###### Abstract

Hexagonal boron nitride is rapidly gaining interest as a platform for photonic
quantum technologies, due to its two-dimensional nature and its ability to
host defects deep within its large band gap that may act as room-temperature
single-photon emitters. In this review paper we provide an overview of (1) the
structure, properties, growth and transfer of hexagonal boron nitride; (2) the
creation and assignment of colour centres in hexagonal boron nitride for
applications in photonic quantum technologies; and (3) heterostructure devices
for the electrical tuning and charge control of colour centres that form the
basis for photonic quantum technology devices. The aim of this review is to
provide readers a summary of progress in both defect engineering and device
fabrication in hexagonal boron nitride based photonic quantum technologies.

###### keywords:

hexagonal boron nitride; quantum photonics; single-photon emitters; spin
qubits; electron paramagnetic resonance; optically detected magnetic
resonance; density functional theory; chemical vapour deposition; molecular
beam epitaxy; van der Waals epitaxy.

1 1 0 https://doi.org/ Hexagonal boron nitride based photonic quantum
technologies Hexagonal boron nitride based photonic quantum technologies
Madhava Krishna Prasad 1, Mike P. C. Taverne2,3, Chung-Che Huang4,*, Jonathan
D. Mar 1,* and Ying-Lung Daniel Ho 2,3,* Madhava Krishna Prasad, Mike P. C.
Taverne, Chung-Che Huang, Jonathan D. Mar and Ying-Lung Daniel Ho Krishna
Prasad, M.; Taverne, M. P. C.; Huang, C.-C.; Mar, J. D.; Ho, Y. L. D.
Correspondence<EMAIL_ADDRESS>(C.-C.H<EMAIL_ADDRESS>(J.D.M<EMAIL_ADDRESS>(Y.-L.D.H.)

##  1 Introduction

Since the advent of graphene, interest in other two-dimensional materials has
dramatically increased. Hexagonal boron nitride (hBN) is a graphene-like two-
dimensional material, where monolayer hBN consists of a single sheet of boron
and nitrogen atoms arranged in a honeycomb structure. It has a large band gap
and shows far ultraviolet light emission. Recently, defects in hBN crystals
have been identified as colour centres and some of these defects are also spin
active, making them suitable as single-photon emitters (SPEs) and spin qubits.
SPEs are essential building-blocks for the realisation of a wide range of
quantum technologies, including quantum computation, quantum communications
and quantum metrology.

In this review paper, we present the unique and advantageous properties of hBN
SPEs which make them ideal candidates for achieving scalable photonic quantum
technologies. We begin by introducing the general material (electronic and
structural) properties of hBN, followed by the methods used for the growth and
transfer of hBN with varying degrees of quality and crystallinity. We then
provide a brief overview of the properties of hBN SPEs when compared to other
candidate solid-state SPEs. We then proceed to describe the methods of
controlling colour centre formation in hBN and theoretical calculations that
have been conducted and correlated to experimental observations to identify
their nature. Furthermore, we explore graphene/hBN based devices, which are
used to tune the emission energies of hBN SPEs and control their charge
states. Finally, we discuss the challenges and future perspectives on the
horizon for hBN based photonic quantum technologies.

###  1.1 Structure of hBN

hBN consists of alternate boron and nitrogen atoms sp2-bonded together in a
honeycomb structure Wang et al. (2017); Bhimanapati et al. (2016). Multilayer
hBN is formed by stacking layers of monolayer hBN on top of each other, held
together by van der Waals forces. Due to weak interlayer forces, hBN is often
used as a lubricant Kimura et al. (1999). The lattice constant of hBN is 2.50
Å (Fig. 1(a)) and the equilibrium interlayer spacing is 3.35 Å. Theoretical
investigations using density functional theory (DFT) predicted that the
preferred stacking is AA′ Constantinescu et al. (2013). This comprises of
switching the position of boron and nitrogen atoms in each layer, resulting in
a stack where each boron (nitrogen) atom is located in-between a nitrogen
(boron) atom in the adjacent layers. The preferred stacking order was
confirmed to be AA′ experimentally by transmission electron microscopy (Fig.
1(c)) Chen et al. (2021); Ji et al. (2017); Alem et al. (2009).

(a)

(b)

(c)

(d)

Figure 1: a) Schematic of hBN with the experimental lattice parameter of 2.50
Å. b) Evolution of the Raman spectrum of hBN from monolayer to multilayer hBN.
c) HRTEM image of hBN of different thicknesses. By measuring the intensity
profile across linear path in the image, it is possible to determine the
stacking. d) Experimental valence-band structures of monolayer hBN films.
Reprinted Fig. 1(b) from ref. Gorbachev et al.,  with permission from John
Wiley and Sons © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. Reprinted
Fig. 1(c) with permission from ref. Alem et al., 2009, Copyright 2009 by the
American Physical Society. Reprinted Fig. 1(d) from ref. Nagashima et al.,
1996, Copyright 1996, with permission from Elsevier.

###  1.2 Electronic and vibrational properties of hBN

There had been a longstanding debate on the nature of the band gap of hBN,
with most early DFT calculations predicting an indirect band gap Ooi et al.
(2005); Blase et al. (1995); Xu and Ching (1991); Gao (2012); Topsakal et al.
(2009) and some calculations suggesting a direct band gap Topsakal et al.
(2009); Paleari et al. (2018). The latter was in line with early experiments
implying a direct band gap Zunger et al. (1976); Evans et al. (2008); Watanabe
et al. (2004). It has now been revealed that hBN exhibits both behaviours
depending on its thickness. Monolayer hBN is a direct band gap insulator with
a band gap of $\sim$ 6 eV, as shown by deep ultraviolet (DUV) reflectance and
photoluminescence measurements in correspondence with some first principles
calculations Elias et al. (2019); Topsakal et al. (2009); Wickramaratne et al.
(2018). However, electron energy loss spectroscopy and two-photon spectroscopy
allowed the identification of the lowest energy indirect exciton to have an
energy of 5.955 eV Cassabois et al. (2016); Schuster et al. (2018), showing an
indirect band gap with the size of the band gap being consistent with DFT
calculations of bulk hBN Blase et al. (1995); Wickramaratne et al. (2018). The
direct to indirect transition for hBN follows the behaviour of another class
of two-dimensional materials called transition metal dichalcogenides (TMDs)
Mak et al. (2010) and occurs immediately from single layer to bilayer hBN
Wickramaratne et al. (2018). Angle-resolved photoemission spectroscopy
(ARPES), angle-resolved ultraviolet photoemission spectroscopy (ARUPS), angle-
resolved secondary electron emission spectroscopy (ARSEES) and X-ray
photoelectron spectroscopy (XPS) have been employed to accurately and directly
visualise the valence band structure of hBN, validating DFT calculations of
the band structure, such as by confirming the location of the valence band
maximum (VBM) to be at the K-point (Fig. 1(d)) Henck et al. (2017); Nagashima
et al. (1995).

In terms of vibrational modes, hBN exibits two degenerate Raman active
$E_{2g}$ modes and an infrared (IR) active $A_{2u}$ mode Geick et al. (1966);
Serrano et al. (2007). The IR mode for hBN occurs at 783 cm-1 and the Raman
mode for bulk hBN has been observed at 1366 cm-1 (1370 cm-1 for monolayer)
Gorbachev et al. . The intensity of the Raman peak increases with the number
of layers and the peak position is usually red shifted by $\sim$ 4 cm-1 (as
shown in Fig. 1(b)) Gorbachev et al. . This can be used to estimate the
thickness of an hBN film.

###  1.3 Growth and transfer of hBN

Highly crystalline and low defect density hBN can be grown at high pressure
and high temperature using a barium boron nitride solvent (Ba-B-N) or using a
Ni-Mo solvent at room temperature and pressure Taniguchi and Watanabe (2007);
Kubota et al. (2007). These high quality crystals can then be exfoliated onto
desired substrates to obtain hBN of various of thicknesses (Fig. 3(a)). The
most common exfoliation processes are mechanical exfoliation (Scotch-tape
method) and solvent assisted liquid phase exfoliation Wang et al. (2016).
Liquid phase exfoliation can be performed by dispersing the flakes in an
organic solvent followed by sonication or by dispersing in an aqueous medium,
allowing for ion interacalation, followed by centrifugation Gonzalez Ortiz et
al. (2018); Rafiei-Sarmazdeh et al. (2016); Khan et al. (2013).

While hBN flakes in powder form obtained from bulk hBN by exfoliation are
pristine, they are usually too small for high throughput device fabrication.
Furthermore, as the growth and transfer process results in a wide range of
flake thicknesses, there is little control in the vertical direction within
the device stack. hBN grown from chemical vapour deposition (CVD) offers an
alternative to this and allows devices to be fabricated on wafer scale Chen et
al. (2020).

CVD growth of hBN is often performed on a Cu or Ni catalyst using ammonia
borane or borazine precursors Shi et al. (2010); Kim et al. (2012); Song et
al. (2010). By controlling parameters such as the catalyst, deposition
temperature and pressure, the thickness of hBN can be controlled to a
monolayer, as shown in Fig. 3(c) Shi et al. (2010); Kim et al. (2015, 2012).
For example, by moving from atmospheric pressure CVD (APCVD) to low pressure
CVD (LPCVD), the number of layers of hBN grown was able to be reduced from a
few layers to monolayer Shi et al. (2010); Kim et al. (2012). LPCVD can also
be used to grow multilayer hBN, with a higher crystallinity than APCVD, by
slowing the cooling rate Kim et al. (2015). It was found that the electronic
properties of hBN is largely independent of the metallic substrate used as a
catalyst for growth Nagashima et al. (1995). Due to the small mismatch in the
lattice parameters of Ni and bulk hBN, it offers an advantage in hBN growth
compared to other catalysts such as Cu Nagashima et al. (1995, 1996).
Homoepitaxy offers a promising way to synthesise hBN by overcoming the
constraint of finding a substrate with a similar lattice parameter Binder et
al. (2024). Furthermore, controlling the surface morphology of the catalyst to
achieve a greater flatness and grain size leads to the growth of hBN with
fewer impurities and allotropes, such as cubic boron nitride (cBN) Lee et al.
(2012). Once large areas of hBN of a desired thickness have been grown on a
catalyst, it can be transferred to the desired substrate Reina et al. (2009);
Fukamachi et al. (2023).

A common method of transfer of 2D materials, such as graphene and hBN, from
the catalyst to the desired substrate is by a wet transfer process. This is
outlined in Fig. 2. Briefly, this involves spin coating a supporting polymer
layer on top of hBN, removing hBN grown on the underside of the catalyst using
a plasma, and exposing the catalyst to an etchant solution. Once the catalyst
has been etched, the floating polymer/hBN film is transferred to a bath of
deionised water a couple of times to remove any residual etchant and is
”fished out” onto the desired substrate and dried. The polymer layer is then
removed by a suitable solvent to leave behind a sheet of hBNScheuer et al.
(2021). While this is a typical process, there are a myriad of other methods
that currently exist to address various issues of the transfer process to
varying degrees of success Fukamachi et al. (2023); Wang et al. (2019); Zhang
et al. (2016).

Figure 2: A typical wet transfer process for hBN from the catalyst to the
desired substrate. Reprinted from Scheuer et al. (2021).

A drawback of CVD hBN is that it usually results in a higher defect density
and thus a poorer quality hBN when compared to hBN flakes obtained via
exfoliation. However, both of these techniques usually involve a polymer
support layer which is difficult to completely remove after transfer,
resulting in contamination. A possible method of removing the polymer post-
transfer is by heating the transferred films in an oxygen environment beyond
the decomposition temperature of the polymer Garcia et al. (2012); Stewart et
al. (2021).

To avoid the issues of transfer, epitaxial growth of hBN directly on the
desired substrate has gained significant interest. For devices that require
encapsulating graphene with hBN, van der Waals epitaxy (vdW-E) allows the
synthesis of hBN directly onto graphene substrates Song et al. (2014); Liu et
al. (2011). Interestingly, if the hBN layer is sufficiently thick and grown on
a suitable substrate, a polymer support may not be needed for transfer as the
film self-delaminates from the catalyst and is not torn by the surface tension
of the water. Recently, continuous and thick films have been grown on sapphire
using metal-oxide vapour phase epitaxy (MOVPE) (Fig. 3(b)) Li et al. (2016),
with some being 1.295 µm thick Zhu et al. (2023); Li et al. (2016), allowing
for self-delamination to be used as an effective means of polymer-free
transfer Chugh et al. (2018).

(a)

(b)

(c)

Figure 3: a) Two images of hBN flakes grown at room temperature and pressure
with a Ni-Mo solvent. (A) is a differential interference microscopy image and
(B) is a 215-nm band cathodoluminescence image. b) hBN films of various
thicknesses grown on a sapphire substrate by MOVPE. c) AFM image of monolayer
hBN grains grown on a Cu catalyst. The step height of 0.420 nm across the line
profile confirms that the hBN film is monolayer. An SEM image of a continuous
monolayer is also shown, with the yellow arrow indicating a wrinkle. Fig. 3(a)
from Kubota et al. (2007). Reprinted with permission from AAAS. Fig. 3(b) was
adapted with permission from Li et al. (2016). Copyright 2016 American
Chemical Society. Fig. 3(c) was adapted with permission from Kim et al.
(2012). Copyright 2011 American Chemical Society.

###  1.4 Single-photon emitters in the solid state

It is common to find point defects formed in hBN during the growth process.
Point defects include vacancies, antisites, impurities and their combinations.
Some of these lead to topological defects, such as Stone-Wales defects. In
semiconductors and insulators, these states lead to localised states in the
band gap. If a point defect leads to an occupied and unoccupied localised
state in the band gap, they form a two-level system which may form the basis
for a SPE.

Before delving into SPEs in hBN, it will be useful to have an overview and
comparison of the wide variety of solid-state SPEs studied so far. The
mechanism by which photons are emitted depends on the type of material. In
quantum dots (QDs), such as indium arsenide (InAs) and gallium nitride (GaN),
and transition metal dichalcogenides (TMDs), the mode of light emission is
through recombination of excitons. In both QDs and TMDs, the source of
emission is through an exciton recombination. In QDs, the energy associated
with this recombination is associated with the size of the QD, whereas in TMDs
the single-photon emission is the result of localised excitons, potentially
due to defects in the crystal - although defects in QDs can also lead to
localised excitons and single photon emission Musiał et al. (2020); Koperski
et al. (2015). In wide band gap semiconductors, such as diamond and silicon
carbide (SiC), the source of emission is due to point defects in the crystal
leading to localised states deep within the band gap. The large energy
difference between the defect states involved in the transition allows these
sources to be active at room temperature.

The quality of a SPE is primarily determined by the purity of its single-
photon emission. This is given by the second-order correlation function,
$g^{(2)}$, obtained by Hanbury Brown and Twiss (HBT) interferometry. For a
SPE, $0\leq g^{(2)}\leq 0.5$, where $g^{(2)}=0$ for an ideal SPE. Furthermore,
as some quantum cryptography protocols require two photons to be entangled,
single photons must be indistinguishable. This not only requires
$g^{(2)}<<0.5$ but also a narrow zero-phonon line (ZPL) with most of the
emission being in the ZPL. The latter is represented by the Debye-Waller (DW)
factor, which is the proportion of the total emission in the ZPL. The DW
factor, $W$, is related to the Huang-Rhys (HR) factor, $S$, by $W=e^{-S}$. A
low phonon coupling along with a narrow ZPL is highly desirable for large-
scale fabrication of SPE devices. Table 1 summarises the wide range of solid-
state SPEs studied so far and Fig. 4 and 5 shows representative optical
images, photoluminescence (PL) maps and spectra of these emitters.

###  1.5 Single-photon emitters in hBN

hBN being a large band gap insulator, like SiC and diamond, can possess defect
states deep within its large band gap, leading to room-temperature SPEs.
Furthermore, the two-dimensional nature of monolayer hBN means that the
emitted light undergoes no total internal reflection before reaching the
detector and that the sources can be placed in nanometer proximity to other
photonic devices (however, note that some degree of total internal reflection
will be present in the case of few-layer hBN). These factors lead to a high
photon-extraction efficiency, an advantage over traditional single-photon
sources such as InAs QDs and diamond NV centres. SPEs in hBN have observed
intensities from $4\times 10^{6}$ counts/s Tran et al. (2016); Martínez et al.
(2016) to $13.8\times 10^{6}$ counts/s Grosso et al. (2017), making them the
brightest among existing solid-state SPEs. hBN SPEs exhibit a $W$ of 82%,
implying that majority of the emission is in the ZPL Tran et al. (2016). The
brightness can partially be attributed to a high proportion of emission into
the ZPL. The purity of single-photon emission from SPEs in hBN has been
measured to be $g^{(2)}=0.077$ Grosso et al. (2017). These properties
consistently rank hBN SPEs as one of the most promising solid-state SPEs,
which can be seen when compared to properties of other sources in Table 1.
Furthermore, by embedding the hBN layer hosting the emitters in a multilayer
hBN structure, the spectral properties can be enhanced, such as a significant
narrowing of the linewidth, as seen in Fig. 6(a) Tran et al. (2016).

Amongst the many excellent properties of colour centres in hBN, it also hosts
a wide range of defects and each of these defects have a characteristic
emission spectrum (Fig. 6(b)). The emission energies of these defects range
from ultraviolet to near infrared wavelengths Tran et al. (2016); Bourrellier
et al. (2016); Tran et al. (2016); Xu et al. (2018). It is useful to
categorise the visible emitters in two groups based on their lineshapes, as it
is possible that they might have similar structural and/or chemical origins
Tran et al. (2016). It was also observed that irrespective of the category of
visible light emitter, the phonon sideband (PSB) is separated from its
corresponding ZPL by about $\sim 160\pm 5$ meV. However, a caveat is that no
SPEs emitting at telecommunications wavelengths have been discovered yet,
giving hBN SPEs a significant disadvantage when compared to InAs QDs and TMDs
when considering the compatibility of these sources with existing silicon
technologies Miyazawa et al. (2016); Zhao et al. (2021).

Table 1: Properties of existing solid-state single photon emitters, excluding hBN. RT: Room Temperature, W: Debye-Waller factor. The following abbreviations are used for emitters: NV: Nitrogen-Vacancy, SiV: Silicon-Vacancy and CNT: Carbon Nanotube.  Source |  Bulk or 2D |  T |  Brightness (counts/s) |  Purity ($\boldsymbol{g^{(2)}}$) |  $\boldsymbol{W}$ (%) |  Emission range (nm)
---|---|---|---|---|---|---
Diamond NV- |  Bulk |  RT |  $\sim\,1\times 10^{6}$ Schröder et al. (2011) |  0.1 - 0.3 Schröder et al. (2011) |  4 - 20 Zhao et al. (2012); Pezzagna et al. (2011) |  637 Schröder et al. (2011); Jelezko et al. (2001); Jelezko and Wrachtrup (2006)
Diamond SiV |  Bulk |  RT |  $\sim\,1-5\times 10^{6}$ Neu et al. (2011, 2013) |  < 0.2 Neu et al. (2011, 2013) |  70 - 97 Neu et al. (2011) |  738 Pezzagna et al. (2011); Neu et al. (2011, 2013), 726.5 and 740.8 Lindner et al. (2018)
InAs Quantum Dots |  Bulk |  up to 80 K Dusanowski et al. (2016) |  $\sim 10^{4}$ Sapienza et al. (2015); Chen et al. (2017), |  0.00044 Miyazawa et al. (2016), 0.006 Musiał et al. (2020) |  |  1500 Miyazawa et al. (2016), 1550 Dusanowski et al. (2016)
SiC |  Bulk |  RT |  $\sim 2\times 10^{6}$ Castelletto et al. (2014) |  < 0.13 Castelletto et al. (2014); Wang et al. (2018) |  8-40 Nagy et al. (2018); Udvarhelyi et al. (2020) |  427-745 Lohrmann et al. (2015), 858, Nagy et al. (2018) 862, 917 Udvarhelyi et al. (2020); Ivády et al. (2017),1033 - 1137 Koehl et al. (2011), 1540 Babunts et al. (2000), 726.5 and 740.8 Lindner et al. (2018)
TMDs |  2D |  4 K |  $0.37\times 10^{6}$ He et al. (2015) |  <0.21 He et al. (2015) |  0.01-0.64 Lee et al. (2022) |  708-757 Koperski et al. (2015), 1080-1550 Zhao et al. (2021)
CNTs |  Nanotubes |  RT |  $\sim\,10^{4}$ He et al. (2017); Endo et al. (2015) |  0.01 He et al. (2017), 0.04 - 0.39 Ma et al. (2015) |  |  980 and 1120 Ghosh et al. (2010), 975 and 1137 Piao et al. (2013), 991 and 1158 Miyauchi et al. (2013), 1140-1580 He et al. (2017)
GaN |  Bulk |  RT |  $\sim 10^{7}$ Tamariz et al. (2020) |  0.01 - 0.3 Kako et al. (2006); Arita et al. (2017); Meunier et al. (2023) |  |  270 nm - 290 Tamariz et al. (2020); Holmes et al. (2014),338 nmArita et al. (2017), 1120 nm, 1225 nm, and 1300 nm Meunier et al. (2023)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 4: a) Spectra of the $NV^{-}$ centre in diamond. b) Confocal PL map of
NV centres embedded in a solid immersion lens. c) µPL spectra and polarisation
resolved measurement of InAs/InP quantum dots. d) PL spectra of SiV centre in
diamond. e) Confocal PL map of colour centres in SiC. f) Typical spectra of
defects in SiC which are SPEs. g) Wid-field PL maps of unfunctionalised and
functionalised (by 3,5-dichlorobenzene diazonium (Cl2-Dz)) single-walled
carbon nanotubes (SWCNTs) on glass and doped SWCNTs on polystyrene and their
respective ensemble PL spectra. h) (Top) An image of a thick WSe2 flake
obtained using an optical microscope. (Middle) Micro-photoluminescence scan of
the flake, showing intensity in the range 1.71–1.75 eV. (Bottom) Emission
spectra found at specific locations on the edges (S4–S6). These locations are
indicated in (Middle) with a red contrast contour plot of the intensity of the
PL signal observed at E = 1.687 eV. Fig. 4(a) reprinted with permission from
Jelezko and Wrachtrup (2006). © 2006 WILEY-VCH Verlag GmbH & Co. KGaA,
Weinheim. Fig. 4(b) reprinted from Schröder et al. (2011) and used under
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.
Fig. 4(c) reprinted from Dusanowski et al. (2016), with the permission of AIP
Publishing. Fig. 4(d) adapted from Lindner et al. (2018) (plots re-arranged)
and used under Creative Commons Attribution 3.0 license. Fig. 4(e) and Fig.
4(f) adapted from Castelletto et al. (2014) with permission from Springer
Nature. Fig. 4(g) reproduced from He et al. (2017) with permission from
Springer Nature. Fig. 4(h) reproduced from Koperski et al. (2015) with
permission from Springer Nature.

(a)

(b)

Figure 5: a) Atomic force microscopy (AFM) of a GaN QD that is uncovered and a
cross-sectional TEM of a covered GaN/AlN QD. b) PL spectra of a GaN/AlN QD
obtained at different excitation powers. Reproduced from Kako et al. (2006)
with permission from Springer Nature.

(a)

(b)

Figure 6: a) (Left) Confocal PL map of colour centres in hBN. A subset of
these are SPEs. (Right) Representative spectra of a visible light SPE in
multilayer and monolayer hBN. Emitters have a significantly narrower linewidth
when embedded in multilayer hBN. b) (Left) Wide range of spectra obtained from
different emitters. Due to their similar lineshapes, it is common to divide
these spectra into two groups. (Centre) shows that both categories of emitters
have PSBs a similar distance away from the ZPL. (Right) g(2) measurements
confirming antibunching from emitters in both groups. Fig. 6(a) reproduced
from Tran et al. (2016) with permission from Springer Nature. Fig. 6(b)
Adapted with permission from Tran et al. (2016). Copyright 2016 American
Chemical Society.

##  2 Colour centres in hBN

As mentioned earlier, due to the wide range of defects present, hBN hosts SPEs
emitting within a wide wavelength range, from UV to near IR. Significant
effort has been invested in controlling the type and location of defects in
hBN, a crucial step in creating arrays of emitters for use in scalable
photonic quantum technologies based on hBN SPEs. The ultimate goal is to
deterministically fabricate a specific type of defect at a pre-determined
location in a high-quality crystal.

Defects are naturally formed during the growth process of hBN. Flakes grown
using high pressure and high temperature (HPHT) have the lowest defect
densities Taniguchi and Watanabe (2007); Kubota et al. (2007); Watanabe et al.
(2004). Hence, they are a suitable platform for the deterministic fabrication
of defects. However, flakes obtained from exfoliated layers from a larger bulk
crystal have no deterministic control over the thickness or lateral size of
the exfoliated flakes. Hence, high throughput fabrication of devices is
unsuitable using this source of hBN. hBN obtained from CVD allows wafer scale
fabrication and thickness control of devices, however they have a high density
of defects and the transfer process from the CVD catalyst to a suitable
substrate can lead to significant contamination Garcia et al. (2012); Ma et
al. (2019).

###  2.1 Creation of colour centres in hBN

####  2.1.1 Annealing

Despite the natural occurence of defects, some of which are colour centres in
hBN, they are usually unstable Tran et al. (2016). In order to improve the
stability of these colour centres, and also create a larger number of colour
centres, annealing in an Ar flow at 850 °C is employed Tran et al. (2016);
Choi et al. (2016); Tran et al. (2016). It was found the defect densities
increased with annealing temperature, suggesting that the defect was vacancy
related, and that they were likely to be neutrally charged as they were
unaffected by annealing in hydrogen, oxygen and ammonia environments, which
are known to change the charge states of defects Tran et al. (2016). Beyond
argon, exfoliated flakes annealed in a CH4 environment at 1000 °C showed a
nine-fold increase in the density of emitters when compared to argon annealing
at 1000 °C Lyu et al. (2020). Purely annealing seems to produce emitters with
a wide range of emission wavelengths, from 565 nm to 775 nm when annealed in
an argon environment at 850 °C Tran et al. (2016) and from 520 nm to 720 nm
(with most emitters at 540 nm) with CH4 annealing at 1000 °C Lyu et al.
(2020). Unlike in Ar annealing, which resulted in a low density of emitters
(0.009 µm2) concentrated around flake edges, annealing of hBN flakes in an O2
flow led to 0.327 emitters/µm2 and the defects seemed to be uniformly
distributed throughout the flake. While annealing can stabilise and create new
emitters, it can also lead to the loss of some existing colour centres. For
example, blue emitters (ZPL at 436 nm) fabricated in carbon-doped hBN flakes
were stable under annealing in 1 Torr of Ar for 30 mins, the standard
annealing recipe to generate and stabilise emitters, for up to 800 °C, but
disappeared when the annealing temperature was raised to 1000 °C and was
followed by the creation of new emitters with a distribution of ZPL energies
Chen et al. (2023).

####  2.1.2 Ion implantation, electron beam and laser pulse irradiation

In hBN crystals with low defect densities, ion and electron beam irradiation
is effective in creating defects Tran et al. (2016); Choi et al. (2016); Guo
et al. (2022); Chejanovsky et al. (2016); Fournier et al. (2021); Zabelotsky
et al. (2023); Grosso et al. (2017). Ion beam irradiation usually requires an
additional annealing process to stabilise the emitters Chejanovsky et al.
(2016); Choi et al. (2016). A study exploring ion beam implantation performed
using B, N, BN, Si and O ions on exfoliated hBN flakes followed by annealing
in argon at 850 °C all produced defects with similar PL spectra consisting of
a peak around 600 nm with a phonon side band 160 meV from the ZPL Choi et al.
(2016). In the same study, a reference sample that was only annealed in argon
without any implantation also produced emitters with similar characteristic
spectra, albeit at a lower density, suggesting that the defects created had
similar structures. Furthermore, after annealing, the emitters were mostly
found on the edges of the flakes, indicating the role of strain in defect
formation. In a different investigation, ion implantation done using He and N
atoms followed by argon annealing increased the emitter density by orders of
magnitude, however the defects were still predominantly located on flake edges
Chejanovsky et al. (2016). However, unlike in the previous study, the spectral
characteristics of the colour centres are spread over a broad range, with ZPLs
from 569 nm to 697 nm. In Fig. 7(a), we can see that the problem of spatial
localisation can be addressed by the use of a focused ion beam (FIB) to
achieve precise localisation of defects Kianinia et al. (2020); Zabelotsky et
al. (2023); Ziegler et al. (2019); Venturi et al. (2024); Glushkov et al.
(2022). Defect creation using FIB involves the breaking of the B-N bond using
high energy ions, leaving behind vacancies. By the use of Xe+ Kianinia et al.
(2020), and N and O ions Zabelotsky et al. (2023), the negatively charged
boron vacancy was able to be deterministically generated, having a ZPL at
approximately 820 nm.

Similar to ion implantation, electron beam irradiation has been a popular way
to controllably generate emitters Tran et al. (2016); Choi et al. (2016);
Fournier et al. (2021). The irradiation is performed at energies much lower
than threshold at which electron beam induced etching of hBN occurs. Unlike
ion implantation, electron beam irradiation allows both the creation and
activation of emitters in a single step, since no additional annealing process
is required to stabilise emitters Tran et al. (2016); Choi et al. (2016);
Fournier et al. (2021). In terms of the types of emitters produced, exposing a
large region, such as a whole flake, to irradiation, results in a wide range
of defects Choi et al. (2016), although in some cases some emitter types may
occur at a higher frequency than others Tran et al. (2016) and in all cases
are predominantly located at flake edges. An approach that was successful in
also creating emitters in flatter regions of the hBN flake was to increase the
energy of the incident electron from the typical values of 15 keV Tran et al.
(2016); Choi et al. (2016) to a few MeV Ngoc My Duong et al. (2018). Localised
doses of electron beam irradiation have been successful in the creation of
spectrally and spatially well-defined defects Gale et al. (2022); Murzakhanov
et al. (2021); Fournier et al. (2021). In Fig. 7(b), we can see that by
focusing the beam radius to around 33 nm at low energies of 15 keV, colour
centres emitting at 435 nm were able to be reproducibly generated Fournier et
al. (2021); Gale et al. (2022). However, while such a process can allow
control over defect creation, the yield of SPEs was quite low, as it was more
likely to form an ensemble of defects than single emitters Gale et al. (2022).
Although there are no studies on the site-controlled creation of boron
vacancies, high energy (2 MeV) electron beam irradiation has been used to
create boron vacancies in hBN flakes Murzakhanov et al. (2021).

Femtosecond pulsed laser irradiation has also been a reliable technique to
generate emitter arrays on demand Yang et al. (2023); Gan et al. (2022); Hou
et al. (2017). The laser pulse can be used to induce a hole in the hBN, around
which colour centres form. It was shown that vacuum annealing also resulted in
the conversion of the defects into paramagnetic colour centres and that the
defect density around the ablation site could be controlled by manipulating
the pulse energy Yang et al. (2023), leading to the possibility of optimising
the pulse energy to produce single emitters Hou et al. (2017); Gan et al.
(2022). It was shown that for pulse energies of 38 nJ and 46 nJ, there was 100
% yield of SPEs Gan et al. (2022). A reduction in the laser pulse energy not
only reduced the density of emitters but their ZPL energy distributions as
well, with a lower pulse energy generally resulting in fewer distinct types of
PL spectra Gan et al. (2022). It is also interesting to note the role of
annealing in SPE creation by laser writing is not conclusive, with some
reporting that UV/ozone annealing is crucial for the activation of defects
Yang et al. (2023); Gan et al. (2022) and others reporting the contrary Hou et
al. (2017). In each of these studies, the ZPL energies were distributed in the
visible light range, from 550 nm to 800 nm Yang et al. (2023). The negatively
charged boron vacancy can also be created reproducibly using laser writing
using 1 µJ pulses and less than 200 pulses Gao et al. (2021).

Building on the above irradiation methods, neutron irradiation also resulted
in the creation of negatively charged boron vacancies Gottscholl et al.
(2020). Like electron irradiation and unlike ion implantation, annealing was
not performed to activate or stabilise the defects.

####  2.1.3 Chemical and plasma etching

Etching of hBN in reactive environments is an effective way of creating colour
centres. Plasma etching in O2 and subsequent annealing in argon, a step that
was found to be necessary in order to have bright and stable emitters, led to
the formation of emitters spanning the visible light wavelength range Vogl et
al. (2018). Other combinations of plasma etching and annealing include CH4 and
H2 plasma etching followed by annealing in air at 850 °C and Ar plasma etching
and Ar annealing at 850 °C or air annealing at 750 °C Chen et al. (2021); Xu
et al. (2018). Ar plasma etching and annealing at 850 °C led to an 8-fold
increase in emitter density Xu et al. (2018).

Chemical etching has been performed using both peroxymonosulfuric acid
(H2O2:H2SO4) and additional (H3PO4 $+$ H2SO4) solutions Chejanovsky et al.
(2016). Process 1 involved etching in a 3:6 solution of H2O2:H2SO4 for 2 hours
at 135 °C. The second process involved performing Process 1 for 20 minutes
followed by etching in a 1:8 solution of H3PO4:H2SO4. After both processes,
annealing at 850 °C in Ar was performed. The emitter density due to Process 1
was 0.09 emitters/µm2, however it dramatically increased to 0.57 when Process
2 was used.

####  2.1.4 CVD hBN

As mentioned earlier, CVD hBN allows wafer scale production of hBN quantum
emitter based devices and vertical control over emitter localisation as the
thickness of the hBN can be controlled during growth. The CVD growth process
leads naturally to the existence of a high density of defects throughout the
film, with relatively low distributions of ZPL energies Stern et al. (2019).
While the natural existence of a high density of emitters is advantageous, the
lack of control over the defect location and type is a limitation. Therefore,
significant effort has been invested in the development of specific emitter
types during growth. A study focused on using LPCVD growth using ammonia
borane (BH3NH3) as a precursor in a quartz tube furnace, at a temperature of
1030 °C, with Ar/H2 as a carrier gas producing a uniform, few layer hBN film
when a very low partial pressue of H2 (0.05 %) and gas flow rate (50 sccm)
Mendelson et al. (2019) is used. The emitter density was uniform throughout
the sample and not localised to areas of high strain (edges or wrinkles), and
had a narrow distribution of ZPL wavelengths. It was found that more than 85 %
of the emitters exhibited ZPL wavelengths in the 580 $\pm$ 10 nm spectral
range, and up to 56 % in the 580 $\pm$ 5 nm range. Furthermore, the PSB of
these emitters were almost always located 165 meV below the ZPL, suggesting a
similar structure for all the defects. It was also noted that a high emitter
density, an overall density of 2.2 emitters/µm2 and a single emitter density
of 0.84 /µm2 was achieved without the need for annealing, a marked improved
over 0.04 emitters /µm2 Stern et al. (2019). Efforts have also been made to
spatially localise emitters during the growth process. It was found that LPCVD
growth of hBN on Ni led to preferential formation of the brightest emitters on
Ni (100) grains Mendelson et al. (2021). In most CVD grown hBN, the spectral
window in which the emitters occur is limited to 580 $\pm$ 10 nm, with
practically no emitters emitting beyond 600 nm Stern et al. (2019); Mendelson
et al. (2019, 2021). It was also found that controlling the diffusion of boron
through the Cu catalyst offered a mode of controlling the type of emitters
formed during CVD growth of hBN Abidi et al. (2019). Using a process labelled
as ’backside boron gettering (BBG)’, hBN growth was controlled by stacking the
oxidised Cu catalyst on a Ni substrate rather than a quartz substrate. As the
solubility of B atoms is higher in Ni than Cu, the B atoms predominantly
diffuse through the Ni substrate than Cu, leading to a significantly slower
growth rate of hBN than when compared to when oxidised Cu was placed on a
quartz substrate. Analysis of the SPEs generated during hBN synthesis revealed
that hBN grown using BBG hosted 87 % of its emitters in the 550 nm to 600 nm
region, while hBN grown on oxidised Cu on quartz led to the formation of 87 %
of its color centres in the 600-650 nm region. Standard growth of unoxidised
Cu on quartz resulted in all the emitters being in the 600-650 nm window.
While this last result is contradictory to Mendelson et al. (2019) and
Mendelson et al. (2021), the difference in the dominant spectral window for
emitter creation can be attributed to the growth in Abidi et al. (2019) being
performed in atmospheric pressue rather than low pressure, an effect that is
commonly observed during hBN growth processes Fernandes et al. (2022).
Controlling boron diffusion also served as a useful way to control emitter
densities as emitters grown using BBG, oxidised Cu on quartz and standard Cu
on quartz resulted in SPE densities of 1.00 emitters/ µm2, 1.66 emitters/ µm2
and 3.11 emitters/ µm2, respectively.

####  2.1.5 Strain activation

From the ubiquitous observation of emitters concentrated around flake edges,
it became apparent that strain played a role in the formation of defects. This
has inspired attempts at exploiting strain to localise emitter creation. One
study etched SiO2 nanopillars of various diameters and directly grew hBN using
CVD on these nanopillars (Fig. 7(c)), and it was found that when the pillar
diameters were 250 nm and 650 nm high, there was an 80 % yield of SPEs at the
pillar site Li et al. (2021). Furthermore, the distribution of ZPLs was
between 559 nm and 639 nm, a much smaller distribution in ZPL wavelengths than
when annealing alone or when using large-area electron/ion beam irradiation.
An important note is that no post-growth annealing was performed on the sample
to increase/stabilise emitters. In a different investigation, hBN flakes were
exfoliated onto silica microspheres to introduce strain fields and intense
fluorescence was observed from 560 nm to 780 nm Chen et al. (2024). In the
latter work, emitters were found only in the region of hBN directly lying on
the microspheres and these emitters were active before and after annealing in
Ar at 850 °C. A near-deterministic activation of defects was also observed
when CVD hBN was transferred onto an array SiO2 micropillars Proscia et al.
(2018). An average of 2 emitters per pillar was found on pillars with a
diameter of 75 nm and height of 155 nm, with some hosting SPEs. Like the first
investigation Li et al. (2021), the emitter activation did not require
annealing. The role of strain was confirmed by a repetition of Proscia et al.
(2018), albeit for pillar diameters ranging from 0.6 µm to 2 µm and even a
bullseye cavity and an optimised transfer process of the CVD hBN. The
brightest emitters were observed at the location of the pillars and cavities,
emphasising the role of strain in defect activation Scheuer et al. (2021).

####  2.1.6 Other methods

Molecular beam epitaxy (MBE) of hBN is an alternative to CVD when growing
large-area hBN. In a study investigating the role of carbon in the formation
of SPEs in hBN, MBE of hBN on sapphire was performed by placing the boron
source in a carbon crucible. Sharp spectral lines were observed which did not
exist during standard MBE of hBN without the carbon crucible Mendelson et al.
(2021). As the carbon crucible showed sidewall etching, it suggested that
carbon was present in gaseous phase during growth and the emergence of the new
spectral lines could be strongly attributed to the carbon doping of hBN. This
conclusion was supported by the observation of a high emitter density when
other methods of increasing carbon incorporation into hBN was employed. These
methods include varying the flow rates of triethylboron (TEB) during metal
organic vapor phase epitaxy (MOVPE) growth of hBN, known to systematically
alter the concentrations of carbon present, exploring the possibility of
carbon incorporation from the substrate by performing high-temperature MBE on
different orientations of SiC and converting highly orientated pyrolytic
graphite (HOPG) into hBN. An increase in emitter intensities and densities
with increasing TEB flow rates, variations in SiC orientation during MBE
growth and conversion of HOPG into hBN offers strong support to the
correlation between carbon doping and SPE creation. Furthermore, the PL
spectra observed using each method of growth was mostly similar, suggesting
similar defect structures.

An interesting technique for spatially localising emitters was using atomic
force microscopy (AFM) to perform nanoindentation in exfoliated hBN flakes. In
these samples, there was a 32 % yield in SPEs for an indent of 400 nm in size.
The ZPL wavelengths produced using this method can be categorised into three
classes: 582 $\pm$ 6 nm, 602 $\pm$ 9 nm, and 633 $\pm$ 5 nm. More than 80 % of
the SPEs show ZPLs being positioned in the 580 nm and 602 nm groups Xu et al.
(2021).

(a)

(b)

(c)

Figure 7: a) (Left) Negatively charged boron vacancies observed in a confocal
scan, created using a focused ion beam of Xe+ ions, with the fluence of ions
increasing with each row and constant across each row, (Scale bar 20 µm).
(Right) Variation of PL intensity with Xe+ fluence. The inset shows a
representative PL spectrum for each fluence. b) (Left-most) Image taken using
a scanning electron microscope (SEM) of a hBN flake, with the blue rectangle
indicating the region irradiated with an electron beam. (Centre-left) Confocal
map of rectangle zone. (Centre-right) and (Right) are PL spectra taken at low
temperature (5 K) at two different spectral resolutions, showing a
reproducible 0.7 nm spectral linewidth. c) (Left) Confocal PL intensity maps
of strain induced colour centres in hBN. The hBN was directly grown using CVD
onto the nanopillars. The pillar diameters are 250, 450, 650, and 950 nm and
the scale bar is 10 µm. The unit for the intensity is photon counts/s. (Right)
Wide-field images of each pillar array with hBN deposited on it. White circles
indicate pillars with multiple emitters. The scale bar is 2 µm. Fig. 7(a)
adapted with permission from Kianinia et al. (2020). Copyright 2020 American
Chemical Society. Fig. 7(b) reprinted from Fournier et al. (2021) and used
under a Creative Commons Attribution 4.0 International license. Fig. 7(c)
adapted with permission from Li et al. (2021). Copyright 2021 American
Chemical Society.

###  2.2 Defect assignment

In order to understand the nature of defects observed in experiment,
comparisons with theoretical calculations need to be made. The most common
method of calculating the electronic structure of defects and subsequently the
structure for comparison with experiment is density functional theory (DFT).
In DFT, the derived values can vary significantly between choice of exchange-
correlation functional. For example, the hBN band gap obtained using the
Perdew-Wang (PW91) generalised gradient functional (GGA) is 4.6 eV Perdew et
al. (1992); Topsakal et al. (2009), which is much smaller than the value of
6.47 eV obtained using Heyd-Scuseria-Ernzerhof (HSE), screened exchange
functionals Heyd et al. (2003); Wickramaratne et al. (2018). Unless explicitly
stated, all DFT derived values have been calculated using HSE functionals as
it is the current de facto standard for calculating these values.

A range of defects have been studied theoretically, such as vacancies,
anitsites, impurities, complexes of antisites and impurities with vacancies,
and Stone-Wales defects, to name a few Tran et al. (2016); Tawfik et al.
(2017); Hamdi et al. (2020). In the following discussion regarding defects,
the following notation is used to describe defects. The species being replaced
is indicated as a subscript of the species that it is being substituted for.
For example, a nitrogen vacancy is represented by VN, as a vacancy is
substituting a single nitrogen atom. Similarly, the antisite nitrogen vacancy
complex is symbolically written as NBVN, as the nitrogen atom is replacing
replacing the boron atom (NB) and is coupled to a nitrogen vacancy (VN).

The NBVN defect was one of the first candidate defects suggested to be a SPE
Tran et al. (2016). Some calculations predicted a planar defect geometry (Fig.
8(a)) Tran et al. (2016); Tawfik et al. (2017); Zhang et al. (2014), and
others found the ground state configuration to involve an out-of-plane
displacement of the nitrogen atom Noh et al. (2018). The defect is also
expected to have a spin doublet ground state and therefore has gained interest
as a spin qubit Tawfik et al. (2017); Zhang et al. (2014). The electronic
structure of the neutrally charged defect involves three defect states in both
spin channels within the band gap (2 occupied in the spin majority and 1
occupied in the minority spin channel), Fig. 8(b) Tran et al. (2016); Zhang et
al. (2014). The ZPL transition for this defect has an energy of 2.12 eV, which
is in the range observed experimentally, but the Huang-Rhys factor is 0.66.
The latter makes the defect less likely to be a candidate as it predicts a
large phonon coupling, something not observed in experiment Tawfik et al.
(2017).

A candidate similar in nature to NBVN is the carbon impurity and nitrogen
vacancy complex, CBVN. Early work on this defect suggested that the defect had
a triplet ground state with $C_{2v}$ geometry, i.e. the carbon atom was in
plane Tawfik et al. (2017); Wu et al. (2017). Like NBVN, CBVN has three states
in the band gap of each spin channel, with two occupied states in the majority
spin channel. The transition energy of this defect is calculated to be 2 eV
with a HR factor of 1.50 Sajid and Thygesen (2020), which is very close to the
HR factor of 1.45 obtained from some experimentally obtained PL spectra
Mendelson et al. (2021), making it a suitable candidate for visible light
emitters centered around 600 nm. From Fig. 8(f), it can be seen that the
theoretical and experimental spectra agree well. However, it was later found
that the true ground state of the CBVN defect is the singlet ground state,
with an out-of-plane distortion of the carbon atom giving it a $C_{1h}$
symmetry Noh et al. (2018); Sajid et al. (2018); Linderälv et al. (2021).
While the ZPL energy associated with this defect is 2.08 eV, putting it within
the observed ZPL energy range, it was shown that the excited state has a
significant lattice distortion when compared to the ground state, implying
large phonon coupling and contradicting observations of the ZPL contributing
to the majority of the emission Sajid et al. (2018); Linderälv et al. (2021).
This finding makes it less likely that the transition is due to this defect.

Beyond the visible light emitters, the nature of the UV light emitters has
gained significant interest. Some studies suggested that the source of this
emission is a topological defect, specifically the Stone-Wales defect which
leads to two six-member rings transforming into a five-member and seven-member
ring Wang et al. (2016). The Stone-Wales defect is formed by a 90° rotation
about the axis perpendicular to the hBN sheet which automatically introduces a
nitrogen antisite and a boron antisite, creating a nitrogen-nitrogen and
boron-boron bond. It was found from first principles calculations using DFT
that the N-N bond leads to a level that is 0.44 eV from the valence band
maximum and the B-B bond leads to an energy level 0.4 eV below the conduction
band Hamdi et al. (2020). The lowest defect state in the band gap is fully
occupied, leading to a singlet ground state. The calculated ZPL energy and
simulated HR factor of this defect is 4.08 eV and 2, respectively, in good
agreement with spectra observed in Museur et al. (2008); Vokhmintsev et al.
(2019). Despite the excellent agreement between theoretical and experimental
spectra, the formation energy of the Stone-Wales defect is relatively high at
7.2 eV suggesting that the defect should occur in low abundance Hamdi et al.
(2020). However, regions of high strain in the hBN crystal could lower the
formation energy of such defects, leading to a greater concentration Hamdi et
al. (2020). In Fig. 8(h), we can see the structure, simulated spectra and band
structure of a Stone-Wales defect.

A competing theory for the nature of the 4.1 eV emission is the carbon dimer.
It has been seen experimentaly that the intensity of the 4.1 eV peak increases
with carbon doping Uddin et al. (2017); Era et al. (1981), indicating that the
nature of the defect is carbon related. The carbon dimer is formed by
substituting neighbouring B and N atoms to form CBCN. The formation energy of
the neutral charge state of this defect is 2.2 eV Mackoit-Sinkevičienė et al.
(2019), 5 eV less than the Stone-Wales defect, making it significantly more
likely to form. The calculated values of the ZPL and HR factor for this defect
range from 4.31 eV Mackoit-Sinkevičienė et al. (2019) to 4.36 Winter et al.
(2021) and 1.37 Winter et al. (2021) to 2 Mackoit-Sinkevičienė et al. (2019),
respectively. Like the Stone-Wales defect, the carbon dimer has a planar
$C_{2v}$ structure Winter et al. (2021). The carbon dimer can be thought of as
a combination of two defects, the substitutional carbon on the boron site and
nitrogen site. Both impurity defects lead to a single defect state in each
spin channel, with spin splitting leading to the majority spin channel having
a lower energy Huang et al. (2022). The CB defect creates a donor state below
the conduction band and the CN creates an acceptor state below the conduction
band. The formation of the CBCN defect leads to a combination of the
electronic structures of CB and CN, with the highest occupied molecular
orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels
residing above the valence band and conduction band a similar energy
difference from the band edges for isolated CB and CN. As seen in Fig. 8(e),
the fully occupied HOMO and LUMO leads to a singlet ground state and loss of
spin splitting existing in the isolated components of the dimer. The excellent
spectral agreement between theory and experiment, and the low formation
energies makes the carbon dimer one of the most likely candidate defects for
UV light emission. It was also discovered that every donor-acceptor pair CBCN
present in a carbon cluster led to a reduction in formation energy of the
cluster. This results in carbon clusters being increasingly stabilised when
there is an equal number of CB and CN, with the stabilisation energy of the
six-member carbon ring (three CBCN pairs in a ring) being the largest. The
stabilisation can be attributed to the formation of a delocalised $\pi$
electron orbital similar to the benzene molecule, leading to a reduction in
the kinetic energy of electrons. Among larger carbon clusters, carbon trimers,
C2CN and C2CB, have been calculated to have spectral characteristics that show
a striking resemblance to the visible light emitters, Fig. 8(d), i.e. a 1.6 eV
ZPL and a PSB 160 meV from the ZPL Jara et al. (2021); Golami et al. (2022),
although some calculations suggest that C2CB has a ZPL energy of 1.36 eV
Auburger and Gali (2021). The reason for this discrepancy is unknown.

Out of the many candidate defects, the negatively charged boron vacancy,
V${}_{\text{B}}^{-}$ is the only defect that has been conclusively identified.
The neutral boron vacancy, VB, has a $C_{2V}$ geometry due to a Jahn-Teller
distortion lowering its symmetry from $D_{3h}$ Huang and Lee (2012). The
formation energy of the neutral defect is 7.65 eV using HSE functionals, where
such a high formation energy is typical for vacancies Huang and Lee (2012).
Previous studies Weston et al. (2018) indicate VB is a triple acceptor, and a
single acceptor level is located at 1.4 eV Huang and Lee (2012); Weston et al.
(2018); Liu et al. (2020) and the double acceptor level has been estimated to
be in the range of 3.9 eV Huang and Lee (2012); Weston et al. (2018). The
triple acceptor level is very close to the conduction band and is not found to
be stable Weston et al. (2018). The defect states of VB are largely derived
from valence-band orbitals. There are three defect levels in each spin
channel, with two (one) occupied and one (two) unoccupied states in the spin
majority (minority) channel Huang and Lee (2012). The negatively charged boron
vacancy, shown in Fig. 8(c), is a spin triplet with $D_{3h}$ symmetry Huang
and Lee (2012); Weston et al. (2018); Ivády et al. (2020) and zero field
splitting causes the triplet degeneracy to be fully lifted Ivády et al.
(2020). Electron paramagnetic resonance (EPR) and optically detected magnetic
resonance (ODMR) measurements of defects induced in hBN flakes by neutron
irradiation, which emitted at 800 nm, led to the conclusive assignment of
these emitters as V${}_{\text{B}}^{-}$ Gottscholl et al. (2020). This was
later further confirmed by DFT calculations which found that the
V${}_{\text{B}}^{-}$ has a ZPL transition at 1.65 eV (765 nm) and a large HR
factor of 3.5, implying a significant phonon coupling, unlike other defects
Ivády et al. (2020).

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 8: a) Schematic of structures of a selection of defects in hBN. b) Band
structure of the NBVN defect. c) (Left) Band structure of V${}_{\text{B}}^{-}$
and (Right) geometry with spin polarised DFT calculation of spin density. d)
(Top left) Band structure and geometry, (Top right) spectral function (inset
shows the phonon mode at $\sim$ 160 meV) and (Bottom) calculated PL spectrum
superimposed on the experiment spectrum from ref. Martínez et al., 2016 of
C2CN. The ZPL has been shifted by 0.5 eV to align with the experimental
spectrum. e) Band structure and wavefunctions of CBCN defect. f) Simulated PL
spectra of CBVN compared to the experimental spectrum from ref. Mendelson et
al., 2021. g) geometry and allowed transitions of CBVN with a triplet ground
state Sajid and Thygesen (2020). h) Geometry, simulated spectra (both Perdew,
Burke, and Ernzerhof (PBE) and Heyd, Scuseria, and Ernzerhof (HSE)
calculations) and band structure of Stone-Wales defect. Fig. 8(a) and Fig.
8(b) reprinted with permission from Abdi et al. (2018). Copyright 2018
American Chemical Society. Fig. 8(c) adapted from Ivády et al. (2020) and used
under a Creative Commons Attribution 4.0 International license. Fig. 8(d)
adapted with permission from Jara et al. (2021). Copyright 2021 American
Chemical Society. Fig. 8(e) reprinted from Mackoit-Sinkevičienė et al. (2019),
with the permission of AIP Publishing. Fig. 8(f) and Fig. 8(g) used with
permission of IOP Publishing Ltd, from Sajid and Thygesen (2020); permission
conveyed through Copyright Clearance Center, Inc. Fig. 8(h) adapted from Hamdi
et al. (2020) and used under a Creative Commons Attribution 4.0 International
license.

##  3 Graphene/hBN heterostructure devices for electrical control of hBN SPEs

###  3.1 Stark tuning of hBN SPEs

(a)

(b)

(c)

Figure 9: a) Giant Stark shift by using an in-plane nanoscale four-electrode
device (device structure shown in inset). b) Gr/hBN/Gr stack used to apply
vertical electric fields across defects embedded in hBN. c) Various types of
Stark shifts observed using the device stack in b), corresponding to the
existence of defects with vastly different dipole orientations. Fig. 9(a)
reprinted with permission from Xia et al. (2019). Copyright 2019 American
Chemical Society. Fig. 9(b) and Fig. 9(c) adapted with permission from Noh et
al. (2018). Copyright 2018 American Chemical Society.

As the understanding of hBN based defects developed, fabrication of hBN based
devices to further control SPE properties gained significant interest. A
popular way of establishing electrical control over hBN SPEs is to assemble
graphene (Gr)/hBN heterostructure devices. Monolayer graphene has a similar
honeycomb crystal structure and lattice parameter to hBN (a mismatch of 2 %),
which makes them commensurate materials, and naturally suitable to form a
heterostructure when the SPE’s geometrical properties need to be protected
from strain. Furthermore, the two-dimensional nature of monolayer graphene
lends to its large transparency, making it a suitable top layer when coupling
SPEs to detectors.

A common way to tune emission lines is to apply an electric field across a SPE
to induce a Stark shift in its ZPL emission energy. An early study on the
Stark shift of emitters in hBN was performed by forming a Gr/hBN/Gr
heterostructure (with multilayer hBN exfoliated from flakes) and using
graphene as a top and bottom electrode (Fig. 9(b)) Noh et al. (2018). Due to
the low electric field that was able to be applied, there was not a
significant shift in the ZPL emission energy. An efficient Stark effect tuning
requires a ZPL shift greater than the linewidth, and in such a structure it
was not possible to effect such a shift at room temperature. However, a tuning
was more obvious when the measurements were performed at 10 K as the thermal
broadening of the linewidth was reduced. A key reason behind the limitation
over the applied voltages has been the low out-of-plane dielectric constant of
hBN, which results in shorting of the device at very low voltages. From Fig.
9(c), we can see that in this investigation, linear, quadratic and V-shaped
Stark shifts were observed. The occurence of the linear Stark shift supports
the existence of defects with an out-of-plane dipole. Hence, defects of the
form V${}_{\text{N}}$X${}_{\text{B}}$ which have a ground state with $C_{1h}$
symmetry cannot be ruled out. Colour centres manifesting quadratic Stark
shifts are likely to have a degenerate excited state. In addition to this, it
was found that SPEs showing quadratic Stark shifts also had large misalignment
between the excitation and emission dipoles, possibly due to them possessing
multiple excitation pathways for the relevant electronic transitions. The
permanent dipole of the defects exhibiting linear Stark shift were calculated
and existed in the range form $-$0.9 D to 0.9 D and those exhibiting quadratic
Stark shifts had a polarisability of $\sim 150$ Å3. For defects with $C_{1h}$
symmetry due to an out-of-plane displacement of the antisite or impurity atom,
it is possible to possess a double well potential as the displacement could
occur on either side of the host hBN plane. A strong enough electric field and
a small energy barrier between the two sites could allow the defect to
transition between the two sites and change the sign of the dipole.

A mode of inducing larger shifts is to be able to apply larger electric fields
without causing breakdown of the device. An example of this was done in an
experiment where hBN was deposited on 285 nm of SiO2 (a high $k$ dielectric)
on Si, followed by a Gr top gate on the hBN Scavuzzo et al. (2019). The
silicon chip was then back-gated allowing larger fields to be applied. In this
study, Stark shifts as large as 24 meV per V/nm was observed at 15 K, which is
currently the largest reported Stark shift due to an electric field
perpendicular to the plane of the host hBN. Vertical electrical fields can
also override charge fluctuations at the hBN/SiO2 interface and lead to
lifetime limited ZPLs at 6.5 K Akbari et al. (2022).

The two-dimensional nature of hBN leads to defects having an in-plane dipole
significantly stronger than a dipole normal to the plane. This motivates the
application of an in-plane electric field to effect giant Stark shifts. In a
lateral device, a 100 nm thick hBN flake was exfoliated onto two gold
electrodes such that an electric field between the electrodes would result in
an in-plane electric field Zhigulin et al. (2023). In this device, the Stark
shift of blue emitters (transition eneryg of 4.1 eV) was studied and it was
found that the Stark shift due to an electric field along the plane was 200
times larger than the shift due to a vertical electric field. DFT calculations
of the intrinsic dipole suggests that the defect responsible could be a split
interstitial rather than the popular candidate, CBCN. Other studies report
giant room-temperature Stark shifts of up to 43 meV/(V/nm) by using a
nanoscale four-electrode device to perform angle-resolved Stark shifts, shown
in Fig. 9(a), Xia et al. (2019). This allowed shifts 4 times larger than the
linewidth of the emitter and, unlike the previous study, was performed on
visible light emitters.

###  3.2 Electrical charge control of hBN SPEs

A key step in the scaling up of hBN based photonic quantum technologies is in
the fabrication of electrically driven single-photon emitters. Such devices
would require on demand charge control of the defects. Recently, it was found
that when hBN was deposited on graphene, the majority of SPEs were quenched,
possibility due to a combination of charge and energy transfer Xu et al.
(2020). It was especially interesting to note that it was only emitters that
possessed ZPLs above 600 nm that were quenched. In a recent DFT study of a
hBN/Gr bilayer, with the hBN layer hosting native defects, charge transfer was
observed between certain defects and absent among others. A deeper
investigation of the charge transition levels (CTLs) of the defects, which are
the values of the electron chemical potential, $\mu_{e}$ at which there is an
equal probability of two charge states of the defect existing (the formation
energy both charge states of the defect is the same at this $mu_{e}$),
indicated that their location with respect to the Dirac point of graphene
determined whether or not charge transfer was thermodynamically favoured. If
the donor (acceptor) level was above (below) the Dirac point, charge transfer
was favoured a whole electron was donated (accepted) to (from) Gr Prasad et
al. (2023). This supported the observation that quenching of emission could be
controlled by changing the Fermi level of Gr by functionalising Gr with NMP Xu
et al. (2020). However, this does not rule out the role of energy transfer in
quenching.

Therefore, interfacing hBN with graphene is a possible scheme to exploit
charge control of emitters. This was shown to be possible when studies showed
that changing the Fermi level of the graphene layer adjacent to hBN can lead
to charging and discharging of the defect, leading to the defect turning
on/off Yu et al. (2022); White et al. (2022). Although the defects in the
latter studies were optically excited and not electrically pumped, these
studies represented important first steps towards achieving electrical pumping
of hBN SPEs. Quenching of emitters due to graphene was also used to spatially
localise emitters in hBN Stewart et al. (2021). A host hBN layer with emitters
activated by Ar annealing was embedded in a trilayer hBN structure, with the
encapsulating hBN layer, which was oxygen treated to remove emitters, serving
the role of protecting the host layer from the environment. The trilayer stack
was then placed on top of a Gr layer with windows patterned using electron
beam lithography. Quenching occured only in areas surrounding the windows
where the Gr was in contact with hBN, with emitters directly above the window
remaining active. By activating only the emitters in a host layer in the
stack, vertical localisation was acheived, and using graphene windows allowed
for lateral localisation.

(a)

(b)

(c)

Figure 10: a) Charge transition levels (CTLs) of native defects in hBN with
the Dirac point in Gr as a reference. The position of the donor/acceptor
relative to the Dirac point determines the directionality and possibility of
charge transfer. b) Using a Gr mask and trilayer stack of hBN (with layer
hosting emitters embedded in the middle), lateral and vertical localisation of
emitters can be achieved by exploiting quenching due to graphene. c) Charge
transfer between defects in hBN and graphene can be controlled by manipulating
the Fermi level of graphene. This can then be used to turn emitters on/off.
Fig. 10(a) adapted from Prasad et al. (2023) and used under a Creative Commons
Attribution 4.0 International license. Fig. 10(b) reprinted with permission
from Stewart et al. (2021). Copyright 2021 American Chemical Society. Fig.
10(c) adapted from White et al. (2022) and used under a Creative Commons
Attribution 4.0 International license.

##  4 Challenges and Future Perspectives

In the rapidly evolving field of photonic quantum technologies, hBN has
emerged as a material of significant interest. The discovery of room
temperature single-photon emitters in a 2D material has opened several
prospects in the realisation of large scale quantum photonic technologies. In
addition to the topics discussed in the review, significant work is being done
in coupling of hBN based emitters to integrated photonic circuits. Integration
of single photon emitters (SPEs) with photonic circuits is crucial, as it
enables scalable components packaged on a single chip. Generation and coupling
of emitters on chip is imperative to package the SPEs with other components
that will allow manipulation of light for quantum technology. Early work in
this field has focused on flakes of hBN being deposited on silicon nitride
(SiN) Elshaari et al. (2021) or aluminium nitride (AlN) waveguides Kim et al.
(2019). AlN and SiN are advantageous over Si due to their wide band gap,
allowing the full range of emitters to couple into the waveguide without
suffering from significant absorption. While successful in demonstrating
coupling to waveguides, the efficiency was very low, at about 12 % Elshaari et
al. (2021). Monolithic integration of quantum emitters in hBN to waveguides
has been demonstrated Li et al. (2021); Gérard et al. (2023). The advantage of
monolithic integration is that it avoids issues of index mismatch present in
hybrid integration. In doing so, waveguide coupling and grating coupler
efficiencies of $\sim 40\%$ was achieved Li et al. (2021). Furthermore, by
using electron beam irradiation, localisation of emitters to the waveguide
could be realised Gérard et al. (2023). However, significant work is yet to do
be done for high throughput fabrication of such devices. Firstly, the process
of using hBN flakes makes deterministic aligning of emitter dipoles to the
waveguide challenging and secondly, the dimensions of the flakes prevents
wafer scale fabrication of these devices. It is therefore of interest to
design a protocol which allows control over dipole alignment, emitter
placement and wafer scale processing. For example, the CVD process for hBN on
(SiN) substrates represents a promising advancement.

Enhancement of SPE intensities to achieve high bit rates across communications
platforms is also an area that needs to be advanced. This can be achieved by
coupling emitters to resonant cavities Fröch et al. (2020); Tran et al.
(2017). Present challenges to this is similar to the coupling of waveguides to
emitters, i.e alignment of dipoles to the cavity to achieve maximal Purcell
enhancement. Current work has only been able to achieve moderate enhancement
on emitters in hBN flakes of 2 to 6 times Tran et al. (2017); Fröch et al.
(2020).

The introduction of dopants into hBN to create resonant peaks suitable for
single-photon sources is an innovative approach that warrants further
exploration. Precise engineering of defects with desirable optical and spin
properties will allow major leaps in quantum computation and communications
relying on optically addressable spin qubits.

Finally, in order to fully realise a compact quantum technology that can be
integrated with other electrical or photonic components. It becomes necessary
to be able to electrically drive emission. While some work has be done on
emitters in InGaN/GaN QDs, Deshpande et al. (2014), and TMDs Palacios-
Berraquero et al. (2016), these sources are not as feasible for scaling due to
their bulk (GaN) or low temperature (TMDs) nature. Therefore, further study
needs to be performed on controlled carrier injection into defects in hBN to
achieve electroluminescence.

In conclusion, the future of photonic quantum technologies based on hBN holds
immense promise. The continued refinement of fabrication processes, such as
the CVD process for hBN on SiN substrates, will be instrumental in harnessing
the full potential of this field. As our understanding of quantum phenomena
deepens and our ability to manipulate quantum systems improves, we anticipate
a wealth of exciting breakthroughs in the coming years for hBN based photonic
quantum technologies.

Conceptualization, M.K.P., C-C.H., J.D.M. and Y.-L.D.H.; methodology, M.K.P.,
C-C.H., J.D.M. and Y.-L.D.H.; investigation, M.K.P. and M.P.C.T.;
writing—original draft preparation, M.K.P.; writing—review and editing,
M.K.P., M.P.C.T., C-C.H., J.D.M. and Y.-L.D.H; supervision, C-C.H., J.D.M. and
Y.-L.D.H. All authors have read and agreed to the published version of the
manuscript.

The work was supported by the Engineering and Physical Sciences Research
Council (EPSRC), grant number EP/N00762X/1, EP/V040030/1 and EP/Y003551/1.

Not applicable.

The raw data supporting the conclusions of this article will be made available
by the authors on request.

The authors declare no conflict of interest.

References

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