Letter pubs.acs.org/NanoLett
Size-Dependence of Acceptor and Donor Levels of Boron and Phosphorus Codoped Colloidal Silicon Nanocrystals Yusuke Hori, Shinya Kano, Hiroshi Sugimoto, Kenji Imakita, and Minoru Fujii* Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan S Supporting Information *
ABSTRACT: Size dependence of the boron (B) acceptor and phosphorus (P) donor levels of silicon (Si) nanocrystals (NCs) measured from the vacuum level was obtained in a very wide size range from 1 to 9 nm in diameter by photoemission yield spectroscopy and photoluminescence spectroscopy for B and P codoped Si-NCs. In relatively large Si-NCs, both levels are within the bulk Si band gap. The levels exhibited much smaller size dependence compared to the valence band and conduction band edges. The Fermi level of B and P codoped SiNCs was also studied. It was found that the Fermi level of relatively large codoped Si-NCs is close to the valence band and it approaches the middle of the band gap with decreasing the size. The results suggest that below a certain size perfectly compensated Si-NCs, that is, Si-NCs with exactly the same number of active B and P, are preferentially grown, irrespective of average B and P concentrations in samples. KEYWORDS: Silicon, nanocrystal, quantum dot, impurity, doping, codoping, size dependence, acceptor level, donor level, HOMO, LUMO, Fermi level
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emerges.14 Another quantity revealed by EPR measurements is a doping efficiency (activation efficiency) of P in Si-NCs, that is, the ratio of electrically active P atoms and a total amount of doped P atoms. The efficiency decreases significantly below ∼10 nm.11 This has been explained by large formation energy of doped Si-NCs compared to that of intrinsic Si-NCs with an identical size.15,16 The activation efficiency is also estimated by electrical17 and optical methods.18 Apart from the binding energy and the activation efficiency, size dependence of the impurity-related physical quantities of Si-NCs has scarcely been experimentally determined, which impedes direct comparison between experiments and theory and makes understanding of the physics of impurity-doped Si nanostructures difficult. In this work, we first experimentally determine size dependence of the highest occupied (HO) and lowest unoccupied (LU) molecular orbitals (MO) of impuritydoped Si-NCs. The largest difficulty of the work is to prepare Si-NCs having electrically active impurities with controlling the size in a wide range. In particular, to make direct comparison between experiments and calculations possible doped Si-NCs smaller than 2 nm are required. In this size range, one impurity atom corresponds to the doping concentration of more than 1020 cm−3, which is larger than solid solubility of boron (B) and P in bulk Si crystal. Therefore, doping either B or P in the substitutional sites of the small NCs in a thermal equilibrium
ontrolling electrical properties by shallow impurity doping is the basis of modern semiconductor technology. In bulk semiconductor crystal, theoretical modeling and technology of doping have been well established while they have been a subject of recent intensive research in the nanostructures. There have been numerous theoretical studies on the electronic structure of doped semiconductor nanocrystals and nanowires.1−5 In contrast, the experimental studies are still limited especially on silicon (Si) nanostructures despite the growing importance with the continuous miniaturization of semiconductor devices. This is mainly due to the difficulty in controlling the size, shape, impurity concentration, impurity sites, and so forth of Si nanostructures.6−9 Because the energy of impurity states depends strongly on these parameters, their small fluctuation often smears impurity-related physical phenomena by inhomogeneous broadening. As a result, clear size dependence capable of detailed comparison with theoretical calculations has not been obtained except for a few physical quantities. One of the relatively well-studied physical quantities is the binding energy of phosphorus (P) donors in Si nanocrystals (NCs).9−13 Analyses of the hyperfine structure of electron paramagnetic resonance (EPR) spectroscopy reveal that the binding energy of a P donor starts to increase gradually when the size of a crystallite decreases to ∼12 nm due to the reduction in the dielectric screening relative to the bulk.8 When the size is further decreased (∼4 nm), the quantum confinement effect of donor electrons, which squeezes donors below the size of the P donor Bohr radius in bulk Si crystal, © XXXX American Chemical Society
Received: January 19, 2016 Revised: March 16, 2016
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DOI: 10.1021/acs.nanolett.6b00225 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters condition is expected to be very difficult,14 although several attempts have been made to dope impurities to Si-NCs exceeding solid solubility.19 To overcome the problem the strategy we employed is simultaneous doping of B and P in a Si-NC. It has been demonstrated that the codoping reduces the formation energy of Si-NCs significantly compared to those of B or P singly doped Si-NCs and even to that of undoped Si-NCs,16 and thus codoped Si-NCs can be preferentially grown in a thermal equilibrium condition if enough amounts of B and P are available during NC growth. In our previous work,20,21 we demonstrated that B and P codoped Si-NCs with the diameters from 1 to 14 nm can be produced by phase separation of oxygen deficient borophosphosilicate (BPSG) glasses by hightemperature annealing. The codoped Si-NCs exhibit sizecontrollable photoluminescence (PL) in an extremely wide energy range (0.85−1.85 eV),22 which covers both above and below bulk Si band gap. The PL energy of codoped Si-NCs are always 300−400 meV lower than that of undoped Si-NCs with comparable sizes, suggesting that impurity states are involved in the optical transition.22 In this work, we first study the size dependence of the HOMO level of B and P codoped Si-NCs by photoemission yield spectroscopy (PYS).23−26 The PYS allows us to determine the energy of the HOMO levels with respect to the vacuum level directly. By combining the PYS data with PL data, we determine the size dependence of the LUMO level. We also measure the valence band spectra by X-ray photoelectron spectroscopy (XPS) and discuss the size dependence of the valence band density of states (DOS). From the onset of the DOS spectra, we determine the size dependence of the Fermi level. We show that relatively large codoped Si-NCs are p-type semiconductor and with decreasing the size the Fermi level approaches the middle of the bandgap. Finally, we discuss the correlation between the energy state structures and the PL properties. B and P codoped Si-NCs were prepared by a method described in our previous papers.27 Si-rich BPSG thin films were deposited on a thin stainless steel plate by cosputtering Si, SiO2, B2O3, and P2O5. The BPSG films were peeled from the plates and annealed in a N2 gas atmosphere at different temperatures (900−1250 °C) for 30 min to grow Si-NCs in BPSG matrices. Si-NCs were then liberated from BPSG matrices by etching out the matrices in hydrofluoric acid (HF) solution (46 wt %). Finally, isolated Si-NCs were transferred to methanol. Figure 1a shows a picture of a methanol solution in which codoped Si-NCs about 5 nm in diameter are dispersed. The solution is very clear and light scattering by agglomerates is not seen.28 The high dispersibility in polar solvents without organic ligands is a unique feature of B and P codoped Si-NCs28 and is not usually observed in any kind of semiconductor NCs. Because codoped Si-NCs can also be dispersed in water in a wide pH range,29 they are very promising in biomedical applications. The high solution dispersibility is explained by the formation of very heavily B and P doped shells on the surface of NCs and the inducement of negative potential on the surface.30,31 Figure 1b shows a transmission electron microscope (TEM) image of the Si-NCs. The sample for the TEM observation was prepared by drop-casting the solution on a carbon-coated TEM mesh. Because of the perfect dispersion of codoped Si-NCs in methanol, the NCs are aligned twodimensionally and no three-dimensional agglomerates are
Figure 1. (a) Photograph of colloidal dispersion of codoped Si-NCs (methanol solution). (b) TEM image of Si-NCs. Inset is a highresolution image of a Si-NC. (c) PL spectra of codoped Si-NCs with different sizes, that is, grown at different temperatures.
formed.27 Therefore, we can prepare high density NC films with very small roughness by printing processes.32,33 The inset of Figure 1b shows a high-resolution TEM image of a NC. The lattice fringe corresponds to the {111} plane of Si crystal (0.31 nm).28 The average diameter of Si-NCs estimated from Figure 1b is 7 nm with the standard deviation of 1.2 nm. In this work, we changed the average diameter from 1 to 9 nm by controlling the growth temperature from 900 to 1250 °C.22 Because very small NCs, typically smaller than about 2.5 nm in diameter, are hard to be observed by TEM, the size of small NCs is estimated by extrapolating the relation between the size and the growth temperature obtained for larger NCs under the assumption that the activation energy of Si diffusion in BPSG is constant.22 The standard deviation of the size distribution estimated by TEM observations is ∼20−30% of the average diameter. For NCs smaller than 2.5 nm in diameter, we assume that it is 30% of the average diameter and use the value in discussing size dependence of the HOMO, LUMO, and Fermi levels. The B and P concentration is almost independent of the growth temperature and is about 15 and 3 atom %, respectively.22 Figure 1c shows normalized PL spectra of codoped colloidal Si-NCs in methanol solution. The excitation wavelength is 488 nm. The PL peak energy is changed from 0.90 to 1.85 eV by varying the diameter from 9 to 1 nm.22 As discussed in a previous paper,22 after dispersing Si-NCs in methanol the PL peak shifts slightly to higher energy with increasing the storage time and is stabilized within a month. This is considered to be due to termination of the surface dangling bonds by oxygen (O) molecules and slight oxidation of the back-bonds of the surface Si-hydrogen (H) bonds. For the PYS and XPS measurements, codoped Si-NCs about 100 nm in thickness were prepared by drop-casting the colloidal dispersion on gold (Au)-coated Si wafers and aluminum (Al) plates, respectively. PYS measurements were B
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for the Si wafer is 4.93 eV, which is smaller than that of the literature value (5.15 eV).35 This slight shift is usually attributed to dipoles induced by organic molecules adsorbed on the surface during storage.36,37 In codoped Si-NCs with the average diameter of 9 nm, the onset of the photoelectron yield is about 0.09 eV smaller than that of bulk Si crystal. With decreasing the size, the onset shifts to higher energy. Figure 2b shows the size dependence of the ionization energy. The error bars in the horizontal axis represent the standard deviation of the size distribution. The data obtained for bulk Si crystal is shown by a horizontal blue line. We can clearly see the size-dependent deepening of the HOMO level. In codoped Si-NCs, in principle the acceptor level corresponds to the HOMO level, the energy of which is determined by the size dependence of the valence band edge and that of the binding energy of a B acceptor. In the largest SiNCs in Figure 2, the quantum size effect is considered to be negligible, because the average diameter (9 nm) is almost twice of the bulk exciton Bohr radius (4.9 nm).38 In fact, the PL energy of undoped Si-NCs with the diameter of 9 nm is very close to the bulk band gap.39 Therefore, the shift of the HOMO level from that of bulk Si crystal is due to the formation of the acceptor level in the band gap. The observed shift (0.09 eV) is larger than the binding energy of a B acceptor in bulk Si crystal (0.044 eV). This may be attributed to the reduction of the dielectric screening in NCs.8 With decreasing the size, the valence band edge deepens, while the binding energy of a B acceptor increases, which compensates the deepening of the HOMO level. However, in general the binding energy of a B acceptor is less sensitive to NC size than the energy of the valence band edge due to smaller Bohr radius of an acceptor (1.67 nm)40 than that of an exciton (4.9 nm). Therefore, as can be seen in Figure 2b, the HOMO level deepens with decreasing the size by mainly reflecting the shift of the valence band edge. In general, the derivative of the PYS spectra is proportional to the DOS.41,42 In the derivative spectra (see Supporting Information, Figure S2a), we can see that the shift of the HOMO level by decreasing the size is accompanied with the decrease of the DOS near the HOMO level. For example, at 5.4 eV the DOS decreases more than 2 orders of magnitude when the size decreases from 9 to 1 nm (Figure S2b). Figure 3a shows the valence band XPS spectra of codoped SiNCs with different sizes. To avoid the signal from surface oxides, we employed Si-NCs 1 day after preparation. The spectra correspond to the DOS of the valence band.43 The binding energy is measured with respect to the Fermi level energy.44 In the spectra of relatively large codoped Si-NCs, two broad peaks appear around 2.8 and 9.1 eV. From the comparison of the DOS of bulk Si crystal, the 2.8 eV peak is attributed to the highest energy p-like band, while the 9.1 eV peak to the lower energy s-like band.43,45 The shape of the valence band spectra changes with decreasing the size. The intensity of the 2.8 eV peak decreases, while that of the 9.1 eV peak is almost independent of the size (Figure 3b). The decrease of the DOS near the band edge with decreasing the size is consistent with the PYS data (Figure S2) and is explained by the quantization of the valence band. The valence band spectra are broader than that of bulk Si crystal (Figure S3).46 The broadening is considered to be due to lattice distortion on the surface of Si-NCs. Similar broadening of the valence band spectra is observed in amorphous Si.46
performed in air with the excitation energy range from 4.2 to 6.2 eV (AC-2, RIKEN KEIKI). The excitation power was fixed to 500 nW. XPS measurements (PHI X-tool, ULVAC-PHI) were carried out using an Al Kα X-ray source. The reason to choose Al instead of Au as a substrate was to avoid strong background signal of Au in the measurement of the valence band spectra of Si-NCs. The photoelectron energy was calibrated by the energy of the C 1s peak at 285 eV. First, we determine the size dependence of the HOMO level of codoped Si-NCs measured from the vacuum level (i.e., ionization energy) by PYS (see Supporting Information, Figure S1, for the definition of the ionization energy). We employ samples aged more than one month to obtain reliable and reproducible data. Figure 2a shows the PYS spectra of codoped
Figure 2. (a) PYS spectra of Si-NCs with different sizes. The diameter is changed from 1 to 9 nm. The data of bulk Si crystal is also shown as a reference. (b) Size dependence of the HOMO level energy measured from the vacuum level obtained from PYS spectra.
Si-NCs with different sizes. As a reference, the spectrum of bulk Si crystal (p-type, 10 Ωcm) is also shown. The yield, Y, of photoelectrons in a semiconductor is empirically given by Y1/3 ∝ (hν − IE), where hν is the energy of the excitation photon and IE is the ionization energy.26,34 Therefore, by extrapolating the linear region of the Y1/3 versus hν spectra in Figure 2a, the ionization energy is obtained. The ionization energy obtained C
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Figure 4. HOMO (●), LUMO (■), and Fermi level (▲) energies measured from the vacuum level of B and P codoped Si-NCs. The horizontal dashed lines are the conduction and valence band edges of bulk Si crystal. Valence band and conduction band edges of undoped Si-NCs calculated by tight binding approximation (solid curves)1 and first principle calculations (open triangle)47 are also shown. Broken curves are acceptor and donor levels calculated by tight binding approximations.1
Figure 3. (a) Valence band XPS spectra of codoped Si-NCs. The origin of the coordinate corresponds to the Fermi level. The diameter is changed from 1.2 to 9 nm. (b) Intensity of valence band spectra at 2.8 and 9.1 eV. Lines are guide to eyes. (c) Energy difference between Fermi level and HOMO level as a function of diameter. The error bars in the horizontal axis represent the standard deviation of the size distribution.
Derelue et al. calculated the energy levels of hydrogen-type impurities in hydrogen-terminated Si-NCs.1 The data are shown by broken curves in Figure 4. The calculated energy levels again do not agree with the present results. To quantitatively explain the size dependence of the HOMO and LUMO levels of the codoped Si-NCs, more precise theoretical modeling by taking into account the realistic surface termination and also the fact that B and P are simultaneously doped in a NC is indispensable. In Figure 4, when the size is relatively large, the Fermi level of codoped Si-NCs is very close to the HOMO level. With decreasing the size, it approaches the middle of the band gap. To show this more clearly, we plot the normalized position of the Fermi level with respect to the HOMO level, that is, EF − EHOMO divided by ELUMO − EHOMO, in Figure 5a. Above about 4 nm, it is around 15% and it approaches 50% when the size is decreased to 1 nm. This means that relatively large codoped SiNCs are p-type semiconductor. In our previous work, we demonstrated by ICP-AES22 and XPS31 that in the present preparation procedure, irrespective of the B and P concentration in starting materials for the production process, B concentration is always larger than P concentration in final products.22 This is consistent with the p-type behavior of codoped Si-NCs when the size is relatively large. On the other hand, approaching the Fermi level to the middle of the band gap with decreasing the size suggests that in small codoped Si-NCs, donors and acceptors are compensated. More precisely, the fraction of perfectly compensated Si-NCs increases with a decrease in the size. The group of Ossicini calculated the formation energy of B and/or P codoped Si-NCs with the diameter of 1.1 and 1.8 nm.16,50 They demonstrated that the formation energy of Si-NCs with exactly the same numbers of B and P is much smaller than those of B or P singly doped Si-NCs and is even smaller than that of undoped SiNCs. They also show that the formation energy is the smallest when B and P atoms are doped as pairs near the surface of SiNCs.16 Therefore, in very small codoped Si-NCs in this work B and P are considered to be doped as pairs near the surface and perfectly compensated.
From the onset of the valence band spectra, the energy of the Fermi level (EF) measured from the HOMO level (EHOMO) is obtained. The lines in Figure 3a are the results of linear fitting of the onset of the valence band spectra. The x-intersect corresponds to EF − EHOMO. Figure 3c shows EF − EHOMO as a function of a NC diameter. At large sizes, the Fermi level is very close to the HOMO level and EF − EHOMO increases with decreasing the size. The valence band spectra and the values of EF − EHOMO are not strongly modified by aging Si-NCs in methanol (Figures S4 and S5). By adding the data in Figure 3c to that in Figure 2b, the energy of the Fermi level measured from the vacuum level is obtained. The results are summarized in Figure 4. In addition, the energies of the LUMO level, which are obtained by adding the PL peak energies to those of the HOMO levels, are shown. The horizontal lines correspond to the valence band and conduction band edges of bulk Si crystal. In codoped Si-NCs with relatively large sizes, both the HOMO and LUMO levels are within the band gap of bulk Si crystal. This confirms that the acceptor and donor levels are HOMO and LUMO levels, respectively. With decreasing the size from 9 to 1 nm, the HOMO level becomes about 0.46 eV deep and the LUMO level about 0.47 eV shallow. The observed size dependence of the HOMO and LUMO level energies are significantly different from those of undoped Si-NCs experimentally48 and theoretically1,47,49 determined. In Figure 4, size dependence of the HOMO and LUMO levels obtained by tight binding approximation (solid curves)1 and by first principle calculations for several sizes (1.5, 3.0, and 3.4 nm) (open triangle)47 are shown. The two theoretical results agree fairly well. On the other hand, the size-dependent shifts of the HOMO and LUMO levels of the present work are much smaller than the theoretical predictions. The discrepancy suggests that acceptor and donor states are the HOMO and LUMO levels, respectively, in codoped Si-NCs. D
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comparable or sometimes larger than that around 3 nm.53−55 On the other hand, it decreases about 2 orders of magnitude in codoped Si-NCs (Figure 5b). Therefore, it is plausible that the observed sharp drop of the QY in Figure 5b is related to doping. Figure 5a suggests that majority of large codoped SiNCs are p-type semiconductor. In p-type semiconductor NCs, Auger recombination of photogenerated carriers with the interaction of holes supplied by doping is possible. The Auger time is estimated to be of the order of nsec or even shorter,56 which is more than 3 orders of magnitude shorter than the exciton radiative recombination time. Therefore, PL QY of ptype Si-NCs is more than 3 orders of magnitude smaller than that of intrinsic Si-NCs and they are practically not luminescing, that is, “dark”. With decreasing the average size, a fraction of perfectly compensated NCs increases. In perfectly compensated Si-NCs, Auger recombination is not possible and excitons recombine radiatively. This is the reason for relatively large external QY of small codoped Si-NCs. In Figure 5b, the QY decreases below ∼1.5 nm. In this range, the quenching is accompanied by the shortening of the lifetime. This suggests that nonradiative processes probably arising from surface defects are responsible for the quenching. It might be possible that enhanced Coulomb interaction on donor−acceptor pair recombination is the cause of the shortening of the lifetime.57 However, we do not have experimental data to discuss it. In summary, we have studied the size dependence of the HOMO and LUMO levels of B and P codoped Si-NCs by PYS and PL. The observed shifts of the levels are much smaller than those predicted by theoretical calculations of undoped Si-NCs. This indicates that the HOMO and LUMO levels of codoped Si-NCs are the acceptor and donor levels, respectively, and thus we have successfully determine the size dependence of the acceptor and donor levels of Si-NCs for the first time. We also studied the Fermi level of B and P codoped Si-NCs and found that relatively large codoped Si-NCs are p-type semiconductor. The Fermi level approaches the middle of the band gap with decreasing the size, despite larger concentration of B than that of P in samples. The result is consistent with theoretical prediction that B and P are doped preferentially as pairs in very small Si-NCs.
Figure 5. (a) Normalized position of Fermi level ((E − EHOMO)/ (ELUMO − EHOMO)) as a function of NC size. (b) PL quantum yield (▲),22 lifetime (■)22 and (c) PL peak energy22 of codoped colloidal Si-NCs as a function of NC diameter.
The result that the majority of NCs are perfectly compensated is inconsistent with the composition analysis in which B concentration is larger than P concentration.22 The discrepancy suggests that when the average size is very small, only fractions of B and P are electrically active and contribute to the formation of impurity-states in the band gap. Others are probably on the surface of Si-NCs and play a role for the high solution dispersibility. Unfortunately, the formation energy calculation by the Ossicini group covers only a limited size range of the present work.16,50 However, we can expect that formation energy difference between perfectly compensated Si-NCs and those with nonequal numbers of B and P atoms decreases with increasing the size, that is, with increasing the number of impurity atoms per a NC. If this assumption is correct, the average size increase results in the increase of a fraction of notperfectly compensated NCs, which makes the whole system ptype reflecting larger average concentration of B than that of P. The observed size dependence of the Fermi level gives us insight into the size dependence of the PL quantum yield (QY) of codoped Si-NCs reported previously.22 In Figure 5b, the QY and the lifetime of the PL are plotted as a function of the size.22 The corresponding PL energies are also shown in Figure 5c.22 The most important fact is that above around 4−5 nm, the QY decreases significantly with increasing the size, while the lifetime is almost independent of the size. This suggests that in large codoped Si-NCs, the majority of NCs are “dark” and do not contribute to the PL and only a small fraction of NCs are “bright”.51,52 The fraction of bright NCs decreases with increasing the average size, resulting in the sharp drop of the QY. The question is what the origin of almost complete quenching of PL in “dark” Si-NCs is. In undoped Si-NCs, the PL QY does not decrease drastically around 4−6 nm; it is
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b00225. Energy state structures of codoped Si-NCs (Figure S1) and the terms used in this work. Derivative of PYS spectra (Figure S2a) and the intensity at 5.4 eV as a function of the diameter (Figure S2b). Valence band XPS spectra of p-type Si wafer (Figure S3). Valence band XPS spectra of codoped Si-NCs aged more than one month (Figure S4) and the energy differences between Fermi Levels and HOMO levels (Figure S5). (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. E
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ACKNOWLEDGMENTS
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REFERENCES
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The authors thank Dr. Y. Nakajima (RIKEN KEIKI Co., Ltd.) for PYS measurements. This work is partly supported by 2014 JSPS Bilateral Joint Research Projects (Japan-Czech Republic) and 2015 Visegrad Group (V4)-Japan Joint Research Project on Advanced Materials. S.K. acknowledges Grant-in-Aid for Research Activity Start-up (26886008) and Casio Science Promotion Foundation. H.S. acknowledges Grant-in-Aid for JSPS Fellows (26-3120).
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DOI: 10.1021/acs.nanolett.6b00225 Nano Lett. XXXX, XXX, XXX−XXX
