Direct Measurement of Quantum Efficiency of Single Photon Emitters in Hexagonal Boron Nitride

Single photon emitters in two-dimensional materials are promising candidates for future generation of quantum photonic technologies. In this work, we experimentally determine the quantum efficiency (QE) of single photon emitters (SPE) in few-layer hexagonal boron nitride (hBN). We employ a metal hemisphere that is attached to the tip of an atomic force microscope to directly measure the lifetime variation of the SPEs as the tip approaches the hBN. This technique enables non-destructive, yet direct and absolute measurement of the QE of SPEs. We find that the emitters exhibit very high QEs approaching $(87 \pm 7)\,\%$ at wavelengths of $\approx\,580\,\mathrm{nm}$, which is amongst the highest QEs recorded for a solid state single photon emitter.

An important parameter that up to now has been unknown for the family of SPEs in hBN is their quantum e ciency (QE). e QE is an important parameter of any light source to be considered for implementation in practical devices. However, measuring the quantum e ciency of solid state sources is challenging due to the signi cantly varying surrounding electromagnetic environment.
In this work, we utilise a recently engineered family of SPEs in a few nm thick hBN lms, grown by chemical vapor deposition (CVD). ese exhibit less wavelength variability than commercial hBN sources and also provide a at topography over large area [17][18][19], which is advantageous for our experiments. To measure the QE, we utilise a method that was pioneered by Drexhage in the 1970s, [20] who investigated changes in the intrinsic radiative decay rate of europium ions as a function of distance to a silver mirror. e underlying modi cation of spontaneous emission of the emi ers in close proximity to a metal surface is a quantum electrodynamic e ect and related to local density of states (LDOS) [21][22][23][24][25]. Since the intrinsic non-radiative decay rate is not modi ed by the LDOS, changes in the total decay rate can be a ributed to an alteration of the radiative decay rate alone. In this way, radiative and non-radiative decay rate components can be separated by recording the emi er's excited state lifetime as a function of its distance to a mirror. Hence, this fundamental technique to directly measure the QE from decay rate components has been used for organic dyes, rare earth ions, quantum dots, and color centers in diamond. [26][27][28][29]

II. EXPERIMENTAL SETUP
e schematics of the measurement setup is shown in Fig. 1  a). A wavelength tunable pulsed laser (Solea, Picoquant) is focused through the cover slide onto the hBN ake with an oil immersion objective lens (NA 1.4, 100x). e SPE uorescence is collected via the same objective lens and guided through a confocal setup into a Hanbury-Brown and Twiss setup, consisting of a polarizing beam spli er (PBS) and two avalanche photon diodes (APD) (Excelitas). With a /2-plate before the PBS we analyzed the uorescence polarization, nding it to be parallel to the glass substrate, an example of which is shown in the suplemental material . e SPEs in hBN were grown using a CVD method as described elsewhere [17].  ent glass substrate, to enable simultaneous atomic force microscope (AFM) and photo luminescence (PL) measurements. Two examples of single emi ers in the hBN akes are shown in Fig. 1 b. To measure the QE of the SPEs, modi cation of their LDOS was achieved by employing a hemispherical tip with a radius of = 2.75 µm covered by gold. Modi cations of the emi er's lifetime were obtained by changing the distance of the AFM tip to the emi er. e lateral position of the tip and focus of the excitation laser were matched by scanning the tip over a large area while recording laser light re ected by the tip. Once matched, the mirrors' vertical position could be changed precisely via the build-in AFM piezo, allowing distance-dependent measurements of the SPE properties.
e QE can be considered as a scaling factor between a change in LDOS and a change in emission rate, as nonradiative processes are una ected by a changed LDOS. A detailed discussion can be found in Ref. [20]. e equation used to relate QE and LDOS is given by: With the distance-dependent lifetimes ( ), LDOS ( ) and QE , analogue to Ref. [30,31]. Accordingly, a change in LDOS is mediated by changing the mirror distance, which nally reveals the QE.  Fig. 2 d).

III. SIMULATION OF EXPECTED LIFETIME CHANGES
In order to relate the change in distance of emi er and mirror to a change in LDOS, we performed a simulation of an emi er exhibiting a horizontally polarized dipole hosted in the center of a 10 nm thick hBN layer (refractive index of = 1.65) situated on top of a glass substrate. A hemisphere made from gold with a tip radius = 2.75 µm is centered at a distance from the dipole acting as a mirror that changes the local density of states (LDOS) ( ). e LDOS can be expressed [22] by with the distance dependent emi ed power , which can be extracted from the simulation. Only SPEs with in-plane polarization were found (e.g. shown in the supplemental material ), therefore the simulations were performed with an in-plane polarized dipole. An intensity distribution with = 1240 nm and an emission wavelength of = 600 nm is shown in Fig. 2 a). In this situation, a standing wave pattern between dipole and mirror with three nodes can be seen. Similar simulations at di erent wavelength and distances were performed and relative lifetime changes extracted, results are shown in Fig. 2 b).

IV. QUANTUM EFFICIENCY MEASUREMENT
Once an SPE was identi ed, we performed distantdependent lifetime measurements for various tip to the emitter distances. First, we xed the AFM tip to emi er distance at approximately 1.2 µm. At this point, we performed a lifetime measurement for 1 s-2 s. Next we reduced the distance by 15 nm and performed the next lifetime measurement, re-peating this process until reaching the surface. e built-in AFM laser points at the end of the cantilever and gets reected to a build-in four quadrant photo diode. A bending of the cantilever results in a change in position of the laser on the photo diode, which was used to indicate a completed approach to the surface and thus stopped the QE measurement. Since this method has an error margin of at least one step (15 nm) and we don't know the emi er's depth, we keep a distance o set 0 as a t parameter.
e emission wavelength is also kept as a t parameter within reasonable limits deducted from the measured spectrum. e maximum distance for lifetime measurements was 1.2 µm which was sucient to produce robust values for the lifetime at in nity ∞ when le as a t parameter.
To determine the QE, we ed the following function to the distance-dependent lifetime measurements: ( To determine the error margins of the QE values, we performed 10 measurements on the same emi er shown by dots in Fig. 2 d). From this data set we calculated the average and the standard deviation of 6.6 %, represented by the solid line and the shaded area, respectively. In the following discussion and gures, we used this standard deviation. In a reference measurement, ∞ changed within minutes by about one standard deviation, uncorrelated to AFM tip approaches (see supplementary material ). us we speculate that photoinduced changes of the environment may cause lifetime and QE variations. Fig. 3 a) shows the QE dependence on the excitation wavelength, conducted at an emi er with a ZPL wavelength of 595 nm emi er. In addition, a power dependent QE measurement was performed on the same emi er, using an excitation wavelength of 540 nm. However, no systematic trend can be seen, as shown in Fig. 3 b). We therefore conclude that the QE of the hBN emi ers are independent of the excitation wavelength or power, which indicates an isolated electronic structure without shelving or additional non radiative states. Most SPEs in the CVD grown hBN sample show ZPL central positions at 570 nm − 590 nm [17] when excited with wavelength of (540.0 ± 1.5) nm. We denote this family as 580 . Consequently, we selected 12 emi ers from this family at random and performed QE measurements on each of them. Interestingly, however, when we switched the excitation laser to (580 ± 15) nm, a second family of emi ers shows up with ZPL central positions at 660 = (661 ± 4) nm, which we term 660 emi ers [18]. ese emi ers were less common throughout the samples, and we were only able to identify ve SPEs with clear ZPL (see Fig. 1 b for example of the SPE). e 660 family may be associated with a di erent charge state or an altered absorption cross-section pathway. Exciting the same area of hBN with a laser wavelength in between 540.0 nm and 580.0 nm, didn't show any emi ers with ZPL positions in between the original ZPL wavelengths. Consequently, we compared the QE of these two families, with the results plotted in Fig. 4 a). We nd clear evidence that the emi ers with the higher energy ZPL possess a higher QE. e QE of the 580 = (62 ± 9) % obtained from averaging over 12 SPEs, while the QE of the family with the longer ZPLs is 660 = (36 ± 8) %, averaged over 5 emi ers, respectively. We also compared the full width at half maximum (FWHM) of the emi ers in both families, as shown in Fig. 4 b). According to our results, there was no clear trend between the FWHM and the QE, for both families.
is might be counter-intuitive, since it indicates that the coupling to low energy phonons does not result in non radiative transitions. Nevertheless, the clear di erence in the QE values indicate that the two families have isolated electronic structures (rather than being same emi er that is shi ed by strain or electric elds).

V. SUMMARY
To summarize, we presented a method to measure the absolute QE of SPEs in hBN. Accompanied by a simulation of the change in LDOS, we found record high QEs of single SPEs in hBN approaching (87 ± 7) %. By measuring the QE of 17 SPEs and relating them to the respective ZPL wavelength, we could identify two SPE families, well separated in ZPL position, with di erent QEs. One family showing ZPLs clustered around 580 nm showed an average QE of (62 ± 9) %, while the other family operating at 660 nm showed an average QE of (36 ± 8) %. While the crystallographic origin of the defects is yet unknown, our results suggest that these emitters possess two distinct electronic structures. Having ultra thin (few nm) solid state SPEs with high QEs opens up fascinating opportunities for advanced quantum photonic experiments. For instance, combining these emi ers with dielectric antennas that have near unity collection e ciency, may result in a room temperature "single photon gun" [32]. Such sources can also nd use in quantum cryptography, that has traditionally been utilizing faint laser sources due to lack of ultra bright and ultra-pure SPEs. e SPEs in hBN that possess the higher QE can potentially meet this demand. Finally, the presented method can be extended to measure QE of localized and interlayer excitons in other 2D materials [33]. To determine the quantum e ciency, we related a change in local density of states (LDOS) to the changes in lifetime (see main text for detailed explanation). By approaching the single photon emi er (SPE) with a spherical mirror, a lifetime change could be observed. A typical lifetime -distance measurement can be seen in Fig. S1 a). Corresponding lifetime measurements and ts at the marked extreme points are shown in b). antum e ciency and corresponding lifetime measurement. a) antum e ciency measurement with 146 points and 6 s integration time per point, with an average count rate of 200 kcps. b) Lifetime measurement (dots) and ts (straight line), corresponding to a minimum (marked green in a) and b)) and a maximum (marked orange in a) and b)).
As described in the supplemental material of Ref.
[S1], we determined the excited state lifetime by recording time di erences between the applied laser pulse and the photon arrival time at the avalanche photodiodes (APDs). A normalized histogram is shown in Fig. S1 b). e t represented by the solid line is given by a circular convolution (denoted by * ) of a double exponential decay with the instrument response function (IRF): ( ) = * (S1) = 1 e − / 1 + 2 e − / 2 + .
With the amplitudes 1 and 2 , the lifetimes 1 and the xed lifetime 2 = 0.5 ns and the o set .

II. DIPOLE ORIENTATION
To reduce the free parameters needed to t the quantum efciency, i.e. Eq. 3 in the main text, we veri ed the horizontal alignment of the emi ing dipole by a polarization measurement, analogous to what was described in the supplemental material of Ref. [S1]. e uorescence was guided through a /2 plate and subsequently split by a polarizing beam spli er. Each output port was directed to an avalanche photo diode (APD). e recorded intensity will be denoted as APD 1 and APD 2 . e relative intensity detected at one port is shown in Fig. S2 and was calculated by (additionally we normalized the relative signal to its value averaged over 2 , denoted by the horizontal line): with the polarization angle . e high contrast (di erence between minimal and maximal point) of (0.797 ± 0.001) arb. units indicates for a horizontally aligned dipole [S2].