and
heterostructure. The linear correlation parameters between the threshold and
other key parameters were calculated for each group. This includes material
(from PL and lifetime measurements), cavity (dimensions and reflectivity) and
performance (lasing wavelength) properties for each group, shown in Fig. 3(a).
This provides an at-a-glance means of assessing the performance, averaging
over any inter-type variation in NW growths, and enables global trends to be
observed that are related to the underlying physics and performance of NWLs.

These results elucidate the importance of the laser cavity on all classes of
NWLs. In all cases, the NW length has a significant negative correlation with
threshold, which confirms the conclusions from Figure 2 in a statistically
rigorous manner. This dictates a clear route towards optimising the threshold
of all types of NWLs: minimise the length variation between each NW. A similar
effect is also observed for increasing the width of “bulk” and excitonic NWLs,
which is compounded by an additional increase in the optical confinement
factor. However, no width correlation is observed for heterostructure samples:
this suggests that the optical gain is decoupled from the NW width and
confinement factor, instead depending on the QW width and QW-lasing mode
overlap 5.

The strength of the length correlation reduces from excitonic (r = -0.17), to
“bulk” (r = -0.11) and to heterostructure (r = -0.05) lasers. This suggests
that the length has different degree of impact on the threshold for different
NW classes. A possible explanation for this is due to differences in
distributed losses between the NW classes, which would partially counter-
balance the increased gain. For example, for heterostructure NWLs, the
overgrowth of the shells can lead to distortions in the NW cross-section shape
and consequently enhance the optical losses 74.

The cavity reflectivity also plays a crucial role in the performance, which
shows a negative correlation with threshold for “bulk” and heterostructure
lasers, indicating that a higher reflectivity reduces the optical losses and,
thus, the threshold. No trend is observed for the excitonic NWs, although this
may be due to a small sample size (90 wires in total). Another route to reduce
variation in NWL performance is therefore to optimise the end facets, either
by optimising the NW transfer 63 or standardising the NW width during growth
49.

In contrast, the material properties of the NWLs do not show consistent
correlations with threshold. The PL FWHM, an often-used measure of the
inhomogeneity in the material 6, has no statistically significant impact on
the threshold. The carrier lifetime also shows no correlation for “bulk” NWLs,
which suggests that, despite the variation in lifetime shown in Fig. 2(d),
there is little significant change in the quantum efficiency of these classes
across their populations. In contrast, the heterostructure and excitonic
lasers show a negative correlation between lifetime and threshold. This
correlation has been discussed in detail previously 36, and is attributed to a
variation in the non-radiative recombination rate (and quantum efficiency)
which is related to a change in defect density within the gain medium. For
these samples, there remains scope to improve the lasing performance by
improving the IQE of the active layer by optimising the growth conditions to
reduce the defect density.

The PL peak energy in “bulk” and heterostructure NWs show a positive
correlation with threshold. The mechanism for the energy variation is related
to composition, strain or heterostructure fluctuations, depending on the
sample, and this also leads to shifts in the laser gain spectrum. These
correlations are a consequence of the strong negative correlations between
lasing wavelength and threshold which have been previously attributed to
reabsorption 1 and band-filling effects 36. Intertestingly, the excitonic
devices show an opposite negative correlation between PL peak energy and
threshold. This is consistent with previous studies that demonstrate the
importance of strong exciton binding to achieve lasing 75: NWs with more
strongly bound excitons are more likely to have a lower lasing threshold. This
is despite the lasing action being sustained by an electron-hole plasma which
forms at high fluences 76.

The wavelength correlation for each NW class shows the same effects to a
different degree. The excitonic devices, shown in Figure 3(b), have minimal
reabsorption since the peak of the gain spectrum lies in the material bandgap,
the 3D density of states and excitonic recombination also reduces the impact
of band-filling and so the correlation between wavelength and threshold is the
lowest of the three classes. The “bulk” class (Fig. 3(c)) has more
reabsorption, and so the correlation is increased. Finally, the
heterostructure NWs (Fig. 3(d)) exhibit reabsorption into core and cap layers,
and will exhibit more band-filling due to a reduced 2D density of states 36
and thus have the highest observed correlation.

Figure 3: A correlative analysis of the lasing threshold pumping fluence. (a)
Statistically significant (with a p-value $<$0.05) Pearson’s linear
correlation coefficients between normalised NW parameters and the lasing
pumping threshold, grouped into three NW classes. White indicates parameters
where $p>0.05$ and so there is no statistically significant correlation,
whereas red and blue are significant positive and negative correlations
respectively. Yellow is representative of a strong negative correlation with
$r<-0.2$. GaAsP/GaAs - 2 and AlGaAs/GaAs NWs are removed from the reflectivity
analysis due to selection bias in the distributions. GaN and ZnO NWs are also
removed from the reflectivity analysis due to a lack of sensitivity to UV
light. Zn:GaAs NWs are removed from the lifetime analysis due to experimental
resolution issues. Normalised 2D histograms are also shown, which display the
relationship between normalised lasing wavelength and threshold for each
class: (b) excitonic, (c) “bulk” and (d) heterostructure.

In summary, we have demonstrated a data-driven experimental approach to study
large numbers of micron-scale opto-electronic devices. We have applied this to
investigate the properties of 55,516 individual NWLs with nine different
designs and have extracted parameters that describe how the gain medium,
lasing cavity and performance vary across the population. We have shown how
the approach can be used to effectively screen for the best-in-class devices
and we have quantified the statistical distribution of each parameter and used
this to compare the properties of different NWL types in a statistically
robust manner. Through a correlative analysis, it was determined that the
properties of the laser cavity are consistently a driving factor in the
performance of NWLs and this elucidates a route towards achieving homogeneous
performance across a population of any type of NWLs: by optimising the NW
length and end-facet reflectivity.

Supporting information is available for this paper, which includes the growth
details for each type of nanowire. This can be found at DOI: ????.

This work was funded by UKRI under grants MR/T021519/1, EP/V036343/1 and
EP/W002302/1, by the Deutsche Forschungsgemeinschaft within the frame of the
collaborative research center CRC 1375 (project C5), by the Australian
Research Council, the Australian National Fabrication Facility ACT node, as
well as China special Grant (134000-E62201ZJ); Zhejiang Provincial Natural
Science Foundation of China (Z24F040009), Zhejiang University Education
Foundation Qizhen Scholar Foundation (K20240015), and CMOS Special Program of
Zhejiang University (04010000-K2A033208). Research data supporting this
publication will be made available at DOI: (DOI to be provide in due course),
and the code to perform the analysis will be made available at DOI: (DOI to be
provide in due course), and on github: (URL to be provide in due course).

CRediT author statement: Stephen Church: Formal analysis, Investigation,
Methodology, Software, Visualisation, Writing - original draft. Francesco
Vitale, Aswani Gopakumar, Nikita Gagrani,Yunyan Zhang, Nian Jiang, Hark Hoe
Tan, Chennupati Jagadish, Huiyun Liu, Hannah Joyce and Carsten Ronning:
Resources, Writing - review and editing. Patrick Parkinson: Conceptualization,
Data curation, Funding acquisition, Methodology, Software, Supervision,
Writing - review and editing.

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##  1 Supporting Information

The nanowires studied in this work were grown using various approaches that
are summarized in this document. For high-throughput investigation, each
sample of nanowires was suspended in IPA using ultrasonication for 5s, and
transferred to quartz substrates using drop-casting 1. These nanowires were
then studied using a number of high-throughput experiments. The details of
these experiments can be found in a previous publication 2.

##  2 Nanowire growth details

###  2.1 InP

InP nanowires were grown using selective area epitaxy (SAE) with metal-organic
chemical vapour deposition (MOCVD). A 150 nm thick SiO2 mask was deposited on
InP (111) wafers, followed by electron beam lithography and dry etching. This
produced a mask with dimensions of 100 ×
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which were placed in a close
coupled showerhead MOCVD reactor, where trimethyl (TM) Indium and phosphine
(PH3) were used as precursors with molar flow rates of 6 × 10-6 and 4.91 ×
10-4 $\mathrm{mol}\text{\,}{\mathrm{min}}^{-1}$, respectively. Nanowires were
grown at $730\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and base pressure of 100
mbar with H2 as the carrier gas at a total flow rate of
$14.5\text{\,}\mathrm{L}\text{\,}{\mathrm{min}}^{-1}$. More details can be
found in reference 3.

###  2.2 GaAs

GaAs nanowires were grown on (111) GaAs substrates using a vapor-liquid-solid
(VLS) approach via MOCVD in a similar manner to those in ref 4. Au particles
were used to catalyse the growth, which was achieved using TMGa, TMAl and
arsine (AsH3) precursors for Ga, Al and As respectively.

The growth process involved a two-temperature procedure for the GaAs core.
Initially, a 1- minute nucleation step growth at
$450\text{\,}\mathrm{\SIUnitSymbolCelsius}$, followed by 45 minutes of growth
at $375\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Subsequently, the temperature
was raised to $750\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in an AsH3
atmosphere, and an AlGaAs shell was grown for 0.5 minutes with a TMAl/(TMGa +
TMAl) ratio of 0.5. Finally, a GaAs cap layer was deposited for 1.5 minutes at
$750\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to shield the AlGaAs shell from
oxidation. More details can be found in reference 4.

###  2.3 ZnGaAs

Zn doped GaAs nanowires were grown using a similar Au-catalysed VLS growth
approach to the GaAs wires, on (111) GaAs substrates. In this case, the doping
was achieved using diethylzinc (DEZn) as a precursor. A capping layer was not
included: more information on these wires can be found in reference 1.

###  2.4 AlGaAs/GaAs

AlGaAs/GaAs quantum well nanowires were produced in a similar manner to the
GaAs wires: this included a GaAs core which grown using a Au-catalyst mediated
two-temperature VLS approach, and an AlGaAs shell layer. This was followed by
8 GaAs/AlGaAs quantum well and barrier layers using an established recipe
provided in reference 5. These wires were also used in a previous optical
study 6.

###  2.5 GaAsP/GaAs

GaAsP/GaAs quantum well nanowires were grown using self-catalysed VLS growth
in a molecular beam epitaxy (MBE) approach onto p-type (111) Si substrates. A
GaAsP nanowire core was grown was grown at a temperature of
$640\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for 90 minutes. The remaining Ga
droplet was then consumed by saturating the growth with As and P flux. 3
GaAs/GaAsP quantum well/barrier shell layers were grown at
$550\text{\,}\mathrm{\SIUnitSymbolCelsius}$, followed by outer shell layers of
AlGaAsP and GaAsP. Full details of the growth can be found in reference 7.

###  2.6 CdS

CdS nanowires were grown using the VLS technique via CVD inside a horizontal-
tube vacuum furnace. CdS powder was sublimated at temperatures of
$800\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and the vapor was transported by
Ar carrier gas towards the growth substrates, which were kept at lower
temperatures. The growth substrates (001-Si) were coated with a 10-15 nm Au
layer, acting as a catalyst for the growth of CdS NWs, which was carried out
for 30 minutes at temperatures between 720 and
$600\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Further details on the growth of
these CdS NWs can be found in reference 8.

###  2.7 GaN

GaN nanowires were grown using a self-catalysed approach via MOCVD on c-plane
sapphire substrates. The substrates were annealed in H2 at a temperature of
$1060\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and then nitrided at 1080 using
NH3 gas. TMGa and NH3 were used as precursor gases for a GaN nucleation layer,
and nanowire growth was performed at a temperature of
$750\text{\,}\mathrm{\SIUnitSymbolCelsius}$, using silane (SiH4) as an
additional precursor to prevent lateral growth. Full growth details can be
found in reference 9.

###  2.8 ZnO

ZnO nanowires were grown via VLS in a similar manner to the CdS samples. In
this case, a mixture of ZnO and graphite powder with molar ratio 1:1 was used
as the precursor and was sublimated at a temperature of
$1050\text{\,}\mathrm{\SIUnitSymbolCelsius}$. The vapor was transported using
Ar + O2 as the carrier gas and the growth occured at temperatures between 960
and $1150\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Further details on the
growth of ZnO NWs are given in reference 10.

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