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Abstract
The doping effect and mechanism on optical property of Si nanocrystals is particularly an interesting issue in order to further broaden their applications in the next generation of electronic and optoelectronic devices. A quenching of photoluminescence in B-doped Si nanocrystals was reported before and there is no consensus on the mechanism. Herein, we fabricate boron-doped Si nanocrystals/SiO2 multilayers with the ultra-small dot sizes near 3.0 nm. It’s found B dopants exhibit a low doping efficiency in ultra-small Si nanocrystals, and are mainly located at the surfaces regions. Electron spin resonance results manifest B dopants lead to defects in Si nanocrystals/SiO2 multilayers, which transform from Pb centers to EX centers. The EX centers, rather than Auger recombination, cause the reduction on the intensities and lifetimes of 840 nm near-infrared emission. Our results give an insight into luminescence quenching of ultra-small Si nanocrystals due to boron doping.
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1. Introduction
Si nanocrystals (Si NCs) have attracted extensive attentions due to its size-dependent bandgap, high quantum yield (>60%) and nontoxicity, and been widely applied in synaptic devices, light emitting devices and bioimaging [1–3]. Further, doping is gradually regarded as the necessary method to expand the electronic and optical properties of Si NCs [4–7]. As reported, phosphorus (P) dopants can enhance the photoluminescence intensities of Si NCs by passivating the surfaces defects [8]. In our previous works, we found P can induce the radiative levels in Si NCs bandgap and obtained the sub-band emission with the wavelength compatible for optical telecommunication [9–11].
However, boron (B) dopants exhibit different doping behaviors from P in Si NCs. In early reports, B dopants induced the photoluminescence quenching of Si NCs, and the quenching mechanism was tentatively ascribed to the Auger recombination, i.e., non-radiative recombinations among the photo-excited excitons and B-provided holes [12–14]. Recently, D. Hiller et al. debated the possibility of Auger recombination leading to luminescence quenching of B-doped Si NCs, and pointed the B-induced defect states might be responsible for the luminescence quenching through DFT calculation, which have received much attentions [15]. Meanwhile, we observed B dopants exhibited low doping efficiency (substitutional dopants) than P [16]. In this work, we fabricate B-doped ultra-small Si NCs (∼3 nm) /SiO2 multilayers. It is found that B dopants are hardly incorporated into Si NCs inner to provide carriers to arise the Auger recombination. More interesting, a new surface defects (EX centers) are experimentally detected after B doping, which is responsible for the photoluminescence quenching. Meanwhile, the B-doping behaviors and physics mechanism is briefly discussed.
2. Experiment
B-doped Si NCs/SiO2 multilayers were prepared by a traditional plasma enhanced chemical vapor deposition (PECVD) system. Briefly, SiH4 and B2H6 (0.1%, H2 dilution) gases were ionized to deposit the B-doped amorphous Si (a-Si) sublayer on (100) Si wafers and fused quartz. Then, in-situ plasma oxidation was performed in pure oxygen plasma to achieve the SiO2 sublayer. The a-Si sublayer depositions and oxidation processes were alternately repeated to form a-Si/SiO2 stacked multilayers. The as-deposited samples were dehydrogenated at 450 °C followed annealing at 1000 °C under nitrogen gas atmosphere for 1 h. B doping ratios of the Si NCs were defined as the gas ratios of B2H6 and SiH4.
Microstructures of B-doped Si NCs/SiO2 multilayers were measured by transmission electron microscopy (TEM, TECNAI G2F20 FEI) and Raman spectra (Horiba HR 800 Raman system, 514 nm laser). Hall effect measurements were studied by LakeShore 8400 series based on Van der Pauw geometry. Low temperature (2K) X-band electron spin resonance (ESR) was measured by Bruker EMX-12 with a liquid-He cooled spectrometer. Steady-state photoluminescence spectra were measured by a HORIBA Jobin Yvon synapse with a PMT detector under the excitation of 325 nm He-Cd laser. Time-resolved photoluminescence (TRPL) spectra were determined by Edinburgh FLS 980 spectrophotometer equipped with a 355 nm nanosecond-pulsed laser.
3. Results and discussions
Figure 1(a) shows the cross-sectional microstructure of Si NCs/SiO2 multilayers investigated by TEM. Periodically stacked structures of Si NCs sublayers and SiO2 sublayers can be clearly observed. As shown in Fig. 1(b), the average thicknesses of Si and SiO2 sublayers are about 3.0 nm and 9.0 nm, respectively. Size-constrained Si NCs with the sphere or ellipse shapes are uniformly distributed in the Si sublayers. Magnified image of a single Si NC with the ultra-small size of 3.1 nm is illustrated in Fig. 1(c). Statistical-averaged size of Si NCs is about 3.0 nm with a standard deviation of 0.4 nm (Fig. 1(d)), which is strictly in accord with the thickness of Si sublayers due to the constrained crystallization of multilayers.
Fig. 1. Cross-sectional TEM images of B-doped Si NCs/SiO2 multilayers with doping ratio of 0.04%. (a) 50nm scale; (b) 10nm scale; (c) magnified image of a single Si NC; (d) size distribution of Si NCs
Figure 2 shows the Raman spectra of B-doped Si NCs/SiO2 multilayers with various doping ratios. Broad Raman envelop near 492 cm−1 is related to the transverse optical (TO) mode of amorphous Si. Meanwhile, an asymmetric Raman peak around 518 cm−1 is also observed for all B-doped samples, which is corresponding to the TO mode of crystallized Si phases. The results are in accord with the TEM images that a-Si sublayers are crystallized to form Si NCs after high temperature annealing. However, the characteristic Raman peaks of Si-B bonds around 618 and 640 cm−1 are not observed [17]. It may indicate B dopants exhibit a low doping efficiency in ultra-small Si NCs (∼3 nm).
The room temperature carrier concentrations of B-doped Si NCs/SiO2 multilayers with different doping ratios are plotted in Fig. 3(a). It is found the carrier concentrations are around 1.2 × 1013 cm−3 for un-doped and B-doped Si NCs samples. Further, the high temperature (500-660 K) dark conduction of Si NCs are studied. As shown in Fig. 3(b), the conductivities (σ) of Si NCs samples exhibit a linear relationship in lnσ-T−1 plot, which matches the Arrhenius relationship:
where σ0 is the pre-factor, ${E_a}$ is the conductivity activation energy, kB refers to the Boltzmann constant. It indicates the high-temperature transport behavior of carriers in Si NCs samples are thermal activation conduction mechanism. As shown in Fig. 3(b), the ${E_a}$ of un-doped samples is about 1.01 eV, which implies the Fermi level locates at the mid gap of the Si NCs [18]. With the increasing of B-doping ratios, the ${E_a}$ is gradually reduced to 0.56 eV. The physical meaning of activation energy needs further understanding. One possibility is the energy distance between the Fermi level and the top of the valence band. With increasing the B doping level, the Fermi level is shifted to the valence band. Another possibility is the energy barrier of grain boundary between the Si NCs or Si NCs/a-Si. The addition of B impurities can reduce the barrier to make carrier transport more easily. It is worth pointing out that we measured the conductivity in co-planar configuration and the alloying process was carried out to make the sufficient diffusion of Al into the sample. Therefore, the carrier transport properties mainly dominant of the layer containing Si NCs and the influence of SiO2 layers is negligible in our case.In previous studies of low P-doped Si NCs (∼ 8.0 nm), the ${E_a}$ can reduced to 48 meV with the room temperature carrier concentration near 3.2 × 1018 cm−3 [16]. Meanwhile, we observed the hyperfine structure of ESR spectra, which indicated only one P dopants were incorporated into Si NCs inner [10]. For the B-doped Si NCs (∼ 8.0 nm), the carrier concentrations can be enhanced about 7 orders of magnitude after B-doping. Even so, the doping efficiency was as low as 3.1% and majority of B dopants gathered at the surfaces of Si NCs, i.e. the SiO2 interfaces regions in multilayers [16]. The slight variation of carrier concentration and ${E_a}$ in Fig. 3 indicate that B dopants are hardly incorporated into ultra-small Si NCs (∼3 nm) inner compared with the counterparts with larger size. Further, B atoms usually introduce structural distortions and tensile stress in Si nanocrystals when substitutionally incorporating, which lead to the redshifts of Si-Si Raman peaks [19]. However, the Raman peaks Si NCs multilayers in Fig. 2 keep unchanged rather than redshifted with the B-doping ratios, which also indicates the low doping efficiency of B dopants in Si NCs.
Fig. 3. (a) The room temperature carrier concentration and (b) high temperature conductivity σ in ln σ-T−1 plot for B-doped Si NCs/SiO2 multilayers with different doping ratios.
Figure 4 shows the room temperature photoluminescence spectra of B-doped Si NCs/SiO2 multilayers with different B-doping ratios. A strong photoluminescence peak near 840 nm is observed for the un-doped Si NCs/SiO2 sample, which is originated from the radiative recombination via luminescence centers in Si oxide adjacent to nanoscale silicon particles (NSPs) [20]. G. Qin group has comprehensively studied the photoluminescence mechanism for nanoscale Si-SiO2 materials and point out the quantum confinement/luminescence centers (QCLC) model [21]. It is that most electrons and holes photoexcited in NSPs enter the adjacent luminescence centers in the Si oxide covering the NSPs, and recombine in the luminescence centers to emit light. After B-doping, the photoluminescence peaks keep unchanged at 840nm, which implies the radiative recombination centers in B-doped samples are identical to the un-doped one. However, the luminescence intensities are sensitive to B dopants and decrease rapidly with the increase of B doping ratios. At 0.4% B-doping ratio, the luminescence is almost quenching.
G. A. Kachurin et al. have reported B ions implantation induces the lattice deformations in Si nanocrystals and leads to the quenching of emission at 790 nm. Meanwhile, the quenching can be eliminated after an additional thermal annealing or subsequent laser annealing [22]. In the reports of B-doped Si NCs embedded in SiO2 matrix, the quenching of photoluminescence was tentatively ascribed to Auger recombination, i.e., non-radiative recombination of the photo-excited exciton with the B-induced carriers [4–7]. However, Hall results have indicated B dopants are hardly incorporated into ultra-small Si NCs to provide carriers. Hence, the reduced 840 nm emission intensities of B-doped Si NCs/SiO2 multilayers are hardly due to the Auger recombination.
Considering the 840 nm emission centers are located at the Si NCs/SiO2 interface regions, and the majority of B-atoms reside at the surrounding surfaces of Si NCs. Low temperature (2K) ESR are used to detect the surface states of un-doped and B-doped Si NCs multilayers. As shown in Fig. 5, a strong ESR signal with g≈2.006 is observed for the un-doped Si NCs sample, which is corresponding to the dangling bonds (Pb centers) on Si nanocrystals surfaces, and also appear in silicon-based materials as the intrinsic defects [23]. After B-doping, the dangling bonds signal disappears, and a new ESR signal with g≈2.003 is detected. This new unpaired electron signal of g≈2.003 is originated from the silicon vacancy (EX centers), which exist in the SiO2 interfaces [24]. Raman and electrical results have indicated that B dopants are mainly distributed at Si NCs surfaces/SiO2 interfaces regions. The disappearance of Pb centers signal after B-doping indicates the dangling bonds can be passivated by B dopants. P. Veettil et al. also reported the B dopants passivated the dangling bonds of self-assembled Si nanocrystals [25].
Fig. 5. Low temperature (2K) ESR spectra of B-doped Si NCs/SiO2 multilayers with different doping ratios.
Z. Ni et al. have calculated that B dopants near Si nanocrystals surfaces are easily entered the surrounding SiO2 layers due to the large electronegativity differences between B and O atoms [26]. K. Nomoto et al. have experimentally observed the B-rich layers are formed and coated on the B-doped and P/B co-doped Si NCs which are embedded in SiO2 matrix [27]. S. Zhou et al. have found the B-doping enhanced the oxidation of free-standing Si nanocrystals [28]. These studies have directly or indirectly demonstrated the strong interaction between B and O atoms. For B-doped Si NCs/SiO2 multilayers, the distribution of B dopants and the strong interaction between B and O atoms may accelerate the formation of silicon vacancy nearby SiO2 interfaces. Meanwhile, silicon vacancy concentration is enhanced with the increasing of B-doping ratios as shown in Fig. 5.
We estimated the integrated PL intensity after B doping. It is found that the PL integrated intensity is reduce by over one order of magnitude for 0.4% B doped sample compared with the un-doped one, while the integrated PL intensity is decreased to 30% with increasing the B doping concentrations from 0.2% to 0.4%. It is also found that the ESR signal intensity is enhanced by 3 folds for 0.4% B doped sample compared to that of 0.2% B doped one, which suggests that the reduction of PL intensity is mainly due to the existence of EX centers after B doping. In our previous work, we found that the PL intensity can be enhanced by adding P dopants at quite low concentration in Si NCs due to the passivation of Pb centers [29]. However, at that case, part of P impurities can enter into the inner sites of Si NCs to provide the free conduction electrons other than generate new type of defects states. For B doping, we found that the doping efficiency of B is quite low compare to P in Si NCs as revealed by Hall measurements. It is suggested that the most of B located at the near surface region and caused the deterioration of film to generate the EX centers. Generally, the Pb centers and EX centers are both the nonradiative recombination defects at room temperature, and the EX centers exhibit a shorter recombination lifetime than Pb centers to suppress the PL intensity more obviously [29,30].
In order to gain more insights into the B-doping induced the variation of surface states and reduction of emission intensities, the dynamics recombination process of 840 nm emission is studied under the excitation of a nanosecond-pulsed laser (355nm). Figure 6(a) exhibits the TRPL spectra of B-doped Si NCs samples with various doping ratios. Comparing with the un-doped Si NCs, the TRPL spectra of B-doped Si NCs exhibit faster dynamic process with the increase of B-doping ratios. The decay curves are well fitted by double exponential function, and the fitting results of 0.04% B-doped samples is inset in Fig. 6(a) [31]. Further, the calculated mean luminescence lifetime τmeans is plotted in Fig. 6(b). We find the τmeans is in the hundred microseconds range, which is in agreement with the lifetime of silicon-oxygen recombination centers in Si-based optical materials as reported [32]. It is noticed that the τmeans exhibits the similar variation trend as photoluminescence intensities, which is gradually decreased from 132 to 78 µs with the increase of B-doping ratios. Combing with the decrease of photoluminescence intensities, the attenuation of τmeans indicates the radiative recombination process is reduced, which is usually companied with the improved proportion of nonradiative recombination. The enhanced nonradiative recombination are attributed to the transformation of surface states from Pb centers to EX centers, while the concentration of EX centers is increasing with B-doping ratios, as verified by the ESR results.
Fig. 6. (a) TRPL spectra of B-doped Si NCs/SiO2 multilayers, inset is the fitting results of TRPL by double exponential function; (b) Mean photoluminescence lifetime τmeans as function of B-doping ratios.
4. Conclusions
In summary, we have fabricated un-doped and B-doped Si NCs/SiO2 multilayers by PECVD. Raman spectra and TEM results reveal that the Si NCs with ultra-small sizes near 3.0 nm are uniformly distributed in Si sublayers. We find the intensity of 840 nm light emission originated from the Si oxide centers covering Si NCs is decreased with the increasing of B-doping ratios. Hall measurements indicate the B-doping efficiency in ultra-small Si NCs is quite low, and B dopants are mainly located at the surface regions of Si NCs. Meanwhile, ESR results reveals B-doping lead to the surface defects of Si NCs transforming from Pb centers to EX centers, which is responsible for the decrease of 840 nm emission intensities and lifetimes.
Funding
National Key Research and Development Program of China (2018YFB2200101); National Natural Science Foundation of China (62004078, 11774155); Natural Science Foundation of Jiangsu Province (BK20201073);Natural Science Research of Jiangsu Higher Education Institutions of China (20KJB510017).
Acknowledgements
Low temperature ESR test was performed on the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, CAS.
Disclosures
The authors declare not conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. H. Tan, Z. Y. Ni, W. B. Peng, S. C. Du, X. K. Liu, S. Y. Zhao, W. Li, Z. Ye, M. S. Xu, Y. Xu, X. D. Pi, and D. R. Yang, “Broadband optoelectronic synaptic devices based on silicon nanocrystals for neuromorphic computing,” Nano Energy 52, 422–430 (2018). [CrossRef]
2. J. H. Liang, C. B. Huang, and X. Gong, “Silicon Nanocrystals and Their Composites: Syntheses, Fluorescence Mechanisms, and Biological Applications,” ACS Sustainable Chem. Eng. 7(22), 18213–18227 (2019). [CrossRef]
3. A. Angi, M. Loch, R. Sinelnikov, J. G. C. Veinot, M. Becherer, P. Lugli, and B. Rieger, “The influence of surface functionalization methods on the performance of silicon nanocrystal LEDs,” Nanoscale 10(22), 10337–10342 (2018). [CrossRef]
4. S. Milliken, K. Cui, B. A. Klein, I. T. Cheong, H. Y. Yu, V. K. Michaelis, and J. G. C. Veinot, “Tailoring B-doped silicon nanocrystal surface chemistry via phosphorous pentachloride - mediated surface alkoxylation,” Nanoscale 13(43), 18281–18292 (2021). [CrossRef]
5. P. Rohani, S. Banerjee, S. Sharifi-Asl, M. Malekzadeh, R. Shahbazian-Yassar, S. J. L. Billinge, and M. T. Swihart, “Synthesis and Properties of Plasmonic Boron-Hyperdoped Silicon Nanoparticles,” Adv. Funct. Mater. 29(8), 1807788 (2019). [CrossRef]
6. Z. Y. Ni, S. Zhou, S. Y. Zhao, W. B. Peng, D. R. Yang, and X. D. Pi, “Silicon nanocrystals: unfading silicon materials for optoelectronics,” Mat. Sci. Eng. R 138, 85–117 (2019). [CrossRef]
7. D. K. Li, Y. C. Jiang, P. Zhang, D. Shan, J. Xu, W. Li, and K. J. Chen, “The phosphorus and boron co-doping behaviors at nanoscale in Si nanocrystals/SiO2 multilayers,” Appl. Phys. Lett. 110(23), 233105 (2017). [CrossRef]
8. M. Fujii, A. Mimura, S. Hayashi, Y. Yamamoto, and K. Murakami, “Hyperfine structure of the electron spin resonance of phosphorus-doped Si nanocrystals,” Phys. Rev. Lett. 89(20), 206805 (2002). [CrossRef]
9. P. Lu, D. K. Li, P. Zhang, D. M. Tan, W. W. Mu, J. Xu, W. Li, and K. J. Chen, “Time-resolved and temperature-dependent photoluminescence study on phosphorus doped Si quantum dots/SiO2 multilayers with ultra-small dot sizes,” Opt. Mater. Express 6(10), 3233–3241 (2016). [CrossRef]
10. P. Lu, W. W. Mu, J. Xu, X. W. Zhang, W. P. Zhang, W. Li, L. Xu, and K. J. Chen, “Phosphorus Doping in Si Nanocrystals/SiO2 Multilayers and Light Emission with Wavelength Compatible for Optical Telecommunication,” Sci Rep 6(1), 22888 (2016). [CrossRef]
11. D. K. Li, J. M. Chen, T. Sun, Y. Y. Zhang, J. Xu, W. Li, and K. J. Chen, “Enhanced subband light emission from Si quantum dots/SiO2 multilayers via phosphorus and boron co-doping,” Opt. Express 30(8), 12308–12315 (2022). [CrossRef]
12. M. Fujii, S. Hayashi, and K. Yamamoto, “Photoluminescence from B-doped Si nanocrystals,” J. Appl. Phys. 83(12), 7953–7957 (1998). [CrossRef]
13. N. Salivati, N. Shuall, J. M. McCrate, and J. G. Ekerdt, “Effect of subsurface boron on photoluminescence from silicon nanocrystals,” Surf. Sci. 605(7-8), 799–801 (2011). [CrossRef]
14. T. Zhang, B. Puthen-Veettil, L. F. Wu, X. G. Jia, Z. Y. Lin, T. C. J. Yang, G. Conibeer, and I. Perez-Wurfl, “Determination of active doping in highly resistive boron doped silicon nanocrystals embedded in SiO2 by capacitance voltage measurement on inverted metal oxide semiconductor structure,” J. Appl. Phys. 118(15), 154305 (2015). [CrossRef]
15. D. Hiller, J. Lopez-Vidrier, S. Gutsch, M. Zacharias, M. Wahl, W. Bock, A. Brodyanski, M. Kopnarski, K. Nomoto, J. Valenta, and D. Konig, “Boron-Incorporating Silicon Nanocrystals Embedded in SiO2: Absence of Free Carriers vs. B-Induced Defects,” Sci Rep 7(1), 8337 (2017). [CrossRef]
16. J. M. Chen, D. K. Li, Y. Y. Zhang, Y. C. Jiang, J. Xu, and K. J. Chen, “Comparative study on P and B doped nano-crystalline Si multilayers,” Appl. Surf. Sci. 529(5), 146971 (2020). [CrossRef]
17. H. Sugimoto, M. Yamamura, M. Sakiyama, and M. Fujii, “Visualizing a core-shell structure of heavily doped silicon quantum dots by electron microscopy using an atomically thin support film,” Nanoscale 10(16), 7357–7362 (2018). [CrossRef]
18. C. Delerue, G. Allan, and M. Lannoo, “Theoretical Aspects of the Luminescence of Porous Silicon,” Phys. Rev. B 48(15), 11024–11036 (1993). [CrossRef]
19. R. Saleh and N. H. Nickel, “The influence of boron concentrations on structural properties in disorder silicon films,” Appl. Surf. Sci. 254(2), 580–585 (2007). [CrossRef]
20. M. V. Wolkin, J. Jorne, P. M. Fauchet, G. Allan, and C. Delerue, “Electronic states and luminescence in porous silicon quantum dots: The role of oxygen,” Phys. Rev. Lett. 82(1), 197–200 (1999). [CrossRef]
21. G. G. Qin, G. Z. Ran, K. Sun, and H. J. Xu, “Light Emission from Nanoscale Si/Si Oxide Materials,” J. Nanosci. Nanotechno. 10(3), 1584–1595 (2010). [CrossRef]
22. G. A. Kachurin, S. G. Cherkova, V. A. Volodin, D. M. Marin, D. I. Tetel’baum, and H. Becker, “Effect of boron ion implantation and subsequent anneals on the properties of Si nanocrystals,” Semiconductors 40(1), 72–78 (2006). [CrossRef]
23. M. Fujii, A. Mimura, S. Hayashi, K. Yamamoto, C. Urakawa, and H. Ohta, “Improvement in photoluminescence efficiency of SiO2 films containing Si nanocrystals by P doping: An electron spin resonance study,” J. Appl. Phys. 87(4), 1855–1857 (2000). [CrossRef]
24. K. Fujio, M. Fujii, K. Sumida, S. Hayashi, M. Fujisawa, and H. Ohta, “Electron spin resonance studies of P and B codoped Si nanocrystals,” Appl. Phys. Lett. 93(2), 021920 (2008). [CrossRef]
25. B. P. Veettil, T. Zhang, R. L. Chin, X. G. Jia, K. Nomoto, T. C. J. Yang, Z. Y. Lin, L. F. Wu, R. Rexiati, S. Gutsch, G. Conibeer, and I. Perez-Wurfl, “Characterisation of active dopants in boron-doped self-assembled silicon nanostructures,” Appl. Phys. Lett. 109(15), 153106 (2016). [CrossRef]
26. Z. Y. Ni, X. D. Pi, S. Cottenier, and D. R. Yang, “Density functional theory study on the B doping and B/P codoping of Si nanocrystals embedded in SiO2 (vol 95, 075307, 2017),” Phys. Rev. B 95(7), 075307 (2017). [CrossRef]
27. K. Nomoto, H. Sugimoto, A. Breen, A. V. Cezguerra, T. Kanno, S. P. Ringer, I. P. Wurfl, G. Conibeer, and M. Fujii, “Atom Probe Tomography Analysis of Boron and/or Phosphorus Distribution in Doped Silicon Nanocrystals,” J. Phys. Chem. C 120(31), 17845–17852 (2016). [CrossRef]
28. S. Zhou, X. Pi, Z. Ni, Q. Luan, Y. Jiang, C. Jin, T. Nozaki, and D. Yang, “Boron- and Phosphorus-Hyperdoped Silicon Nanocrystals,” Part. Part. Syst. Charact. 32(2), 213–221 (2015). [CrossRef]
29. S. Dannefaer, “Defects and Oxygen in Silicon Studied by Positrons,” Phys. Stat. Sol. (a) 102(2), 481–491 (1987). [CrossRef]
30. P. Asokakumar, K. G. Lynn, and D. O. Welch, “Characterization of Defects in Si and SiO2-Si Using Positrons,” J. Appl. Phys. 76(9), 4935–4982 (1994). [CrossRef]
31. D. K. Li, Y. C. Jiang, J. J. Liu, P. Zhang, J. Xu, W. Li, and K. J. Chen, “Modulation of surface states by phosphorus to improve the optical properties of ultra-small Si nanocrystals,” Nanotechnology 28(47), 475704 (2017). [CrossRef]
32. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408(6811), 440–444 (2000). [CrossRef]
