Decay rate enhancement of diamond NV-centers on diamond thin films

We demonstrate experimentally two-fold enhancement of the decay rate of NV$^0$ centers on diamond/Si substrate as opposed to a bare Si substrate. We link the decay enhancement to the interplay between the excitation of substrate modes and the presence of non-radiative decay channels. We show that the radiative decay rate can vary by up to 90% depending on the thickness of the diamond film.

resting on a thin diamond film, as compared to a bare silicon substrate, which we observed experimentally using time-resolved cathodoluminescence (TR-CL). We attribute such an increase to the existence of non-radiative channels and coupling of the emitters to Fabry-Perot modes of the thin film. In our experiments, we considered ~120 nm large nanodiamonds containing ~10 3 NV centers. The nanodiamonds were diluted in methanol and the solution was mixed for 10 min in an ultrasonic bath. The nanodiamonds were then deposited by drop casting on two different substrates: a 200 nm thick diamond film on silicon and a bare silicon wafer (see Fig. 1(b)). We characterized NV centers in the deposited nanodiamonds at room temperature using a scanning electron microscope (SEM) operating in fixed-spot mode. The electron beam was incident on the samples through a small hole in a parabolic mirror, which collected and collimated the emitted light. The collected light was subsequently directed to the entrance of a VIS/NIR spectrometer, as shown in Fig. 1 (a).
The spectrometer selected photons within a 3.6 nm wavelength range around the central wavelength of 575 nm and directed them to the input of a single photon detector. The beam blanker driven with a wave function generator produced a pulsed electron beam and also provided the synchronization required to implement time-correlated single-photon counting 20 . A beam current of ~1.8 nA was maintained in each TR-CL measurement. Our system can measure reliably lifetimes as short as ~3 ns.
We selected 60 nanodiamond clusters on each type of substrate with sizes in the range 120-1500 nm (see Fig. 1(c) and Supporting Information S3) and studied the emission of the neutral NV 0 centers at the zero phonon line, as shown in Fig. 1  We argue that the changes in the lifetime distribution observed for NV centers on a diamond film are a result of strong interactions between diamond nanoparticles and guided optical modes in the diamond film. To demonstrate this we performed full-wave 3D electromagnetic modeling of the emission from a dipole embedded in a diamond nanoparticle placed on a diamond film of varying thickness. The modeling also allowed us to distinguish between radiative and nonradiative decay channels. A comparison of computationally obtained and experimentally measured total lifetimes is presented in Table 1. In agreement with our experimental results, our simulations show that the lifetime is shorter in the presence of a thin diamond film (81 ns) than in the case of a bare Si substrate (91 ns). We attribute the difference between the values of experimental and numerical lifetimes mainly to the fact that in our numerical calculations we considered single nanodiamond particles, whereas experimental measurements involved clusters of nanodiamonds.
In particular, our numerical results indicate that the faster decay rates obtained for thin diamond films are due mainly to non-radiative loss in the underlying bulk Si (see Supporting Information   table S1). Importantly, the enhancement or suppression of radiative and non-radiative decay rate depends strongly on the film thickness (see Fig. 3(a)), which indicates coupling to slab modes in the film 21 . Indeed, at the thickness of the experimentally measured samples (90 nm) radiative (nonradiative) decay rates are suppressed (enhanced), whereas at 160 nm film thickness the situation is reversed. This is further illustrated in radiated field maps plotted in Figs = 120 nm. We, therefore, conclude that the decay rate can be efficiently controlled by changing the thickness of the supporting thin film. In particular, the tuning depth of NV radiative decay rate for a thin diamond film can be as high as   In conclusion, we experimentally demonstrate two-fold enhancement of the decay rate of NV 0 centers in nanodiamonds when deposited on a thin diamond film. We attribute the enhancement to the presence of non-radiative decay channels and coupling of NV 0 centers to the optical slab modes supported by the film, which leads to increase of both radiative and non-radiative decay rates. As such, we show that varying the thickness of the diamond film allows tuning of the radiative decay rate by up to 90%. Our study provides insights into the mechanism of Purcell enhancement of NV emission from nanodiamonds deposited on thin films and puts forward simple means of controlling the corresponding emission statistics.

S2. Fitting of CL measured photon counting histograms
The photon counting histograms (see Fig. 1d in main text) were fitted using the following formula: where is the normalized peak photon number, is the sample irradiation time, is the background noise, the faster characteristic time, , is related to the carrier time 22 , while the slower corresponds to the NV 0 center lifetime.

S3. ND Cluster size and aspect ratio distributions
The correlation between the recorded lifetimes and ND cluster geometry are examined in Fig. S1 for diamond nanoparticles placed on a diamond film or a bare Si substrate. The decay rates are presented as function of size ( Fig. S1(a)) and shape ( Fig. S1(b)). In both cases, the decay rate is nearly independent of both ND cluster size and cluster aspect ratio.

S4. Simulation of emission from a nanodiamond with NV center
Numerical simulations were performed by a commercial software (COMSOL 5.3a) based on the finite-element method. We set the refractive index of diamond and Si at the wavelength of 575 nm as ndiamond=2.40 23 and nSi=4.00+0.03i 24 , respectively. The simulation domain represents a cylinder with the radius of 1500 nm and height 3000 nm, terminated by scattering boundaries on all sides (see Fig. S2). The NV 0 center excitation at λ=575 nm was introduced via a volume polarization density oscillating inside a 10 nm sphere. The total radiated power, Ptot, is calculated as the integral of power flow P ⃗ ⃗ over the surface of a 12 nm large sphere encapsulating the emitting center.
The nanodiamond was modeled as a dielectric sphere with radius of 60 nm and with the NV 0 center placed at its center. The lifetime of NV 0 center on a substrate was given by =  Table S1. The NV 0 center is introduced as a volume polarization density with the orientation along the x-axis (in the plane of the substrate) or z-axis (normal to the substrate) oscillating inside a sphere of radius =5 nm.

S5. Collection efficiency of the parabolic mirror
The collection efficiency of the parabolic mirror in our TR-CL system depends on the orientation of the electric dipole of an NV 0 center, as shown in Fig. S3. In our experiments, the nanodiamonds are at the focus of the parabolic mirror. We define the quantities ∥ = P x P x +P y +P z , ∥ = P y P x +P y +P z , ⊥ = P z P x +P y +P z , where P x , P y , P z are the radiated powers collected by the parabolic mirror for dipoles moments of NV 0 centers orientated along x, y, z directions, respectively. The average lifetime can then be calculated as: