# 3D-mapping and manipulation of photocurrent in an optoelectronic diamond
device

A. A. Wood<EMAIL_ADDRESS>School of Physics, University of
Melbourne, Parkville, Victoria 3010, Australia  D. J. McCloskey  School of
Physics, University of Melbourne, Parkville, Victoria 3010, Australia  N.
Dontschuk  School of Physics, University of Melbourne, Parkville, Victoria
3010, Australia  A. Lozovoi  CUNY-The City College of New York, New York
10031, USA  R. M. Goldblatt  School of Physics, University of Melbourne,
Parkville, Victoria 3010, Australia  T. Delord  CUNY-The City College of New
York, New York 10031, USA  D. A. Broadway  School of Science, RMIT University,
Melbourne Victoria 3000, Australia  J.-P. Tetienne  School of Science, RMIT
University, Melbourne Victoria 3000, Australia  B. C. Johnson  School of
Science, RMIT University, Melbourne Victoria 3000, Australia  K. T. Mitchell
School of Physics, University of Melbourne, Parkville, Victoria 3010,
Australia  C. T.-K. Lew  School of Physics, University of Melbourne,
Parkville, Victoria 3010, Australia  C. A. Meriles  CUNY-The City College of
New York, New York 10031, USA  CUNY - The Graduate Center, New York, NY 10016,
USA  A. M. Martin  School of Physics, University of Melbourne, Parkville,
Victoria 3010, Australia

(August 31, 2024)

###### Abstract

Characterising charge transport in a material is central to the understanding
of its electrical properties, and can usually only be inferred from bulk
measurements of derived quantities such as current flow. Establishing
connections between host material impurities and transport properties in
emerging electronics materials, such as wide bandgap semiconductors, demands
new diagnostic methods tailored to these unique systems, and the presence of
optically-active defect centers in these materials offers a non-perturbative,
_in-situ_ characterisation system. Here, we combine charge-state sensitive
optical microscopy and photoelectric detection of nitrogen-vacancy (NV)
centres to directly image the flow of charge carriers inside a diamond
optoelectronic device, in 3D and with temporal resolution. We optically
control the charge state of background impurities inside the diamond on-
demand, resulting in drastically different current flow such as filamentary
channels nucleating from specific, defective regions of the device. We then
optically engineered conducting channels that control carrier flow, key steps
towards optically reconfigurable, wide bandgap designer optoelectronics. We
anticipate our approach might be extended to probe other wide-bandgap
semiconductors (SiC, GaN) relevant to present and emerging electronic
technologies.

Characterising a material, however exotic, for use in electronics applications
amounts to determining how charges enter, leave, and most importantly, move
through it. Imaging charge carriers directly is generally not possible, so an
ideal diagnostic platform would thus consist of an array of minimally-
perturbative probes embedded throughout a material that detect electrons and
holes as they traverse the device. Exactly this situation occurs in several
wide bandgap semiconductors, where impurities give rise to optically-active
defect centres [1, 2, 3] distributed throughout the material. Some of these
defects even exhibit coherent spin properties at room temperature [4], such as
the nitrogen-vacancy (NV) centre in diamond [5] or the silicon-vacancy and
divacancy in SiC [6, 7]. Recently, it has been shown that exploiting the spin
properties of these defects provides a powerful means of characterising
optoelectronic devices [8, 9, 10, 11, 12, 13, 14, 15]. However, not all such
defects exhibit sufficient sensitivity to electric fields, especially at room
temperature. In comparison, the electronic charge state of a deep-level defect
in a wide bandgap semiconductor is a stable and optically addressable resource
[16, 17] for the study of charge transport [18, 19]. In this work, we
introduce a new imaging scheme based on single-shot charge-state-sensitive
optical microscopy to reveal the generation and flow of currents inside
diamond at room temperature in three dimensions. Our technique is distinct
from scanning photocurrent microscopy, where optical excitation generates a
photocurrent signal at remote electrodes [20]: here, we image the actual
photocurrent as it flows between electrical contacts and the point of optical
illumination, a measurement simultaneously _in-situ_ yet also weakly
perturbing.

Figure 1: Photocurrent generation and detection within an optoelectronic
diamond device. a) Experimental setup: two planar electrodes are deposited on
the surface of a diamond hosting NV centres. Optical protocols (bottom frame)
are used to prepare the NV centres and other defects in particular charge
states, which can then be measured using optical confocal microscopy or
detection of photocurrent (PC) via the electrodes and lock-in amplification.
(b) Images of NV- photoluminescence after an 8 mW (80 Hz modulated) green
laser beam is positioned near the left electrode, held at -120 V, while the
right-hand electrode (positive) connects to ground through a current
amplifier, and (c) corresponding photocurrent vs. time. All images are
80$\times$80$\,\upmu$m scans. The formation of dark, NV0-rich filaments
connecting the charge capture halo surrounding the illumination spot to the
left-hand electrode is correlated with distinct features in the photocurrent,
which corresponds to predominantly-hole photocurrent flowing in local channels
before a general ‘breakdown’ event at later times. Holes move from right to
left in these images. (d)(i-x) The dark ‘filaments’ nucleate from specific
regions of the electrodes, as these scans over a 200 $\upmu$m region shows.
Plots of the time-dependent photocurrent are shown inset for each confocal
scan, and the coloured circle on each plot indicates the corresponding time
where the image is taken (3-4.5 s, where the filaments are most clearly
resolved for each case). At each point, the onset of filaments always precedes
a general increase in photocurrent.

Our method works on the basis that a charge carrier induces a measurable
change in the fluorescence of a colour centre defect upon capture, for
instance NV- \+ h${}^{+}\rightarrow$ NV0. With charge-state selective
excitation and spectral filtering, we detect only the NV- fluorescence,
consequently, the spatial profile and time evolution of current flow is
imprinted on the charge state of an ensemble of NV centres embedded throughout
the device, enabling micoscale mapping in three dimensions. Optical confocal
microscopy is augmented by the simultaneous electrical detection of time-
dependent currents, allowing us to make clear associations between spatial
structures observed in images and current transients. We employ our technique
to detect local electric field inhomogeneities and preferential charge
injection in a metal-semiconductor interface, revealing points in the metal-
diamond junction that nucleate thin filament-like channels of charge carriers.
Next, we show that the spatial structure and temporal variation of
photocurrent is determined by the charge state of nonfluorescent defects,
assumed to be substitutional nitrogen impurities [21]. We can control and even
mimic the naturally-occurring filament structures by creating optically-
defined patterns of varied conductivity with laser scans, and then image these
patterns in three spatial dimensions with temporal resolution.

Experiment. Our experiment, depicted schematically in Fig. 1(a) and detailed
further in Methods, uses a diamond sample equipped with a pair of coplanar
Au/Cr electrodes ($500\,\times 500\,\upmu$m, 50$\,\upmu$m spacing) fabricated
on the oxygen-terminated diamond surface via photolithography (see Methods).
The nitrogen and NV concentrations are $1$ ppm and $0.01$ ppm, respectively. A
purpose-built confocal microscope enables two-colour optical illumination (532
nm and 633 nm) and charge-state-selective imaging via collection of only NV-
fluorescence within a limited band (691-731 nm). One of the electrodes is held
at a potential $V$, while the other connects to ground via a low-noise current
preamplifer and lock-in amplifier in a standard setup to detect photocurrent
[22, 23]. The voltage-current characteristics of the device were measured and
found to exhibit the characteristic back-to-back Schottky-diode shape of
similar semiconductor-metal interface devices [24], preventing efficient
injection of charge into the diamond from the electrodes. We thus generated a
photocurrent inside the diamond using optical illumination and charge cycling
[25] of the NV centres, which injects free electrons and holes into the
conduction and valence bands of the diamond, respectively. These freely-
diffusing charge carriers are then trapped by various defects, or drift
towards the electrodes and detected as a photocurrent [26]. In the former
case, and in the absence of an electric field, positively-charged holes are
efficiently captured by negatively-charged NV- centres, resulting in a
characteristic ‘halo’-like charge capture pattern (CCP) of NV0 and thus
reduced fluorescence around the illumination point in an NV--selective image.
Combining photoelectric detection with charge-sensitive imaging allows us to
then track where photocurrent flows when an electric field is applied.

Prior to inducing the photocurrent, we utilise two protocols, _green
initialisation_ (GI) and _defocused preparation_ (DP), depicted in Fig. 1(a),
to initialise the charge state of both the NV centres and nitrogen in the
diamond into NV-/N+ (see Methods). While other defects are expected to play a
similar role [27], we focus on nitrogen given it is the highest abundance
impurity in our sample. A full understanding of the charge environment we
initialise necessarily includes consideration of other defects, including
vacancies, as discussed later. After initialisation, we apply a -120 V bias
voltage to the left-hand electrode and position a focused green laser beam (8
mW, $1\,\upmu$m diameter) near the same electrode for a variable duration. The
position of the laser beam was chosen to maximise the measured steady-state
photocurrent (see Supplementary Material). The green light is modulated at 80
Hz to facilitate lock-in detection of the photocurrent, the modulation itself
was not observed to have any confounding effects on the measurements. While
the measured photocurrent originates from various sources [28], we verified
that a significant fraction derives from NV charge cycling by performing a
photoelectrically-detected magnetic resonance measurement with an applied
microwave field (see Supplementary material).

In Fig. 1(b,c), we study the time dependence of the NV population and
photocurrent, respectively. We first observe the characteristic circular CCP
of NV0 that quickly grows to a radius of 10-15$\,\upmu$m within the first 0.5
s of the photocurrent laser application. This feature expands almost
isotropically regardless of the applied field and is driven by charge carrier
diffusion and space charge effects [29]. At later times, we observe the
formation of filamentary structures of NV0 that connect the CCP to the ground
(positive) electrode. The formation of these features correlates with sudden
increases in photocurrent, indicating that hole photocurrent flows from the
ground electrode into the CCP via these channel-like filaments. Later, a
significant ‘breakdown’-like event is observed, corresponding to an almost
doubled photocurrent and complicated, unstable temporal dynamics. We also
studied how the photocurrent and filaments depend on position of the laser,
laser power and applied electric field (see Supplementary material).

In-situ device characterisation. The filamentary current channels are observed
to nucleate from specific regions of the ground (positive) electrode, and grow
from right to left, starting as dark patches near the electrode that
eventually reach out to join the CCP. In some cases, a matching filament from
the CCP is observed to join the approaching filament from the electrode. In
Fig. 1(d) we shift the vertical position where the photocurrent beam is
applied across the full 200 $\upmu$m field of view of our microscope, and
observe consistent sites where the filaments form, sometimes taking nontrivial
paths [e.g. Fig. 1(d, ii, iv)] to join to the source CCP. The onset of
filaments is always accompanied by a steep increase in photocurrent (inset).

A hint to the origin of these photocurrent filament channels is found in the
observed nucleation points along the electrode, and a consistent nucleation
point appears to be the top corner of the electrode, where field bunching
results in a locally stronger electric field. We hypothesise then that
filaments nucleate at similar points of higher field along the electrode,
whether due to localised intrinsic interface defects and damage or
imperfections in the metal-semiconductor junction. This latter point is of
considerable interest, given the difficulty in fabricating electrical contacts
on diamond and the lack of existing characterisation techniques. We note that
for all applied electric fields in this work, estimated to be of order
$10$-$20\,$kV cm-1, NV electrometry [30, 31, 32] could not detect any
electric-field induced splittings or shifts. In contrast, optical measurement
of the photocurrent via NV charge state conversion yields a striking and
highly specific _in-situ_ detection method for local electric field
inhomogeneity.

Tailoring photoconductivity with dark impurities. We now draw special
attention to the role of charge-state preparation, not just of the NV centres
but of other, non-luminescent defects in the diamond. Indeed, for the charge
state of the NV centres to be a non-perturbative detector carrier transport,
the extent to which the probes affect the photocurrent dynamics must first be
understood. We first remove the DP step, which generates the NV- charge state,
resulting in initialisation into optically dark NV0/N0 (see also Methods).
Figure 2(a) shows the photocurrent as a function of time following
initialisation with and without DP, with almost twice as much photocurrent
observed without the DP step, and lacking the intervening filament nucleation
step. While this might initially point to the NV charge state playing a
significant role in photocurrent transport, further investigation reveals the
opposite. We introduce another step, consisting of a 300 $\upmu$W red (633 nm)
scan (RS) that follows either GI or DP. Illumination with weak red light
results in one-way ionisation of the NV- to NV0 [33], but with a photon energy
of 1.96 eV, below the 2.2 eV photoionisation threshold of N0 [34], the red
light leaves the nitrogen charge state unchanged.

Figure 2: Optically engineering the initial conductivity. (a) Three optical
preparation steps control the charge state of NV centres and nitrogen
impurities between the electrodes. GI prepares mostly NV0 and N0 due to charge
cycling and carrier capture, DP creates NV- and N+ while an RS scan ionises
NV- and leaves N0 and N+ untouched. Photocurrent measurements following
initialisation steps are independent of the NV charge state, but strongly
dependent on the assumed N charge state. (b) Drawing horizontal or (c)
vertical paths with a varied-power green laser defines conductive channels,
with wider horizontal channels resulting in greater photocurrent generation,
and wider vertical channels parallel to the negative electrode nucleating
filaments at earlier times, with concomitantly higher photocurrents.

In Fig. 2(a) we compare the previous intialisation stages with the addition of
a RS step. Notably, the photocurrent is unchanged following initialisation to
NV- and subsequent ionisation with red scanning, and essentially identical
when a red scan follows a GI-only initialisation. The nearly identical
photocurrent profiles correlate with the expected nitrogen charge state and
confirm the NV plays a negligible role in the photocurrent dynamics, serving
only to detect the spatial distribution of holes.

Photocurrent appears to flow readily in N0-rich regions, and less so in
N+-rich regions. Rather than scanning across the whole inter-electrode region
as in a GI step, we can optically engineer specific regions by ‘painting’
patterns of NV0/N0 with green light. In Fig. 2(b), we scan a green laser beam
with power $P_{\text{ch}}$ between the electrodes, making a horizontal
conducting channel with width set by $P_{\text{ch}}$: as the channel is
widened with increasing power, the time taken for the photocurrent to reach
the same saturation value decreases. The time-dependence mirrors the
signatures of filament formation, with a characteristic step in photocurrent
signal occurring at earlier times as the channel width, effectively an
artificial filament, is increased. Similarly, in Fig. 2(c), we paint a
vertical line parallel to the right-hand electrode. Now, filaments form
between the source CCP and the painted region, accompanied by the same
photocurrent signatures observed for filaments formed between the CCP and the
bare electrode. Interestingly, this observation implies the processes that
drive filament nucleation at the diamond-electrode interface are replicated in
the defect charge environment following green laser application, which we
assume generates N0 in its vicinity.

Figure 3: 3D-spatiotemporal mapping of photocurrent flow. (a) Illustration
(bottom) and protocol (top) for time-resolved 3D photocurrent imaging with
charge sensitive microscopy. Here, a ‘target’ CCP is generated with a 0.50 s,
1.5 mW laser park 15 $\upmu$m below the diamond surface. Varying the $z$-plane
where the $x$-$y$ confocal scan is performed reveals the near-spherical shape
of the target CCP, which is fully disconnected from the metal electrodes (the
dark sections on the sides are the result of shadows cast by the electrodes).
(b) Applying an opacity mask to display only the NV0 concentration, we reveal
the full 3D spatiotemporal dynamics of photocurrent generation, filamentation
and breakdown. The source photocurrent laser is applied for time $t$, 7.5
$\upmu$m below the surface, the uppermost $z$-position corresponds to
$z=5\,\upmu$m below the diamond surface. We note the distortion and eventual
filament nucleation from the target CCP, 15 $\upmu$m below the surface. (c) A
simple cartoon model of filament formation and corresponding photocurrent
accumulation. i), electrons generated by the photocurrent laser drift under
the applied field, being captured by N+ and consequently forming channels of
N0 (ii) that act as conduction pathways for holes, at later times individual
filaments are washed out and hole flow saturates (iii). The proposed role of
the target CCP in this picture is to gather and bunch hole trajectories
towards the CCP, which explains the bulging observed in (b).

3D imaging of photocurrent flow. The electrical conductivity of diamond is
strongly dependent on the surface chemistry [35], which can also be modified
by light [27]. An important question then arises as to whether the surface of
the diamond plays a significant role in our own experiments. Due to the
lateral electrode geometry of our device, the electric field strength
decreases linearly with depth (see Supplementary Material), meaning the
strongest carrier drift is found at or near the surface. We extended our
photocurrent imaging scheme into three dimensions (Fig. 3(a)) by incrementally
changing the $z$-plane where the red readout scan is performed, with all other
optical manipulation steps as before. To probe the depth dependence of
photocurrent transport, we first apply a green laser beam ($P=1.2$ mW, for 0.5
s) 15 $\upmu$m below the surface of the diamond and $10\,\upmu$m from the
ground electrode to generate an isolated, ‘target’ CCP, analogous to the
painted regions depicted in Fig. 2(b,c) though entirely separate from the
electrodes. 3D charge-sensitive confocal scanning (Fig. 3(a,b)) reveals the
characteristic shape of the CCP, consisting of a spherical region of dark NV0
punctured by the conical regions exposed to the entering and exiting laser
beam, which remain NV- [33].

With the target CCP in place, we made a photocurrent measurement as before,
with the ‘source’ laser positioned 7.5$\upmu$m below the surface for a varied
time $t_{p}$. Figure 3(b) shows a sequence of 3D maps of the resulting NV0
distributions following variable time photocurrent laser measurements. As time
progresses, we see filament formation extending more than 10 $\upmu$m into the
diamond bulk prior to the onset of photocurrent breakdown. More significantly,
we observe a distinct, isolated filament form to join the source and target
CCP. These measurements show unambiguously that the photocurrent spatial
dynamics result from charged defects inside the diamond bulk, rather than
surface conduction effects. Prior to formation of a connecting filament, the
target CCP bulges _toward_ the photocurrent-induced CCP (see accompanying
videos in the Extended Data). This observation, while in concordance to some
degree with our measurements showing filament nucleation from both the bare
electrodes and the ‘painted’ regions in Fig. 2(c), is unexplained, as the
‘target’ CCP is assumed to be fully disconnected from the ground electrode.

Discussion. Our measurements provide an intricate picture of the origin and
phenomenology of photocurrent propagation in diamond. We first note that holes
appear to cross the metal-diamond junction of the ground electrode and
converge towards the CCP, first as channel-like filaments and then as a
breakdown-like flow that converges towards the CCP in a broad “V”-like shape.
To understand this, we must again take into consideration that the charge
state of nonfluorescent defects has a significant effect on the spatio-
temporal dynamics of the current flow. While holes travel from right to left
in images such as Fig. 1(b) and leave visible evidence in the form of NV0,
electrons are to be assumed to follow similar, unseen trajectories but from
left to right. Electrons generated by the photocurrent laser remain invisible
to our imaging technique, as the dominant interaction expected is capture by
N+, which does not change the NV fluorescence, but does significantly alter
the photoconductivity. From Fig. 1(d), hole injection is observed to occur at
specific, reproducible regions of the ground electrode, and we expect that
these same sites also attract electron flow towards regions of stronger
electric field. Electrons create channels of N0 as they are drawn to these
defective sites, and then build up on the diamond-electrode Schottky
interface. Eventually, sufficient negative charge buildup occurs to reduce the
Schottky barrier height and facilitate hole (minority carrier) injection [36],
which in turn preferentially flows along the channels passivated by the
electrons.

We can thus posit a model where charged impurity scattering sets the electron
and hole mobilities, and the filaments are first traced by electrons
propagating away from the photocurrent laser beam, as depicted in Fig. 3(c).
Open questions remain as to the microscopic charge environment, and whether
the nitrogen is initialised into a positive charge state alone (as an
optically-defined space charge region), or compensated by electron capture by
neutral defects such as neutral vacancies V0 [37]. In the latter case, the
charge environment is neutral, though possesses equal numbers of ionised
impurities acting as electron and hole traps, resulting in the observed
impeded current flow. In both pictures, carrier capture drives the charge
environment towards a state composed of neutrally-charged defects (N0, V0)
which results in higher carrier mobilities. The time-dependence of the
photocurrent, which resembles the archetypal case for extrinsic, defect-
mediated photoconductivity [38] offers further insights. Given a significant
photocurrent flows before any filaments are observed optically, we can deduce
that the initial photocurrent is due to electrons, which gradually passivate
the N+ population that impedes hole flow. With a high hole mobility corridor
of N0 connecting the CCP to the electrode, hole current now flows and is
observed through charge state conversion of the NV centres.

We now apply our model to explain the phenomenology observed in Fig. 2(c) and
Fig. 3(b). Of particular note is the somewhat anomalous finding that an
isolated target CCP appears to bulge or distort in the direction of the
photocurrent CCP. We note that no bulging or distortion is observed for an
equivalent experiment without the applied electric field, or without the
photocurrent laser but with an applied field. Due to the the very short
carrier lifetime ($\sim 1\,\upmu$s [39]), no free charge is stored in the
isolated target CCP, which is created several seconds before the photocurrent
beam is turned on. We propose that the isolated target CCP acts essentially as
a focal point first for electron current, which is drawn to the isolated
region of NV0/N0 in the same way as it is focused on defective sites along the
electrode and the painted regions in Fig. 2(c). This in turn attracts holes,
which flow along various defect-nucleated paths from the electrode towards the
target CCP. Here, the paths bunch up, resulting in a higher hole concentration
and stronger NV0 signal than closer to the positive electrode. Further work is
needed to fully understand this observation.

Our work demonstrates a powerful new measurement modality for the study of
charge transport in a semiconductor, and poses questions that motivate an
improved understanding of photoelectric physics in diamond. In this work we
have focused on diamond, which is arguably the most technologically mature
platform for our technique, possessing well-characterised photochromic defects
which are stable at room-temperature, while also being a promising material
for select high-power electronics [40, 41, 42]. With further work, our method
could be extended to materials more advanced in terms of power-efficient
semiconductor applications which host similar optically active defect centres
[43], i.e., SiC [44] or GaN [45], or in emerging platforms for quantum sensing
such as hBN [46]. Focusing on diamond, our work has immediate implications for
photoelectric detection of NV centres [47, 48]. Photoelectric detection of NV
magnetic resonance promises fully-integrated sensors unconstrained by the
diffraction limit and limitations of optical collection efficiency [47].
Indeed, the complicated spatial dynamics of photocurrent we measure here are
at play, unseen, in many photoelectric detection schemes. Similar issues are
encountered in diamond radiation detectors, where impurities capture charge
carriers generated by high-energy particles [49], leading to space-charge
effects that impact performance. However, photocurrent cannot be spectrally
filtered like photoluminescence, and the carrier capture by other defects we
observe here translates to reduced photocurrent yield. Both these points are
addressed in our work, where we show careful control of the nitrogen charge
state yields significantly enhanced photocurrents, and observation of filament
formation allows us to attribute sources of photocurrent injection to from the
electrodes rather than from particular defects. More ambitiously, optical
manipulation of specific defect concentrations and regions could be used to
create junctions, current pathways, interconnects and potentially even entire
optically-defined devices using charged defects.

##  I Methods

###  I.1 Initialisation scans.

Green initialisation (GI) An initial high-intensity (8 mw) green scan serves
to erase any spatial charge distributions left by preceding experiments, and
due to the continuous generation of electrons and holes from NV charge cycling
originating from the scanning laser beam, prepares a region of predominantly
NV0 (via NV- hole capture) and N0 (via N+ electron capture) [50]. Typical scan
ranges are $(80\times 80)\,\upmu$m and take 30 s to complete. The electric
field is off during the initialisation scans.

Defocused preparation (DP) Following the (GI) scan, we elevate the microscope
objective 50 $\upmu$m above the surface of the diamond and repeat the scan.
The corresponding optical intensity at the diamond is significantly reduced,
and as a result two-photon NV charge cycling is markedly suppressed. However,
single-photon ionisation of N0 continues. Following this defocused preparation
(DP) step, we observe an increased fraction of NV-, which we attribute to
photoionisation of N0 generating electrons that are eventually captured by the
NV0 defects. The extended optical interaction time ($>10\,$s) prevents
electron recapture by N+ and effectively forces electrons into traps,
resulting in a higher fraction of positively charged nitrogen. More details
about how the DP step functions to increase N+ density are provided in the
Supplementary Information.

###  I.2 Electrode fabrication.

Square $500\,\times 500\,\upmu$m electrodes were fabricated following a
photolithographic patterning and lift-off process. The diamond substrate was
first cleaned by boiling in a 1:20 (by weight) mixture of sodium nitrate and
sulphuric acid for 20 minutes followed by a 10 minute immersion in piranha
etching solution at 90 degrees C and subsequent ultrasonic immersion in
deionized water. The sample was coated with image-reversal photoresist
(AZ1514E – MicroChemicals GmbH) by spin-coating. After baking to remove resist
solvent, the sample underwent a brief flood exposure under a standard mercury
vapor lamp in a mask aligner (Quintel), after which the sample underwent
image-reversal baking in order to partially crosslink the uppermost layer of
the resist film. Electrode patterns were then written on the sample using a
direct-write UV lithography system (POLOS NanoWriter), after which the resist
was developed in AZ 726 MIF developer for 90 seconds. The crosslinked upper
layer of resist results in an undercut sidewall profile, thereby allowing for
evaporation and lift-off to create the electrodes. The sample was exposed to
oxygen-argon plasma in a benchtop plasma ashing system (Diener Femto) for 30
seconds to remove photoresist residues from the sample surface prior to
electron-beam evaporation of a 15nm/100nm Cr/Au stack. Lift-off was performed
by ultrasonication in acetone followed by deionized water. No post-fabrication
annealing of the electrodes was performed, and the sample preparation steps
leave the diamond with an oxygen-terminated surface.

## Acknowledgments

We thank R. E. Scholten for a careful reading of the manuscript. This work was
supported by the Australian Research Council (DE210101093). R. M. G. and K. T.
M. were supported by an Australian Governement Research Training Program (RTP)
Scholarship. D. A. B. was supported by an ARC DECRA Fellowship (DE230100192).
A.L. acknowledges support from the National Science Foundation under grant
NSF-2216838. T.D. and C.A.M. acknowledge support by the U.S. Department of
Energy, Office of Science, National Quantum Information Science Research
Centers, Co-design Center for Quantum Advantage (C2QA) under contract number
DE-SC0012704. A.L., T.D., and C.A.M. acknowledge access to the facilities and
research infrastructure of NSF CREST-IDEALS, grant number NSFHRD- 1547830.

## Author contributions

A. A. W. conceived and led the work with guidance from C. A. M. and A. M. M.
Data was collected and analysed by A. A. W. with assistance by R. M. G. The
devices were fabricated by D. J. M., simulations of the device electric fields
were carried out by K. T. M, and the electrical characteristics of the device
were assisted by C. T-K. L. The theoretical model was developed by A. A. W, N.
D., D. J. M., A. L., T. D. and C. A. M. with inputs from D. A. B., J-P. T. and
B. C. J. All authors contributed to the preparation of the manuscript.

## Competing interests

The authors declare no competing interests.

## Data availability

All raw data and analysis code is available from the corresponding author (A.
A. W.) upon reasonable request.

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SUPPLEMENTARY INFORMATION

##  II Experimental Setup

The experimental setup was briefly outlined in the main text and methods, and
a full description including all important part numbers is provided here and
shown schematically in Fig. S1. The apparatus is a home-built confocal
microscope featuring a three-axis scanning microscope objective and paths for
multiple wavelength excitation, and a single-photon counting module for
detection of NV fluorescence. We use a Nikon TU Plan ELWD 50$\times$ NA =
$0.6$ microscope objective and a Physik Instrumente P-545 scanning piezo stage
with 200$\,\upmu$m travel in each direction. Excitation light at 633 nm from a
diode laser (Coherent Obis 633) and 532 nm from a Laser Quantum opus 532 via a
double-passed AOM setup (AA Optoelectronic MT200-A0,5-VIS) for intensity
control is combined with free space optics and dichroic mirrors into a single-
mode, polarisation-maintaining fiber (Thorlabs P3-488PM-FC). Light from the
fiber is collimated with an achromatic microscope objective (Nikon TU Plan EPI
SLWD 0.3 NA) and expanded to fill the back aperture of the imaging objective
(5 mm). A Thorlabs 638 nm longpass dichroic mirror reflects green and red
light onto the microscope objective and permits the transmission of NV
fluorescence. A 650 nm longpass filter (Thorlabs) and a 695-725 nm bandpass
filter (Semrock) set of optical filters is used to selectively transmit only
NV- fluorescence via an $f$ = 100 mm doublet lens into 50 $\upmu$m multi-mode
fiber, and inally into a single-photon counting module (SPCM, Excelitas SPCM-
AQRH-14). Despite the filters, we still detect residual 633 nm light from
surface reflections in our signal, though at the level of a few thousand
counts per second can be generally ignored, contributing only a baseline
background signal to the NV0 signal.

The diamond sample is mounted using PDMS on a microscope cover slip glued onto
a custom printed circuit board. Care is taken to avoid any glue (Norland
Optical Adhesive no. 61) contacting electrical pads as it has been found to
exhibit conductivity. Square $500\,\times 500\,\upmu$m electrodes were
fabricated following a photolithographic patterning and lift-off process. The
diamond substrate was first cleaned by boiling in a 1:20 (by weight) mixture
of sodium nitrate and sulphuric acid for 20 minutes followed by a 10 minute
immersion in piranha etching solution at 90 degrees C and subsequent
ultrasonic immersion in deionized water. The sample was coated with image-
reversal photoresist (AZ1514E – MicroChemicals GmbH) by spin-coating. After
baking to remove resist solvent, the sample underwent a brief flood exposure
under a standard mercury vapor lamp in a mask aligner (Quintel), after which
the sample underwent image-reversal baking in order to partially crosslink the
uppermost layer of the resist film. Electrode patterns were then written on
the sample using a direct-write UV lithography system (POLOS NanoWriter),
after which the resist was developed in AZ 726 MIF developer for 90 seconds.
The crosslinked upper layer of resist resulted in an undercut sidewall
profile, thereby allowing for evaporation and lift-off to create the
electrodes. The sample was exposed to oxygen-argon plasma in a benchtop plasma
ashing system (Diener Femto) for 30 seconds to remove photoresist residues
from the sample surface prior to electron-beam evaporation of a 15nm/100nm
Cr/Au stack. Lift-off was performed by ultrasonication in acetone followed by
deionized water. No post-fabrication annealing of the electrodes was
performed, and the sample preparation steps leave the diamond with an oxygen-
terminated surface.

The diamond electrodes are connected to the PCB via wirebonds, and an
electrically-insulated 100 $\upmu$m copper wire is placed 100 $\upmu$m above
the electrodes for the application of microwaves, which are sourced from a
Windfreak SynthHD connected to a Microwave Amplifiers AM6-1-3.5-47-47 50 W
amplifier. We use a high-voltage amplifier (Thorlabs HVA200) to supply
voltages to one electrode between $\pm 200\,$V during usual operation or a
high-voltage DC source (Stanford PS325) for higher voltages (up to $\pm
500\,$V) for I-V characterisation. High-voltage control signals are sourced
from a 16-bit analog voltage source (NI-PCI6733). The second electrode is
connected to the photocurrent signal measurement chain, consisting of a low-
noise current preamplifier (Stanford SR570) whose output is connected to a
lock-in amplifier (Stanford SR850), the output of which is directed to a
National Instruments data acquisition board (NI-PCIe-6323). For photocurrent
measurements, the lock-in reference signal is provided by a Rigol DG4162
function generator that modulates the AOM drive amplitude in the 532 nm
double-pass setup. Typical gain settings for the current amplifier are 100-500
pA/V, no filtering, high-BW mode and no input offsets. The lock-in amplifier
has 20 dB of gain (the lowest setting) and a 30 ms time constant, with the
modulation frequency set to 80 Hz, square-wave. We do not require the lock-in
amplifier to see a photocurrent signal, but find it essential to remove
anomalous drifts in the observed DC signal following optical preparation
steps, where a slowly-damped (60 s) DC component of between 10-100 pA often
accompanies the photocurrent signal, discussed further in Sec. IV. The origin
of this effect is not precisely known, though is potentially related to the
unavoidable optical excitation of the metal-diamond interface during
initialisation scans[1]. Our experimental hardware and data analysis is
controlled using the Python-based Qudi experimental control suite [2].

Figure S1: Experimental setup, showing relevant experimental hardware and
geometry. Inset on the schematic diagram of the diamond is a photograph of the
actual device, the electrode pads are $500\,\times 500\,\upmu$m for scale.

##  III Photoelectrically-detected magnetic resonance

We confirmed that the measured photocurrent originates from charge cycling of
the NV by performing photoelectrically-detected magnetic resonance (PDMR). In
a PDMR experiment, a change in photocurrent signal is observed when microwaves
resonantly drive the $|m_{S}=0\rangle\leftrightarrow|m_{S}=\pm 1\rangle$
transitions. This originates from the spin-selectivity of the NV- ionisation
process, as green-mediated ionisation is more probable from the excited state
spin triplet of the NV rather than the metastable spin singlet states that are
populated preferentially by $m_{S}=\pm 1$ states following optical excitation
and passage through the intersystem crossing [3]. A similar effect has also
been observed for charge-capture patterns (CCPs), since equivalent physics
drives the expansion of the NV0 region around the illumination spot [4]. Here,
observation of PDMR serves primarily to confirm that NV centres are the source
for a fraction of the photocurrent. To observe PDMR, a 50 G magnetic field is
applied that makes a 21.1∘ angle to the diamond surface normal, and we apply
the protocol depicted in Fig. S2(a), identical to a cw-ODMR experiment except
that the 8 mW green laser is modulated at 80 Hz to enable lock-in detection of
the photocurrent. PDMR (orange) and ODMR (blue) traces are shown in Fig.
S2(b). The observed PDMR contrast is typically less than one percent, and sits
on a strong background variation that persists when the laser is switched off,
we attribute this to coupling of the microwave signal into the photocurrent
detection signal chain. The slight offset between ODMR and PDMR traces is due
to the long time constant of the lock in amplifier making the photocurrent lag
behind the time-varying microwave frequency sweep. The observation of PDMR
indicates a fraction of the photocurrent originates from charge cycling of NV
centres. While negative ODMR contrast is the norm, PDMR contrast can vary
significantly in amplitude and even become positive for certain samples [5].
Thus, the low amplitude of the PDMR signal does not necessarily indicate a
very small photocurrent of purely NV origin.

Figure S2: Experimental protocol (a) for photoelectrically-detected magnetic
resonance (PDMR), consisting of 300 mW varied-frequency cw microwave and a -80
V electric field applied while the 8 mW 532 nm laser is modulated at 80 Hz.
(b) ODMR (blue, left-axis) and PDMR (orange, right axis) results. The slight
offset between ODMR and PDMR traces is due to the long time constant of the
lock in amplifier making the photocurrent lag behind the time-varying
microwave frequency sweep.

##  IV Electric field geometry and device characterisation

To estimate the electric field geometry, we used the COMSOL Multiphysics
Electrostatics module. We recreated the geometry of the electrodes placed on
the surface of the diamond and used the in-built diamond material which
assumes the relative electric permittivity of diamond is $5.7\varepsilon_{0}$.
One electrode was held at a potential of -120 V and the other at ground.
Figure S3 shows how the electric field strength ($\left|E\right|$) varies with
depth inside the diamond. All points were calculated along a line passing
through the centre of both electrodes. The 25 $\upmu$m line is at the mid-
point between the electrodes. The 5 $\upmu$m point is closest to the grounded
electrode. Only the electric fields on the side of the grounded electrodes
were calculated as the electric field is symmetrical. It should be noted that
the simple model described here does not include surface or internal,
N-dominated Debye screening effects by charges diamond created via laser
illumination, which reduces the electric field strength at the location of the
NVs [6, 7].

Figure S3: Simulated electric field strength $|E_{x}|$ as a function of depth
into the diamond $z$ for various distances $|\Delta x$ from the ground
electrode. All experiments conducted in this work were within 20 $\upmu$m of
the surface.

The diamond sample equipped with metallic electrodes constitutes an electrical
device that is composed of a metal-semiconductor-metal junction, each of which
form Schottky-type barriers. The electrical characteristics of such a device
exhibits a characteristic V-I curve at low bias voltages, where a very small
leakage current flows: while one Schottky junction is forward-biased, the
other is reverse biased and this limits the overall current. At higher bias
voltages, the measured current abruptly increases, and for the voltages we can
apply without damaging the device ($<$400 V) we observe no saturation. A
measured I-V curve of the device used in the experiments described in the main
text is depicted in Fig. S4. After a prolonged exposure to higher voltages and
significant current flow, the I-V curves are observed to change, though
gradually return to that depicted in Fig S4.

Though much information, including the barrier heights and ideality factors
for each junction can be deduced from I-V measurements [8], it should be noted
that the I-V curves represent the electrical characteristics of the _entire_
500 $\upmu$m of the diamond-metal contact rather than the comparatively
smaller spatial region probed in experiments (80$\times$80$\,\upmu$m). In
principle, one could additionally study how the IV curves respond to the
various optical initialisation protocols conducted in this work, though the
presence of an unexplained systematic vexes these measurements. Following
optical scanning (either GI or DP were observed to have the same effect) and
application of a bias voltage, we observe a significant current transient with
a slow decay time, typically of order 30 s (Fig. S4(c)). The magnitude of the
current transient is observed to depend on the applied electric field, as
shown in Fig. S4(d), though the time constant is observed to be nearly
completely independent, with time spent at zero electric field having the same
effect as application of an electric field. We performed experiments to
determine if this current transient had any role in the photocurrent
measurements or spatial features in confocal measurements we study in the main
text by pausing for 180 s after optical preparation and application of the
electric field, and found no significant difference in confocal images or
photocurrent time dependence.

Figure S4: Voltage-vs-current characteristics for the diamond photoelectric
device used in experiments. a) logarithmic scale, where the current magnitude
at negative bias voltages is plotted, and b) detail on a linear scale of the
low-voltage region, showing low leakage current. c) Current measured through
device immediately following green initialisation scanning (GI) and
application of a voltage $V_{0}$ for time $t_{V}$, and d) peak current
transient vs applied voltage $V_{0}$.

##  V Optical preparation of nitrogen charge state

As the most abundant defect in our diamond (1 ppm), substitutional nitrogen is
the prime candidate for the nonfluorescent defect that dictates the
photoconductivity of the sample. All NV-hosting diamonds contain nitrogen to
varying degrees, as it is an essential precursor in the formation on the NV
centre itself and the negative charge state of the NV centre is hypothesised
to arise from a nitrogen donor [9, 10]. Three charge states of
N${}_{\text{S}}$ have been reported, though only N+ and N0 exist stably at
room temperature in the bulk of the diamond [11], the negatively-charged state
N- having only a 10 ns lifetime [12]. Early photoconductivity measurements put
the N0 donor level at the commonly accepted value of 1.7 eV below the
conduction band [13], in agreement with ab initio modelling [14]. However,
more recent measurements reported low ionisation cross sections below 2.2 eV,
the now commonly reported ‘photoionisation threshold’ for N0 [15, 16, 11]. The
difference is attributed to the additional energy required for rearrangement
of the N and C atoms upon ionisation [14]. Practically, this results in
minimal charge interconversion of N under red (1.95 eV) light.

###  V.1 Generation of N0 and NV0: green initialisation

We consider first the green initialisation scan (GI), where a high power (8
mW) green laser is scanned over the entire region of interest between the
electrodes. The laser focus is approximately 7.5 $\upmu$m below the surface of
the diamond, and corresponds to an intensity of order 1 MW/cm2. For this high-
intensity regime, charge cycling of the NV is very strong and results in rapid
generation of free holes and electrons, which are captured by any NV- and N+
surrounding the laser spot. Weaker processes, such as NV0 electron capture and
N0 hole capture are not explicitly forbidden, though any generation of NV- or
N+ is quickly suppressed by the Coulombic attraction of holes and electrons,
respectively. Under the laser spot itself, a steady state charge distribution
is established with a significant NV- population, as evidenced by the bright
spot at the centre of the CCP. The details of this charge distribution are
unimportant, since scanning the laser beam (quasistatically on the $\sim$MHz
timescales of ionisation and recombination) quickly swamps the bright areas
with charge carriers generated under the new laser focus that subsequently
result in NV0 and N0. While only NV- population can be definitively inferred
from confocal measurements (at the noise floor after only one green scan), it
is reasonable to assume a significant fraction of the nitrogen charge state
population is converted to N0 under the sustained generation of electrons from
NV charge cycling. The 3D nature of the CCP generation means the NV0/N0
generation extends some 50 $\upmu$m into the bulk of the diamond. The GI step
is also effective at deleting old patterns imprinted on both the NV and N
charge states, and thus forms the first initialisation step in every one of
our experiments.

###  V.2 Generation of N+ and NV-: defocused preparation

We found that defocusing the green laser (while kept at the same power of 8
mW) resulted in an increase in NV- generation. While not in itself evidence of
a similarly dramatic change in the N0 population, the two processes are
intimately linked. For the NA = 0.6 objective lens used in our experiment,
raising the objective lens 50 $\upmu$m above the imaging plane (i.e. where the
GI step was performed) reduces the optical intensity by a factor of 1900, but
reduces the two-photon charge cycling rate of the NV ($\propto I^{2}$) by a
factor of 3$\times 10^{6}$, effectively suppressing it compared to the single-
photon ionisation rate of N0. The reduced optical intensity, extended
interaction time and inhomogeneous intensity profile of the light is the key
to the DP step. An equivalent process to the formation of a CCP occurs, albeit
with one-way photoionisation of N0 being the dominant effect and this time,
the steady-state charge distribution under the laser spot is the important
part.

Under sustained, low intensity green illumination, single-photon ionisation of
N0 occurs. The electrons generated by this process either 1) recombine with
the host N+ (geminate recombination), 2) diffuse some distance before capture
by another N+ or 3) be captured by a trap that is optically inactive. For
cases 1 and 2, subsequent photoionisation always occurs, resulting in multiple
capture and ionisation cycles between N+ centres before eventual pumping into
traps. Electron capture by NV0 is weak due to the lack of coulombic
attraction, but over the multiple seconds of exposure to light such processes
may become significant. Once an NV0 has captured the electron, the low optical
intensity suppresses ionisation and extends the trap lifetime, resulting in
efficient NV- generation. Further, without NV charge cycling occuring, hole
generation and diffusion is assumed to be negligible, meaning trapping by NV-
is a dead-end for the electron. After saturation of the NV and potentially
other traps, the end result is local N+ enrichment. As discussed in the main
text, the exact charge composition of other defects is currently unknown.
Defining a charge environment composed of only neutrally-charged defects, we
consider a mesoscopic charge-neutral situation, with equal numbers of
positively- and negatively-charged defects coexisting with no spatial
structure. With this assumption, it is reasonable to assume that the
generation of N+ is accompanied by a concomitant increase in a negatively
charged defect that is not the NV centre. This second inference stems from the
observation that ionising the NV- population generated following a DP scan
with red light (Main text, Fig 2(a)) has no bearing on the photoconductivity,
and implies a neutral charge trap T0 with a concentration significantly higher
than the NV yet lower than substitutional nitrogen,

$[\text{N}]>[\text{T}]\gg[\text{NV}].$ (S1)

Thus, the change in the N charge state after a DP scan is limited by the T0
population rather than the NV population. The lack of an observed GR1
fluorescence feature from V0 in this diamond (ZPL at 741 nm [17]) raises
doubts about this model. An alternative picture, mentioned in the Main Text,
is that the electrons liberated from N0 photoionisation in the DP step diffuse
away from the illumination region, to be captured by other defects in the bulk
or surface of the diamond, thus leaving a significant N+-rich, charge-
uncompensated region. Charge compensation thus occurs over a macroscopic
region.

###  V.3 Generation of N0 and NV-: Weak green preparation

Reducing the laser power to a sufficiently low level and keeping the laser
focus scanning in-plane should serve to emulate the defocused preparation
step, assuming only the intensity of the light, rather than its spatial
extent, matters. We compared weak green (WG) scanning to defocused
preparation. With both initialisation steps preceded by a GI scan that is
assumed to make N0/NV0 (Fig. S5)(a,b), we varied the intensity in the DP step
by changing the height above the diamond and laser power to span 7 orders of
magnitude in intensity and measured the PL within a 30 $\upmu$m circle between
the electrodes to assess NV- generation. Three regimes are apparent in Fig.
S5(c): when the intensity is too low, little to no photoionisation of N0
occurs and thus no NV- population is generated. For high intensities,
$I>10^{5}\,$W/cm2, NV- charge cycling is strong and so hole generation and
capture result in NV0 formation, akin to a GI scan. In between,
$10^{3}<I<10^{5}$ W/cm2, NV- generation is maximised due to photoionisation of
N0 and electron capture by NV0. We typically used intensities of $10^{4}$
W/cm2 in DP scans.

Figure S5: Defocused preparation vs. weak green scanning. a) Sequence of
intialisation and readout steps. $N_{R}$ denotes the number of repeated green
scans. b) Schematic depicting differences between the DP and WG sequences:
while DP photoionises N0 over an extended region, WG only does so under the
laser spot. During a scan, the moving laser overwrites the previously prepared
region with electrons, resulting in N0 generation. c) Optimisation of
defocused preparation. NV- PL counts are indicative of the NV- population
generated in a fixed region of the diamond (a 30 $\upmu$m circle between the
electrodes). High intensities result in NV- charge cycling and hole
generation, while low intensities do not photoionise N0. In between, N0
photoionisation is dominant over NV- charge cycling, resulting in N+/NV-
generation. d) Optimisation of WG: NV- generation vs number of repeated 90
$\upmu$W scans, and (inset) power dependence for a single scan. We use
$N_{R}=6$ henceforth. e) Generation of a CCP with an 2 s, 8 mW laser pulse (no
applied electric field) on a background prepared with DP (left) and 6 WG scans
(right). All images are $(80\upmu\text{m})^{2}$ scans. The dashed lines depict
the CCP radius in the opposing image: charges propagate slightly further under
a WG preparation. f) Same as (e) but with $V=-120$ V. While no filaments are
present in the DP initialised background, clear filaments appear at earlier
times with WG. g) Photocurrent vs time for an 8 mW green laser park on
standard DP background and with various $N_{R}$.

Optimising the WG scan for NV- generation was achieved by first reducing the
green laser power to find the point at which NV- generation was highest in a
single scan ($90\,\upmu$W), and then repeating the scan six times (Fig.
S5)(d). We then compared formation of a CCP (8 mW, 2 s park) without (Fig.
S5(e)) and then with (Fig. S5(f)) an applied electric field. We observed that
the radius of the CCP is slightly larger with WG preparation, which is assumed
to generate more N0 than N+. Under a $-120$ V voltage applied to the left-hand
electrode, the difference between the two initialisations is far more
apparent. While no filaments are discernable under DP preparation at 2 s park
time, with WG a clear V-shaped filament structure is resolved. In the main
text we correlated formation of filaments with increases in photocurrent, and
we clearly observe this here also. In Fig. S5(g) we show the photocurrent vs
time for DP initialisation (dashed blue line) and compare this for WG with
various $N_{R}$. As the number of green scans increases, the photocurrent time
dependence appears to smoothly change from the characteristic profile of
purely GI initialisation (fast saturation, no plateaus) towards what we see
with DP (plateaus and filaments).

Changing the number of WG scans appears to be able to vary the N+
concentration. This can be explained by invoking the model of nitrogen charge
conversion in the macroscopic charge neutrality case, and would seem to
confirm this model. Here, the optically-prepared region is limited to the
micron-sized laser spot. N0 is still ionised here, and NV- charge cycling
suppressed, but with the assumption of macroscopic charge neutrality,
electrons need only diffuse a a micron or so to escape the laser. As the laser
scans, a similar overwriting effect that occurs with the GI scan occurs,
except that this time only electrons are present, meaning a weak green scan
prepares NV- (since no holes are generated in the wake of the scanning laser,
NV- production is unaffected) and N0 from electron capture by N+. However,
this inference is based on the assumed N0 initial charge composition. Complete
experimental verification of one model or the other is not readily apparent,
and further work – ideally using an independent metric for nitrogen
concentration, such as electron paramagnetic resonance – is needed to reveal
the exact charge composition following DP scans.

##  VI Power, position and field strength dependence

###  VI.1 Position of the photocurrent laser

In all measurements reported in the main text, the photocurrent laser was
positioned within 5-10 $\upmu$m of the electrode held at $-120\,$V. This
position was chosen as it corresponds to the point at which maximum
photocurrent was detected when the laser position was scanned. Fig. S6(a)
depicts a scanning-photocurrent measurement of the inter-electrode gap, each
line scan taking 4 s to complete (20 ms dwell time per 0.8 $\upmu$m pixel plus
dead time). We thus measure the steady-state photocurrent rather than the
photocurrent at a given time as before, as no well-defined initialisation
steps are taken before each scan. We measure maximum photocurrent yields near
the negatively biased electrode, and such observations were also made in Ref.
[18]. We now know from this current work that the increase in photocurrent
near the negative electrode corresponds to hole current flowing in the
‘breakdown regime’ from the ground electrode towards the CCP. This is observed
vividly in the following experimental data.

Figure S6: a) Scanning the laser beam while measuring photocurrent ($P$ = 8
mW, $V=-80$ V) reveals that the optimum point for maximised photocurrent
generation is near the negative electrode. b) Changing the laser park position
from optimum ($\delta x=0$) during a photocurrent measurement (after GI and DP
initialisation) affects the spatial distribution of CCP and filament
formation. c) Same as (b) but with reversed electric field, here, the
filaments form left to right. d) Time-dependence of the photocurrent for
negative bias and (e) positive bias. All images are $(80\upmu\text{m})^{2}$
scans.

We studied the spatiotemporal dynamics of photocurrent using the methods we
developed in this current work, changing the position where the photocurrent
laser is applied between the electrodes. Fig. S6(b-e) shows the relevant data.
Starting with green initialisation and defocused preparation, the photocurrent
laser (8 mW) is parked for a variable time and the resulting CCP distribution
is imaged while photocurrent simultaneously detected. When the photocurrent
laser is parked close to the more negatively biased electrode, filaments form
from the ground electrode: from right to left when negatively biased and from
left to right when positively biased, in the direction of the applied electric
field. As the laser park position is moved from the negative electrode, the
CCP radius is observed to increase, and distort towards the negative
electrode. These observations can be understood by noting that when the CCP
overlaps with the negative electrode, photogenerated holes that would
otherwise contribute to the CCP are drawn under or into the electrode. As the
laser position is moved further away, holes are still drawn towards the
negative electrode, resulting in a distorted shape, but now more holes
contribute to the expanding front of the CCP. The time-dependence of the
simultaneously measured photocurrent reflects the formation of filaments
observed in images. When filaments are present, the photocurrent is observed
to first rapidly increase, plateau, and then increase again upon the formation
of filaments. When no filaments are visible we observe only the rapid initial
increase and plateau. In both cases we also observe the magnitude of the
photocurrent to slowly drift down, consistent with the time dependent
transient reported in Sec. IV. We note here that we have reverted to signed
photocurrents to reflect the different device biases, whereas in the main text
we plot the absolute value of photocurrent.

Varying the position of the laser offers considerable insight into the
photoelectric mechanisms taking place. From Fig. S6, it is evident that
filaments only occur between the CCP and the more positively biased electrode.
We summarise the inferred dynamics of photocurrent in Fig. S7. Since the
filaments are interpreted as hole current flowing _towards_ the CCP, this
implies holes crossing the metal-diamond interface. However, without the
photoelectric laser generating charges inside the diamond, no such current
flow is observed to take place. We hypothesised in the main text that the hole
current is able to flow when electrons from the photocurrent laser create
corridors within the N+ regions that are focused on defective sites along the
electrode. We identified the flowing photocurrent prior to instigation of
filaments as electron current. Under reverse bias, electrons are unable to
overcome the metal-diamond Schottky barrier (evidenced by the very low DC
current flowing at these voltages), but appear to traverse the diamond-metal
junction (_i.e._ from inside the diamond, effectively forward biased) without
difficulty.

Figure S7: Photocurrent generation explained in terms of Schottky barriers. a)
Application of the photocurrent laser near the negatively-biased electrode
generates electrons and holes via NV charge cycling. Holes are swept towards
the left and electrons to the right, and a photocurrent $i_{1}$ is
established. As electrons pass through the diamond towards localised point
defects on the right hand electrode, N+ is converted to N0 via electron
capture. Holes cannot flow from the right to the left since the Schottky
barrier is too high, both junctions are reverse-biased for charges on the
metallic electrodes. b) Photoelectrons generated by the laser are trapped at
the diamond-metal interface and form a space charge, which results in
localised band bending and reduction of the Schottky barrier height for hole
injection. Holes enter the diamond and flow along the channels of N0 created
by the electron current, which we observe as filaments of NV0 and photocurrent
begins to increase (to $i_{F}$). c) following a steep increase in photocurrent
from hole injection, holes now flow through the diamond and a saturated
electron-hole photocurrent $i_{2}$ is reached. Figure S8: a) To study the
effects on temporal and spatial photocurrent dynamics, we quantify the time
corresponding to the onset of filaments (left) and measure the $y$-extent of
the CCP (right). b) Increasing the laser power is observed to result in faster
growth of larger CCP patterns (right) and consequently larger photocurrents
and earlier onset of filaments and breakdown (left). At this applied electric
field, (-80 V), when the CCP diameter approaches $35-40\,\upmu$m,
filamentation and subsequent breakdown occurs (dark trace). c) Increasing the
electric field strength results in increased photocurrent and earlier onset of
filamentation and breakdown. This is accompanied by a reduction in the CCP
diameter, consistent with more charge carriers (holes) being swept towards the
negative electrode. Overlaid on the right-hand panel is the CCP diameter when
filamentation and breakdown occur. Solid lines on the right in (b), (c) are
fits of the form $Ae^{-\gamma t^{0.25}}$.

The model depicted in Fig. S7 can then be used to explain the data in Fig.
S6(a-c). When the photocurrent laser is parked near the more positively-biased
electrode, no filaments or breakdown are observed, and the photocurrent even
in the steady state is less. In this case, holes drift slightly towards the
negative electrode, but always experience an N+ rich environment: with no
electrons to passivate the N+, hole mobility is reduced and they do not flow
across the device. Without a space charge growing near the negative electrode
to slightly forward-bias the Schottky junction, no electron injection occurs
either. One might expect that at sufficiently high voltages, electrons can
overcome the Schottky barrier and flow into the diamond, _i.e._ facilitating
reverse filament formation, from photocurrent laser (generating holes) to the
electrode. Electron injection at defective points along the electrode would be
expected to nucleate filaments. However, an important distinction must be
drawn here. The characteristic pattern of holes converging upon the
photocurrent laser illumination point is a consequence of the paths through
the N+ space-charge region created by electrons that are generated at a point
source. We never saw any filament-like features following current excursions
at high bias voltages, i.e. in Fig. S4.

###  VI.2 Photocurrent laser power and electric field

We then studied the spatiotemporal dynamics of photocurrent as a function of
the two most pertinent parameters at our disposal, namely, laser power and
electric field strength. We focus our analysis on the onset time of filament
formation and then subsequent ‘breakdown’ that are apparent from the
photocurrent trace, and correspondingly the diameter of the CCP which is
deduced from confocal images following the photocurrent measurement as shown
in Fig. S8(a). We define the CCP diameter as the FWHM extent of the dark
charge pattern in the $y$-direction, since the strong distortion accompanying
a breakdown event precludes reliable extraction of a characteristic horizontal
spatial extent. While the halo is not necessarily radially symmetric (though
approximately so in the space-charge dominated regime we are in), the
$y$-diameter nevertheless constitutes a useful figure of merit to quantify the
physical extent of the charge capture region.

As the laser power is increased, we observe that the CCP grows faster, and
subsequently that filaments and breakdown occur at earlier times, as shown in
Fig. S8(b). Indeed, when the CCP diameter nears 35-40$\,\upmu$m this
corresponds to the onset of filament formation and subsequently breakdown.
This observation implies that the formation of filament channels (at a given
electric field strength) are mediated by the proximity of the CCP boundary to
the ground electrode. When the electric field strength is increased in Fig.
S8(c), we again observe that breakdown events happen at earlier times,
however, the charge capture halo diameter is observed to saturate to smaller
values. We interpret this latter observation to essentially the same
phenomenology discussed in Fig. S6(b,c), with the stronger electric field
pulling holes from the CCP into the electrode, thus preventing the expansion
of the CCP.

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