Supplementary Information: Lifetime measurements well below the diffraction limit

Transcription

1 Supplementary Information: Lifetime measurements well below the diffraction limit S. Meuret, L. H. G. Tizei, T.Auzelle, B. Daudin, B. Gayral and M. Kociak 1 High Angle Annular Dark Field acquired during the spectral image of Figure 1 of the main text Figure S 1: Original HAADF image and CL filtered image of Fig. 1 in the main text. Scale bar 50 nm. 1

2 2 Energy versus lifetimes for different QDiscs Figure S 2: Emission energy vs beam position for the nanowire of Fig. 1 in the main text. a, HAADF image acquired in parallel to the spectrum image. b, Emission intensity energy as a function of the beam position along the growth direction. Emissions from individual QDiscs can be isolated and related to the HAADF (see Ref. [1, 2]). The lifetimes measured for each QDisc (dashed white rectangle) are indicated in nanoseconds. 2

3 Figure S 3: QDiscs energy vs lifetime. a,b, HADF image (top), projection of a spectrum image along the growth direction (middle) and the correlation function g (2) (τ) taken on each QDisc (bottom). The dashed rectangles represent the QDisc location. Scale bar is 20 nm. c, Lifetime as a function of the emission energy for the QDiscs contained in the fifteen studied nanowires. Only QDiscs with an easily identifiable single emission energy are reported. For QDiscs emissions overlapping spectrally and spatially at scales below the diffusion length (typically the distance between two QDiscs), a contribution from the neighbor QDiscs may be expected, explaining partly the distribution of lifetimes for a given energy. 3

4 3 Comparison of lifetimes measured in PL and SRTC-CL Figure S 4: Comparison of lifetimes measured in PL and CL. QDiscs lifetimes have been measured using (top) TR-PL and (bottom) the CL technique in NWs containing a single QDisc. In each experiment, different NWs have been probed, but all from the same batch. In the µ-pl experiment multiple NWs are excited and single NW selection is achieved by energy filtering (sketch at the left of the top figure), while in the CL experiment this is achieved taking advantage of the small size of the electron probe (sketch in the bottom figure). Using both photons (top) and electrons (Bottom) spectral (center) and lifetime (right) information is retrieved for individual NWs. 4 Monte Carlo simulation with two lifetimes In complex structures like GaN/AlN nanowires or defects in materials, it is often the case that despite an excitation at the nanometer scale, the electron beam excites more than one emission center at a time, due to the diffusion of carriers in the material. We restrict here to the case of two different emissions E 1 and E 2 which spatially overlap. To know if we can accurately retrieve the two emissions lifetimes, we have performed Monte Carlo simulations with two emissions E 1 and E 2 (with lifetimes τ 1 and τ 2 ). In a real experiment, the ratio of the intensities of E 1 and E 2 would be typically monitored by moving the beam closer to one of the emitter (and further away from the other). The principle of the Monte Carlo simulation is the same as described in [3], but here for each incoming electron the number of created h pairs n eh is distributed between E 1 and E 2 (rather than exciting only one emitter in [3]) by generating n eh random number r and [0, 1]. We define r e as the probability for the e-h pair to excite E 1 rather than E 2. If the j th random number r j and < r e, then the j th e-h pair interacts with E 1 otherwise it interacts with E 2. Depending on which emitter the e-h pair interacts with, it will decay with the radiative probability P 1 rad or P 2 rad associated with the lifetime τ 1 or τ 2, respectively. Results of simulations show that by fitting the g (2) (τ) function with the sum of two exponentials (equation 1; a and b are the weighting components of E 1 and E 2 ) we can retrieve the two lifetimes τ 1 and τ 2, independently. g (2) (τ) = 1 + a exp ( τ τ 1 ) + b exp ( τ τ 2 ) (1) 4

5 The accuracy of the fit depends on the signal to noise ratio, on how close the two lifetimes are and on the emission intensity ratio between the two emitters. On Supplementary Fig. 5, results are shown for a single value of τ 1 (τ 1 = 1 ns) and two different values for τ 2 (τ 2 = 2 ns and τ 2 = 5 ns). The other parameters are set to I = 5 pa, and a thickness to mean free path ratio of 1. For each case, 300 Monte Carlo simulations have been performed. The different lifetimes distributions retrieved for both emitters are shown as well as the typical g (2) (τ) functions for r e = 0.3, 0.5 and 0.7. The total number of incoming electrons is 50000, which correspond to an integration time of about 200 s for a 10 4 counts/s on the HBT detectors. Supplementary Fig. 5 shows that the precision increases when the difference between the two lifetimes increases. Some simulations at higher current have been realized showing that the accuracy decreases if the current increases, as it is expected since g (2) (0) decreases when I increases. However, even for I = 50 pa, the accuracy is still sufficient to retrieve the two lifetimes with a precision of about 20 %. As a conclusion, even in a situation where two emitters are excited at the same time, our method allows for the two emitters lifetime retrieval. 5 Applicability of SRTC-CL to lower energy incident electron beam Figure S 6: Monte Carlo simulation of the bunching effect at lower acceleration voltage. Monte Carlo Simulation of the g (2) (τ) function obtained for two different lifetimes τ = 19 ns and τ = 10 ns at 30 kev for I = 25 pa. This condition can be obtained in a SEM. The curve for τ = 19 ns at 100 kev is drawn (dashed line) as a comparison point. 5

6 Figure S 5: Monte Carlo simulation for two emissions with different lifetimes and relative intensities. a, Simulated correlation functions for two emissions E 1 and E 2 with different weights (the percentage represents the weight of the intensity of E 1 ). The nominal lifetime τ 1 = 1 ns for E 1 and τ 2 = 2 ns for E 2. The time sampling was 100 ps, I = 5 pa, and a thickness to mean free path ratio of 1. b, Histograms of the fitted lifetimes for emission 1, when the correlation functions are fitted with the trial function g (2) (τ) = 1+a exp( τ/τ 1 ) +b exp( τ/τ 2 ), where a and b represent the intensity of emission E 1 and E 2 respectively. In order to get the generated histogram, simulations have been re-iterate 300 times. The input parameters for the Monte Carlo simulations where a/b = 0.3, 0.5 and 0.7 c,d, same as a,b, for τ 1 = 1 ns and τ 2 = 5 ns. 6

7 References [1] L. F. Zagonel, S. Mazzucco, M. Tence, K. March, R. Bernard, B. Laslier, G. Jacopin, M. Tchernycheva, L. Rigutti, F. H. Julien, R. Songmuang, and M. Kociak, Nanometer scale spectral imaging of quantum emitters in nanowires and its correlation to their atomically resolved structure, Nano Letters, vol. 11, pp , Feb [2] L. F. Zagonel, L. Rigutti, M. Tchernycheva, G. Jacopin, R. Songmuang, and M. Kociak, Visualizing highly localized luminescence in gan/aln heterostructures in nanowires, Nanotechnology, vol. 23, p , Nov [3] S. Meuret, L. H. G. Tizei, T. Cazimajou, R. Bourrellier, H. C. Chang, F. Treussart, and M. Kociak, Photon bunching in cathodoluminescence, Physical Review Letters, vol. 114, p , May