Method and device for localizing charge traps in a crystal lattice

Abstract

The present disclosure relates to a method for locating charge traps in a crystal lattice, comprising the following steps: arranging, on a crystal lattice (13), a local probe (11) having an inversion-symmetric lattice defect, wherein energy levels of the lattice defect are non-linearly Stark-shifted by means of charge traps (12) in the crystal lattice (13); determining, using a readout unit (10), Stark-shifted photoluminescence emission spectra (62), wherein each of the photoluminescence emission spectra (62) is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice (13); determining an integrated spectrum (61) by integrating the photoluminescence emission spectra (62);Determining jump probabilities (92) from successive photoluminescence emission spectra (62) and determining a charge trap configuration from the jump probabilities (92), wherein the charge trap configuration comprises a set of charge trap states of charge traps (12) adjacent to the local probe (11); determining simulated spectra (60) by means of Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, wherein spatial arrangements of the adjacent charge traps (12) are varied; and determining an optimal spatial arrangement of the adjacent charge traps (12) by comparing the integrated spectrum (61) with the simulated spectra (60). Furthermore, a device for localizing charge traps in a crystal lattice is disclosed.

Description

background

[0001] Until now, the local detection of charges with a local probe on a nanoscopic scale was mainly possible by measuring charges in a magnetic field and for charges with a free spin in their localized state. Furthermore, applications were limited to the nanometer scale and could not resolve atomic scales on an angstrom scale. A well-known example is the nitrogen vacancy defect center in diamond (see US 10,620,251 B2). Using nitrogen vacancy centers, these charges could not be localized with angstrom resolution or time resolution using known methods.

[0002] Alternatively, electric fields can also be measured spectroscopically, for example, using Rydberg atoms (see US 11,585,841 B1). However, such measurements rely on the linear Stark effect to induce a spectral shift in the atom-like system. This linear response is prone to saturation of the sensor, reducing its resolution and applicability.

[0003] The detection and quantification of desirable and undesired charge carriers can be of great importance at both the macroscopic and nanoscopic scales. Electric charges can be measured with electrometers, which have a wide range of applications in everyday life and for fundamental scientific investigations. Electrometers are currently not capable of detecting individual charges with time resolution in the subnanometer range.

[0004] However, the precise localization and temporal analysis of charge traps or individual charges at the atomic lattice level is becoming increasingly important. As silicon transistors become smaller, down to a few nanometers, they become increasingly susceptible to unknown and uncontrollable charge-induced noise. In ion quantum computers, for example, localized electronic states are suspected of causing decoherence through motional heating. Superconducting qubits, in turn, suffer from defect-induced charge noise, which impairs the performance of even the most advanced quantum computers. Finally, in atom-like spin qubits in wide-bandgap semiconductors, unpredictable charge noise leads to optical and spin decoherence, significantly limiting the development of quantum networks.Investigating and addressing the underlying mechanisms of such adverse processes in each of these platforms is essential to further improve the performance and application scope of nanoscale electronic and photonic devices. Summary

[0005] The object of the invention is to provide a method and a device with which charge traps in a crystal lattice can be localized with high accuracy.

[0006] The problem is solved by a method and a device for locating charge traps in a crystal lattice according to the main claim and the subordinate claim, respectively. Further embodiments are the subject of dependent subclaims.

[0007] According to one aspect, a method for locating charge traps in a crystal lattice comprises the following steps: - Arranging, on a crystal lattice, a local probe with an inversion-symmetric lattice defect, wherein energy levels of the lattice defect are non-linearly Stark-shiftable by means of charge traps in the crystal lattice; - determining, using a readout unit, strongly shifted photoluminescence emission spectra, wherein each of the photoluminescence emission spectra is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum by integrating the photoluminescence emission spectra; - determining jump probabilities from successive ones of the photoluminescence emission spectra and determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration comprises a set of charge trap states of charge traps adjacent to the local probe; - Determination of simulated spectra by means of Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, whereby spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0008] According to another aspect, a device for locating charge traps in a crystal lattice comprises: - a local probe with an inversion-symmetric lattice defect, which is arranged on a crystal lattice, wherein energy levels of the lattice defect are non-linearly Stark-shiftable by means of charge traps in the crystal lattice; - a readout unit for photoluminescence spectroscopy and - a data processing facility.

[0009] The data processing device is designed to perform at least one of the following steps: - determining, using the readout unit, strongly shifted photoluminescence emission spectra, wherein each of the photoluminescence emission spectra is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum by integrating the photoluminescence emission spectra; - determining jump probabilities from successive ones of the photoluminescence emission spectra and determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration comprises a set of charge trap states of charge traps adjacent to the local probe; - Determining simulated spectra by means of Monte Carlo simulation based on the determined charge trap configuration and preferably the resulting Stark shift, whereby spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0010] Using the proposed method and device, Stark shifts of a local electric field can be used to determine the spatial positions of individual or multiple elementary charges in a time-resolved manner and with a spatial resolution of up to a few (~3) angstroms. In particular, a device with a nonlinear response can be realized.

[0011] The local probe can be an atomic solid-state defect with a typical optical energy level structure and a nonlinear electric field response due to its inversion symmetry, for example in the D 3d -point group. In contrast to non-inversion symmetric configurations of color centers, such as a nitrogen vacancy center in diamond or a silicon vacancy center in silicon carbide, the linear polarizability of point defects with an inversion center (e.g. the D 3d-point group) can be largely neglected, and higher-order terms can lead to a strongly nonlinear response. This property can make local probes with an inversion center particularly sensitive to closely spaced charges and insensitive to background electric field noise, while still allowing sufficient measurement ranges to be maintained in low-noise environments. Consequently, the spectral readout can provide exceptionally high spatial resolution, down to several angstroms, even at charge densities as low as tens of ppm, due to the spectral shift and linewidth broadening of the charge-induced optical transitions.

[0012] By utilizing a nonlinear response of the local probe's electric fields to spatially sense the environment of charge traps with angstrom resolution and to temporally observe the dynamics of individual traps with nanosecond resolution, the spatial resolution can be increased to several angstroms, while the sensor / device can still function in an environment with relatively high electric field background and electric field background noise. Furthermore, the sensor can be used to determine the local charge trap density of solid materials and solid surfaces. In combination with an electro-optical modulator for fast spectral readout of the sensor, the sensor could achieve nanosecond temporal resolution.The detection and quantification of desired and undesired charge carriers can be of particular interest in semiconductors, quantum computers, quantum electrometers, material quality control sensors, materials science probes, or biological sensors.

[0013] In particular, by means of charge traps in the crystal lattice (lattice) that contain charged vacancies, the energy levels of the lattice defect can be nonlinearly Stark-shifted and / or nonlinearly Stark-shifted. The charge trap states of the charge traps adjacent to the local probe can each indicate charges of the charge traps adjacent to the local probe or distributions of (discrete) charges of the charge traps adjacent to the local probe.

[0014] The lattice defect (of the local probe) can cause a D 3d -symmetry. In other words, the local probe can have a D 3d-symmetric lattice defect (a lattice defect with D 3d -point group symmetry).

[0015] The energy levels of the lattice defect can be (essentially) nonlinearly DC Stark shifted / shiftable. In particular, the energy levels of the lattice defect can be (essentially) quadratically (DC) Stark shifted / shiftable.

[0016] The local probe can comprise a tin vacancy (SnV), a silicon vacancy (SiV), a germanium vacancy (GeV), or a group IV vacancy. The tin vacancy can occupy two lattice sites of the crystal lattice, with a tin atom, in particular, being located substantially in the center of the two lattice sites. The same can be provided for the silicon vacancy or the germanium vacancy.

[0017] The tin vacancy, silicon vacancy or germanium vacancy can be (electrically) negatively charged.

[0018] The charge traps in the crystal lattice can comprise electrically charged single vacancies (monovacancy) and / or double vacancies (two adjacent single vacancies - divacancy), or void complexes containing N vacancies.

[0019] The crystal lattice can be a diamond lattice or a silicon lattice. The crystal lattice can be part of a solid.

[0020] Arranging the local probe on the crystal lattice may involve implanting the local probe within the crystal lattice. The local probe may (after placement) be stationary in the crystal lattice (in particular, the bulk crystal).

[0021] Arranging the local probe on the crystal lattice can comprise arranging the local probe close to and / or adjacent to and / or spaced from the crystal lattice. In particular, the local probe can be embedded in a scanning probe microscope tip (e.g., for position-dependent measurements in the context of magnetometry), a nanocrystal (e.g., for integration with other materials), or a biological sample.

[0022] A sensing capability of the local probe can be demonstrated by analyzing time-varying optical transition frequencies, which can be associated with the charging of all charge traps / crystal defects in the surrounding crystal lattice under laser irradiation.

[0023] A (charge-induced) local electric field can be determined from the spectral shift. Using the determined local electric field (and the polarizability), the spatial arrangement of charge traps and, in particular, charge trap-probe distances can be determined.

[0024] Each of the photoluminescence emission spectra can be determined in a respective scan using photoluminescence excitation (PLE) in the crystal lattice under irradiation with laser light (from a laser, especially a narrowband laser), particularly continuous orange laser light. The charge traps can be additionally excited during each scan using a blue or green laser pulse.

[0025] The orange laser light can have a wavelength of 619 nm. The blue laser pulse can have a wavelength of 445 nm or 450 nm. The green laser pulse can have a wavelength of 520 nm. Each of the photoluminescence emission spectra can be determined with a scan duration (acquisition time) of five seconds.

[0026] The readout unit can comprise or be at least one of a microscope, a spectrometer, and a CCD camera. The device, in particular the readout unit, can comprise one or more lasers, in particular for irradiating laser pulses and / or laser light, in particular green and / or blue laser pulses and / or orange laser light.

[0027] During scanning, the frequency of the laser light (laser frequency) can be controlled by applying an external voltage signal to the laser. The laser frequency can be monitored via a pick-off path directed to a wavemeter. The photoluminescence emission spectra can be recorded as voltages and fluorescence signals. The voltages can be converted to frequencies by matching timestamps.

[0028] Individual scans can be mapped to a frequency axis by selecting a single line scan / scan. The scan spectra can be binned (discretized / divided into bins) according to frequency (frequency binning). If multiple data points fall into the same bin (frequency interval), the data points can be averaged. If no data points fall into a bin, the value for the bin can be determined as the average of the previous and next bins.

[0029] The integration of the scan process spectra can be achieved by (bin-wise) summation of the photoluminescence emission spectra. Specifically, the integrated spectrum can be determined by summing corresponding bins (bins of the same frequency range) of the photoluminescence emission spectra. The integrated spectrum can then be normalized.

[0030] The method may further comprise the following steps: - Determining a plurality of peak frequencies (central frequencies) of peaks (peak values) from the integrated spectrum as well as frequency ranges (configuration ranges) of the integrated spectrum assigned to the peaks; - determining scanning peak frequencies of scanning peaks for each of the photoluminescence emission spectra and assigning the scanning peak frequencies to one of the associated frequency ranges of the integrated spectrum (and / or to a charge trap state), and - Determine the jump probabilities from the respective assigned frequency ranges (for the consecutive photoluminescence emission spectra).

[0031] Boundaries of frequency ranges of the integrated spectrum associated with the peaks, which are adjacent, may correspond to half of the spectral distance between two adjacent peaks of the integrated spectrum.

[0032] For example, a particular scan peak of a particular scan can be assigned to a particular frequency range if the scan peak frequency of the particular scan peak is in the particular frequency range.

[0033] The jump probabilities can each indicate a probability of the change of the charge trap state, in particular a probability p(i → j) of the change from charge trap state i to charge trap state j.

[0034] The jump probabilities can be determined by determining how often (as a proportion of all scans) a jump from one charge trap state i to another charge trap state j has occurred. Whether a jump from one charge trap state i to another charge trap state j has occurred can be determined by comparing a specific scan peak from a specific scan to the following scan peak of the subsequent scan. If the specific scan peak does not match the following scan peak, a jump can be determined to have occurred.

[0035] The determined jumps from one charge trap state i to another charge trap state j can each be normalized with respect to a total number of all jumps to obtain (jump) probabilities. The jump probabilities can additionally be determined by multiplying them by uncertainty factors.

[0036] The method may further comprise: determining a brightness duration of a charge trap state (or multiple brightness durations of charge trap states) from the respective associated frequency ranges of the photoluminescence emission spectra as a time span of consecutive scan spectra for which a scan peak is maintained (no other scan peak is determined for any of the scan spectra). The brightness durations may be summarized into a histogram according to the respective frequency with which they were observed, preferably to determine average lifetimes and / or switching rates. A probability density may be determined from the histogram. The probability density may be fitted (adjusted) with a Poisson distribution. A lifetime τ(i) for the charge trap state i and / or a conditional spectral jump rate Γ ct(i → j) can be determined from an average value of the fitted Poisson distribution.

[0037] Determining the cargo trap configuration may include at least one of the following steps: - determining a number of peaks of the integrated spectrum and a number of jump probabilities which are greater than a predetermined threshold; - Determining charge trap states of the charge trap configuration, in particular a number of (detectable) charge traps of the charge trap configuration, from the number of peaks and the number of jump probabilities.

[0038] The charge trap configuration may specify a (charge trap) number of the neighboring charge traps. The charge trap configuration may further specify at least one charge (within) the neighboring charge traps.

[0039] For a number M of peaks of the integrated spectrum, a smallest possible number for the number N of detectable charge traps can be calculated using M <= 2 N-1 be determined and a largest possible number for the number N of detectable charge traps would be the number M.

[0040] The determined charge trap configuration may be a most probable charge trap configuration and / or a least-assumption charge trap configuration (a set of charge trap configurations compatible with the integrated spectrum).

[0041] Determining the charge trap configuration may in particular comprise at least one of the following steps: - Determine the number of peaks of the integrated spectrum as M; - Determining the number of jump probabilities which are greater than the predetermined threshold, for example greater than 3% / M; - Setting the number N of detectable charge traps equal to M; - Iteratively decrementing N, determining the possible charge trap states and comparing the possible charge trap states with the number of jump probabilities greater than the predetermined threshold until they agree.

[0042] For M peaks, a simplest charge trap configuration can have N = M - 1 charge traps with N charge trap states. If only single ionization events are likely, 2 * (M - 1) values are expected that are different from zero (larger than the threshold) and are all correlated with the least redshifted peak.

[0043] For N = M - 2 charge traps, M - 2 peaks can result from the ionization of M - 2 individual traps, with one peak corresponding to no ionization and a remaining peak resulting from a charge trap state with two ionized charge traps. The = M - 2 case can be distinguished from the N = M - 1 case by those (e.g., four) jump probabilities that are greater than zero (or greater than the threshold) and are not correlated with the least redshifted peak. These non-zero elements can uniquely correlate each peak with a charge trap state.

[0044] For N = M - 3 charge traps, M - 3 peaks can result, which are correlated with the individual ionized charge trap states. One peak can correspond to a non-ionized trap state, and the remaining two peaks can be assigned to two charge trap configurations, comprising either two distinguishable, simultaneously ionized charge trap states or two charge trap states with two and three simultaneously ionized charge trap states.

[0045] To further distinguish these two possible charge trap configurations, higher-order correlations can be used to determine whether subsequent ionization processes have occurred. In particular, a highest-order correlation can be determined.

[0046] To determine the charge trap configuration, the jump probabilities can be arranged in a correlation matrix (probability matrix). The correlation matrix can indicate probabilities for switching from one charge trap state to another. The correlation matrix can have M · (M - 1) entries, with original diagonal elements (no state change) discarded. The rows and columns of the correlation matrix can be ordered according to peaks (charge trap states) from the lowest redshift (no ionization) to the highest redshift.

[0047] The jump probabilities that are not greater than the predetermined threshold can be set to zero in the correlation matrix.

[0048] The jump probabilities can be determined starting with a non-ionized case (least redshifted peak) and reaching a certain peak step by step: p(0->i->...T-3 steps...- >k) (higher order correlation matrix).

[0049] The peaks of the integrated spectrum (in particular the number of peaks and / or peak frequencies) and / or scanning peaks (in particular a number of scanning peaks and / or scanning peak frequencies) can be determined by means of a peak-finding algorithm.

[0050] A scan duration can be adjusted so that a maximum of two peaks are detected between scans and / or two peaks per scan. This allows a maximum of two ionization events to occur simultaneously during this time interval. Consequently, the complexity of detectable charge trap configurations can be reduced.

[0051] Starting from the determined charge trap configuration, the positions (the optimal spatial arrangement) of the neighboring charge traps can be determined in several ways. Firstly, charge trap positions can be initialized at random positions with the distances corresponding to the spectral (Stark) shifts of the assigned peaks. These distances are determined by a set of (Stark shift) equations that govern DC Stark shifts. Secondly, the remaining free parameters (relative angles and distances) can be determined by minimizing a χ 2 -tests are fine-tuned. Based on this χ 2 Tests can determine the most likely cargo trap configuration and positions.

[0052] When determining simulated spectra using Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, the spatial arrangements of the neighboring charge traps and the charges of the neighboring charge traps can be varied. When determining simulated spectra using Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, the spatial arrangements of the distant charge traps and / or the charges of the distant charge traps can also be varied.

[0053] Determining the simulated spectra may include at least one of the following steps: - Determining approximate values for first position values of the spatial arrangements from relative Stark shifts from the integrated spectrum and - Fine-tuning the first location values by means of Monte Carlo simulation(s), wherein the first location values and second location values of the spatial arrangements are varied. In particular, the optimal spatial arrangement can have fine-tuned first location values and optimal second location values.

[0054] Alternatively, (both first and second) location values can be determined by means of Monte Carlo simulation, whereby the (first and second) location values of the spatial arrangements are varied so that preferably a χ 2 distribution from the integrated spectrum and the simulated spectra can be minimized.

[0055] Furthermore, when fine-tuning the first location values using Monte Carlo simulation, a charge trap density ρ trap of the distant charge traps can be varied. Alternatively, the charge trap density ρ trapand / or a spatial distribution of remote charges must be predefined. For example, the spatial distribution of remote charges can be estimated using a physical model (e.g., the distribution of implantation damage). Without a physical model, a predefined charge distribution (e.g., cylindrically symmetric) can be specified.

[0056] The first and / or second location values may comprise spherical coordinates that indicate spatial arrangements of the neighboring charge traps (relative to the local probe).

[0057] The first location values may, for example, comprise at least one of the following quantities: a first distance r1 of a first charge trap from the local probe, a first azimuth angle or polar angle θ1 of the first charge trap with respect to the local probe, a second distance r2 of a second charge trap from the local probe, a second azimuth angle or polar angle θ2 of the second charge trap with respect to the local probe, a third distance r3 of a third charge trap from the local probe, and a third azimuth angle or polar angle θ3 of the third charge trap with respect to the local probe.

[0058] The first location values may in particular comprise at least one of the following quantities: the first distance r1 of the first charge trap from the local probe, the third distance r3 of the third charge trap from the local probe and the third azimuth angle or polar angle θ3 of the third charge trap with respect to the local probe.

[0059] The first position values (in particular the first distance r1, the third distance r3 and the third azimuth angle or polar angle θ3) can be determined (for example in the case of two charge traps and / or four peaks) from the relative Stark shifts Δ ◯◯ , Δ ◯⊙ , Δ ⊙◯ , Δ ⊙⊙ can be determined using the following (Stark shift) equations: Δ◯◯=−Δα2E(−1,r→2)2 Δ◯⊙=−Δα2[E(−1,r→2)+E(−1,r→1)]2 Δ⊙◯=−Δα2[E(−1,r→2)+E(−1,r→3)]2 Δ⊙⊙=−Δα2[E(−1,r→2)+E(−1,r→1)+E(−1,r→3)]2

[0060] Δα represents the second-order polarizability and E(−1,r→i)2 the square of the electric field of the electric trap i with elementary charge -1 (E(qi,r))=qi4πε0εrrr3,qi∈e⋅{−1,0,+1}, Elementary charge e). A neutral charge trap is denoted by ◯ and a negatively charged charge trap by ⊙. Consequently, a charge trap state with, for example, a neutral first charge trap and a negatively charged second (or third) charge trap is denoted by ◯ ⊙.

[0061] The relative Stark shifts Δ ◯◯ , Δ ◯⊙ , Δ ⊙◯ , Δ ⊙⊙ can be determined from the integrated spectrum, in particular from the peak frequencies of the peaks of the integrated spectrum, whereby the peaks are each fitted using Voigt profiles.

[0062] The first, second, and third charge traps can be arranged in a common plane. In particular, the first and second charge traps can be arranged in a common plane. The azimuth angles and / or polar angles can be defined with respect to the common plane. The second charge trap can be arranged with respect to the local probe along a direction of implantation of the local probe. The first charge trap can be arranged with respect to the local probe perpendicular to the direction of implantation.

[0063] For example, the spatial arrangements of the first, second, and third charge traps can be parameterized as follows: r→1=r1[cos(θ1),0,sin(θ1)],r→2=[0,0,r2],r→3=[cos(θ3),0,sin(θ3)].

[0064] When determining the simulated spectra, the charges of neighboring charge traps as well as the charges of distant charge traps can be varied. For example, distant charge traps can be at least 2.5 nm (25 Å) away from the local probe. In contrast, neighboring charge traps can be less than 2.5 nm (25 Å) away from the local probe.

[0065] The second location values may, for example, comprise at least one of the following quantities: the first azimuth angle or polar angle θ1 of the first charge trap with respect to the local probe and the second distance r2 of the second charge trap to the local probe.

[0066] Comparing the integrated spectrum with the simulated spectra can minimize a χ 2 -distribution and / or a χ 2 -Tests from the integrated spectrum and the simulated spectra.

[0067] The minimization can be done using a global optimization algorithm, in particular simplicial homology global optimization (shgo).

[0068] The χ 2 -Distribution can be represented by the following function: ∑iχ(θ,i)=∑n=0,iN(on(θ,i)−En,i)2En,i with values O n (θ, i) of the simulated spectra and values E n,i of the integrated spectrum for bin n (especially with 0 n (θ, i) as the number of expected counts for peak i and bin n and the corresponding value E n,i of the integrated spectrum, where a vector θ indicates at least one of the first location values). For example, the vector θ can indicate the first and third distances, specifically θ = [α, b] with fine-tuning factors α, b, where r1'=ar1 and r3'=br3.

[0069] In other words, comparing the integrated spectrum with the simulated spectra can minimize ∑iχ(θ,i)=∑n=0,iN(On(θ,i)−En,i)2En,i with values 0 n (θ, i) of the simulated spectra and values E n,i of the integrated spectrum for bin (interval) n, peak i, and vector θ of initial position values. For example, 170 bins of equal width can be provided over a frequency range of 4 GHz.

[0070] The simulated spectra and / or the integrated spectrum can be divided into subspectra (parts of the spectra). The values {0 n (θ, i)} n or {E n,i} n can be considered as parts of the total simulated spectra or the total integrated spectrum {0 n (θ, i)} n,i or {E n,i} n,i The parts of the spectra can also be partially combined. For example, the spectra can be partitioned according to i ∈ (◯◯, ◯ ⊙,⊙ ◯ +⊙⊙}.

[0071] The integrated spectrum (and / or its parts / subspectra) can be fitted using (single or double) Voigt profile fitting (Voigt profile fits) before comparison with the simulated spectra.

[0072] The values 0 n (θ, i) of the simulated spectra can be calculated using the formula S(ω) = 1 / NΣ n Lγ(ω-Δ stark,n ) can be determined (with normalization constant N (so that max S(ω) = 1), simulation step index n, Stark shift Δ stark,n for simulation step n and Lorentz curve L γ with half-width y (e.g. y = 35 MHz for local probe SnV -1 )). For the simulated spectra, determining the Stark shift Δ stark,n terms of linear and higher order. In particular, the Stark shift Δ stark,n for each simulation step n using the formula Δstrong=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4 be determined (with dipole moment Δµ = 6.1 × 10 -4 GHz / (MV / m)2 and differences between higher order polarizabilities Δα = -5.1 × 10 -5 GHz / (MV / m) 2 , Δβ = -5.5 × 10 -8 GHz / (MV / m) 2 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 2 ), where E s depends on the simulation step n.

[0073] The determination of the simulated spectra may further comprise the following: The second location values (e.g. the first azimuth angle or polar angle θ1 and the second distance r2) and / or the charge trap density ρ trap can be varied (within optimization intervals), for example ρ trap ∈ [35, 100] ppm or θ1 ∈ [0; 0.6] rad. This variation can be done, for example, over 500 iterations.

[0074] Within each of the iterations, that is, for fixed second location values (e.g. the one first azimuth angle or polar angle θ1 and the second distance r2) and / or fixed charge trap density ρ trapof the remote charge traps, the remote charge sites can each be positioned relative to the local probe according to the charge trap density ρ trap randomly distributed spatially (when implanting the local probe within a cone volume (z > 0 nm, the local probe is located at the origin) with an opening angle of 45°, where r q < 2.5 nm to the local probe, no distant charge sites are distributed). The spatial distribution can be carried out according to a uniform distribution. Furthermore, the neighboring charge traps can be charged according to charge probabilities. In the case of two neighboring charge traps with time-varying charge, the charge probabilities can be, for example, p ⊙⊙ = 0.041 , p ⊙◯ = 0.017, p ◯⊙ = 0.63 and p ◯◯ = 0.31. The charges for the neighboring charge traps can have values qi · e with q i∈ {-1,0, +1} and elementary charge e, where charge neutrality is ensured including the negative charge of the local probe (-e + e Σ i q i = 0). Accordingly, the field strength at the location of the local probe can be E = E i E(q i , r i ).

[0075] The spatial distribution of the distant charge traps and the charging of the neighboring charge traps can be carried out for fixed second location values and / or fixed charge trap density ρ trap For example, this can be repeated 1000 times. The charge probabilities of the neighboring traps can be determined from the (possibly normalized) peak heights of the peaks of the integrated spectrum.

[0076] At least one of the neighboring charge traps (e.g., the second charge trap) can be determined to be permanently charged. A permanently charged charge trap can lead to peak broadening.

[0077] For fixed second position values and / or fixed charge trap density ρ trap as well as distributed remote charge sites and charged neighboring charge traps, the first position values (or parts thereof, in particular r1 and r3) can be fine-tuned (within the framework of a Monte Carlo simulation). For this purpose, the χ 2 -Distribution with ∑iχ(θ,i)=∑n=0,iN(On(θ,i)−En)2En with θ = [a, b] and fine-tuning factors a, b, where r1'=ar1 and r3'=br3. The minimization is carried out using simplicial homology global optimization (shgo).

[0078] The fine-tuned first location values (or parts thereof, in particular r1 and r3 or r1' and r3' ) can (together with the corresponding χ 2 -values) for the (varied) second location values and / or the (varied) charge trap density ρ trapcompiled (especially tabulated).

[0079] The optimal spatial arrangement of (neighboring) charge traps can be the fine-tuned first position values and the second position values with the smallest χ 2 -value or alternatively from a respective weighted mean of several smallest (for example the 50 smallest) χ 2 The optimal spatial arrangement can also include further optimized (first) location values, which were determined from the remaining first or second location values using the Stark displacement equations. In particular, the (optimized, first) location value θ3 can be determined from the (optimized) second location value θ1 using the Stark displacement equations.

[0080] Confidence intervals for the (first and / or second) location values and / or further values of the optimal spatial arrangement can be determined using χ 2-values (for example, a weighted mean of the 50 smallest χ 2 -values including an offset value). In particular, 68% confidence intervals for ρ trap and / or θ1 using min{χ 2} + 3.5 can be determined.

[0081] The data processing device may comprise a processor and / or a memory. At least one, preferably each, of the steps of determining the plurality of strongly shifted photoluminescence emission spectra, determining the integrated spectrum, determining the jump probabilities, determining the simulated spectra, and determining the optimal spatial arrangement, as well as intermediate steps or further steps, may be performed by means of a data processing device.

[0082] According to the disclosure, a method may further be provided, preferably for locating charge traps in a crystal lattice, comprising at least one of the following steps: - arranging, preferably on a crystal lattice, a local probe with an inversion-symmetric lattice defect, wherein further preferably by means of charge traps in the crystal lattice energy levels of the lattice defect are (essentially) non-linearly Stark-shiftable (Stark-shifted); - determining, preferably using a readout unit, strongly shifted photoluminescence emission spectra (line scan spectra), wherein preferably each of the photoluminescence emission spectra is determined in a respective scanning process (line scan) by means of photoluminescence excitation in the crystal lattice; - determining an integrated spectrum, preferably by integrating the photoluminescence emission spectra; - determining jump probabilities, preferably from successive ones of the photoluminescence emission spectra, and / or determining a charge trap configuration from(s) jump probabilities, wherein further preferably the charge trap configuration comprises a set of charge trap states of charge trap(s) adjacent to the local probe; - Determining simulated spectra by means of Monte Carlo simulation(s) (based on the determined charge trap configuration) and preferably resulting Stark shift(s), whereby spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0083] According to the disclosure, a device may further be provided, preferably for locating charge traps in a crystal lattice, which comprises at least one of the following: - a local probe with an inversion-symmetric lattice defect, which is preferably arranged on a crystal lattice, wherein further preferably energy levels of the lattice defect are non-linearly Stark-shiftable by means of charge traps in the crystal lattice; - a readout unit for photoluminescence spectroscopy and - a data processing facility.

[0084] The data processing device is in particular designed to carry out at least one of the following steps: - determining, preferably using the readout unit, strongly shifted photoluminescence emission spectra, wherein further preferably each of the photoluminescence emission spectra is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice; - determining an integrated spectrum, preferably by integrating the photoluminescence emission spectra; - determining jump probabilities, preferably from successive ones of the photoluminescence emission spectra, and / or determining a charge trap configuration from(s) jump probabilities, wherein further preferably the charge trap configuration comprises a set of charge trap states of charge trap(s) adjacent to the local probe; - Determining simulated spectra by means of Monte Carlo simulation(s), preferably based on the determined charge trap configuration, and further preferably Stark shift(s) resulting therefrom, wherein in particular spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0085] In connection with the device for locating charge traps in a crystal lattice, the embodiments described above in connection with the method can be provided accordingly. Description of implementation examples

[0086] Further embodiments are explained in more detail below with reference to the figures of a drawing. Herein: Fig. 1 a schematic representation of a device for locating charge traps, Fig. 2 a schematic representation of the device for localizing charge traps in a crystal lattice by means of Stark shift, Fig. 3 a plot of a relative sensitivity |ΔE| / E to changes in an electric field as a function of an electric field E s and a charge trap density ρ trap , Fig. 4 a plot of the resolution of the sensor in determining the distance of an elementary charge based on the discrimination of two different charge traps as a function of the charge trap density ρ trap and the distances, Fig. 5 a schematic representation of a crystal lattice with a tin vacancy and lattice defects, Fig. 6 a plot of the integrated spectrum and the simulated spectrum with assignment of the peaks to the charge trap states and plot of the photoluminescence emission spectra as a function of the Stark shift, Fig. 7 a schematic representation of the relative positions of the charge traps and their probability distribution with respect to an SnV probe and a table indicating the charge trap states and the position of the identified charge traps, Fig. 8 a schematic representation of the SnV probe, the ionized and neutral lattice defects in the band gap, Fig. 9 example histograms showing how long the charge remains in one charge trap state until it changes to another and a table with jump probabilities and jump rates for the corresponding spectral jumps, Fig. 10 plots of the inhomogeneous broadening of the SnV zero-phonon line due to bulk and surface charges, Fig. 11 a schematic representation of the formation of double charge traps in the crystal lattice during an annealing process, Fig. 12 plots of the simulated densities of the double charge traps versus the single charge traps for three different species of color centers, Fig. 13 a plot of the inhomogeneous broadening as a function of the local bias field, Fig. 14 a plot of the normalized uncertainty to the homogeneous linewidth for three different values of the relative sensitivity of the electric field, Fig. 15 a plot of the uncertainty extracted from a fit as a function of the SNR and the Gaussian component of the Voigt profile, both normalized to the homogeneous linewidth, Fig. 16 a plot for the experimental estimation of the bias field at the sensor, Fig. 17 plots of control experiments, Fig. 18 plots of extracted parameters from autocorrelation measurements for an emitter E1, Fig. 19 plots showing the influence of laser misalignment on the photoluminescence emission spectra, Fig. 20 plots of photoluminescence excitations of the C junction under different charge stabilization schemes at emitter E1, Fig. 21 plots of photoluminescence excitation of the C transition under different colored stabilization schemes of the emitter E2, Fig. 22 plots comparing different stabilization pulse powers and Fig. 23 shows a plot comparing the different stabilization powers at the emitter E20.

[0087] The detection of individual charges plays a crucial role in fundamental materials science and in the advancement of classical and quantum high-performance technologies that operate with low noise. However, it has not yet been possible to determine charges at the lattice scale in a time-resolved manner. The development of an electrometer is presented that utilizes the spectroscopy of an optically active spin defect embedded in a solid-state material with a nonlinear Stark response. By applying the approach in diamond (diamond lattice), a widely used platform for applications in quantum technology, it is possible to detect charge traps 12 (traps, multivacancies, double vacancies, vacancies, V n, vacancies), quantify their influence on transport dynamics and noise generation, analyze relevant material properties, and develop strategies for material optimization.

[0088] Free charge carriers such as electrons are essential components of the modern world. They enable devices such as smartphones and computers. Uncontrolled or unwanted charges, however, can cause damage and reduce the performance of such devices. Prominent examples are gate oxide breakdown in flash memory and charge noise at the nanoscopic level. The detection and quantification of desired and unwanted charge carriers using electrometers is of great technological importance at the nanoscale.

[0089] Despite significant advances, electrometers have so far been unable to measure elementary charges with subnanometer resolution. However, the precise localization and temporal analysis of charges at atomic lattice scales is becoming increasingly important. For example, the study of 2D ferroelectric systems would greatly benefit from the use of a highly sensitive electrometer, which could provide crucial insights into the unresolved fundamental aspects of their physical properties. Furthermore, silicon transistors, with a size of a few nanometers, are becoming increasingly susceptible to charge-induced noise.

[0090] Quantum technology applications, in particular, face challenges: In ion-based quantum computers, localized electronic states are suspected of causing decoherence due to motional heating; superconducting qubits suffer from defect-induced charge noise; and in atom-like spin qubits in wide-bandgap semiconductors, charge noise leads to optical and spin decoherence, significantly limiting the development of quantum networks and sensing. Understanding the underlying mechanisms of such platform-specific adverse processes is essential to improve the performance and application scope of electronic and photonic nanodevices, including open questions regarding decoherence processes, electron dynamics, and material issues related to lattice defect formation.

[0091] A device (electrometer, quantum electrometer) is presented that allows the detection of electric fields generated by single and multiple elementary charges with a relative sensitivity of 10 -7 and enables the localization of their relative position on the Angstrom scale while providing time-resolved access to the dynamics of individual charges, down to nanoseconds.

[0092] The electrometer consists of an optically active, local probe 11 (probe, atom sensor probe, spectral sensor, sensor probe) sensitive to electric fields and a readout unit 10 (cf. Fig. 1). The local probe 11 can be a negatively charged tin vacancy color center 21 (tin vacancy color center, SnV, SnV color center, SnV center) in a diamond (cf. Fig. 2), a solid-state defect with fluorescent transitions and a nonlinear response to the electric field, typical for defects in the D 3d -point group. The optical transition energies depend on the DC Stark effect Δ stark = -µ ind (E s )E s directly from the local electric field, where µ ind the induced dipole moment of the atomic defect and E s is the sum of all static electric fields generated by surrounding charges that shift the optical energies ( Fig. 2).

[0093] The readout unit 10 is a microscope used for photoluminescence excitation spectroscopy at the local probe 11 and therefore does not require magnetic resonance methods. The measurement of the energy shift indicates the magnitude of the electric field at the sensor probe 11 E. s about the DC Stark shift Δstrong=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4, with Δµ as the change in the dipole moment and Δα, Δβ, and Δγ as differences between the higher-order polarizabilities. In contrast to non-inversion-symmetric configurations of color centers, such as the nitrogen vacancy center in diamond and the silicon vacancy center in silicon carbide, the negligible linear and strongly nonlinear response due to the inversion symmetry makes the sensor applicable for typical semiconductor dopant and defect densities. When Δα dominates and the observed Δ Stark comes from a localized elementary charge e at a distance r from the sensor 20, then: ΔStark(r)~Δα / r4.

[0094] As the distance of the charges from the sensor 20 decreases, increasingly large spectral shifts occur. This property makes sensors 20 with an inversion center remarkably sensitive to charges in close proximity and insensitive to the background noise of electric fields.

[0095] The relative sensitivity of the electric field ~ 10 -7 (cf. Fig. 3) enables the readout of a spectral sensor with exceptionally high spatial resolution, even at charge trap densities (charge density, trap density, density) of up to one hundred ppm (cf. Fig. 4) down to a few µm.

[0096] In Fig. Figure 2 shows a schematic representation of the device for localizing charge traps 12 in a crystal lattice (atomic lattice) using Stark shifts. The local probe 20 is an optically active atomic defect with nonlinear Stark-sensitive energy levels. The readout unit 10 is a microscope with photoluminescence excitation spectroscopy. A nearby charge (neighboring charges, neighboring charge trap 12, short-range trap, near-trap) shifts the optical transition from C0 to C s by Δ s (r) as a function of their distance r. In addition, an ensemble of distant fluctuating charges (distant charge traps, long-range traps, far-range traps) broadens the signal of C s to C s,b depending on the charge density ρ trap . In Fig. 3, the relative sensitivity |ΔE| / E to changes in the electric field is given as a function of the electric field E s and the trap density ρ trapshown. To the left of the dashed line, Stark shifts are not large enough to be resolved by the Rayleigh criterion. Larger field strengths correlate with larger inhomogeneous broadening. In Eq. 1, Δµ = 6.1 × 10 -4 GHz / (MV / m) 2 , Δα = -5.1 × 10 -5 GHz / (MV / m) 2 , Δβ = -5.5 × 10 -8 GHz / (MV / m) 3 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 4 assumed.

[0097] In Fig. Figure 4 shows the resolution of sensor 20 in determining the distance of an elementary charge based on the discrimination of two different charge traps 12 as a function of the charge trap density and the distances. The resolution was determined for a trap 12 with a variable distance r and a bias field corresponding to a trap distance of 0.8 nm. The dashed white lines indicate the inscribed resolution thresholds.

[0098] In the present embodiment, the local SnV probe 20 is stationary in a bulk crystal, but it could also be integrated into the tip of a scanning probe microscope 14 for position-dependent measurements, which are well established in magnetometry, or into a nanodiamond 15 for integration with other materials or biological samples. As an alternative to SnV, other D 3d Symmetric defects such as silicon or germanium defects and other inversion-symmetric defects in other materials, for example, silicon, can be used as local probes 11. To demonstrate the nonlinear sensor principle, a single SnV created by ion implantation and annealing is used. Determination of charge trap positions at the level of the atomic lattice

[0099] Probe 20 and its surroundings are in Fig. 5. To demonstrate the sensor capability, the time-varying quasi-static electric field caused by the charging and neutralization of crystal defects in the surrounding lattice 13 under laser irradiation 22 is analyzed. Based on the recorded field strength for different charge distribution configurations, the position of the surrounding crystal defects can be extracted with lattice-scale resolution.

[0100] If all traps 12 are neutral, the total field at the position of the local probe 20 is zero and the optical transition of the SnV is undisturbed. A charged trap 12 induces an electric field It→, which Stark-shifts the energy of the optical transition according to Equation 1. If a single elementary charge is located near probe 20, the C transition is shifted by more than its own linewidth, resulting in a spectral jump (jumps, spectral jumps, charge state change, state change) (cf. Fig. 2). The magnitude of the spectral shift can be determined by comparison with the unperturbed case. The addition of both resonances in one spectrum results in a unique optical fingerprint with two peaks.

[0101] To capture spectra 62 (cf. Fig. 6), the fluorescence of sensor 20 is measured under photoluminescence (PLE) excitation with a narrowband laser. The charge-induced electric field is extracted from the spectral shift. Knowledge of the local field and the use of polarizability allow the trap-probe distance to be determined.

[0102] For N charged traps 12 near the probe 20, the electric fields add up to It'→ and the individual charges cannot be directly separated. To distinguish the 2 N To distinguish charge states, the strongly shifted PLE spectra 62 (photoluminescence emission spectra, PLE line scans, PLE line scans, scan, PLE scan, PLE spectrum) are recorded repeatedly. Laser irradiation randomly ionizes and neutralizes the traps 12. By scanning a large number of configurations, complex trap distributions can be analyzed.

[0103] In addition to the nearby charges 12, which cause significant spectral line shifts, the numerous randomly distributed traps in the distant environment also contribute. These distant traps exhibit fluctuating charge states, resulting in a fluctuating electric field δEs→ which causes an inhomogeneous broadening. Consequently, the density of charge traps ρ trap within the grating 13 by linewidth measurements. It is found that traps can be resolved with subnanometer resolution. For trap densities ρ trap ≈ 0.3 ppm, detection volumes of 150 3 Å are possible. Fluctuating charge traps at larger distances mainly contribute to the inhomogeneous broadening.

[0104] To fully calibrate the electrometer, the nonlinear response to external fields is taken into account, which causes an interdependence of the various external field components. For example, the effective Stark shift induced by two charges is not equal to their sum. This phenomenon enables high resolution but makes the analysis of the recorded fingerprints very complex. Therefore, a theoretical database of simulated spectra 60 for a variety of discrete charge positions near and far from trap densities is created using Equation 1.

[0105] The complex experimental four-peak fingerprint from Fig. 6 can be quantitatively analyzed as follows. Experimentally determined polarizabilities are used. By comparing the experimental and simulated fingerprints, several possible trap configurations (charge trap configuration, charge state configuration, state configuration, charge trap state configuration) are found. Of these possible configurations, the most plausible one is identified based on specific physical considerations.

[0106] The most likely configuration of Trap 12 nearby consists of a permanent Ebias,→ which is generated, for example, by a permanently ionized trap 12, and two additional traps 12 that cause spectral jumps. The spectral peaks in Fig. 6 are assigned designations based on the charge state of the two additional traps 12 in the vicinity ◯◯, ◯ ⊙,⊙ ◯,⊙⊙ where ◯ stands for an uncharged trap (neutral charge trap) and ⊙ a charged trap (ionized charge trap). Subsequently, the position of these charge traps 12 is determined up to an azimuthal angle using Monte Carlo simulations. The relative Stark shifts corresponding to the distances between the neighboring traps r1 = 8(1) Å,r2 = 11(2) Å, r3 = 26(3) Å ( Fig. 7) and a remote charge trap density of 74(22) ppm is extracted.

[0107] In Fig. Figure 5 shows a schematic representation of a crystal lattice 13 with a tin vacancy (SnV) 21 and lattice defects. The 12 localized charges in this case cause a Stark shift in the energy levels of the atom sensor probe 20. From very near to far, the spectral effect of an elementary charge can be categorized as follows: a >30 GHz spectral shift detectable by photoluminescence spectroscopy, a ~GHz shift detectable by photoluminescence excitation spectroscopy (PLE), and inhomogeneous broadening detectable by PLE. Charges in the very far region have negligible effects.

[0108] In Fig. 6 shows a plot of the integrated spectrum 61 (multimodal spectrum) and a simulated spectrum 60 with assignment of the peaks to the charge trap states (trap states, state) and a plot of the photoluminescence emission spectra 62 as a function of the Stark shift. Fig. Figure 6 shows an integrated multimodal PLE spectrum 61, recorded with the SnV sensor 20 (blue) and modeled with Monte Carlo simulations (integrated spectrum 61 with error bars representing the statistical standard deviation) to determine a nearby charge trap configuration (states above the peaks, ⊙ and O stand for ionized and neutral traps 12, respectively) and the surrounding charge density. Fig. 6 shows time-resolved photoluminescence emission spectra 62 and an SnV level scheme.

[0109] In Fig. Figure 7 shows a representation of the relative positions of the charge traps 12 and their probability distribution with respect to the SnV probe 20, as well as a table indicating the charge trap states and the position of the identified charge traps 12. On the left side, the identified charge trap configuration, their relative (optimal) positions, and their probability distribution with respect to the SnV probe 20 are shown. The distributions resemble a donut shape due to the direction-independent calibration of the sensor 20. On the right side, a diagram indicating the charge trap states and the position of the identified traps 12 is shown. Dynamics of the load

[0110] To identify the position of charge traps 12, accumulated spectral fingerprints were used, which comprise the integrated spectrum 61 for the entire set of charge states UC={○○, ○⊙, ⊙○, ⊙⊙, SnV−2}, including the dark state SnV -2 The comparison of individual electrometer reading events, ie individual PLE line scans between different charge configurations within UC provides access to time-resolved charge transfer dynamics.

[0111] The charge state changes are described using a simplified charge transfer diagram (cf. Fig. 8) interpreted: charge traps 12, which were later called multivacancy complexes V nidentified can be ionized under laser illumination by two different processes: negative charge, which occurs when the trap 12 captures an electron promoted from the valence band, leaving a positively charged hole in the band; and positive charge, when an electron is promoted from the trap 12 into the conduction band. The created holes and the promoted electrons then diffuse and recombine with other charge traps 12, resulting in an overall charge-neutral environment. The event ◯◯→ ◯ ⊙ is called ionization, and the reverse case ◯ ⊙→ OO is called a neutralization event. The charge transfer picture is consistent with the time-resolved correlation measurements performed, assuming that charge events are triggered by single-photon processes.

[0112] To characterize the local charge environment and dynamics, the transition probabilities 92 of the charge states p(i → j) and the conditional transfer rates (jump rate 93, state change rate, charge state change rate) Γ ct (i → j) between charge states i and j of the near traps 12, where i,j∈UC introduced. p(i → j) and Γ ct (i → j) extracted from histograms 90 constructed from the charge transfer events and the intervals between them (cf. Fig. 9). In addition, the lifetimes of each configuration are defined as τ(i).

[0113] In Fig. Figure 8 shows a schematic representation for SnV of the ionized and neutral lattice defects (V x,y) in the band gap. Ionization occurs when either an electron is transported from the valence band into the charge trap 12 or an electron is transported from the trap to the conduction band by an illumination field. Neutralization occurs when the trap 12 captures either a hole from the valence band or an electron from the conduction band.

[0114] In Fig. Figure 9 shows example histograms 90 showing how long the charge remains in one charge trap state before changing to another and a table with jump probabilities 92 p(i → j) and jump rates 93 Γ ct (i → j) to the corresponding spectral jumps 91 i → j. The example histograms 90 show how long the resonance remains in one charge state until it changes to another. The data are fitted to a Poisson distribution to estimate a mean time. The temporal values can be obtained from the sensor data in Fig. 6. The experiment is performed under 0.5 nW 619 nm light, with a 2 µW (CW power) blue 450 nm pulse with a duration of 4 ms applied between linescans. p(i → j) and Γ ct (i → j) represent conditional spectral jump probabilities 92 and rates 93, respectively, where i, j are the initial and final charge state configurations, respectively. Missing rates are due to insufficient data points. Γ S is the sampling rate. The uncertainties are estimated from the overlap of the individual peaks for p(i → j) and the 95% confidence intervals obtained from the fits for Γ ct (i → j) were extracted.

[0115] The analysis begins with the quantification of the smallest jump probabilities 92 p(i → j). The occurrence of a charge exchange event, given the current linescan time of 5 seconds, given by p(◯ ⊙→⊙ O)=0.03(1), indicates an unlikely direct transfer between the two nearby traps 12. Furthermore, the occurrence of a two-trap charging event p(◯◯ →⊙⊙)=0.03(1) is also unlikely, indicating that these events are uncorrelated.

[0116] Furthermore, the relationship between the reinitialization of the bright SnV charge state SnV -2 → SnV -1 and the charge states of trap 12. The probabilities p(SnV -2 → O ⊙) = 0.61(12) and p(SnV -2 → ◯◯) = 0.38(9) are close to the corresponding peak intensities in spectrum 61 (0.63(5) and 0.31(3) respectively), which may indicate that the trap states are not correlated with the charge state of the SnV.

[0117] In the following, the ionization and neutralization rates for a single trap 12 are compared, Σ X=◯,⊙ Γ ct (◯X →⊙ X) / 2 =0.075(1) Hz or Σ X=◯,⊙ Γ ct (⊙ X → ◯X) / 2 >> Γ s = 0.2 Hz, where Γ s The more than three-fold higher ionization rate may reflect the different physical mechanism compared to neutralization. The ionization rates of the other trap 12 change abruptly with time: for the line scans 0-250 Γ ct (⊙ ◯ → ◯ ⊙) =0.07(2) Hz and 250-500 Γ ct (⊙ ◯ → ◯ ⊙) » Γ s = 0.2 Hz. The trend is reversed for the neutralization rate. This change in rates 93 is attributed to discrete changes in the trap environment. Furthermore, the different ionization rates, Γ ct {(◯◯ → ◯ ⊙})=0.09(1) Hz and Γ ct(⊙ ◯ → ⊙ ◯) =0.19(4) Hz observed under the same illumination laser field, either indicate large variations in the local electrostatic potentials in a ~1 nm range that alter the charge dynamics or the presence of multiple charge trap types. Further investigations could distinguish between the different V n be distinguished.

[0118] Furthermore, the total lifetime of the charge states τ(i), which provides a reference for experiments requiring spectral stability, is determined and interpreted. τ(◯⊙) = 2.3(1) s and τ(◯◯) = 4(1) s are found, which roughly correspond to the duration of a line scan. The measurement procedure involves a blue 445 nm charge initialization pulse between each line scan, accompanied by continuous orange 619 nm laser illumination. From these timescales, it is clear that the blue laser is the primary driver for changes in the charge trap states ( Fig. 20), suggesting that the stability of the trap states can be maintained during optical operations resonating with SnV transitions. Since the trap states are stable much longer than the measured SnV ionization time of 50 ms and the spin coherence time of about 1 ms, albeit non-deterministic, the emitter can still act as an optically coherent spin-photon interface. Evaluation of spectral scattering

[0119] The spectral dynamics induced by charge transfer are extremely detrimental for applications in quantum technology. Spectral diffusion, a term that describes the probabilistic nature of the observed spectral dynamics, leads to optical decoherence, which results in reduced entanglement fidelity in quantum network nodes.

[0120] Knowing the nonlinear susceptibility of the quantum electrometer to charge noise, predictions are now made about how a particular charge distribution affects the spectral properties of a color center. Based on the model, an overview is given of the inhomogeneous broadening caused by a particular charge trap density ρ. trap The details of the calculation are described in the sections below.

[0121] First, the bulk case (cf. Fig. 10) and surface charge traps are considered ρtraps for two different surface geometries, planar and cylindrical. It is found that an implantation depth of d > 21 nm and a cylinder with a radius of r > 45 nm ensure that the surface charges do not degrade the spectral properties of an SnV color center with a linewidth broadening of less than 1%. Such broadening results in 90% interference visibility and more than 87% entanglement fidelity. Similar estimates can be performed for any defect with known polarizability. Control measurements of spectral diffusion as a function of the illumination field are included in the supplementary materials.

[0122] Due to the estimated minimal damaging distances, SnVs and similar color centers are well suited for integration into nanostructures that increase photon collection efficiency and provide tailored emission properties for quantum information applications via the Purcell effect.

[0123] In Fig. 10 shows plots of the inhomogeneous broadening of the SnV zero-phonon line due to bulk and surface charges. The inhomogeneous broadening of an SnV line with a lifetime-limited linewidth of 35 MHz is plotted as a function of ρ trap in units of ppm in a bulk diamond. The brightnesses in the plots indicate the linewidth distribution. The mean and variance of the distribution are represented by the white dots and the error bars. The inhomogeneous broadening as a function of the distance of an SnV from a planar surface and the surface trap density ρtraps is defined as the fraction of surface lattice sites. The dashed lines show the threshold of 1 % and 10 % of the broadening compared to the lifetime-limited linewidth of 35 MHz. The inhomogeneous broadening of an SnV located centrally in a cylinder with radius r is a function of ρtraps. The dashed lines indicate 1% and 10% widening, respectively. Identification of material properties: double vacancy formation

[0124] Based on the electrometer's ability to quantify the charge trap density, the investigation of the material properties will be expanded and the sensor data will be combined with additional simulations. In particular, the physical origin of charge traps 12 in the implanted diamond will be determined. For a sample with less than 1 ppb nitrogen and boron and even lower lattice defect concentrations, the estimated charge trap density of 74(22) ppm must originate from the damage caused by the Sn ion implantation and the subsequent annealing process. The ion implantation creates Frenkel pairs: a pair consisting of a single vacancy V1 and a dislocated interstitial carbon atom. During annealing, V n mobile and can form vacancy complexes, a process that is not well understood and is an active area of research (cf. Fig. 11).

[0125] Here, the V1 to double vacancy V2 conversion yield is estimated using a kinetic Monte Carlo simulation in combination with a simple stochastic diffusion model.

[0126] The density V2 is used as a proxy for higher order vacancy complexes V n Annealing up to 1100 °C primarily converts V2 into V3 and V4. Indeed, wavelength-dependent spectral diffusion and jumps (cf. Fig. 21) are observed, which indicate different ionization energies of the multiple trap types. The estimated density of V2 both as an approximation of an order of magnitude and as an upper limit for the total density of the charge trap 12. ρ V2 = 40.0(2.1) ppm is compared with the experimentally estimated trap density of ρ Exp = 74.1(22.5) ppm. Due to the charge neutrality, the total charge density ρ Sim = twice the density of V2 with ρ Sim = ρ V2× 2 = 80.0 (4.2) ppm. The small deviation is attributed to a reduction in the density of V n compared to the V2 estimate.

[0127] Understanding the origin of charge traps 12 also provides a clear path to creating optically noise-free group 4 vacancy defects in diamond. Single-peak fingerprints indicating a low V n density are more frequently found in high pressure, high temperature (HPHT) annealed samples at 2000 °C, which is consistent with electron spin resonance measurements.

[0128] Spectral jumps have already been observed for group IV vacancy defects. A comparison of the V n -density for the atomic types Si, Ge and Sn and different implantation energies ( Fig. 12) shows that Si implantation leads to the lowest V2 density. This observation is consistent with the more frequent reports of spectrally stable SiV compared to SnV, which can now be explained by the analysis that heavier ions cause increasing V n -cause densities.

[0129] In Fig. Figure 11 shows a schematic representation of the formation of double charge traps (V2) in the crystal lattice 13 during an annealing process. A spatial distribution of the single vacancies (V1) created by 400 keV Sn implantation, predicted by SRIM simulations, is shown. Furthermore, the formation of V2 during annealing at 800 °C is shown. At higher temperatures, V1 begins to diffuse. Then, V1 either moves to the interfaces, recombines with interstitial carbons, or forms V2. Furthermore, the distribution of V1 and V2 distributed near the damage channel caused by the Sn implantation is shown.

[0130] In Fig. Figure 12 shows plots of the simulated densities of the double-charge traps V2 versus the single-charge trap V1 implantation yield (% of participating V1, estimated by SRIM simulations) for three different species: tin, germanium, and silicon. A lower yield of V1 is attributed to recombination with interstitial carbons. The implantation energies are chosen to achieve an average implantation depth of 100 nm. V2 densities for 100 keV implantation energy are shown. The error bands shown represent the statistical standard deviation. Overview of Monte Carlo simulation

[0131] The following provides an overview of the general methodology for simulating single and multimodal spectra 60 ( Fig. 6). The simulations begin with the uniform distribution of charge traps 12 within a certain volume or surface. For multimodal spectra 61, such as the one in Fig. As shown in Figure 6, the distribution of charge traps 12 is divided into two categories: near-range traps 12 and far-range traps. Proximity traps 12 are positioned at fixed locations, while far-range traps are distributed at a fixed density within a given volume. The SnV -1 -Probe 20 is always located at the origin of the coordinate space.

[0132] Once a spatial trap configuration has been created, a single iteration of the Monte Carlo simulation can be performed. This consists of assigning charges to the trap locations (charging the traps 12). A fixed number of charges 12 are distributed under the assumption of charge neutrality: -e + e Σ i q i = 0 with elementary charge e and charge state qi ∈ {-1,0, +1}. The field strength at the location of the SnV -1 then becomes: E→=∑iE→(qi, ri→), where r→i the position of a trap is 12 and E→(qi, r→i) is the electric field of a point charge in the medium, chosen to adequately reflect the boundary conditions for the solution of Maxwell's equations. The nonlinear Stark shift Δ Stark according to the size of the field E→(qi, r→i) is calculated using Eq. 1, where It=|It→| and the parameters Δµ = 6.1 × 10 -4 GHz / (MV / m) 2 , Δα = -5.1 × 10 -5 GHz / (MV / m) 2 , Δβ = -5.5 × 10 -8 GHz / (MV / m) 3 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 4 Unless explicitly stated otherwise, the procedure is repeated 1000 times, and for spectrum 61, which corresponds to the distribution of Stark shifts, the following applies: S(ω)=1N∑nLγ(ω−ΔStark, n), where N is a normalization constant (max S(ω) = 1), n is the simulation step index and L γ (ω) is a Lorentzian line profile with half-width y = 35 MHz, which corresponds to the lifetime-limited line width of the SnV -1 It is assumed that there is neither additional power broadening nor a reduction in lifetime due to Purcell amplification. Relative sensitivity to electric fields

[0133] The sensitivity of the relative electric field δ ∈ = ΔE / E s for a given ρ trap can be calculated by ΔE corresponding to the smallest spectral shift Δ Stark can be resolved according to a modified Rayleigh criterion as described below.

[0134] ΔE is calculated in a two-step procedure: First, the expected inhomogeneously broadened linewidth in the presence of an electric field It→ (see Fig. 13), which is generated either by a charged near-trap 12 or by a non-neutral charge state of the entire spatial trap configuration. The total field at the sensor position can be divided into two components: E→=Es→+δEs→, where δEs→ a fluctuating electric field generated by the varying charge states of the remote trap configuration.

[0135] In Fig. 13 shows a plot of the inhomogeneous broadening as a function of the local bias field E s The line width decreases with increasing E s or ρ trap to.

[0136] The average value of the nonlinear Stark shift is given by 〈ΔStark〉=−Δα(Es2+σ2). Its variance is σΔStark=Δα2(4Es2σ2+2σ4) (assuming that δEs→ is normally distributed with variance σ). The expressions show that a field induces both a discrete spectral shift and a quasi-permanent dipole moment, which leads to an inhomogeneous broadening of the lines depending on the quantities E s and σ.

[0137] In the second step, ΔE is calculated for a given ρ trap calculated using a modified Rayleigh criterion: Two spectral peaks originating from different fields E s and It' are considered separable if the sum of the two individually standardized line shapes resulting from E→=Es→+δEs→ and E→=Es'→+δEs→ have a contrast of at least 26.3% between their local maxima.

[0138] For Fig. 7 is It→=(0,0,It) chosen. To determine the 〈Δ Stark 〉 and the inhomogeneously broadened linewidth, a Monte Carlo simulation is used as described in the simulation overview. The traps that δEs→ were generated with a fixed density ρ trap placed in a conical volume z > 0 with an opening angle of 45°, which mimics the anisotropic distribution of the traps created by implantation and annealing (cf. e.g. Fig. 5 and Fig. 6). The conical volume was capped at z = 30 nm. A spherical volume of 2.5 nm was left free of traps 12 to reduce the appearance of exaggerated multimodal spectral features.

[0139] The for Fig. 3 required averaged line widths are calculated with γFWHM=aσohm+(bσhom2+σinhom2)1 / 2, where σ hom and σ inhomare the half-width of the Lorentz and Gaussian contributions to the Voigt profile and α = 0.5346, b = 0.2166 . In total, the Gaussian and Lorentzian components of 100 different spatial trap configurations at a certain ρ trap averaged. For each ρ trap 2500 randomly generated charge states are taken to simulate a single spectrum 60. The averaged spectral profiles correspond E→=Es→+δEs→ and E'→=Es'→+δEs→ are then used to determine ΔEs→=|Es−Es'| using the Rayleigh criterion.

[0140] Finally, the Fig. 3 calculated by δ ∈ = ΔE / E s for a given ρ trap is divided. resolution

[0141] To determine the spatial resolution Δr=|r→−r'→|, where r→ and r→' are two different positions of point charges, the same calculation is performed as for the relative sensitivity of the electric field. However, it is additionally assumed that the charges generate electric fields: E→(q, r→)=qi4πϵ0ϵrr3, where ∈0 is the permittivity of the vacuum and ∈ r = 5.5 is the relative dielectric constant of diamond. The use of the bulk expression and the neglect of surface contributions is justified due to the dimensions of the column, r > 40 nm ( Fig. 4) when the SnV is located on the symmetry axis of the column. In Fig. 4, the resolution of the sensor 20 in the presence of a constant static field E→rc shown, which is generated by a negatively charged trap 12 at a fixed location, r→0=(0; 0; 0, 8) nm. As described in the previous section, Fig. 4 was created in a two-step procedure: First, the expected spectral profiles for a given ρ trap and E→=E→(−1, r0→)+E→(−1, r1→)+δEs→ Then the resolution was calculated using the Rayleigh criterion.

[0142] The position vector r→1=(0, 0, d) is in line with r→0 The averaged profiles are then used to determine the smallest resolvable distance Δr=|r→−r'→| from the spectral profiles, with the fields Ebias→=E→(−1, r0→)+E→(−1, r1→)+δEs→ and Ebias→=E→(−1, r0→)+E→(−1, r1'→)+δEs→. Multimodal spectra

[0143] The most likely trap configuration is determined in three steps. First, the spectral positions of the (in this case) four peaks observed in the measured multimodal spectrum 61 are determined to identify the near traps 12 that generate the Stark shifts observed in the experiment. Next, the predetermined positions of the near traps 12 are fine-tuned using an optimization procedure that uses a comprehensive collection of simulated spectra 60. Finally, using an objective function (χ 2 -test) the most likely near-trap configuration by comparing the simulated spectra 60 with the experimental observations. Modeling of glow

[0144] A kinetic Monte Carlo simulation of the annealing process was performed, in which an initial distribution of single vacancies was calculated using SRIM for a given set of implantation parameters. Subsequently, a spatial distribution of double vacancies was calculated by randomly migrating the single vacancies on the fcc diamond lattice until they encountered another single vacancy, forming a double vacancy. sample

[0145] The sample used (E001) is an electronic diamond (element 6) grown by chemical vapor deposition (CVD). The sample was first cleaned in a boiling triacidic solution (H2SO4:HNO3:HClO4, 1:1:1) and then dissolved in Cl2 / He and O / CF 24 etched to remove organic contaminants and structural defects from the surface. Subsequently, Sn (spin-0) ions were introduced with a fluence of 5 x 10 10 atoms cm -2and an implantation energy of 400 keV, corresponding to a penetration depth of 100 nm, as estimated by SRIM simulations. The formation of the SnV color centers was finally achieved by annealing the diamond at a temperature of 1050 °C for about 12 hours in a vacuum (pressure 7.5 x 10 -8 mbar).

[0146] The nanopillars were fabricated using a combination of electron beam lithography and plasma etching. First, 200 nm of Si3N4 was deposited on the diamond surface using an inductively coupled plasma (ICP) CVD system. After coating the sample with 300 nm of electrosensitive resist (ZEP520A), pillars with nominal diameters ranging from 180 nm to 340 nm were exposed using electron beam lithography in 40 nm increments. After development, the pattern was transferred onto the Si3N4 layer using a reactive ion etching plasma (RIE) (10 sccm CF4, RF power = 100 W, P = 1 Pa) and then etched into the diamond using an ICP process in an O2 plasma (80 sccm, ICP power = 750 W, RF power = 200 W, P = 0.3 Pa). The remaining nitride layer was finally dissolved in a buffered HF solution. Optical setup and experimental details

[0147] The sample is cooled to 4 K in a closed-loop helium cryostat (Montana s50). A confocal scanning microscope is used to locate and optically address nanopillars with SnV. The SnV is initialized with a blue diode laser at 450 nm (Thorlabs LP450-SF15 or Hübner Cobolt 06-MLD). Off-resonant measurements are performed with a green diode laser at 520 nm (DLnsec). The PLE spectra were measured using a spectrometer (Princeton Instruments HR500) and a CCD camera (Princeton Instruments Excelon ProEM:400BX3). The photons collected by the cryogenic setup are coupled into a fiber and counted via avalanche photodiodes (Excelitas SPCM-AQ4C or SPCM-AQRH). The experiments are controlled with the Qudi software package.

[0148] A highly tunable laser at 619 nm (Sirah Matisse, DCM in EPL / EG solution) and a SHG laser source (TOPTICA SHG DLC PRO) are used for PLE scans. The frequency of the resonant excitation laser is scanned across the C transition of an SnV center and the phonon sideband of the fluorescence is collected. The analyzed measurement ( Fig. 6) was under P = 0.5~nW « P sat to minimize power broadening and SnV ionization. Between each line scan, 4 ms of 2 µW (average CW power) blue laser irradiation were performed. Temporal analysis of sensor data

[0149] As described, emitters with inversion symmetry can be used to investigate aspects of charge dynamics near the emitter. Details of the data analysis of the long-term PLE scans to estimate the lifetime of the charge configuration in the vicinity and the switching rates are presented below.

[0150] Wavemeter correction: During scanning, the laser frequency is controlled by applying an external voltage signal. The laser frequency is monitored via a pick-off path directed to a wavemeter. The PLE spectra 62 are initially recorded as voltages and fluorescence signals. The voltages can then be converted to frequencies by matching the timestamps. This takes into account any nonlinear frequency changes that occur during the scan.

[0151] Binning: Individual scans are mapped to a frequency axis by selecting a single line scan and then frequency binning. If multiple data points fall into the same bin, they are averaged. If a bin remains empty, the average of the previous and next bins is used.

[0152] Histogramming scans: The binned scans are summed and normalized to create histograms for PLE spectra 62.

[0153] Configuration identification: A peak-finding algorithm (MATLAB: findpeaks) is used to identify the frequencies of the (in this case, four) peaks. These peaks are then labeled and used to average the spectral position corresponding to a specific charge configuration of near traps 12.

[0154] Configuration regions: The state configurations are separated by assigning a spectral region to each central peak position. These regions can be determined by half the spectral distance between two neighboring peaks.

[0155] Scan-by-scan peak detection: The same peak finder algorithm is used to find peaks for each individual scan.

[0156] Scan-by-scan configuration identification: The identified peaks are then assigned to a charge state configuration based on their central frequencies.

[0157] Determination of brightness durations: A brightness duration is determined by the time period during which a peak value is associated with the same charge configuration until a change occurs. Each brightness duration is recorded along with the changes in the charge state configuration.

[0158] Histogramming of brightness durations: The brightness durations are summarized in histograms 90 according to the frequency with which they were observed in order to extract averaged lifetimes and switching rates 93.

[0159] Probability 92 of a charge state change p(i → j): The frequency with which a spectral jump 91 from one charge state i to another j has occurred is recorded. It is then normalized to the total number of jumps from configuration i to obtain a probability. There are two factors that can limit the quantification of uncertainties. First, jump events depend on the individual identification of peak positions per line. The implemented peak finder algorithm locates the maximum of a line for each scan. Due to spectral dispersion, it is not possible to fit each individual line and extract a central frequency uncertainty. Second, in the integrated spectrum 61 in Fig. 6 Overlaps of individual spectral peaks. Although a cutoff position in the center of the peaks was chosen, some of the identified peaks may actually belong to the tail of the neighboring spectral peak rather than to the identified position. Therefore, a total uncertainty factor is assigned by calculating the overlap of the individual integrated fits of the individual peaks. These factors are then multiplied by the extracted probabilities 92.

[0160] Poisson fitting: The 90 histograms are converted to probability densities and then fitted to a Poisson distribution. After fitting, the 90 histogram and the fit are scaled back to the original occurrences. The brightness durations are then converted to real time units using the duration of a single scan.

[0161] Lifetime τ(i) and determination of the conditional spectral hopping rate 93 Γ ct(i → j): The means of the Poisson distribution fits and their uncertainties are given as lifetimes of the near-charge configurations or their inverse as rates of state change between the configurations. Simulation detailsMultimodal spectra

[0162] In the following, the simulation of the multimodal spectrum in Fig. 6 is shown in detail. It is described that there is a spatial trap configuration that stores the experimental data in Fig. 6 can reproduce.

[0163] The process for determining the most likely trap configuration can be divided into three main steps. First, the four peaks observed in the measured multimodal spectrum 61 are used to determine the positions of near-trap 12 that produce Stark shifts consistent with the experimental observations. This first step provides a rough estimate of the positions of the near-trap 12. Next, an optimization procedure is applied to fine-tune the predetermined positions of the near-trap 12. By optimizing the relevant parameters, a comprehensive collection of simulated spectra 60 is generated. Finally, using the objective function (χ 2-test) used during the optimization procedure, the large data set of simulated spectra 60 is analyzed to determine the most likely configuration of the near traps 12. This objective function serves as a measure of the agreement between the simulated spectra 60 and the experimental observations. By comparing the calculated spectra 60 with the measured data, the configuration that best matches the experimental results can be determined. Each step is described in detail below.

[0164] The four peaks of the measured spectrum 61 in Fig. 6 are used as a reference to estimate the position of a charged near trap 12 relative to the SnV using the following equation: ΔStark=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4.

[0165] It is assumed here that the scenario with three traps 12 contributing to the multimodal spectrum 61 is the most likely. Trap 12, which is located at r→2=(0,0,r2) is assumed to be permanently charged. The charge state of the other two traps 12 is then given by {◯◯, ◯⊙, ⊙ ◯, ⊙⊙}, where the left circle represents a trap 12 at the position r→1 and the right circle a trap 12 at the position r→3 An empty circle represents a neutral trap 12, while a filled circle represents a negatively charged trap 12. The peaks corresponding to each charge state are shown in Fig. 6. The negative charge, which is located at a distance r→2 increases the response of the SnV to distant charges and produces the observed inhomogeneous broadening. The choice r→2=(0,0,r2) is not universally valid, but due to the anisotropy expected from the implantation procedure, it can be assumed. Furthermore, the inclusion of the position r→2 with two additional degrees of freedom, the free parameter space is increased.

[0166] The arrangement of the three near traps is limited to one level, further reducing the complexity of the problem. The starting positions r→1,r→2,r→3 are approximated by solving the following system of equations: Δ◯◯=−Δα2E(−1,r→2)2 Δ◯⊙=−Δα2[E(−1,r→2)+E(−1,r→1)]2 Δ⊙◯=−Δα2[E(−1,r→2)+E(−1,r→3)]2 Δ⊙⊙=−Δα2[E(−1,r→2)+E(−1,r→1)+E(−1,r→3)]2.

[0167] The positions are parameterized according to: r→1=r1[cos(θ1),0,sin(θ1)] r→3=r3[cos(θ3),0,sin(θ3)].

[0168] The above equations can be solved for r1(θ1), r3(θ1) and θ3(θ1). The relative displacements Δ ◯◯ ,Δ ◯⊙ ,Δ ⊙◯ ,Δ ⊙⊙ are estimated from the central peak positions using a fitting procedure, where the integrated spectrum is Fig. 6 is fitted with four Voigt profiles simultaneously.

[0169] The fine-tuning of the near-trap positions in the second step is again carried out using a Monte Carlo simulation in combination with an optimization procedure. For the optimization procedure, the far-trap positions are randomly placed in a conical volume z > 0 nm with an opening angle of 45° and a fixed density ρ trap distributed to mimic the non-isotropic distribution of the traps expected during implantation damage. The volume is capped at 30 nm. E s a volume r q< 2.5 nm for the arrangement of the short-range charge traps 12. It is assumed that a charged trap contributes to the total field E→=∑iE→(qi,r→i), contributes with E→(qi,r→)=qi4πε0εrr→r3, where e is the elementary charge and q i a charge state with q i ∈ {-1,0, +1}, ∈0 is the dielectric constant of the vacuum and ∈ r = 5.5 is the relative dielectric constant of diamond.

[0170] For each choice of ρ trap . r2 and θ1 a Monte Carlo simulation of the spectral fingerprint is performed.

[0171] In order to adequately take into account the charge state of the near traps 12, they are detected with a probability p i charged according to the relative peak heights in each simulation step. The following probabilities p i were used: p⊙⊙ = 0.041 , p ⊙◯ = 0.017, p ◯⊙ = 0.63 and p ◯◯ = 0.31.

[0172] The optimization of trap positions for given ρ trap . r2 and θ1 is done by minimizing the χ 2 -Function with: ∑iχ(θ,i)=∑n=0,iN[On(θ,i)−En,i]2En using the simplicial homology global optimization (shgo) algorithm. An implementation of the shgo algorithm provided by the Python library SciPy is used. In Eq. S10, θ = [a, b, p], where a, b are fine-tuned as follows: r1'=ar1 and r3'=br3.

[0173] The spectrum is split into three parts, denoted by i ∈ {◯◯, ◯ ⊙,⊙ ◯ +⊙⊙}. For each part, the respective single and double Voigt profile fits are used for comparison with the simulated spectra 60 using Eq. S10. In Eq. S10, E n,ithe expected counts in the nth bin, which was determined by binning the (normalized) single and double Voigt profiles fitted to the measured spectrum 61 into 170 equal-sized bins over an interval containing the 4 GHz wide profile. 0 n (θ, i) is the number of expected counts of the respective i for the simulated spectrum in the n-th bin.

[0174] Finally, the values χ2,r1',r3' r3 tabulated for ρ trap ∈ [35,100] ppm, (Δ ⊙⊙ ∈ [0.5; 1.7] GHz) and θ1 ∈ [0; 0.6] rad. 500 iterations of optimization over different spatial configurations of the remote traps for each value of ρ trap , r2 and θ1 are performed. Only the 50 lowest values of χ 2 (the others are considered as outliers) are used and a weighted average is applied to determine 〈χ 2 > carried out.

[0175] The 68% confidence interval for ρ trap , (Δ ⊙⊙ ) and θ1 by min{〈χ 2 〉} + 3.5. The results are shown in Fig. 6 and Fig. 7. The Fig. 6 and Fig. The statistical error shown in Figure 7 results from all simulated spectra within the 68% confidence interval. Effects of noise

[0176] The Fig. The relative sensitivity to electric fields shown in Figure 3 depends on how well the peak frequency of a spectral peak can be determined. The determination of peak position is influenced by uncertainties caused by noise other than the stochastic shifts of the C transition. Sources of such noise can be dark counts of the detector or unwanted background fluorescence. The signal-to-noise ratio (SNR) required to determine the Fig. To allow for the relative sensitivities shown in Figure 3, the relative sensitivities are estimated. It is first assumed that α dominates the sensor's response to the interaction with an electric field, so that the relative Stark shift according to Eq. S1, which arises from two different resolvable electric fields E1 and E2, becomes the following equation: |δω|=α2|E12−E22| =αδεE12,

[0177] Here, the definition of the relative sensitivity of the electric field δ ∈ = |E1 - E2| / E1 and assuming that E1 + E2 ≈ 2E1. The normalized uncertainty is given as A = |δω| / γ hom where the homogeneous linewidth of the SnV γ hom = 35 MHz has been chosen as the reference. A is the smallest Stark shift difference that must be resolved to achieve a relative electric field sensitivity of δ ∈ can be achieved.

[0178] In Fig. 14 the normalized uncertainty for three values of δ ∈ which are representative values from Fig. 3. The uncertainty normalized to the homogeneous linewidth for three different values of the relative electric field sensitivity is δ ∈ = 1, 4, 7 · 10 -7 . For the range of relevant field strengths it is determined that 2.5 · 10 -5 < Λ ≤ 10 -4 To understand the normalized uncertainty, the normalized uncertainty of the central peak position δω0 / γ hom a spectral fit with a centered Voigt profile V(ω - ω0, γ hom , σ) with ω0 = 0 a Lorentzian component γ hom and a Gaussian component σ in the presence of noise. If δω0 / γ hom, resulting from the fitting, does not exceed the threshold required by Λ, it is assumed that the corresponding relative sensitivity of the electric field can be achieved. In Fig. The result of the simulations is shown in Figure 15. The Gaussian component of the Voigt profile is calculated according to σ norm = σ / γ hom normalized. SNR=10 log10(A2 / δnoise2) calculated, where the amplitude of the Voigt profile A = 1 and δnoise2 the amplitude of the white noise is: S(ω) = V(ω, γ hom , σ) + δ noise .

[0179] Fig. 15 shows the required SNR as a function of σ normThe uncertainty extracted from the fit as a function of SNR and the component of the Voigt profile are both normalized to the homogeneous linewidth. Although these requirements are demanding, they do not represent a fundamental limitation of the proposed sensor. For the multimodal spectrum in Fig. 6, the standardized uncertainties are between 10 -2 ≤ Λ < 7 · 10 -1 The unfavorable A in the experiment is mainly due to experimental deficiencies and does not represent a fundamental limitation of the sensor principle.

[0180] Even if Λ in the implementation does not reach the simulated requirement to generate the simulated limit of the relative sensitivity of the proposed electrometer, they are sufficient for the claimed Ångström resolution of the sensor. A similar estimation of the normalized sensitivity as a function of the relative resolution δ∈ r= (r1 - r2) / r1, making similar assumptions as above (r1 + r2 ≈ 2r1), so that Λ=2δεra2αγ(1rbias2r12+1r14), where α = 1 / 4π∈0∈ r . It is determined that 18 < Λ < 166 for δ∈ r = 1, r bias = 10 Å and r1 ∈ (10,30) Å, which far exceeds the stated relative fitting uncertainties. Most likely spatial trap configuration

[0181] The integrated multimodal spectrum in Fig. 6 can arise from different spatial charge configurations, which can lead to identical results. However, the possible spatial charge configurations can be narrowed down.

[0182] The integrated spectrum in Fig. Figure 6 shows four peaks. The two simplest configurations that produce such a spectrum are: A) three traps 12, where one trap 12 is permanently charged and the other two are in the states [◯ O, ◯ ⊙,⊙ ◯,⊙⊙] or B) four near-trap 12, where one trap 12 is permanently charged and the other three are in the charge states [◯◯◯, ◯◯⊙,◯ ⊙ ◯,⊙ ◯◯]. In both cases, a bias field / a permanently charged trap 12 is required to explain the inhomogeneous broadening of the right peak. There are many other trap configurations that could produce the same features, but these are less likely because they require more and more traps, 12 with only a subset of all possible charge-state combinations contributing to the observed spectrum. Of the two scenarios, scenario A) requires the fewest additional assumptions.

[0183] The strongest argument for A) is the rate p(◯◯ →⊙⊙) = 3(1)%. If the traps are assumed to ionize independently with a probability P, then the corresponding rates for B) are p(◯◯◯ →⊙ ◯◯) ≈ P. However, it is one of the most unlikely processes. Scenario A) would require two ionization events of the order of P 2 which is much closer to the observation. The same argument can be made for p(◯ ⊙→⊙⊙) = 33(6)%. For B), the corresponding event would be p(O ⊙ ◯ →⊙ ◯◯) ≈ P 2 , which seems unlikely. However, the single ionization event p(◯ ⊙→⊙⊙) is more likely and is therefore more consistent with the two-trap scenario.

[0184] The bias field to which the sensor is exposed is estimated by positioning a constantly ionized charge trap such that the inhomogeneous broadening of the simulations matches the observed linewidths. The simulations yield a bias field that causes a spectral shift of 1.27(0.4) GHz. This result is compared with the integrated spectrum 61 for lines between 0 and 200 from the spectrum in Fig. 6 and evidence of a small blue-shifted peak with a spectral shift of 1.24(2) GHz compared to the ◯◯ peak is found (cf. Fig. 16). Fig. Figure 16 illustrates the experimental estimation of the bias field on the sensor using a background-subtracted integrated spectrum of the line scans between 0 and 200 as in Fig. 6. The fit centered at 1.24 GHz indicates the existence of an additional charge trap 12 that is ionized most of the time. This experimentally demonstrates that there is indeed a third charge trap 12 that is ionized most of the time. Analysis of the inhomogeneous linewidth with Monte Carlo simulations and experimental data independently confirms the estimated magnitude of the bias field. This agreement also demonstrates that the simulations can reproduce the charge environment and are capable of detecting traps that do not dynamically change their charge on the timescales of the distant traps. Glow

[0185] The formation of V2 is understood to be a consequence of implantation damage and the annealing process: The implantation damage occurs during the collision cascade in the diamond lattice, which decelerates the implanted ion. Collisions with an energy above the displacement threshold (≈ 37.5–47.6 eV, much lower than typical implantation energies) displace carbon atoms and create Frenkel pairs: a pair of V1 and a dislocated carbon atom located at an interstitial site. After implantation, an annealing process is performed to create the color center through vacancy diffusion and heal the lattice damage. At temperatures above 600 K, the interstitial carbon becomes mobile, and at 800 K, the V1 exhibits a high degree of mobility. Consequently, during annealing, the interstitial carbon can either recombine with the V1 or diffuse away from the damage site, eventually leaving the sample via the interfaces.The V1, which is not recombined with the interstitial carbon, can form an immobile V2, vacancy clusters or, together with the implanted ion, a color center.

[0186] The model assumes a single mobile species (V1) and considers the formation of V2 without multiple vacancy complexes. Since multiple species are not considered, the assignment of different hopping frequencies is omitted. The initial number N and the 3D distribution of V1 after implantation are estimated using a SRIM simulation. Assuming a certain percentage of V1 that is not consumed by interstitial carbon, which is referred to as the yield in % of non-recombined Frenkel pairs (V1 yield in Fig. 11 and Fig. 12), a range of concentrations of V2 is found, which in Fig. 12 for the three atomic G4V species Si, Ge, and Sn and different implantation energies. The distribution of V2 in the sample is estimated using a kinetic Monte Carlo simulation. At each time step of the kinetic simulation, V1 can make a random step along one of the neighboring lattice sites. When two V1s are adjacent to each other, they form a static V2 that no longer diffuses. The initial distribution of V1 is estimated using SRIM. For each implantation energy, 50,000 implantation events for a given atomic species and implantation energy are used to determine the probability distribution p(z) of V1 as a function of depth z, measured relative to the diamond surface (001). The p(z) values are then used to realize the spatial distribution of V1 after a single implantation event.The V1s are distributed on the diamond lattice according to the p(z) along a narrow damage channel with a rectangular cross-section of 2α × 2α. The loss of V1s that do not contribute to the formation of V2s by recombination with interstitial carbon atoms is a fixed percentage due to the reduction of the original amount of V1, as determined by the SRIM simulation. Bulk cargo

[0187] Based on the model, an overview of the charge trap densities and the resulting inhomogeneous broadening with specific thresholds, the 90% interference visibility, and > 87% entanglement fidelity is given. First, a Monte Carlo simulation is used to determine the linewidth distributions for a specific trap density p. A carbon density of ρ is assumed. C = 8 / α 3in the bulk and an isotropic distribution of traps 12 in the vicinity of the SnV at a given density ρ are assumed. For each ρ, 500 spatial trap configurations are considered, producing individual spectra with a peak for ρ ∈ (1,100) ppm. Eqs. S9 and S8 are used to calculate the spectra. Surface charges

[0188] The surface density for both the semi-infinite half-space and the cylindrical geometry, which is given in ppm, is calculated with respect to a carbon density of ρ c = 2 / α 2[(001) plane]. For the semi-infinite half-space, the traps 12 are randomly arranged in a square with an edge length of 100 nm. The cylindrical surface has a height of 100 nm. The simulation of the inhomogeneous linewidth was performed in both cases using the Monte Carlo method, using 5000 different charge configurations for a single spatial configuration of traps 12. The electrostatic fields of a point charge on a surface are also used, taking into account the appropriate boundary conditions. The electric field of a charge located on the surface of the semi-infinite half-space is: E→(q,r→q)=q2πε0(εr+1)r→qrq3.

[0189] For the cylindrical surface, a diamond cylinder with radius R is assumed, extending to z = ±∞. Band bending is not considered, which can be advantageous for eliminating surface noise through shielding. Shielding by free charge carriers is also neglected because the strong reduction in sensitivity to charge noise that would be expected even at moderate shielding lengths of a few tens of nanometers is not observed. Control testsVerification of emissions from a single transition

[0190] The sensor can be verified to determine whether the multimodal spectral fingerprint originates from a single transition. Four characterization measurements are provided at zero magnetic field to rule out Zeeman splitting, which indicates that the signal originates from a single source and a single transition. Distribution of jump distance

[0191] For the 19 characterized emitters, hopping distances ranging from a few hundred MHz to a few GHz were determined. In the samples examined, either one or two different hopping processes or combinations thereof were found, which are in complete agreement with the number of estimated lattice defects. The distribution of these distances is shown in Fig. 17 shown on the left. Fig. Figure 17, left, shows the spectral hopping ranges of characterized emitters. Non-hopping emitters were stable during linewidth scans, which took place at various time intervals between minutes and one hour. The error bars indicate the 95% confidence intervals of the central frequency separations extracted from the data.

[0192] The existence of unknown levels with quasi-forbidden transition rules therefore seems unlikely, since the jump distances for each emitter appear to be random. PL spectrum

[0193] In Fig. 17 The middle shows a photoluminescence spectrum of E1 with -850 GHz splitting between C and D transitions. The photoluminescence emission spectrum measured under 520 nm excitation light at 4 K according to Fig. 17 Middle shows a typical SnV spectrum with recognizable spectrometer-limited peaks representing the C (between levels |1〉-|3〉, Fig. 6) and D- (|2〉-|3〉) transitions. Since they are separated by ~ 850 GHz, it can be safely stated that several peaks from the PLE scan do not correspond to these transitions. Measuring autocorrelation

[0194] The autocorrelation measurements presented in the control experiments for the single-photon ionization charge dynamics model are taken from the emitter under investigation. The probability that multiple emitters contribute to the spectrum is determined by an autocorrelation measurement with g (2)(0) = 0.12(9) < 0.5 close to the theoretical expected value of g (2) (0) = 0 made unlikely. Rabi frequencies of different resonances

[0195] Rabi oscillations between the levels |1〉 and |3〉 (C-transition) of an SnV are demonstrated at the emitter E2 at two different resonance frequencies before and after a spectral jump event. Fig. Figure 17 right shows Rabi frequencies of emitter E2 at different powers of both resonances. The values are extracted from a damped oscillation function at different resonant excitation powers (between the levels |1〉 and |3〉). The data points were recorded before and after a spectral jump and thus at different frequencies. The uncertainties and error bars represent 95% confidence intervals extracted from the data. The detailed view shows Rabi oscillations observed with 45.5 nW power at the higher-frequency resonance. The oscillations are achieved by resonant excitation after a green stabilization pulse. The data after the rise time of the resonant laser are fitted to a damped oscillation function. After repeating the measurement at different powers, a slope of 20.9(9) was obtained for the low-frequency resonance. Hz / nW, for the higher frequency a slope of 21.2(1.8) Hz / nW and for the combined dataset a slope of 21.0(5) Hz / nW on a linear frequency Frequency−power line. Line. The fact that the slopes for three data sets remained within the fitting error range strongly suggests that the dipole moment did not change between the spectral jumps and that the same transition is addressed between the two measurements. Demonstration of ionization processes via single-photon processes using autocorrelation measurements

[0196] One of the events that can occur during laser irradiation is the transition of group IV vacancy (G4V) emitters to a dark state. This manifests itself as shoulder-like bunching features around the anti-bunching decay in autocorrelation measurements. Applying the single-photon process assumption from the model used, a linear power dependence is found for both hole creation / capture and electron promotion. These experiments demonstrate that the charge transfer picture is consistent with the photon statistics measurements. The analysis is based on the derivation of the autocorrelation function and the rate equations.

[0197] A system with three levels is assumed, where level 1 is the ground state, level 2 is the excited state and level 3 is a non-radiative shelving state known as G4V -2 Such a system g (2)with a non-zero background follows the following equation: g(2)=1+p2[1−(1+a)exp(−ττa)+a exp(−ττb)], where p determines the contribution of the background, τ α is the anti-bunching time, which refers to the sink at 0 delay, τ b is the bunching time, which determines the shoulders around the anti-bunching drop, and the parameter α is related to the transition rates. To verify the model, g (2) Measurements of an SnV center at different powers (P) were fitted to this equation and the parameters extracted. To predict the transition rates (k InitialFinal ) the following performance relationships are assumed: • At k 12 (incoherent excitation) a linear dependence on the power 'δP' is assumed, since it is a one-photon process in which an electron transitions from the ground state into quasi-continuous phononic bands of the excited state. • k 21 (spontaneous emission) is modeled with a constant rate 'Γ'. • At k 23 (Shelving) a linear power dependence 'αP' is assumed, since this process is known to be a one-photon process that transports electrons from the valence band into an excited G4V. • k 31 (Deshelving) is also modeled as linearly proportional to the power 'βP': Here, hole provision is assumed to be a one-photon process, which is initiated by the transport of an electron from the valence band to a V n Previously, this rate was modeled with a saturation curve, which can be attributed to the limited amount of contributing V1. However, for this case, the Monte Carlo simulations predict a V nDensity is predicted, so saturation can occur. Therefore, a linear model can fit the data well. A saturation curve can mimic a linear relationship at low power levels, and both models can perform consistently across different ranges.

[0198] The bundling time τ b is related to the transition rates by the following equation: τb=1k31+k23k12k12+k21

[0199] If k 12 as much larger than k 21 - as expected with higher performance - is assumed, then k strives 12 / (k 12 + k 21 ) against 1. Consequently: τb=1k31+k23=1(α+β)P

[0200] This shows that τ b effectively by the total rate of k 31 and k 23 at higher power levels. When a 1 / x model is fitted to the extracted data τ b in Fig. 18, it is shown that the model fits the data well, and α + β is extracted as 7.5(1) kHz / µW. The total charge cycle rate of 1 MHz at ~150 µW also seems reasonable, as it is assumed that the charge transfer process is slower than spontaneous emission or excitation.

[0201] To estimate the rate coefficients separately, the α parameter can be determined, which can be calculated by the following equation: a=k23k31+k12k12+k21=αβδPδP+Γ.

[0202] At high powers, the α parameter asymptotically reaches the value α / β. Fig. 17, the extracted α values from the measurements follow a saturation curve where the fit asymptotically approaches 0.40(3). From this relationship in Eq. S17, the shelving and deshelving rates at each power can be derived with α = 2.2(2) kHz / µW and β = 5.4(2) kHz / µW. Since the assumption of linear power dependence is consistent with the observed data, one-photon processes are assumed to be the main cause of the charge dynamics in the sample.

[0203] In Fig. Figure 18 shows plots of the extracted parameters from the autocorrelation measurements for emitter E1. The error bars represent 95% confidence intervals derived from the fits. These measurements on the left show that shelving and deshelving processes can be modeled as single-photon events. The bunching time at different powers is given. The gray points are excluded from the calculation because they do not behave according to the approximated model at low powers and have large errors. The solid line represents the fit to a 1 / (cP) function. In the box in Fig. 18 Selected sample measurements are shown on the left. On the right, the α parameter is plotted at different power levels. The solid line represents the fit to a saturation curve. Interaction between charge trap and illumination field

[0204] The properties of the laser can influence spectral diffusion. Since the illumination triggers the ionization events in the sample, it is shown that the interactions and observed phenomena are consistent with the existence of charge traps. Position dependence of the stabilization laser and measurement of subdiffraction drift

[0205] A special property of the ZPL of an SnV is that the spectral line drifted in correlation with the laboratory's air conditioning cycle. Simulations are performed to reproduce the periodic changes and the inhomogeneous broadening of the PLE measurement. These simulations involve introducing a periodic misalignment of the laser by varying the involved remote charge densities.

[0206] The blue stabilizing laser is assumed to have a Gaussian intensity distribution in the z-direction that oscillates in time: I(z,t)=I0e−[z−z0(t)]2 / 2σ where I0 is the peak intensity of the laser at the focal point, σ is the focal length and z0(t)=a sin(ωt).

[0207] The amplitude α, which describes the extent of misalignment due to temperature fluctuations in the system, is unknown. The frequency ω = 2π / T corresponds to a T = 10 min cycle. To perform the Monte Carlo simulation, the previously described steps are followed, with the field generated by an ionized trap specified as follows: E→(q,r→)=qi2πε0εrr→r3.

[0208] Traps 12 with a density of ρ = 22.7 ppm are randomly distributed in a cubic volume with an edge length of 100 nm. The trap density reproduces well the inhomogeneously broadened linewidth of ≈ 103 MHz and the Fig. 17 for a power-broadened homogeneous linewidth of ≈ 88 MHz. The probability that a trap participates in the ionization is assumed to be given by P(t) = P(z, t) + P0, where P(z, t) ∝ I(z, t) and P0 = 0.1 is a constant background ionization probability. For the Monte Carlo simulation of the inhomogeneous linewidth, 2500 different charge configurations are used at each time step t. Very good agreement with the results is obtained for a laser with a focal spot width of FWHM=240 nm(σ=FWHM / 22log(2)) and a vibration amplitude of a = 200 nm. The results are shown in Fig. 19 can be seen.

[0209] To further confirm the model, a long-term PLE scan was carried out ( Fig. 19) and the xyz control of the confocal microscopy setup is used to optimize the fluorescence signal. By monitoring the changes in the spectral line, a ~200 MHz drift is measured over a period of 3 hours, corresponding to a shift of ~50 nm according to the position optimizer. By reorienting the setup, the original position of the resonance is restored, further supporting the hypothesis.

[0210] Spectral drift relationships ~0.2 MHz / nm and ~4 MHz / nm for Fig. are extracted. This means that, depending on the surrounding charge density, it would be reasonable to estimate a MHz / nm equivalent of the laser position drift to the emission center frequency. Such a spectral test could prove useful for estimating position drift below the diffraction limit. It has been demonstrated that chirped pulses from an EOM can scan a range of 200 MHz in less than one second. Therefore, using a spectral approach would also enable a higher bandwidth, exceeding the readout rates of fluorescence intensity-based systems.

[0211] Overall, an SnV, or generally an emitter with inversion symmetry, can be used to temporally resolve the involved remote charge trap density at any time. By correlating the central frequency, spatial drifts in experimental systems can be tracked.

[0212] In Fig. Figure 19 shows plots of the influence of laser misalignment on the PLE spectra. The left plot shows the simulation of the temporal change in the central position and linewidth of the C transition caused by a periodic change in the alignment of the charge-state stabilizing laser, which can result from temperature changes in the experiment. A power-broadened homogeneous linewidth of FWHM is used. hom = 88 MHz (left line) and an inhomogeneous line width of FWHM hom = 103.3 MHz (extracted from the fit with a Voigt profile, right line) for the specified parameters of the charge-state polarization laser. The right plot shows an example PLE measurement demonstrating a drift of the resonance frequency. After optimizing the xyz position of the sample and the laser spot, the central frequency returns to its original position. Method for stabilizing the emitter

[0213] The spectral properties of the emitters using different methods for charge stabilization with blue laser light are also investigated to determine its interaction with the V n to investigate. Fig. Figure 20 shows PLE scans and spectra using two different stabilization schemes with a charge-stabilizing laser at 450 nm and 300 nW average power. The first scheme uses continuous wave (CW) laser light during each PLE scan (continuous stabilization). The second is a pulsed scheme: Before each PLE scan, the sample is irradiated with a 4 ms blue laser pulse (pulsed stabilization). The PLE scans were performed at emitter E1 with a resonance power of 0.7 nW, which is below the saturation power (>20 nW) and also low enough to avoid ionization during the scan.

[0214] Fig. Figure 20 shows the two resonance peaks (~ 1.4 GHz apart), which are also present in each individual line scan. The individual PLE scans of the pulsed scheme in Fig. 20 show that both resonances correspond to two different spectral positions of the C transition, which is attributed to the Stark shift according to Eq. S1, which is caused by two different charge configurations of the ionized V n near the SnV. With the resonance laser, a quasi-continuous fluorescence signal with the full inhomogeneous linewidth can be observed. Due to the continuous stabilization, the charge state of the surroundings is changed with a spectral jump rate Γ SH » Γ scan cyclically changed, which is much higher than the PLE scan rate, resulting in two detectable peaks in individual PLE scans.

[0215] In Fig. Figure 20 shows plots of the photoluminescence excitations of the C junction under different charge stabilization schemes at emitter E1. During the scans, hopping between two different resonances is observed. The resonant laser has a power of 0.7 nW and the blue laser has a power of 300 nW. The spectra were calculated using Voigt profiles. The uncertainties represent 95% confidence intervals extracted from the spectra. In the left plot, the blue laser at 450 nm continuously illuminates the sample while the resonant laser measures. Continuous operation of the blue laser results in hopping that is faster than a single line scan, resulting in both peaks being observed in every single scan. In the right plot, a 4 ms blue laser pulse is emitted at the beginning of each scan.Without the help of the blue laser, the transition between the two resonances is slower, but still present due to the laser resonating with the C transition.

[0216] Another clear signal for the increased ionization of V n is the more pronounced inhomogeneous broadening of the resonance lines during continuous stabilization. 450 nm CW light results in more traps in the surrounding area being involved in generating the fluctuating electric field at the emitter position during each individual scan. Just as predicted by the Monte Carlo simulation, increased charge trap activity leads to increased inhomogeneous broadening. Wavelength dependence of the stabilization laser

[0217] An indication that charge dynamics and the occupation of nearby traps play a role in the spectral jump phenomena comes from the comparison of charge stabilization with blue (450 nm) and green (520 nm) lasers. In Fig. 21, the PLE spectra of emitter E2, acquired under the same resonant and stabilizing laser powers, show a single peak with the green laser, while a smaller second peak (albeit faint) can be observed when the blue laser is used. Blue laser irradiation has been shown to be more efficient for charge trap ionization. This suggests that with the blue laser, a previously inaccessible charge trap is activated, leading to the new discrete spectral jump. Spectroscopy of charge trap transition rates could help determine the ionization energies for individual charge trap species. For example, it is possible, albeit only qualitatively, to observe a faster-switching fluorescence signal within the PLE acquisition resolution with the blue laser at each individual line, resulting from rapid spectral jumps.

[0218] In Fig. Figure 21 shows plots of the photoluminescence excitations (PLE) of the C transition under different colored stabilization schemes of the emitter E2. The C laser had a power of 1 nW. The spectra were acquired using bimodal Voigt profiles. The uncertainties represent 95% confidence intervals extracted from the spectra. In the left plot, the green laser at 500 nW at 520 nm is continuously switched on while the resonant laser scans. Continuous fluorescence from smaller peaks was sometimes observed. The secondary peak was not observed in this configuration. The spectra were recorded using a Voigt profile. In the right plot, the blue laser at 500 nW at 450 nm is continuously switched on while the resonant laser scans. The blue laser produces a spectral jump leading to a secondary peak. The spectrum was acquired using a bimodal Voigt profile. Power dependence of the stabilization laser

[0219] Extended resonance excitation of SnVs leads to a transition to a dark state. This has been linked to a change in the charge state due to the promotion of an electron from the valance band. A hole capture process induced by blue or green lasers can restore the SnV to its bright state. Using higher powers or longer illumination times increases the probability of charge state stabilization and re-emission.

[0220] This is made possible by the ionization or charging of the defects around the quantum emitter, which act as charge / hole donors. As a result, illumination alters the charge distribution around the color center, leading to spectral diffusion. Therefore, charge stabilization and inhomogeneous broadening become competing effects that must be optimized for high-quality emission.

[0221] In Fig. 22, this trade-off is demonstrated using a measurement on the emitter E14. At a power of 7000 (375) nW, bright lines are observed 30%, 9 / 30 (23%, 7 / 30) of the time, and a histogram linewidth of 871 (204) MHz is obtained. Since charge traps 12 play such a crucial role in stabilizing the bright state, a competition arises between spectral diffusion and the efficiency of stabilizing the charge state η bright expected. The ideal V n-density (or more generally the density of the hole donors) can then be determined by a compromise between minimizing the spectral diffusion and maximizing η bright be determined.

[0222] In Fig. Figure 22 shows plots comparing the different stabilization pulse powers when illuminating the E14 emitter. Both measurements were performed under 0.5 nW resonant laser excitation. Two different blue laser powers of 375 nW and 7000 nW were used. Higher powers resulted in a broader, inhomogeneous linewidth and more pronounced spectral drifts. The spectra were recorded using a Voigt profile. The uncertainties represent 95% confidence intervals extracted from the spectra. The two left plots show the measured fluorescence at each cycle while the laser frequency was scanned. The two right plots show histogram counts for the linewidth determination using a Voigt profile.

[0223] In addition, the contribution of the blue laser to spectral diffusion was determined as a function of its power. Fig. Figure 23 shows measurements of emitter E20, i.e., sample E014, which had the same fabrication parameters as E002 (five times higher dose than sample E001), but with an additional sulfur co-implantation step. It is clearly evident that higher blue laser powers lead to a more pronounced broadening, exhibiting a certain degree of saturation, which again is consistent with the Monte Carlo simulations.

[0224] In Fig.Figure 23 shows a plot comparing the different stabilization powers at emitter E20. The measurements were performed on a different sample that had a five-fold higher Sn implantation dose and was co-implanted with sulfur. All measurements use the same resonant excitation power of 5 nW while varying the power of the continuous blue stabilization laser. As the blue laser power increases, the linewidth broadens and reaches an asymptotic limit. The inset shows an enlargement of the lower powers to better illustrate the saturation trend. The error bars are the 95% confidence intervals, which are strongly influenced by the background fluorescence caused by the high blue laser powers.

[0225] The features disclosed in the above description, the claims and the drawings may be important for the realization of the various embodiments both individually and in any combination. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 10,620,251 B2

[0001] US 11,585,841 B1

[0002]

Claims

[1] Method for locating charge traps in a crystal lattice with the following steps: - arranging, on a crystal lattice (13), a local probe (11) with an inversion-symmetric lattice defect, wherein energy levels of the lattice defect are non-linearly Stark-shiftable by means of charge traps (12) in the crystal lattice (13); - determining, using a readout unit (10), strongly shifted photoluminescence emission spectra (62), wherein each of the photoluminescence emission spectra (62) is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice (13); - determining an integrated spectrum (61) by integrating the photoluminescence emission spectra (62); - determining jump probabilities (92) from successive ones of the photoluminescence emission spectra (62) and determining a charge trap configuration from the jump probabilities (92), wherein the charge trap configuration comprises a set of charge trap states of charge traps (12) adjacent to the local probe (11); - determining simulated spectra (60) by means of Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, wherein spatial arrangements of the adjacent charge traps (12) are varied and - Determining an optimal spatial arrangement of the adjacent charge traps (12) by comparing the integrated spectrum (61) with the simulated spectra (60). [2] Method according to claim 1, wherein the lattice defect of the local probe (11) has a D 3d -symmetry. [3] The method of claim 1 or 2, wherein the local probe (11) comprises a tin vacancy (21), a silicon vacancy, a germanium vacancy, or a group IV vacancy. [4] Method according to at least one of the preceding claims, wherein arranging the local probe (11) on the crystal lattice (13) comprises implanting the local probe (11) within the crystal lattice (13). [5] The method according to at least one of claims 1 to 3, wherein arranging the local probe (11) on the crystal lattice (13) comprises arranging the local probe (11) close to the crystal lattice (13), wherein the local probe (11) is embedded in a scanning probe microscope tip (14), in a nanocrystal (15) or a biological sample. [6] Method according to at least one of the preceding claims, further comprising: - determining a plurality of peak frequencies of peaks from the integrated spectrum (61) as well as frequency ranges of the integrated spectrum (61) associated with the peaks; - determining scanning peak frequencies of scanning peaks for each of the photoluminescence emission spectra (62) and assigning the scanning peak frequencies to one of the assigned frequency ranges of the integrated spectrum (61) and - Determining the jump probabilities (92) from the respective assigned frequency ranges for the successive photoluminescence emission spectra (62). [7] A method according to any one of the preceding claims, wherein determining the charge trap configuration comprises: - determining a number of peaks of the integrated spectrum (61) and a number of jump probabilities which are greater than a predetermined threshold value; - Determine a number of charge traps of the charge trap configuration from the number of peaks and the number of jump probabilities. [8] Method according to at least one of the preceding claims, wherein determining the simulated spectra (60) comprises: - Determining approximate values for first position values of the spatial arrangements from relative Stark shifts from the integrated spectrum (61) and - Fine-tuning the first location values by means of Monte Carlo simulation, whereby the first location values and second location values of the spatial arrangements are varied, whereby the optimal spatial arrangement has fine-tuned first location values and optimal second location values. [9] Method according to at least one of the preceding claims, wherein comparing the integrated spectrum (61) with the simulated spectra (60) involves minimizing a χ 2distribution from the integrated spectrum (61) and the simulated spectra (60). [10] Device for locating charge traps in a crystal lattice, comprising: - a local probe (11) with an inversion-symmetric lattice defect, which is arranged on a crystal lattice (13), wherein energy levels of the lattice defect are non-linearly Stark-shiftable by means of charge traps (12) in the crystal lattice (13); - a readout unit (10) for photoluminescence spectroscopy and - a data processing device which is configured to carry out the following steps: - determining, using the readout unit (10), strongly shifted photoluminescence emission spectra (62), wherein each of the photoluminescence emission spectra (62) is determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice (13); - determining an integrated spectrum (61) by integrating the photoluminescence emission spectra (62); - determining jump probabilities (92) from successive ones of the photoluminescence emission spectra (62) and determining a charge trap configuration from the jump probabilities (92), wherein the charge trap configuration comprises a set of charge trap states of charge traps (12) adjacent to the local probe (11); - determining simulated spectra (60) by means of Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, wherein spatial arrangements of the adjacent charge traps (12) are varied and - Determining an optimal spatial arrangement of the adjacent charge traps (12) by comparing the integrated spectrum (61) with the simulated spectra (60).

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